# Airy stress functions method

The method of Airy stress functions is a method to find the stress distribution in an elastic solid. The method uses a Airy stress function $\varphi$, a scalar potential, and can be used when:

• The problem is two dimensional.
• The body forces are derivable from a potential function $V$, i.e.,
$$\mathbf{b} = -\nabla V\, .$$

## Computation of stresses

The stresses are computed from the Airy functions as

\begin{align} \sigma_{xx} &= \frac{\partial^2 \varphi}{\partial y^2}\\ \sigma_{yy} &= \frac{\partial^2 \varphi}{\partial x^2}\\ \sigma_{xy} &= -\frac{\partial^2 \varphi}{\partial x \partial y}\, , \end{align}

in Cartesian coordinates, and

\begin{align} \sigma_{rr} &= \frac{1}{r}\frac{\partial \varphi}{\partial r} + \frac{1}{r^2}\frac{\partial^2 \varphi}{\partial r^2}\\ \sigma_{\theta\theta} &= \frac{\partial^2 \varphi}{\partial r^2}\\ \sigma_{r\theta} &= -\frac{\partial}{\partial r}\left(\frac{1}{r}\frac{\partial \varphi}{\partial \theta}\right)\, , \end{align}

in polar coordinates.

## Airy stress functions are biharmonic

In 2D, the compatibility equations and equilibrium imply

$$\nabla^2 \sigma_v = \frac{4}{1 + \kappa} \nabla^2 V\, ,$$

where $\sigma_v = \mathrm{Tr}\,(\sigma)$ is the volumetric component of the stress tensor, and

$$\kappa = \begin{cases} 3 - 4\nu\quad \text{plane strain}\\ \frac{3 - \nu}{1 + \nu}\quad \text{plane strain} \end{cases}$$

Then, plugging the Airy stress function into this equation leads to

$$\nabla^2 \nabla^2 \varphi = -\frac{2(\kappa - 1)}{(1 + \kappa)} \nabla^2 V$$

or, just

$$\nabla^4 \varphi = -\frac{2(\kappa - 1)}{(1 + \kappa)} \nabla^2 V$$

for short.

This means that the Airy stress functions are biharmonic, that is, they satisfy the above equation.



In [1]:

from sympy import *
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams




In [2]:

x, y, z, t = symbols('x y z t')
f, g, h = symbols('f g h', cls=Function)
init_printing()




In [3]:

%matplotlib notebook
plt.style.use("seaborn-notebook")
plt.rcParams["image.cmap"] = "RdYlBu_r"



The following cell contains the routines that we will use in the remaining part of the notebook.



In [4]:

def poly_airy(x, y, order, coeff="c"):
"""Return a polynomial of a given order in x and y

The coefficients of the polynomial are returned as a set in the
variable c.
"""
num = (order**2 + 3*order + 2)/2
c = symbols('%s0:%d' % (coeff, num))
terms = [x**(order - k - j) * y**k
for j in range(0, order - 1)
for k in range(0, order + 1 - j)]
phi = sum(c[k]*term for k, term in enumerate(terms))
return phi, c

def airy_stress(phi, x, y):
"""Return stresses from the Airy stress function

The coordinate system is Cartesian
"""
return diff(phi, y, 2), diff(phi, x, 2), -diff(phi, y, 1, x, 1)

def conds2eqs(conds, var=(x, y)):
"""Turn the list of boundary conditions into equations to be solved

In general, the final list can have repeated equations. Thus, we
are removing those before returning it.
"""
eqlist = [coef for cond in conds for coef in Poly(cond, var).coeffs()]
return list(set(eqlist))

def plot_contours(x_coord, y_coord, field, fig=None, figsize=(7, 2), lines=True):
"""Plot the contours for a solution"""
if fig is None:
fig = plt.figure(figsize=figsize)
f_max = max(np.max(field), -np.min(field))
plt.contourf(x_coord, y_coord, field, vmin=-f_max, vmax=f_max)
plt.colorbar()
if lines:
plt.contour(x_coord, y_coord, field, colors="k")
plt.axis("image")
return fig



## Solutions

### Cantilever beam with load at the end

A cantilever beam is a beam that is anchored at one end. In this case, the beam has length $L$ and height $h$. The force $F$ is applied at $x=L$.



In [5]:

L, h, F =  symbols("L h F")



To choose the Airy polynomial we need to fix the maximum power. This seem to be arbitrary, but we can use the intuition that we have grasped in the study of resistance of materials. Taking that into account, we should have stresses with powers of two, then the Airy stress functions should have at least powers of 4.

Picking 4 as maximum power will let us recover the desired solution, but in general we don't know this beforehand, and we should use a trial and error procedure. You could try with a maximum power of 10 for this example and it should still give you the same answer. It will take a while, though.



In [6]:

phi, c = poly_airy(x, y, 4)

phi




Out[6]:

$\displaystyle c_{0} x^{4} + c_{1} x^{3} y + c_{10} x y + c_{11} y^{2} + c_{2} x^{2} y^{2} + c_{3} x y^{3} + c_{4} y^{4} + c_{5} x^{3} + c_{6} x^{2} y + c_{7} x y^{2} + c_{8} y^{3} + c_{9} x^{2}$




In [7]:

s11, s22, s12 = airy_stress(phi, x, y)
display(s11, s22, s12)




$\displaystyle 2 \left(c_{11} + c_{2} x^{2} + 3 c_{3} x y + 6 c_{4} y^{2} + c_{7} x + 3 c_{8} y\right)$

$\displaystyle 2 \left(6 c_{0} x^{2} + 3 c_{1} x y + c_{2} y^{2} + 3 c_{5} x + c_{6} y + c_{9}\right)$

$\displaystyle - 3 c_{1} x^{2} - c_{10} - 4 c_{2} x y - 3 c_{3} y^{2} - 2 c_{6} x - 2 c_{7} y$



The stress boundary conditions for this problem are:

\begin{align} &\sigma_{22}(x, y=h/2) = 0\\ &\sigma_{12}(x, y=h/2) = 0\\ &\sigma_{22}(x, y=-h/2) = 0\\ &\sigma_{12}(x, y=-h/2) = 0 \end{align}

Additionally, we have weak boundary conditions. That means, that we are not satisfying a distribution of tractions point-wise but in an average sense, namely

\begin{align} &\int_{-h/2}^{h/2} \sigma_{11} \mathrm{d}y = 0\\ &\int_{-h/2}^{h/2} \sigma_{12} \mathrm{d}y = F\\ &\int_{-h/2}^{h/2} y\sigma_{11} \mathrm{d}y = 0\, . \end{align}

With the weak conditions we are imposing that the system satisfy global equilibrium



In [8]:

t1 = s22.subs(y, h/2)
t2 = s12.subs(y, h/2)
t3 = s22.subs(y, -h/2)
t4 = s12.subs(y, -h/2)
t5 = s11.subs(x, L)
t6 = s12.subs(x, L)




In [9]:

conds = [t1, t2, t3, t4,
integrate(t5, (y, -h/2, h/2)),
integrate(t6, (y, -h/2, h/2)) - F,
integrate(y*t5, (y, -h/2, h/2)),
diff(phi, x, 4) + diff(phi, y, 4) + 2*diff(phi, x, 2, y, 2)]




In [10]:

eqlist = conds2eqs(conds, (x, y))
eqlist




Out[10]:

$\displaystyle \left[ 12 c_{0}, \ 2 L^{2} c_{2} h + 2 L c_{7} h + 2 c_{11} h + c_{4} h^{3}, \ 24 c_{0} + 8 c_{2} + 24 c_{4}, \ \frac{L c_{3} h^{3}}{2} + \frac{c_{8} h^{3}}{2}, \ - c_{10} - \frac{3 c_{3} h^{2}}{4} - c_{7} h, \ \frac{c_{2} h^{2}}{2} + c_{6} h + 2 c_{9}, \ - F - 3 L^{2} c_{1} h - 2 L c_{6} h - c_{10} h - \frac{c_{3} h^{3}}{4}, \ - 2 c_{2} h - 2 c_{6}, \ 3 c_{1} h + 6 c_{5}, \ - 3 c_{1} h + 6 c_{5}, \ 2 c_{2} h - 2 c_{6}, \ - c_{10} - \frac{3 c_{3} h^{2}}{4} + c_{7} h, \ - 3 c_{1}, \ \frac{c_{2} h^{2}}{2} - c_{6} h + 2 c_{9}\right]$




In [11]:

sol = solve(eqlist, c)




In [12]:

sol




Out[12]:

$\displaystyle \left\{ c_{0} : 0, \ c_{1} : 0, \ c_{10} : - \frac{3 F}{2 h}, \ c_{11} : 0, \ c_{2} : 0, \ c_{3} : \frac{2 F}{h^{3}}, \ c_{4} : 0, \ c_{5} : 0, \ c_{6} : 0, \ c_{7} : 0, \ c_{8} : - \frac{2 F L}{h^{3}}, \ c_{9} : 0\right\}$




In [13]:

s11.subs(sol)




Out[13]:

$\displaystyle - \frac{12 F L y}{h^{3}} + \frac{12 F x y}{h^{3}}$




In [14]:

s12.subs(sol)




Out[14]:

$\displaystyle \frac{3 F}{2 h} - \frac{6 F y^{2}}{h^{3}}$




In [15]:

s22.subs(sol)




Out[15]:

$\displaystyle 0$




In [16]:

x_vec, y_vec = np.mgrid[0:10:100j, -1:1:100j]
s11_fun = lambdify((x, y, h, L, F), s11.subs(sol), "numpy")
s12_fun = lambdify((x, y, h, L, F), s12.subs(sol), "numpy")




In [17]:

s11_vec = s11_fun(x_vec, y_vec, 2, 10, 1)
plot_contours(x_vec, y_vec, s11_vec);




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0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
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mpl.figure.prototype.handle_draw = function(fig, msg) {
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mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

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fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
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var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
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try {
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return;
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callback(fig, msg);
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};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [18]:

s12_vec = s12_fun(x_vec, y_vec, 2, 10, 1)
plot_contours(x_vec, y_vec, s12_vec, lines=False);




var element = $('#7f89dd73-f5cb-41e9-95ff-e1f49faf457c'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}



### Beam under pure bending



In [19]:

L, h, S =  symbols("L h S")




In [20]:

phi, c = poly_airy(x, y, 3)

phi




Out[20]:

$\displaystyle c_{0} x^{3} + c_{1} x^{2} y + c_{2} x y^{2} + c_{3} y^{3} + c_{4} x^{2} + c_{5} x y + c_{6} y^{2}$




In [21]:

s11, s22, s12 = airy_stress(phi, x, y)




In [22]:

conds = [s22.subs(y, h/2),
s12.subs(y, h/2),
s22.subs(y, -h/2),
s12.subs(y, -h/2),
s11.subs(x, L/2) - S*y,
s12.subs(x, L/2),
s11.subs(x, -L/2) - S*y,
s12.subs(x, -L/2)]

conds




Out[22]:

$\displaystyle \left[ 6 c_{0} x + c_{1} h + 2 c_{4}, \ - 2 c_{1} x - c_{2} h - c_{5}, \ 6 c_{0} x - c_{1} h + 2 c_{4}, \ - 2 c_{1} x + c_{2} h - c_{5}, \ L c_{2} - S y + 6 c_{3} y + 2 c_{6}, \ - L c_{1} - 2 c_{2} y - c_{5}, \ - L c_{2} - S y + 6 c_{3} y + 2 c_{6}, \ L c_{1} - 2 c_{2} y - c_{5}\right]$




In [23]:

eqlist = conds2eqs(conds)

eqlist




Out[23]:

$\displaystyle \left[ - c_{1} h + 2 c_{4}, \ - L c_{1} - c_{5}, \ c_{2} h - c_{5}, \ - 2 c_{2}, \ - S + 6 c_{3}, \ - L c_{2} + 2 c_{6}, \ c_{1} h + 2 c_{4}, \ - c_{2} h - c_{5}, \ - 2 c_{1}, \ L c_{2} + 2 c_{6}, \ 6 c_{0}, \ L c_{1} - c_{5}\right]$




In [24]:

sol = solve(eqlist, c)




In [25]:

sol




Out[25]:

$\displaystyle \left\{ c_{0} : 0, \ c_{1} : 0, \ c_{2} : 0, \ c_{3} : \frac{S}{6}, \ c_{4} : 0, \ c_{5} : 0, \ c_{6} : 0\right\}$




In [26]:

s11.subs(sol)




Out[26]:

$\displaystyle S y$




In [27]:

s12.subs(sol)




Out[27]:

$\displaystyle 0$




In [28]:

s22.subs(sol)




Out[28]:

$\displaystyle 0$




In [29]:

s11_fun = lambdify((x, y, S), s11.subs(sol), "numpy")




In [30]:

s11_vec = s11_fun(x_vec, y_vec, 1)
plot_contours(x_vec, y_vec, s11_vec);




var element = $('#c95ee01e-e4ca-4e20-9a88-9f406151c84c'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}



### Simply supported beam with uniform force



In [31]:

L, h, q =  symbols("L h q")




In [32]:

phi, d = poly_airy(x, y, 5)

phi




Out[32]:

$\displaystyle c_{0} x^{5} + c_{1} x^{4} y + c_{10} y^{4} + c_{11} x^{3} + c_{12} x^{2} y + c_{13} x y^{2} + c_{14} y^{3} + c_{15} x^{2} + c_{16} x y + c_{17} y^{2} + c_{2} x^{3} y^{2} + c_{3} x^{2} y^{3} + c_{4} x y^{4} + c_{5} y^{5} + c_{6} x^{4} + c_{7} x^{3} y + c_{8} x^{2} y^{2} + c_{9} x y^{3}$




In [33]:

s11, s22, s12 = airy_stress(phi, x, y)
display(s11, s22, s12)




$\displaystyle 2 \left(6 c_{10} y^{2} + c_{13} x + 3 c_{14} y + c_{17} + c_{2} x^{3} + 3 c_{3} x^{2} y + 6 c_{4} x y^{2} + 10 c_{5} y^{3} + c_{8} x^{2} + 3 c_{9} x y\right)$

$\displaystyle 2 \left(10 c_{0} x^{3} + 6 c_{1} x^{2} y + 3 c_{11} x + c_{12} y + c_{15} + 3 c_{2} x y^{2} + c_{3} y^{3} + 6 c_{6} x^{2} + 3 c_{7} x y + c_{8} y^{2}\right)$

$\displaystyle - 4 c_{1} x^{3} - 2 c_{12} x - 2 c_{13} y - c_{16} - 6 c_{2} x^{2} y - 6 c_{3} x y^{2} - 4 c_{4} y^{3} - 3 c_{7} x^{2} - 4 c_{8} x y - 3 c_{9} y^{2}$




In [34]:

conds = [s22.subs(y, h/2) + q,
s12.subs(y, h/2),
s22.subs(y, -h/2),
s12.subs(y, -h/2),
integrate(s11.subs(x, L/2), (y,-h/2, h/2)),
integrate(s12.subs(x, L/2), (y,-h/2, h/2)) - q*L/2,
integrate(y*s11.subs(x, L/2), (y,-h/2, h/2)),
diff(phi, x, 4) + diff(phi, y, 4) + 2*diff(phi, x, 2, y, 2)]
conds




Out[34]:

$\displaystyle \left[ 20 c_{0} x^{3} + 6 c_{1} h x^{2} + 6 c_{11} x + c_{12} h + 2 c_{15} + \frac{3 c_{2} h^{2} x}{2} + \frac{c_{3} h^{3}}{4} + 12 c_{6} x^{2} + 3 c_{7} h x + \frac{c_{8} h^{2}}{2} + q, \ - 4 c_{1} x^{3} - 2 c_{12} x - c_{13} h - c_{16} - 3 c_{2} h x^{2} - \frac{3 c_{3} h^{2} x}{2} - \frac{c_{4} h^{3}}{2} - 3 c_{7} x^{2} - 2 c_{8} h x - \frac{3 c_{9} h^{2}}{4}, \ 20 c_{0} x^{3} - 6 c_{1} h x^{2} + 6 c_{11} x - c_{12} h + 2 c_{15} + \frac{3 c_{2} h^{2} x}{2} - \frac{c_{3} h^{3}}{4} + 12 c_{6} x^{2} - 3 c_{7} h x + \frac{c_{8} h^{2}}{2}, \ - 4 c_{1} x^{3} - 2 c_{12} x + c_{13} h - c_{16} + 3 c_{2} h x^{2} - \frac{3 c_{3} h^{2} x}{2} + \frac{c_{4} h^{3}}{2} - 3 c_{7} x^{2} + 2 c_{8} h x - \frac{3 c_{9} h^{2}}{4}, \ \frac{h^{3} \left(2 L c_{4} + 4 c_{10}\right)}{4} + h \left(\frac{L^{3} c_{2}}{4} + \frac{L^{2} c_{8}}{2} + L c_{13} + 2 c_{17}\right), \ - \frac{L q}{2} + \frac{h^{3} \left(- L c_{3} - c_{9}\right)}{4} + h \left(- \frac{L^{3} c_{1}}{2} - \frac{3 L^{2} c_{7}}{4} - L c_{12} - c_{16}\right), \ \frac{c_{5} h^{5}}{4} + \frac{h^{3} \left(\frac{L^{2} c_{3}}{2} + L c_{9} + 2 c_{14}\right)}{4}, \ 24 \left(c_{10} + c_{4} x + 5 c_{5} y\right) + 24 \left(5 c_{0} x + c_{1} y + c_{6}\right) + 8 \left(3 c_{2} x + 3 c_{3} y + c_{8}\right)\right]$




In [35]:

eqlist = conds2eqs(conds)

eqlist




Out[35]:

$\displaystyle \left[ - 4 c_{1}, \ c_{12} h + 2 c_{15} + \frac{c_{3} h^{3}}{4} + \frac{c_{8} h^{2}}{2} + q, \ 3 c_{2} h - 3 c_{7}, \ 6 c_{11} + \frac{3 c_{2} h^{2}}{2} - 3 c_{7} h, \ \frac{L^{2} c_{3} h^{3}}{8} + \frac{L c_{9} h^{3}}{4} + \frac{c_{14} h^{3}}{2} + \frac{c_{5} h^{5}}{4}, \ 6 c_{11} + \frac{3 c_{2} h^{2}}{2} + 3 c_{7} h, \ - 2 c_{12} - \frac{3 c_{3} h^{2}}{2} + 2 c_{8} h, \ 20 c_{0}, \ - \frac{L^{3} c_{1} h}{2} - \frac{3 L^{2} c_{7} h}{4} - L c_{12} h - \frac{L c_{3} h^{3}}{4} - \frac{L q}{2} - c_{16} h - \frac{c_{9} h^{3}}{4}, \ 24 c_{10} + 24 c_{6} + 8 c_{8}, \ - 3 c_{2} h - 3 c_{7}, \ \frac{L^{3} c_{2} h}{4} + \frac{L^{2} c_{8} h}{2} + L c_{13} h + \frac{L c_{4} h^{3}}{2} + c_{10} h^{3} + 2 c_{17} h, \ - c_{13} h - c_{16} - \frac{c_{4} h^{3}}{2} - \frac{3 c_{9} h^{2}}{4}, \ 6 c_{1} h + 12 c_{6}, \ 24 c_{1} + 24 c_{3} + 120 c_{5}, \ - 6 c_{1} h + 12 c_{6}, \ 120 c_{0} + 24 c_{2} + 24 c_{4}, \ c_{13} h - c_{16} + \frac{c_{4} h^{3}}{2} - \frac{3 c_{9} h^{2}}{4}, \ - 2 c_{12} - \frac{3 c_{3} h^{2}}{2} - 2 c_{8} h, \ - c_{12} h + 2 c_{15} - \frac{c_{3} h^{3}}{4} + \frac{c_{8} h^{2}}{2}\right]$




In [36]:

sol = solve(eqlist, d)




In [37]:

sol




Out[37]:

$\displaystyle \left\{ c_{0} : 0, \ c_{1} : 0, \ c_{10} : 0, \ c_{11} : 0, \ c_{12} : - \frac{3 q}{4 h}, \ c_{13} : 0, \ c_{14} : - \frac{L^{2} q}{4 h^{3}} + \frac{q}{10 h}, \ c_{15} : - \frac{q}{4}, \ c_{16} : 0, \ c_{17} : 0, \ c_{2} : 0, \ c_{3} : \frac{q}{h^{3}}, \ c_{4} : 0, \ c_{5} : - \frac{q}{5 h^{3}}, \ c_{6} : 0, \ c_{7} : 0, \ c_{8} : 0, \ c_{9} : 0\right\}$




In [38]:

factor(s11.subs(sol))




Out[38]:

$\displaystyle \frac{q y \left(- 15 L^{2} + 6 h^{2} + 60 x^{2} - 40 y^{2}\right)}{10 h^{3}}$




In [39]:

factor(s12.subs(sol))




Out[39]:

$\displaystyle - \frac{3 q x \left(- h + 2 y\right) \left(h + 2 y\right)}{2 h^{3}}$




In [40]:

factor(s22.subs(sol))




Out[40]:

$\displaystyle \frac{q \left(- h + y\right) \left(h + 2 y\right)^{2}}{2 h^{3}}$




In [41]:

x_vec, y_vec = np.mgrid[-5:5:100j, -1:1:100j]
s11_fun = lambdify((x, y, L, h, q), s11.subs(sol), "numpy")
s12_fun = lambdify((x, y, L, h, q), s12.subs(sol), "numpy")
s22_fun = lambdify((x, y, L, h, q), s22.subs(sol), "numpy")




In [42]:

s11_vec = s11_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s11_vec);




var element = $('#16e32d58-500b-4063-aa32-cce1435de41f'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [43]:

s12_vec = s12_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s12_vec);




var element = $('#d0122e07-6e6e-48f8-ad3f-f3df8eabc39c'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [44]:

s22_vec = s22_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s22_vec);




var element = $('#a19a06bf-95f0-4bc2-b7cc-8f41a529954b'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}



## Simply supported beam with triangular force



In [45]:

L, h, q =  symbols("L h q")




In [46]:

phi, d = poly_airy(x, y, 6)

phi




Out[46]:

$\displaystyle c_{0} x^{6} + c_{1} x^{5} y + c_{10} x^{2} y^{3} + c_{11} x y^{4} + c_{12} y^{5} + c_{13} x^{4} + c_{14} x^{3} y + c_{15} x^{2} y^{2} + c_{16} x y^{3} + c_{17} y^{4} + c_{18} x^{3} + c_{19} x^{2} y + c_{2} x^{4} y^{2} + c_{20} x y^{2} + c_{21} y^{3} + c_{22} x^{2} + c_{23} x y + c_{24} y^{2} + c_{3} x^{3} y^{3} + c_{4} x^{2} y^{4} + c_{5} x y^{5} + c_{6} y^{6} + c_{7} x^{5} + c_{8} x^{4} y + c_{9} x^{3} y^{2}$




In [47]:

s11, s22, s12 = airy_stress(phi, x, y)
display(s11, s22, s12)




$\displaystyle 2 \left(3 c_{10} x^{2} y + 6 c_{11} x y^{2} + 10 c_{12} y^{3} + c_{15} x^{2} + 3 c_{16} x y + 6 c_{17} y^{2} + c_{2} x^{4} + c_{20} x + 3 c_{21} y + c_{24} + 3 c_{3} x^{3} y + 6 c_{4} x^{2} y^{2} + 10 c_{5} x y^{3} + 15 c_{6} y^{4} + c_{9} x^{3}\right)$

$\displaystyle 2 \left(15 c_{0} x^{4} + 10 c_{1} x^{3} y + c_{10} y^{3} + 6 c_{13} x^{2} + 3 c_{14} x y + c_{15} y^{2} + 3 c_{18} x + c_{19} y + 6 c_{2} x^{2} y^{2} + c_{22} + 3 c_{3} x y^{3} + c_{4} y^{4} + 10 c_{7} x^{3} + 6 c_{8} x^{2} y + 3 c_{9} x y^{2}\right)$

$\displaystyle - 5 c_{1} x^{4} - 6 c_{10} x y^{2} - 4 c_{11} y^{3} - 3 c_{14} x^{2} - 4 c_{15} x y - 3 c_{16} y^{2} - 2 c_{19} x - 8 c_{2} x^{3} y - 2 c_{20} y - c_{23} - 9 c_{3} x^{2} y^{2} - 8 c_{4} x y^{3} - 5 c_{5} y^{4} - 4 c_{8} x^{3} - 6 c_{9} x^{2} y$




In [48]:

conds = [s22.subs(y, h/2) + (x + L/2)*q/L,
s12.subs(y, h/2),
s22.subs(y, -h/2),
s12.subs(y, -h/2),
integrate(s11.subs(x, L/2), (y,-h/2, h/2)),
integrate(s12.subs(x, L/2), (y,-h/2, h/2)) - q*L/2,
integrate(y*s11.subs(x, L/2), (y,-h/2, h/2)),
diff(phi, x, 4) + diff(phi, y, 4) + 2*diff(phi, x, 2, y, 2)]
conds




Out[48]:

$\displaystyle \left[ 30 c_{0} x^{4} + 10 c_{1} h x^{3} + \frac{c_{10} h^{3}}{4} + 12 c_{13} x^{2} + 3 c_{14} h x + \frac{c_{15} h^{2}}{2} + 6 c_{18} x + c_{19} h + 3 c_{2} h^{2} x^{2} + 2 c_{22} + \frac{3 c_{3} h^{3} x}{4} + \frac{c_{4} h^{4}}{8} + 20 c_{7} x^{3} + 6 c_{8} h x^{2} + \frac{3 c_{9} h^{2} x}{2} + \frac{q \left(\frac{L}{2} + x\right)}{L}, \ - 5 c_{1} x^{4} - \frac{3 c_{10} h^{2} x}{2} - \frac{c_{11} h^{3}}{2} - 3 c_{14} x^{2} - 2 c_{15} h x - \frac{3 c_{16} h^{2}}{4} - 2 c_{19} x - 4 c_{2} h x^{3} - c_{20} h - c_{23} - \frac{9 c_{3} h^{2} x^{2}}{4} - c_{4} h^{3} x - \frac{5 c_{5} h^{4}}{16} - 4 c_{8} x^{3} - 3 c_{9} h x^{2}, \ 30 c_{0} x^{4} - 10 c_{1} h x^{3} - \frac{c_{10} h^{3}}{4} + 12 c_{13} x^{2} - 3 c_{14} h x + \frac{c_{15} h^{2}}{2} + 6 c_{18} x - c_{19} h + 3 c_{2} h^{2} x^{2} + 2 c_{22} - \frac{3 c_{3} h^{3} x}{4} + \frac{c_{4} h^{4}}{8} + 20 c_{7} x^{3} - 6 c_{8} h x^{2} + \frac{3 c_{9} h^{2} x}{2}, \ - 5 c_{1} x^{4} - \frac{3 c_{10} h^{2} x}{2} + \frac{c_{11} h^{3}}{2} - 3 c_{14} x^{2} + 2 c_{15} h x - \frac{3 c_{16} h^{2}}{4} - 2 c_{19} x + 4 c_{2} h x^{3} + c_{20} h - c_{23} - \frac{9 c_{3} h^{2} x^{2}}{4} + c_{4} h^{3} x - \frac{5 c_{5} h^{4}}{16} - 4 c_{8} x^{3} + 3 c_{9} h x^{2}, \ \frac{3 c_{6} h^{5}}{8} + \frac{h^{3} \left(L^{2} c_{4} + 2 L c_{11} + 4 c_{17}\right)}{4} + h \left(\frac{L^{4} c_{2}}{8} + \frac{L^{3} c_{9}}{4} + \frac{L^{2} c_{15}}{2} + L c_{20} + 2 c_{24}\right), \ - \frac{L q}{2} - \frac{c_{5} h^{5}}{16} + \frac{h^{3} \left(- \frac{3 L^{2} c_{3}}{4} - L c_{10} - c_{16}\right)}{4} + h \left(- \frac{5 L^{4} c_{1}}{16} - \frac{L^{3} c_{8}}{2} - \frac{3 L^{2} c_{14}}{4} - L c_{19} - c_{23}\right), \ \frac{h^{5} \left(2 L c_{5} + 4 c_{12}\right)}{16} + \frac{h^{3} \left(\frac{L^{3} c_{3}}{4} + \frac{L^{2} c_{10}}{2} + L c_{16} + 2 c_{21}\right)}{4}, \ 24 \left(15 c_{0} x^{2} + 5 c_{1} x y + c_{13} + c_{2} y^{2} + 5 c_{7} x + c_{8} y\right) + 8 \left(3 c_{10} y + c_{15} + 6 c_{2} x^{2} + 9 c_{3} x y + 6 c_{4} y^{2} + 3 c_{9} x\right) + 24 \left(c_{11} x + 5 c_{12} y + c_{17} + c_{4} x^{2} + 5 c_{5} x y + 15 c_{6} y^{2}\right)\right]$




In [49]:

eqlist = conds2eqs(conds)

eqlist




Out[49]:

$\displaystyle \left[ \frac{L^{4} c_{2} h}{8} + \frac{L^{3} c_{9} h}{4} + \frac{L^{2} c_{15} h}{2} + \frac{L^{2} c_{4} h^{3}}{4} + \frac{L c_{11} h^{3}}{2} + L c_{20} h + c_{17} h^{3} + 2 c_{24} h + \frac{3 c_{6} h^{5}}{8}, \ 10 c_{1} h + 20 c_{7}, \ 12 c_{13} + 3 c_{2} h^{2} - 6 c_{8} h, \ 120 c_{1} + 72 c_{3} + 120 c_{5}, \ 24 c_{10} + 120 c_{12} + 24 c_{8}, \ - 5 c_{1}, \ - 4 c_{2} h - 4 c_{8}, \ 24 c_{13} + 8 c_{15} + 24 c_{17}, \ - \frac{5 L^{4} c_{1} h}{16} - \frac{L^{3} c_{8} h}{2} - \frac{3 L^{2} c_{14} h}{4} - \frac{3 L^{2} c_{3} h^{3}}{16} - \frac{L c_{10} h^{3}}{4} - L c_{19} h - \frac{L q}{2} - \frac{c_{16} h^{3}}{4} - c_{23} h - \frac{c_{5} h^{5}}{16}, \ 24 c_{11} + 120 c_{7} + 24 c_{9}, \ - 3 c_{14} - \frac{9 c_{3} h^{2}}{4} + 3 c_{9} h, \ - 3 c_{14} - \frac{9 c_{3} h^{2}}{4} - 3 c_{9} h, \ - \frac{c_{10} h^{3}}{4} + \frac{c_{15} h^{2}}{2} - c_{19} h + 2 c_{22} + \frac{c_{4} h^{4}}{8}, \ 24 c_{2} + 48 c_{4} + 360 c_{6}, \ \frac{c_{11} h^{3}}{2} - \frac{3 c_{16} h^{2}}{4} + c_{20} h - c_{23} - \frac{5 c_{5} h^{4}}{16}, \ - \frac{3 c_{10} h^{2}}{2} - 2 c_{15} h - 2 c_{19} - c_{4} h^{3}, \ \frac{12 L c_{14} h + 24 L c_{18} + 3 L c_{3} h^{3} + 6 L c_{9} h^{2} + 4 q}{4 L}, \ - \frac{c_{11} h^{3}}{2} - \frac{3 c_{16} h^{2}}{4} - c_{20} h - c_{23} - \frac{5 c_{5} h^{4}}{16}, \ 12 c_{13} + 3 c_{2} h^{2} + 6 c_{8} h, \ - \frac{3 c_{10} h^{2}}{2} + 2 c_{15} h - 2 c_{19} + c_{4} h^{3}, \ \frac{L^{3} c_{3} h^{3}}{16} + \frac{L^{2} c_{10} h^{3}}{8} + \frac{L c_{16} h^{3}}{4} + \frac{L c_{5} h^{5}}{8} + \frac{c_{12} h^{5}}{4} + \frac{c_{21} h^{3}}{2}, \ 4 c_{2} h - 4 c_{8}, \ - 3 c_{14} h + 6 c_{18} - \frac{3 c_{3} h^{3}}{4} + \frac{3 c_{9} h^{2}}{2}, \ 360 c_{0} + 48 c_{2} + 24 c_{4}, \ - 10 c_{1} h + 20 c_{7}, \ 30 c_{0}, \ \frac{c_{10} h^{3}}{4} + \frac{c_{15} h^{2}}{2} + c_{19} h + 2 c_{22} + \frac{c_{4} h^{4}}{8} + \frac{q}{2}\right]$




In [50]:

sol = solve(eqlist, d)




In [51]:

sol




Out[51]:

$\displaystyle \left\{ c_{0} : 0, \ c_{1} : 0, \ c_{10} : \frac{q}{2 h^{3}}, \ c_{11} : 0, \ c_{12} : - \frac{q}{10 h^{3}}, \ c_{13} : 0, \ c_{14} : - \frac{q}{4 L h}, \ c_{15} : 0, \ c_{16} : \frac{L q}{4 h^{3}} + \frac{q}{10 L h}, \ c_{17} : 0, \ c_{18} : - \frac{q}{12 L}, \ c_{19} : - \frac{3 q}{8 h}, \ c_{2} : 0, \ c_{20} : 0, \ c_{21} : \frac{q \left(- 35 L^{2} + 6 h^{2}\right)}{120 h^{3}}, \ c_{22} : - \frac{q}{8}, \ c_{23} : - \frac{q \left(15 L^{2} + h^{2}\right)}{80 L h}, \ c_{24} : 0, \ c_{3} : \frac{q}{3 L h^{3}}, \ c_{4} : 0, \ c_{5} : - \frac{q}{5 L h^{3}}, \ c_{6} : 0, \ c_{7} : 0, \ c_{8} : 0, \ c_{9} : 0\right\}$




In [52]:

factor(s11.subs(sol))




Out[52]:

$\displaystyle \frac{q y \left(- 35 L^{3} + 30 L^{2} x + 6 L h^{2} + 60 L x^{2} - 40 L y^{2} + 12 h^{2} x + 40 x^{3} - 80 x y^{2}\right)}{20 L h^{3}}$




In [53]:

factor(s12.subs(sol))




Out[53]:

$\displaystyle - \frac{q \left(- h + 2 y\right) \left(h + 2 y\right) \left(15 L^{2} + 60 L x + h^{2} + 60 x^{2} - 20 y^{2}\right)}{80 L h^{3}}$




In [54]:

factor(s22.subs(sol))




Out[54]:

$\displaystyle \frac{q \left(L + 2 x\right) \left(- h + y\right) \left(h + 2 y\right)^{2}}{4 L h^{3}}$




In [55]:

x_vec, y_vec = np.mgrid[-5:5:100j, -1:1:100j]
s11_fun = lambdify((x, y, L, h, q), s11.subs(sol), "numpy")
s12_fun = lambdify((x, y, L, h, q), s12.subs(sol), "numpy")
s22_fun = lambdify((x, y, L, h, q), s22.subs(sol), "numpy")




In [56]:

s11_vec = s11_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s11_vec);




var element = $('#da11bda6-3421-417e-a1b8-9a32c4fc7e6b'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [57]:

s12_vec = s12_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s12_vec);




var element = $('#97438ac8-3b85-4253-904a-fe3a554b9a89'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [58]:

s22_vec = s22_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s22_vec);




var element = $('#40af9624-2f9b-4923-8dc4-e96fc3db4500'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}



### Cantilever beam with variying thickness



In [59]:

L, h, q =  symbols("L h q")




In [60]:

phi, d = poly_airy(x, y, 5)

phi




Out[60]:

$\displaystyle c_{0} x^{5} + c_{1} x^{4} y + c_{10} y^{4} + c_{11} x^{3} + c_{12} x^{2} y + c_{13} x y^{2} + c_{14} y^{3} + c_{15} x^{2} + c_{16} x y + c_{17} y^{2} + c_{2} x^{3} y^{2} + c_{3} x^{2} y^{3} + c_{4} x y^{4} + c_{5} y^{5} + c_{6} x^{4} + c_{7} x^{3} y + c_{8} x^{2} y^{2} + c_{9} x y^{3}$




In [61]:

s11, s22, s12 = airy_stress(phi, x, y)
display(s11, s22, s12)




$\displaystyle 2 \left(6 c_{10} y^{2} + c_{13} x + 3 c_{14} y + c_{17} + c_{2} x^{3} + 3 c_{3} x^{2} y + 6 c_{4} x y^{2} + 10 c_{5} y^{3} + c_{8} x^{2} + 3 c_{9} x y\right)$

$\displaystyle 2 \left(10 c_{0} x^{3} + 6 c_{1} x^{2} y + 3 c_{11} x + c_{12} y + c_{15} + 3 c_{2} x y^{2} + c_{3} y^{3} + 6 c_{6} x^{2} + 3 c_{7} x y + c_{8} y^{2}\right)$

$\displaystyle - 4 c_{1} x^{3} - 2 c_{12} x - 2 c_{13} y - c_{16} - 6 c_{2} x^{2} y - 6 c_{3} x y^{2} - 4 c_{4} y^{3} - 3 c_{7} x^{2} - 4 c_{8} x y - 3 c_{9} y^{2}$




In [62]:

conds = [s22.subs(y, h/2) + q,
s12.subs(y, h/2),
s22.subs(y, -h/2),
s12.subs(y, -h/2),
integrate(s11.subs(x, 0), (y,-h/2, h/2)),
integrate(s12.subs(x, 0), (y,-h/2, h/2)) + q*L,
integrate(y*s11.subs(x, 0), (y,-h/2, h/2)) - q*L**2/2,
diff(phi, x, 4) + diff(phi, y, 4) + 2*diff(phi, x, 2, y, 2)]
conds




Out[62]:

$\displaystyle \left[ 20 c_{0} x^{3} + 6 c_{1} h x^{2} + 6 c_{11} x + c_{12} h + 2 c_{15} + \frac{3 c_{2} h^{2} x}{2} + \frac{c_{3} h^{3}}{4} + 12 c_{6} x^{2} + 3 c_{7} h x + \frac{c_{8} h^{2}}{2} + q, \ - 4 c_{1} x^{3} - 2 c_{12} x - c_{13} h - c_{16} - 3 c_{2} h x^{2} - \frac{3 c_{3} h^{2} x}{2} - \frac{c_{4} h^{3}}{2} - 3 c_{7} x^{2} - 2 c_{8} h x - \frac{3 c_{9} h^{2}}{4}, \ 20 c_{0} x^{3} - 6 c_{1} h x^{2} + 6 c_{11} x - c_{12} h + 2 c_{15} + \frac{3 c_{2} h^{2} x}{2} - \frac{c_{3} h^{3}}{4} + 12 c_{6} x^{2} - 3 c_{7} h x + \frac{c_{8} h^{2}}{2}, \ - 4 c_{1} x^{3} - 2 c_{12} x + c_{13} h - c_{16} + 3 c_{2} h x^{2} - \frac{3 c_{3} h^{2} x}{2} + \frac{c_{4} h^{3}}{2} - 3 c_{7} x^{2} + 2 c_{8} h x - \frac{3 c_{9} h^{2}}{4}, \ c_{10} h^{3} + 2 c_{17} h, \ L q - c_{16} h - \frac{c_{9} h^{3}}{4}, \ - \frac{L^{2} q}{2} + \frac{c_{14} h^{3}}{2} + \frac{c_{5} h^{5}}{4}, \ 24 \left(c_{10} + c_{4} x + 5 c_{5} y\right) + 24 \left(5 c_{0} x + c_{1} y + c_{6}\right) + 8 \left(3 c_{2} x + 3 c_{3} y + c_{8}\right)\right]$




In [63]:

eqlist = conds2eqs(conds)
eqlist




Out[63]:

$\displaystyle \left[ - 4 c_{1}, \ c_{12} h + 2 c_{15} + \frac{c_{3} h^{3}}{4} + \frac{c_{8} h^{2}}{2} + q, \ 3 c_{2} h - 3 c_{7}, \ 6 c_{11} + \frac{3 c_{2} h^{2}}{2} - 3 c_{7} h, \ 6 c_{11} + \frac{3 c_{2} h^{2}}{2} + 3 c_{7} h, \ - 2 c_{12} - \frac{3 c_{3} h^{2}}{2} + 2 c_{8} h, \ 20 c_{0}, \ 24 c_{10} + 24 c_{6} + 8 c_{8}, \ - \frac{L^{2} q}{2} + \frac{c_{14} h^{3}}{2} + \frac{c_{5} h^{5}}{4}, \ c_{10} h^{3} + 2 c_{17} h, \ - 3 c_{2} h - 3 c_{7}, \ - c_{13} h - c_{16} - \frac{c_{4} h^{3}}{2} - \frac{3 c_{9} h^{2}}{4}, \ 6 c_{1} h + 12 c_{6}, \ 24 c_{1} + 24 c_{3} + 120 c_{5}, \ L q - c_{16} h - \frac{c_{9} h^{3}}{4}, \ - 6 c_{1} h + 12 c_{6}, \ 120 c_{0} + 24 c_{2} + 24 c_{4}, \ c_{13} h - c_{16} + \frac{c_{4} h^{3}}{2} - \frac{3 c_{9} h^{2}}{4}, \ - 2 c_{12} - \frac{3 c_{3} h^{2}}{2} - 2 c_{8} h, \ - c_{12} h + 2 c_{15} - \frac{c_{3} h^{3}}{4} + \frac{c_{8} h^{2}}{2}\right]$




In [64]:

sol = solve(eqlist, d)




In [65]:

sol




Out[65]:

$\displaystyle \left\{ c_{0} : 0, \ c_{1} : 0, \ c_{10} : 0, \ c_{11} : 0, \ c_{12} : - \frac{3 q}{4 h}, \ c_{13} : 0, \ c_{14} : \frac{L^{2} q}{h^{3}} + \frac{q}{10 h}, \ c_{15} : - \frac{q}{4}, \ c_{16} : \frac{3 L q}{2 h}, \ c_{17} : 0, \ c_{2} : 0, \ c_{3} : \frac{q}{h^{3}}, \ c_{4} : 0, \ c_{5} : - \frac{q}{5 h^{3}}, \ c_{6} : 0, \ c_{7} : 0, \ c_{8} : 0, \ c_{9} : - \frac{2 L q}{h^{3}}\right\}$




In [66]:

factor(s11.subs(sol))




Out[66]:

$\displaystyle \frac{q y \left(30 L^{2} - 60 L x + 3 h^{2} + 30 x^{2} - 20 y^{2}\right)}{5 h^{3}}$




In [67]:

factor(s12.subs(sol))




Out[67]:

$\displaystyle - \frac{3 q \left(- L + x\right) \left(- h + 2 y\right) \left(h + 2 y\right)}{2 h^{3}}$




In [68]:

factor(s22.subs(sol))




Out[68]:

$\displaystyle \frac{q \left(- h + y\right) \left(h + 2 y\right)^{2}}{2 h^{3}}$




In [69]:

x_vec, y_vec = np.mgrid[0:10:100j, -1:1:100j]
s11_fun = lambdify((x, y, L, h, q), s11.subs(sol), "numpy")
s12_fun = lambdify((x, y, L, h, q), s12.subs(sol), "numpy")
s22_fun = lambdify((x, y, L, h, q), s22.subs(sol), "numpy")




In [70]:

s11_vec = s11_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s11_vec);




var element = $('#e2a472ea-e1d7-48bf-a01a-78ecc1d46b2a'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [71]:

s12_vec = s12_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s12_vec);




var element = $('#0a4a1761-b5dc-4970-bdd9-24b3d7f31872'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [72]:

s22_vec = s22_fun(x_vec, y_vec, 10, 2, 1)
plot_contours(x_vec, y_vec, s22_vec);




var element = $('#2055159b-6406-48c0-a91c-47f539a53742'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}



### Cantilever beam with uniform force and triangular shape

We want to check that the stress function

$$\phi = C\left[r^2(\alpha - \theta) + \frac{1}{2}r^2 \sin(2\theta) - r^2\cos^2\theta \tan \alpha\right]$$

satisfy the boundary conditions for this problem.



In [73]:

r, theta, C, alpha, q = symbols("r  theta C alpha q")
phi = C*(r**2*(alpha - theta) + r**2*sin(2*theta)/2 - r**2*cos(theta)**2*tan(alpha))
phi




Out[73]:

$\displaystyle C \left(r^{2} \left(\alpha - \theta\right) + \frac{r^{2} \sin{\left(2 \theta \right)}}{2} - r^{2} \cos^{2}{\left(\theta \right)} \tan{\left(\alpha \right)}\right)$




In [74]:

Srr = simplify(1/r**2*diff(phi, theta, 2) + 1/r*diff(phi, r))
Srr




Out[74]:

$\displaystyle C \left(2 \alpha - 2 \theta - 2 \sin^{2}{\left(\theta \right)} \tan{\left(\alpha \right)} - \sin{\left(2 \theta \right)}\right)$




In [75]:

Stt = simplify(diff(phi, r, 2))
Stt




Out[75]:

$\displaystyle C \left(2 \alpha - 2 \theta + \sin{\left(2 \theta \right)} - 2 \cos^{2}{\left(\theta \right)} \tan{\left(\alpha \right)}\right)$




In [76]:

Srt = -simplify(diff(1/r*diff(phi, theta), r))
Srt




Out[76]:

$\displaystyle - C \left(\sin{\left(2 \theta \right)} \tan{\left(\alpha \right)} + \cos{\left(2 \theta \right)} - 1\right)$



In the upper edge we have that

\begin{align} \sigma_{\theta\theta} &= -q\\ \sigma_{r\theta} &= 0 \end{align}

and in the lower one

\begin{align} \sigma_{\theta\theta} &= 0\\ \sigma_{r\theta} &= 0 \end{align}

The constant $C$ can be inferred from the first boundary condition, i.e.



In [77]:

sol = solve(Stt.subs(theta, 0) + q, C)
sol




Out[77]:

$\displaystyle \left[ - \frac{q}{2 \alpha - 2 \tan{\left(\alpha \right)}}\right]$



And the solution is then



In [78]:

Srr2 = Srr.subs(C, sol[0])
Stt2 = Stt.subs(C, sol[0])
Srt2 = Srt.subs(C, sol[0])

display(Srr2)
display(Stt2)
display(Srt2)




$\displaystyle - \frac{q \left(2 \alpha - 2 \theta - 2 \sin^{2}{\left(\theta \right)} \tan{\left(\alpha \right)} - \sin{\left(2 \theta \right)}\right)}{2 \alpha - 2 \tan{\left(\alpha \right)}}$

$\displaystyle - \frac{q \left(2 \alpha - 2 \theta + \sin{\left(2 \theta \right)} - 2 \cos^{2}{\left(\theta \right)} \tan{\left(\alpha \right)}\right)}{2 \alpha - 2 \tan{\left(\alpha \right)}}$

$\displaystyle \frac{q \left(\sin{\left(2 \theta \right)} \tan{\left(\alpha \right)} + \cos{\left(2 \theta \right)} - 1\right)}{2 \alpha - 2 \tan{\left(\alpha \right)}}$



And we need to check that the other boundary conditions are satisfied.



In [79]:

Srt.subs(theta, 0)




Out[79]:

$\displaystyle 0$




In [80]:

trigsimp(Stt.subs(theta, alpha))




Out[80]:

$\displaystyle 0$



SymPy does not detect that the other expression is zero, but we can help rewriting the expression



In [81]:

simplify((Srt.subs(theta, alpha)).rewrite(sin))




Out[81]:

$\displaystyle 0$



If we want to write the solution in Cartesian coordinates we can change the frame by

$$[\sigma'] = [Q^T] [\sigma] [Q]$$

with

$$Q = \begin{bmatrix} \cos(\theta) &\sin(\theta)\\ -\sin(\theta) &\cos(\theta) \end{bmatrix}$$


In [82]:

Q = Matrix([
[cos(theta), sin(theta)],
[-sin(theta), cos(theta)]])
S_polar = Matrix([
[Srr2, Srt2],
[Srt2, Stt2]])




In [83]:

S_cart = simplify(Q.T *  S_polar * Q)
S_cart




Out[83]:

$\displaystyle \left[\begin{matrix}\frac{q \left(- 2 \alpha + 2 \theta + \sin{\left(2 \theta \right)}\right)}{2 \left(\alpha - \tan{\left(\alpha \right)}\right)} & \frac{q \sin^{2}{\left(\theta \right)}}{\alpha - \tan{\left(\alpha \right)}}\\\frac{q \sin^{2}{\left(\theta \right)}}{\alpha - \tan{\left(\alpha \right)}} & \frac{q \left(- 2 \alpha + 2 \theta - \sin{\left(2 \theta \right)} + 2 \tan{\left(\alpha \right)}\right)}{2 \left(\alpha - \tan{\left(\alpha \right)}\right)}\end{matrix}\right]$




In [84]:

angle = np.pi/10
t_vec, r_vec = np.mgrid[0:angle:100j, 0:5:100j]
x_vec = r_vec * np.cos(t_vec)
y_vec = r_vec * np.sin(t_vec)
s11_fun = lambdify((r, theta, alpha, q), S_cart[0, 0], "numpy")
s12_fun = lambdify((r, theta, alpha, q), S_cart[0, 1], "numpy")
s22_fun = lambdify((r, theta, alpha, q), S_cart[1, 1], "numpy")




In [85]:

s11_vec = s11_fun(r_vec, t_vec, angle, 1)
plot_contours(x_vec, y_vec, s11_vec)
plt.gca().invert_yaxis();




var element = $('#f2aeb9b5-6570-4ec1-9bba-dc7b3cb46840'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [86]:

s12_vec = s12_fun(r_vec, t_vec, angle, 1)
plot_contours(x_vec, y_vec, s12_vec)
plt.gca().invert_yaxis();




var element = $('#67339ddd-de34-4319-afc2-f4d7e9be96eb'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [87]:

s22_vec = s22_fun(r_vec, t_vec, angle, 1)
plot_contours(x_vec, y_vec, s22_vec)
plt.gca().invert_yaxis();




var element = $('#663d5e31-c919-4274-ba3b-e2ff8462efdd'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support. ' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext[0]; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas[0]; this.context = canvas[0].getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>');
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker[0]; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option);
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0]; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info[1]['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>'); nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}




In [ ]:



The following cell changes the style of the notebook



In [88]:

from IPython.core.display import HTML
def css_styling():
return HTML(styles)
css_styling()




Out[88]:

/* Based on Lorena Barba template available at: https://github.com/barbagroup/AeroPython/blob/master/styles/custom.css*/
@font-face {
font-family: "Computer Modern";
src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');
}
div.cell{
width:800px;
margin-left:16% !important;
margin-right:auto;
}
h1 {
font-family: 'Alegreya Sans', sans-serif;
}
h2 {
font-family: 'Fenix', serif;
}
h3{
font-family: 'Fenix', serif;
margin-top:12px;
margin-bottom: 3px;
}
h4{
font-family: 'Fenix', serif;
}
h5 {
font-family: 'Alegreya Sans', sans-serif;
}
div.text_cell_render{
font-family: 'Alegreya Sans',Computer Modern, "Helvetica Neue", Arial, Helvetica, Geneva, sans-serif;
line-height: 135%;
font-size: 120%;
width:600px;
margin-left:auto;
margin-right:auto;
}
.CodeMirror{
font-family: "Source Code Pro";
font-size: 90%;
}
/* .prompt{
display: None;
}*/
.text_cell_render h1 {
font-weight: 200;
font-size: 50pt;
line-height: 100%;
color:#CD2305;
margin-bottom: 0.5em;
margin-top: 0.5em;
display: block;
}
.text_cell_render h5 {
font-weight: 300;
font-size: 16pt;
color: #CD2305;
font-style: italic;
margin-bottom: .5em;
margin-top: 0.5em;
display: block;
}
.warning{
color: rgb( 240, 20, 20 )
}

MathJax.Hub.Config({
TeX: {
extensions: ["AMSmath.js"]
},
tex2jax: {
inlineMath: [ ['$','$'], ["\$","\$"] ],
displayMath: [ ['$$','$$'], ["\$","\$"] ]
},
displayAlign: 'center', // Change this to 'center' to center equations.
"HTML-CSS": {
styles: {'.MathJax_Display': {"margin": 4}}
}
});