To import into another worksheet:
fun_include_ipynb('Worksheet_setup')or
load('Worksheet_setup.sage')Note: This worksheet is prepared for the open source software sage. In sage 7.3, nbconvert is missing dependencies. To rectify, enter the following commands in a terminal:
sage --sh
pip install entrypoints
pip install configparser
In [1]:
%matplotlib inline
import numpy as np # for data array operations
import pylab # for plotting
import json # for reading notebook metadata
list_plot.options["frame"]=True
list_plot.options["axes"]=False
plot.options["frame"]=True
plot.options["axes"]=False
try:
for s in units.amount_of_substance.trait_names():
globals()[s] = getattr(units.amount_of_substance,s)
for s in units.energy.trait_names():
globals()[s] = getattr(units.energy,s)
for s in units.length.trait_names():
globals()[s] = getattr(units.length,s)
for s in units.mass.trait_names():
globals()[s] = getattr(units.mass,s)
for s in units.pressure.trait_names():
globals()[s] = getattr(units.pressure,s)
for s in units.temperature.trait_names():
globals()[s] = getattr(units.temperature,s)
for s in units.time.trait_names():
globals()[s] = getattr(units.time,s)
for s in units.power.trait_names():
globals()[s] = getattr(units.power,s)
except: # in newer versions of sage, need to use _tab_completion() instead of trait_names()
for s in units.amount_of_substance._tab_completion():
globals()[s] = getattr(units.amount_of_substance,s)
for s in units.energy._tab_completion():
globals()[s] = getattr(units.energy,s)
for s in units.length._tab_completion():
globals()[s] = getattr(units.length,s)
for s in units.mass._tab_completion():
globals()[s] = getattr(units.mass,s)
for s in units.pressure._tab_completion():
globals()[s] = getattr(units.pressure,s)
for s in units.temperature._tab_completion():
globals()[s] = getattr(units.temperature,s)
for s in units.time._tab_completion():
globals()[s] = getattr(units.time,s)
for s in units.power._tab_completion():
globals()[s] = getattr(units.power,s)
udict = {}
cdict = {}
docdict = {}
dict_latex = {}
dict_domain = {}
dict_vars ={}
def var2(name, doc='', units=1, domain1='real', latexname='', value = False):
'''
Creates a symbolic variable in the given domain (standard:'real') and with the given
latexname. Further, it adds the string doc to docdict, the units to udict and the value
to cdict. All entries are optional except for name. Note that the information passed as
domain1 is saved as an assumption, e.g. 'a is read'. All assumptions can be viewed as a
list, using the command assumptions().
Usage example:
sage: var2('x', 'Distance' , units=meter, domain1 = 'positive', latexname = 'x_{1-2}', value = 1.0)
'''
if len(latexname)>0:
z = var(name,domain = domain1,latex_name = latexname)
else:
z = var(name,domain = domain1)
var1 = eval(name)
dict_domain[var1] = domain1
dict_latex[var1] = var1._latex_()
docdict[var1] = doc
udict[var1] = units
dict_vars[var1] = {'doc': doc, 'units': units, 'domain1': domain1, 'latexname': latexname, 'value': value}
if value:
cdict[var1] = value
return z
def fun_loadvars(vardict = False):
'''
Loads all information related to symbolic variables defined using var2.
Usage example:
sage: allvars = fun_loadvars()
'''
if vardict:
variables = vardict.keys()
for var1 in variables:
var2(str(var1), doc = vardict[var1]['doc'], units = vardict[var1]['units'], domain1 = vardict[var1]['domain1'],\
latexname = vardict[var1]['latexname'], value = vardict[var1]['value'])
else:
variables = docdict.keys()
for var1 in variables:
if var1 in cdict.keys():
var2(str(var1), doc=docdict[var1], units=udict[var1], domain1 = dict_domain[var1],\
latexname=dict_latex[var1], value=cdict[var1])
else:
var2(str(var1), doc=docdict[var1], units=udict[var1], domain1 = dict_domain[var1],\
latexname=dict_latex[var1])
# Workaround from http://ask.sagemath.org/question/10260/convert-derived-si-units-to-base-units/
def convert(expr):
op = expr.operator()
ops = expr.operands()
if op:
if len(ops) == 2:
return op(*map(convert, ops))
else:
return op(convert(ops[0]), reduce(op, map(convert, ops[1:])))
else:
return expr.convert() if hasattr(expr, 'convert') else expr
def units_check(eq, sfull = True):
'''
Checks whether all arguments are keys in udict and returns simplified units
'''
global udict, dict_units
udict1 = {}
# Need to multiply units with variable, so that we can devide by the symbolic equation later:
for key1 in udict.keys():
udict1[key1] = key1*udict[key1]
for blah in eq.arguments():
udict[blah]
eq.show()
if sfull:
return convert(eq.subs(udict1)/eq).simplify_full()
else:
return convert(eq.subs(udict1)/eq)
def fun_units_formatted(variable):
'''
Returns units of variable expanded to exponential notation.
'''
global udict, subsdict
units1 = (eval(variable)*udict[eval(variable)]/eval(variable)).subs(subsdict) # multiplication and division by the variable ensures that units1 is a symbolic expression, even if udict[var] = 1
facs = units1.factor_list()
str1 = ''
for term1 in facs:
op1 = term1[1]
if op1==1:
str1 = str(term1[0]) + ' ' + str1
if op1!=1:
str1 = str1 +' ' + str(term1[0])
str1 = str1 + '$^{' + str(op1) + '}$ '
return str1
def plot_fit(xdata, ydata, model, initial_guess = None, parameters = None, variables = None):
'''Fits the parameters of model to lists of xdata and ydata and plots the results
Example:
#linear regression through origin
var('x m')
model(x) = m*x
plot_fit(xdata,ydata,model)
'''
data = zip(xdata,ydata)
xdata1 = vector(xdata)
ydata1 = vector(ydata)
p1 = find_fit(data, model,solution_dict=True)
pkeys = p1.keys()
p2 = {}
for i in pkeys: p2[i] = n(p1[i],digits=3)
fitvals = vector([n(model(x1).subs(p1)) for x1 in xdata])
# root mean square deviation
rmsd = sqrt(mean(ydata1 - fitvals)^2)
nrmsd = rmsd/(max(ydata) - min(ydata))
blah = text("y="+str(model(x).subs(p2)),(0,0),fontsize=10,rgbcolor=(1,0,0))
print "y="+str(model(x).subs(p2))
print "NRMSD = "+str(n(nrmsd,digits=5))
lentext = blah.xmax() - blah.xmin()
# plot
P = list_plot(data, frame=True, axes = False, faceted=True, color = "white")
P += plot(model.subs(p1),(x,min(xdata),max(xdata)),color = 'black', legend_label = "y="+str(model(x).subs(p2)) + '\n ' + "NRMSD = "+str(n(nrmsd,digits=5)))
return P
def dict_print(vdict1, list_names = None):
dtype1 = [('name', 'S10'), ('val', object)]
vdict2 = vdict1.copy()
if list_names:
vdict2 = {}
for name1 in list_names:
vdict2[name1] = vdict1[name1]
list1 = np.array(vdict2.items(), dtype = dtype1)
list2 = np.sort(list1,order = 'name')
for k, v in list2:
print "{:<15} {:<15}".format(k,v)
def fun_dict_print(vdict1):
dtype1 = [('name', 'S10'), ('val', object)]
list1 = np.array(vdict1.items(), dtype = dtype1)
list2 = np.sort(list1,order = 'name')
for k, v in list2:
print "{:<15} {:<15}".format(k,v)
def fun_dict(dict1,dict2):
'''
Updates all entries of dict1 with entries co-occurring in dict2
and returns the udated dict1.
'''
dict1.update(dict2)
return dict1
def fun_comp_array(expr1, nparray):
"""
Returns list of values for expr1
corresponding to each row of nparray
where all arguments in expr1 are substituted
by the corresponding values in nparray.
"""
list_args = expr1.args()
return [expr1.subs(dict(zip(list_args, [nparray[str(dummy)][i] for dummy in list_args]))) for i in srange(len(nparray))]
def fun_printvar(varname):
pstring = str(varname)+': ' + docdict[varname]
try:
value = cdict[varname]
pstring1 = pstring + ', ' + str(n(value, prec = 16)) + ' ' + str(udict[varname]/varname)
except: pstring1 = pstring + ', ' + str(udict[varname]/varname)
print pstring1
return
def fun_eq(eq, sfull = True):
print units_check(eq)
return eq
def fun_export_ipynb(worksheet, folder):
'''
Exports worksheet.ipynb to a .py or .sage depending on kernel.
Example:
fun_export_ipynb('Worksheet_setup', 'temp/')
Need to import json before using this function. Unless option output=True is given,
each line of text has a semicolon added in the .py file, preventing any output.
'''
str1 = 'jupyter nbconvert --to=python \'' + worksheet+'.ipynb\''
print str1
print 'Exporting specified worksheet to .py file...'
try:
retcode = os.system(str1)
if retcode < 0:
print >>sys.stderr, "nbconvert was terminated by signal", -retcode
else:
print >>sys.stderr, "nbconvert returned", retcode
except OSError as e:
print >>sys.stderr, "Execution failed:", e
print >>sys.stderr, "Trying ipython nbconvert instead..."
str1 = 'ipython nbconvert --to script \'' + worksheet+'.ipynb\'' # for new version of python
try:
retcode = os.system(str1)
if retcode < 0:
print >>sys.stderr, "nbconvert was terminated by signal", -retcode
else:
print >>sys.stderr, "nbconvert returned", retcode
except OSError as e:
print >>sys.stderr, "Execution failed:", e
str1 = worksheet + '.py'
print 'Checking if specified ipynb file was run with sage kernel...'
with open(worksheet+'.ipynb') as data_file:
data = json.load(data_file)
if data['metadata']['kernelspec']['name'][0:4] == 'sage':
print 'Renaming .py file to .sage if notebook kernel was sage (to avoid exponent error)'
str2 = folder + worksheet + '.sage'
os.rename(str1, str2)
def fun_include_ipynb(worksheet, del1 = True, output = True):
'''
Exports worksheet.ipynb to a sage file and loads it into current worksheet.
Example:
fun_include_ipynb('Worksheet_setup')
Need to import json before using this function. Unless option output=True is given,
each line of text has a semicolon added in the .py file, preventing any output.
'''
str1 = 'jupyter nbconvert --to=python \'' + worksheet+'.ipynb\''
print str1
print 'Exporting specified worksheet to .py file...'
try:
retcode = os.system(str1)
if retcode < 0:
print >>sys.stderr, "nbconvert was terminated by signal", -retcode
else:
print >>sys.stderr, "nbconvert returned", retcode
except OSError as e:
print >>sys.stderr, "Execution failed:", e
print >>sys.stderr, "Trying ipython nbconvert instead..."
str1 = 'ipython nbconvert --to script \'' + worksheet+'.ipynb\'' # for new version of python
try:
retcode = os.system(str1)
if retcode < 0:
print >>sys.stderr, "nbconvert was terminated by signal", -retcode
else:
print >>sys.stderr, "nbconvert returned", retcode
except OSError as e:
print >>sys.stderr, "Execution failed:", e
str1 = worksheet + '.py'
print 'Checking if specified ipynb file was run with sage kernel...'
with open(worksheet+'.ipynb') as data_file:
data = json.load(data_file)
if data['metadata']['kernelspec']['name'][0:4] == 'sage':
print 'Renaming .py file to .sage if notebook kernel was sage (to avoid exponent error)'
str2 = worksheet + '.sage'
os.rename(str1, str2)
str1 = str2
if output == False:
input_file = open(str1, "r")
str2 = '0_'+ str1
output_file = open(str2, "w")
for line in input_file:
line = line.strip() # remove line end marks
final = line+'\n'
if len(line)>0:
if line[-1] != ';':
final= line+';\n'
output_file.write(final)
input_file.close()
os.remove(str1)
output_file.close()
str1 = str2
print 'Loading file into current worksheet...'
load(str1)
if del1:
print 'Removing file generated above...'
os.remove(str1)
Below, we export the above commands to a file called Worksheet_setup.sage in the temp folder, which can be loaded in other worksheets by typing:
load('temp/Worksheet_setup.sage')
However, to avoid re-exporting the file every time it is loaded, we will comment out the command and instead execute it from a different worksheet, Worksheet_update.ipynb.
In [2]:
#fun_export_ipynb('Worksheet_setup', 'temp/')
In [ ]: