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from __future__ import absolute_import


    

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from bokeh.document import Document
from bokeh.session import Session

document = Document()
session = Session()
session.use_doc('taylor_server')
session.load_document(document)


    

In [3]:

    

import numpy as np
import sympy as sy

from bokeh.objects import Plot, DataRange1d, LinearAxis, ColumnDataSource, Glyph, Grid, Legend
from bokeh.widgetobjects import Slider, TextInput, HBox, VBox, Dialog
from bokeh.glyphs import Patch, Line, Text

xs = sy.Symbol('x')
expr = sy.exp(-xs)*sy.sin(xs)
order = 1

def taylor(fx, xs, order, x_range=(0, 1), n=200):
    x0, x1 = x_range
    x = np.linspace(float(x0), float(x1), n)

    fy = sy.lambdify(xs, fx, modules=['numpy'])(x)
    tx = fx.series(xs, n=order).removeO()

    if tx.is_Number:
        ty = np.zeros_like(x)
        ty.fill(float(tx))
    else:
        ty = sy.lambdify(xs, tx, modules=['numpy'])(x)

    return x, fy, ty

def update_data():
    x, fy, ty = taylor(expr, xs, order, (-2*sy.pi, 2*sy.pi), 200)

    plot.title = "%s vs. taylor(%s, n=%d)" % (expr, expr, order)
    legend.legends = {
        "%s"         % expr: [line_f_glyph],
        "taylor(%s)" % expr: [line_t_glyph],
    }
    source.data = dict(x=x, fy=fy, ty=ty)
    slider.value = order

    session.store_document(document)

source = ColumnDataSource(data=dict(
    x  = [],
    fy = [],
    ty = [],
))

xdr = DataRange1d(sources=[source.columns("x")])
ydr = DataRange1d(sources=[source.columns("fy")])

plot = Plot(data_sources=[source], x_range=xdr, y_range=ydr, plot_width=800, plot_height=400)

line_f = Line(x="x", y="fy", line_color="blue", line_width=2)
line_f_glyph = Glyph(data_source=source, xdata_range=xdr, ydata_range=ydr, glyph=line_f)
plot.renderers.append(line_f_glyph)

line_t = Line(x="x", y="ty", line_color="red", line_width=2)
line_t_glyph = Glyph(data_source=source, xdata_range=xdr, ydata_range=ydr, glyph=line_t)
plot.renderers.append(line_t_glyph)

xaxis = LinearAxis(plot=plot, dimension=0)
yaxis = LinearAxis(plot=plot, dimension=1)

xgrid = Grid(plot=plot, dimension=0, axis=xaxis)
ygrid = Grid(plot=plot, dimension=1, axis=yaxis)

legend = Legend(plot=plot, orientation="bottom_left")
plot.renderers.append(legend)

def on_slider_value_change(obj, attr, old, new):
    global order
    order = int(new)
    update_data()

def on_text_value_change(obj, attr, old, new):
    try:
        global expr
        expr = sy.sympify(new, dict(x=xs))
    except (sy.SympifyError, TypeError, ValueError) as exception:
        dialog.content = str(exception)
        dialog.visible = True
        session.store_document(document)
    else:
        update_data()

dialog = Dialog(title="Invalid expression", buttons=["Close"])

slider = Slider(start=1, end=20, value=order, step=1, title="Order:")
slider.on_change('value', on_slider_value_change)

text = TextInput(value=str(expr), title="Expression:")
text.on_change('value', on_text_value_change)

inputs = HBox(children=[slider, text])
layout = VBox(children=[inputs, plot, dialog])

document.add(layout)


    

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update_data()


    

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session.show(layout)


    

In [8]:

    

import time

try:
    while True:
        session.load_document(document)
        time.sleep(0.5)
except KeyboardInterrupt:
    pass


    

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