def main():
x,y,c,f,rd= symbols('x y c f rd')
c= x*4+y*3
f= c**2
radius=3
r=5
p=plot3d(f)
plot3d_parametric_surface, plot3d_parametric_line,
plot3d)
lx = range(5)
ly = [i**2 for i in lx]
x = Symbol('x')
y = Symbol('y')
u = Symbol('u')
v = Symbol('v')
expr = x**2 - 1
b = plot(expr, (x, 2, 4), show=False) # cartesian plot
e = plot(exp(-x), (x, 0, 4), show=False) # cartesian plot (and coloring, see below)
f = plot3d_parametric_line(sin(x), cos(x), x, (x, 0, 10), show=False) # 3d parametric line plot
g = plot3d(sin(x)*cos(y), (x, -5, 5), (y, -10, 10), show=False) # 3d surface cartesian plot
h = plot3d_parametric_surface(cos(u)*v, sin(u)*v, u, (u, 0, 10), (v, -2, 2), show=False) # 3d parametric surface plot
# Some aesthetics
e[0].line_color = lambda x: x / 4
f[0].line_color = lambda x, y, z: z / 10
g[0].surface_color = lambda x, y: sin(x)
# Some more stuff on aesthetics - coloring wrt coordinates or parameters
param_line_2d = plot_parametric((x*cos(x), x*sin(x), (x, 0, 15)), (1.1*x*cos(x), 1.1*x*sin(x), (x, 0, 15)), show=False)
param_line_2d[0].line_color = lambda u: sin(u) # parametric
param_line_2d[1].line_color = lambda u, v: u**2 + v**2 # coordinates
param_line_2d.title = 'The inner one is colored by parameter and the outher one by coordinates'
param_line_3d = plot3d_parametric_line((x*cos(x), x*sin(x), x, (x, 0, 15)),
(1.5*x*cos(x), 1.5*x*sin(x), x, (x, 0, 15)),
def plot_and_save(name):
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x*sin(x),x*cos(x))
p.extend(p)
p[0].line_color = lambda a : a
p[1].line_color='b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1,1)
p.xlim = (-15,20)
p.save(tmp_file('%s_basic_options_and_colors.png' % name))
p.extend(plot(x+1))
p.append(plot(x+3,x**2)[1])
p.save(tmp_file('%s_plot_extend_append.png' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem.png' % name))
p = plot(sin(x),(x,-2*pi,4*pi))
p.save(tmp_file('%s_line_explicit.png' % name))
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range.png' % name))
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range.png' % name))
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range.png' % name))
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple.png' % name))
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges.png' % name))
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
#3d parametric plots
p = plot3d_parametric_line(sin(x),cos(x),x)
p.save(tmp_file('%s_3d_line.png' % name))
p = plot3d_parametric_line((sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface.png' % name))
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
# Multiple 3D plots with different ranges.
p = plot3d((x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface((x*sin(z),x*cos(z),z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface.png' % name))
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a : a
p.save(tmp_file('%s_colors_line_arity1.png' % name))
p[0].line_color = lambda a, b : b
p.save(tmp_file('%s_colors_line_arity2.png' % name))
p = plot(x*sin(x), x*cos(x), (x, 0, 10))
p[0].line_color = lambda a : a
p.save(tmp_file('%s_colors_param_line_arity1.png' % name))
p[0].line_color = lambda a, b : a
p.save(tmp_file('%s_colors_param_line_arity2a.png' % name))
p[0].line_color = lambda a, b : b
p.save(tmp_file('%s_colors_param_line_arity2b.png' % name))
p = plot3d_parametric_line(sin(x)+0.1*sin(x)*cos(7*x),
cos(x)+0.1*cos(x)*cos(7*x),
0.1*sin(7*x),
(x, 0 , 2*pi))
p[0].line_color = lambda a : sin(4*a)
p.save(tmp_file('%s_colors_3d_line_arity1.png' % name))
p[0].line_color = lambda a, b : b
p.save(tmp_file('%s_colors_3d_line_arity2.png' % name))
p[0].line_color = lambda a, b, c : c
p.save(tmp_file('%s_colors_3d_line_arity3.png' % name))
p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
p[0].surface_color = lambda a : a
p.save(tmp_file('%s_colors_surface_arity1.png' % name))
p[0].surface_color = lambda a, b : b
p.save(tmp_file('%s_colors_surface_arity2.png' % name))
p[0].surface_color = lambda a, b, c : c
p.save(tmp_file('%s_colors_surface_arity3a.png' % name))
p[0].surface_color = lambda a, b, c : sqrt((a-3*pi)**2+b**2)
p.save(tmp_file('%s_colors_surface_arity3b.png' % name))
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a : a
p.save(tmp_file('%s_colors_param_surf_arity1.png' % name))
p[0].surface_color = lambda a, b : a*b
p.save(tmp_file('%s_colors_param_surf_arity2.png' % name))
p[0].surface_color = lambda a, b, c : sqrt(a**2+b**2+c**2)
p.save(tmp_file('%s_colors_param_surf_arity3.png' % name))
###
# Examples from the 'advanced' notebook
###
i = Integral(log((sin(x)**2+1)*sqrt(x**2+1)),(x,0,y))
p = plot(i,(y, 1, 5))
p.save(tmp_file('%s_advanced_integral.png' % name))
s = summation(1/x**y,(x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum.png' % name))
p = plot(summation(1/x,(x,1,y)), (y, 2,10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum.png' % name))
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x)+I*cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
import numpy as np
from engine.interpolate import splint2
from sympy.plotting import plot3d
from sympy.abc import x, y
from scipy import misc
image = misc.imread('bitmap_force_input.jpg')
image = image.astype(dtype=np.float)
grey = np.add.reduce(image, 2)/3.0
grey = np.fliplr(np.swapaxes(grey, 1, 0))
(m, n) = grey.shape
xs = np.linspace(0.0, m, num=m)
ys = np.linspace(0.0, n, num=n)
zs = grey
tolerance = 1e-6
print "starting build a spline"
spline_expression = splint2(xs, ys, zs, x, y)
print "end building a spline"
plot3d(spline_expression, (x, 0.0, m), (y, 0.0, n))
print('g ->', sym.factor(x**3 + 12 * x * y * z + 3 * y**2 * z))
print('h ->', sym.solveset(x - 4, x))
matrix1 = sym.Matrix([[5, 12, 40], [30, 70, 2]])
matrix2 = sym.Matrix([2, 1, 0])
print('i ->')
sym.pprint(matrix1 * matrix2)
print()
print('j ->')
plot(x**3 + 3, (x, -10, 10))
print()
print('k ->')
plot3d(x**2 * y**3, (x, -6, 6), (y, -6, 6))
#==============================================================================
print("_________________Question2_______________")
workbook = xlsxwriter.Workbook('sample1.xlsx')
worksheet = workbook.add_worksheet()
str1 = 'This is Example'
str2 = 'My first export examlpe'
format1 = workbook.add_format({
'bold': True,
'font_color': 'red',
'font_size': 15
})
format2 = workbook.add_format({'font_size': 10})
sho_potential_1D = m * omega**2 * x**2 / 2
sho_potential_3D = m * omega**2 * r_sq / 2
sho_ham_1D = hamiltonian_one_dim(func=psi_a,
potential=sho_potential_1D,
var=x,
constants=True)
sho_ham_3D = hamiltonian_three_dim(func=psi_c,
potential=sho_potential_3D,
constants=True)
print(sho_ham_1D)
print(sho_ham_3D)
# Plotting
sho_ham_1D_plot = plot(sho_ham_1D, plot=False)
sho_ham_3D_plot = plot3d(sho_ham_3D, plot=False)
'''
Euler–Lagrange
'''
def lagrangian(kinetic, potential):
l = kinetic - potential
return l
def action(lagra, var, var_1, var_2):
s = sym.integrate(lagra, (var, var_1, var_2))
return s
from sympy import Point, Line, pi, symbols, plot
from sympy.plotting import plot3d, plot3d_parametric_surface
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits import mplot3d
p1, p2 = Point(0, 0), Point(1, 1)
l = Line(p1, p2)
t = symbols('t')
plot(3 + 5 * t, (t, -5, 5))
x, y = symbols('x y')
plot3d(3 + 5 * x, (x, -5, 5), (y, -5, 5))
z = symbols('x y z')
plot3d(x**2 + y**2, (x, -5, 5), (y, -5, 5))
xx, yy = np.meshgrid(range(10), range(10))
z = 0 * xx + 0 * yy + 475
plt3d = plt.figure().gca(projection='3d')
plt3d.plot_surface(xx, yy, z, alpha=0.2)
ar1, ar2, ar3 = t_df['x_kb'], t_df['y_kb'], t_df['z_kb']
#plt3d.plot(ar1, ar2, ar3)
# Ensure that the next plot doesn't overwrite the first plot
ax = plt.gca()
def plot3d(*args, **kwargs):
if "show" in kwargs:
kwargs.pop("show")
return plotter.plot3d(*plotArgs(args), show=False, **kwargs)
def graph3d(calculation, **kwargs):
result = plot3d(sympify(calculation), show=False, **kwargs)
result.save(result_file)
from sympy import *
from sympy.plotting import plot3d
x, y = symbols('x y')
f = 2 * x + 3 * y
plot3d(f)
from sympy import symbols
from sympy.plotting import plot3d
x1, x2, x3 = symbols('x1 x2 x3')
plot3d(x1 + x2 + x3 - 1, (x1, -5, 5), (x2, -5, 5), (x3, -5, 5))
def plot_and_save(name):
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x * sin(x), x * cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors.png' % name))
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append.png' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem.png' % name))
p = plot(sin(x), (x, -2 * pi, 4 * pi))
p.save(tmp_file('%s_line_explicit.png' % name))
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range.png' % name))
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range.png' % name))
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range.png' % name))
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple.png' % name))
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges.png' % name))
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line.png' % name))
p = plot3d_parametric_line((sin(x), cos(x), x, (x, -5, 5)),
(cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface.png' % name))
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
# Multiple 3D plots with different ranges.
p = plot3d((x * y, (x, -3, 3), (y, -3, 3)),
(-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x * sin(z), x * cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface.png' % name))
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1.png' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2.png' % name))
p = plot(x * sin(x), x * cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1.png' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a.png' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b.png' % name))
p = plot3d_parametric_line(
sin(x) + 0.1 * sin(x) * cos(7 * x),
cos(x) + 0.1 * cos(x) * cos(7 * x), 0.1 * sin(7 * x), (x, 0, 2 * pi))
p[0].line_color = lambda a: sin(4 * a)
p.save(tmp_file('%s_colors_3d_line_arity1.png' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2.png' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3.png' % name))
p = plot3d(sin(x) * y, (x, 0, 6 * pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1.png' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2.png' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a.png' % name))
p[0].surface_color = lambda a, b, c: sqrt((a - 3 * pi)**2 + b**2)
p.save(tmp_file('%s_colors_surface_arity3b.png' % name))
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1.png' % name))
p[0].surface_color = lambda a, b: a * b
p.save(tmp_file('%s_colors_param_surf_arity2.png' % name))
p[0].surface_color = lambda a, b, c: sqrt(a**2 + b**2 + c**2)
p.save(tmp_file('%s_colors_param_surf_arity3.png' % name))
###
# Examples from the 'advanced' notebook
###
i = Integral(log((sin(x)**2 + 1) * sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral.png' % name))
s = summation(1 / x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum.png' % name))
p = plot(summation(1 / x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum.png' % name))
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I * cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
def plot_loss(self, expression, path):
from sympy.plotting import plot3d
graph = plot3d(expression, show=False)
graph.save(f"{path}/loss_function")
plt.close("all")
# assumed values
u0 = 1
v0 = 0
omegan = 4.
wd = omegan*sympy.sqrt(1-zeta**2)
ics = {u.subs(t, 0): u0, u.diff(t).subs(t, 0): v0}
sol = dsolve(u.diff(t, t) + 2*zeta*omegan*u.diff(t) + omegan**2*u, ics=ics)
#import matplotlib
#matplotlib.use('TkAgg')
from sympy.plotting import plot3d
p1 = plot3d(sol.rhs, (t, 0, 10), (zeta, 0.05, 0.7),
show=False,
nb_of_points_x=500,
nb_of_points_y=10,
xlabel='$t$',
ylabel='$\zeta$',
zlabel='$u(t)$',
)
p1.show()
def plot_and_save_3(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x*sin(x), x*cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x) + 0.1*sin(x)*cos(7*x),
cos(x) + 0.1*cos(x)*cos(7*x),
0.1*sin(7*x),
(x, 0, 2*pi))
p[0].line_color = lambdify_(x, sin(4*x))
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3*pi)**2 + y**2))
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a*b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
v0 = 0
omegaf = omegan * ratio
f0 = 10.
# solving ODE
f = f0 * sympy.cos(omegaf * t)
ics = {
u.subs(t, 0): u0,
u.diff(t).subs(t, 0): v0,
}
sol = dsolve(u.diff(t, t) + 2 * zeta * omegan * u.diff(t) + omegan**2 * u - f,
ics=ics)
import matplotlib
matplotlib.use('TkAgg')
from sympy.plotting import plot3d
subs = {zeta: 0.2}
p1 = plot3d(
sol.rhs.subs(subs),
(t, 0, 10),
(ratio, 0.1, 2),
show=False,
nb_of_points_x=250,
nb_of_points_y=250,
xlabel='$t$',
ylabel='$\omega_f/\omega_n$',
zlabel='$u(t)$',
)
p1.show()
print(sym.expand((x + y)**2))
print(sym.simplify((4 * x**3 + 21 * x**2 + 10 * x + 12)))
print(sym.limit(1 / (x**2), x, sym.oo))
i, n = sym.symbols('i n')
print(sym.summation(2 * i + i - 1, (i, 5, n)))
print(sym.integrate(sin(x) + exp(x) * cos(x) + tan(x), x))
print(sym.factor(x**3 + 12 * x * y * z + 3 * y**2 * z))
print(sym.solveset(x - 4, x))
m1 = sym.Matrix([[5, 12, 40], [30, 70, 2]])
m2 = sym.Matrix([2, 1, 0])
print(m1 * m2)
plot(x**3 + 3, (x, -10, 10))
f = x**2 * y**3
plot3d(f, (x, -6, 6), (y, -6, 6))
print("==========================Exercise two=====================")
workbook = xlsxwriter.Workbook('forEx.xlsx')
worksheet = workbook.add_worksheet()
text1 = 'This is Example'
text2 = 'My first export examlpe'
Fformat = workbook.add_format({
'bold': True,
'font_color': 'red',
'font_size': 14
})
from sympy import symbols
import numpy as np
from engine.interpolate import splint2
from sympy.plotting import plot3d
x, y = symbols('x y')
m = 5
n = 4
xs = np.array([2.0, 3.0, 6.0, 8.0, 9.0], dtype=np.float)
ys = np.array([1.0, 2.0, 4.0, 8.0], dtype=np.float)
zs = np.random.rand(5, 4)*10.0
tolerance = 1e-6
spline_expression = splint2(xs, ys, zs, x, y)
plot3d(spline_expression, (x, 2.0, 9.0), (y, 1.0, 8.0))
import sympy
from sympy import Function, dsolve, Symbol
# symbols
t = Symbol('t', positive=True)
wf = Symbol('wf', positive=True)
# unknown function
u = Function('u')(t)
# solving ODE with initial conditions
u0 = 0.4
v0 = 2
k = 150
m = 2
F0 = 10
wn = sympy.sqrt(k/m)
#wf = 2*sympy.sqrt(k/m)
F = F0*sympy.sin(wf*t)
ics = {u.subs(t, 0): u0, u.diff(t).subs(t, 0): v0}
sol = dsolve(m*u.diff(t, t) + k*u - F, ics=ics)
import matplotlib
matplotlib.use('TkAgg')
from sympy.plotting import plot3d
p1 = plot3d(sol.rhs, (t, 0, 10), (wf, 0.8*wn, 0.99*wn),
xlabel='$t$', ylabel='$\omega_f$', zlabel='$u(t)$',
nb_of_points_x=250, nb_of_points_y=25)
def newton_multi(request):
x, y, z, w = sympy.symbols('x y z w')
valores = request.POST
n = len(valores)
plt.rcParams.update(plt.rcParamsDefault)
plt.close('all')
if n == 5:
iteraciones = 10
resul = {'titulos': ['n', 'Vector Solución', 'f₁(x, y), f₂(x, y)'], 'filas': []}
f1 = sympy.sympify(valores['f1'])
x0 = float(valores['x0'])
f2 = sympy.sympify(valores['f2'])
y0 = float(valores['y0'])
# derivadas parciales
f1x = sympy.diff(f1, x)
f1y = sympy.diff(f1, y)
f2x = sympy.diff(f2, x)
f2y = sympy.diff(f2, y)
# vector de las funciones iniciales
v = sympy.Matrix([[f1], [f2]])
# inversa,de la jacobiana
j_inv = (sympy.Matrix([[f1x, f1y],
[f2x, f2y]])) ** -1
# lamdify de las matrices
jaco = sympy.lambdify([x, y], j_inv, 'numpy')
fxfy = sympy.lambdify([x, y], v, 'numpy')
solucion = np.array([[x0], [y0]])
for n in range(1, iteraciones + 1):
# Dandole formato a los valores
sol = fxfy(solucion[0][0], solucion[1][0])
xs = f'{solucion[0][0]:.6f}'
ys = f'{solucion[1][0]:.6f}'
fxn = f'{float(sol[0]):.6f}'
fyn = f'{float(sol[1]):.6f}'
resul['filas'].append([n, xs + ' | ' + ys, fxn + ' | ' + fyn])
j = jaco(solucion[0][0], solucion[1][0]).dot(fxfy(solucion[0][0], solucion[1][0]))
solucion = solucion - j
context = {'context': resul}
context["jaco"] = sympy.latex(sympy.Matrix([[f1x, f1y],
[f2x, f2y]])).replace("\left[", ' ').strip("\\right]").replace(
"matrix", "bmatrix")
# graficación
plt.rc_context({'axes.edgecolor': 'w', 'xtick.color': 'w', 'ytick.color': 'w'})
# plt.style.use("dark_background")
xs = solucion[0][0] # x solucion
ys = solucion[1][0] # y solucion
titulo = '\n' + estiliza_string(valores['f1']) + ' and ' + estiliza_string(valores['f2']) + '\n'
plt.rc_context({'axes.edgecolor': 'gray', 'xtick.color': 'gray', 'ytick.color': 'gray'})
p = plot3d(f1, f2, (x, xs - 3, xs + 3), (y, ys - 3, ys + 3), title=titulo, nb_of_points_x=35, nb_of_points_y=35,
xlabel='X', ylabel='Y')
buf = BytesIO()
p._backend.fig.savefig(buf, format='jpg', quality=90, bbox_inches='tight', facecolor="#f3f2f1", dpi=150,
transparent=True)
buf.seek(0)
uri = 'data:image/png;base64,' + parse.quote(b64encode(buf.read()))
context['image'] = uri
p._backend.close()
elif n == 7:
iteraciones = 15
resul = {'titulos': ['n', 'Vector Solución', 'f₁ | f₂ | f₃'], 'filas': []}
f1 = sympy.sympify(valores['f1'])
x0 = float(valores['x0'])
f2 = sympy.sympify(valores['f2'])
y0 = float(valores['y0'])
f3 = sympy.sympify(valores['f3'])
z0 = float(valores['z0'])
# derivadas parciales
f1x = sympy.diff(f1, x)
f1y = sympy.diff(f1, y)
f1z = sympy.diff(f1, z)
f2x = sympy.diff(f2, x)
f2y = sympy.diff(f2, y)
f2z = sympy.diff(f2, z)
f3x = sympy.diff(f3, x)
f3y = sympy.diff(f3, y)
f3z = sympy.diff(f3, z)
# funciones iniciales
v = sympy.Matrix([[f1], [f2], [f3]])
# inversa jacobiana
j_inv = (sympy.Matrix([[f1x, f1y, f1z],
[f2x, f2y, f2z],
[f3x, f3y, f3z]])) ** -1
jaco = sympy.lambdify([x, y, z], j_inv, "numpy")
fxfyfz = sympy.lambdify([x, y, z], v, "numpy")
solucion = np.array([[x0], [y0], [z0]])
for n in range(1, iteraciones + 1):
# Dandole formato a los valores
sol = fxfyfz(solucion[0][0], solucion[1][0], solucion[2][0])
xs = f'{solucion[0][0]:.4f}'
ys = f'{solucion[1][0]:.4f}'
zs = f'{solucion[2][0]:.4f}'
fxn = f'{float(sol[0]):.4f}'
fyn = f'{float(sol[1]):.4f}'
fzn = f'{float(sol[2]):.4f}'
resul['filas'].append([n, xs + ' | ' + ys + ' | ' + zs, fxn + ' | ' + fyn + ' | ' + fzn])
j = jaco(solucion[0][0], solucion[1][0], solucion[2][0]).dot(
fxfyfz(solucion[0][0], solucion[1][0], solucion[2][0]))
solucion -= j
context = {'context': resul}
context["jaco"] = sympy.latex(sympy.Matrix([[f1x, f1y, f1z],
[f2x, f2y, f2z],
[f3x, f3y, f3z]])).replace("\left[", ' ').strip("\\right]").replace(
"matrix", "bmatrix")
context["inv"] = sympy.latex(j_inv).replace("\left[", ' ').strip("\\right]").replace("matrix", "bmatrix")
context["mat"] = sympy.latex(v).replace("\left[", ' ').strip("\\right]").replace("matrix", "bmatrix")
return render(request, "newton_calculado_multi.html", context)
x = sym.Symbol('x')
y = sym.Symbol('y')
f = sy.Function('f')(x, y)
y, yp, N = sym.symbols('y_i, y^p_i, N')
MSE = 1 / n * sy.Sum((y - yp)**2, (i, 1, n))
MSE
sy.Derivative(MSE, y, yp, 1)
MSE = 1 / n * sy.summation((y - yp)**2, (i, 1, n))
MSE
MSE_diff = sy.diff((y**2 + yp**2)**0.5, y, yp, 1)
MSE_diff
plt.ion()
p1 = plot3d(sy.diff((y**2 + yp**2)**0.5, y, yp, 1), (y, -5, 5), (yp, -5, 5))
fg, ax = p1._backend.fig, p1._backend.ax
plt.rcParams["figure.figsize"] = (20, 10)
ax[0].axis('tight')
#ax[0].set_aspect('auto') # 'auto', 'equal' or a positive integer is allowed
ax[0].grid(True)
ax[0].view_init(100, 150)
plt.draw()
plt.ion()
plt.show()
def plot_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x * sin(x), x * cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors' % name))
p._backend.close()
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem' % name))
p._backend.close()
p = plot(sin(x), (x, -2 * pi, 4 * pi))
p.save(tmp_file('%s_line_explicit' % name))
p._backend.close()
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range' % name))
p._backend.close()
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range' % name))
p._backend.close()
raises(ValueError, lambda: plot(x, y))
p = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1))
p.save(tmp_file('%s_plot_piecewise' % name))
p._backend.close()
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line((sin(x), cos(x), x, (x, -5, 5)),
(cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d((x * y, (x, -3, 3), (y, -3, 3)),
(-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x * sin(z), x * cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x * sin(x), x * cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(
sin(x) + 0.1 * sin(x) * cos(7 * x),
cos(x) + 0.1 * cos(x) * cos(7 * x), 0.1 * sin(7 * x), (x, 0, 2 * pi))
p[0].line_color = lambdify_(x, sin(4 * x))
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x) * y, (x, 0, 6 * pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3 * pi)**2 + y**2))
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a * b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
###
# Examples from the 'advanced' notebook
###
# XXX: This raises the warning "The evaluation of the expression is
# problematic. We are trying a failback method that may still work. Please
# report this as a bug." It has to use the fallback because using evalf()
# is the only way to evaluate the integral. We should perhaps just remove
# that warning.
with warnings.catch_warnings(record=True) as w:
i = Integral(log((sin(x)**2 + 1) * sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral' % name))
p._backend.close()
# Make sure no other warnings were raised
assert len(w) == 1
assert issubclass(w[-1].category, UserWarning)
assert "The evaluation of the expression is problematic" in str(
w[0].message)
s = Sum(1 / x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum' % name))
p._backend.close()
p = plot(Sum(1 / x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum' % name))
p._backend.close()
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I * cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
#Characteristic function of a StudentT distribution with nu=10
plot((meijerg(
((1 / 2, ), ()),
((5, 0, 1 / 2), ()), 5 * x**2 * exp_polar(-I * pi) / 2) + meijerg(
((1 / 2, ), ()),
((5, 0, 1 / 2),
()), 5 * x**2 * exp_polar(I * pi) / 2)) / (48 * pi),
(x, 1e-6, 1e-2)).save(tmp_file())
def plot_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x*sin(x), x*cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors' % name))
p._backend.close()
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem' % name))
p._backend.close()
p = plot(sin(x), (x, -2*pi, 4*pi))
p.save(tmp_file('%s_line_explicit' % name))
p._backend.close()
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range' % name))
p._backend.close()
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range' % name))
p._backend.close()
raises(ValueError, lambda: plot(x, y))
p = plot(Piecewise((1, x > 0), (0, True)),(x,-1,1))
p.save(tmp_file('%s_plot_piecewise' % name))
p._backend.close()
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line(
(sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d(
(x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x*sin(z), x*cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x*sin(x), x*cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x) + 0.1*sin(x)*cos(7*x),
cos(x) + 0.1*cos(x)*cos(7*x),
0.1*sin(7*x),
(x, 0, 2*pi))
p[0].line_color = lambda a: sin(4*a)
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambda a, b, c: sqrt((a - 3*pi)**2 + b**2)
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a*b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambda a, b, c: sqrt(a**2 + b**2 + c**2)
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
###
# Examples from the 'advanced' notebook
###
i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral' % name))
p._backend.close()
s = Sum(1/x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum' % name))
p._backend.close()
p = plot(Sum(1/x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum' % name))
p._backend.close()
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I*cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
#Characteristic function of a StudentT distribution with nu=10
plot((meijerg(((1 / 2,), ()), ((5, 0, 1 / 2), ()), 5 * x**2 * exp_polar(-I*pi)/2)
+ meijerg(((1/2,), ()), ((5, 0, 1/2), ()),
5*x**2 * exp_polar(I*pi)/2)) / (48 * pi), (x, 1e-6, 1e-2)).save(tmp_file())
msg = "\tMenu\n\n"
msg += "0. EXIT\n"
msg += "1. Show graph for f1\n"
msg += "2. Show graph for the first Taylor polynomial of f1\n"
msg += "3. Show graph for the second Taylor polynomial of f1\n"
msg += "4. Show graph for f1, T1 of f1 and T2 of f1 together.\n"
msg += "5. Show graph for f2\n"
msg += "6. Show graph for the first Taylor polynomial of f2\n"
msg += "7. Show graph for the second Taylor polynomial of f2\n"
msg += "8. Show graph for f1, T1 of f2 and T2 of f2 together.\n"
print msg
while True:
cmd = raw_input("Enter command: ").strip()
if(cmd == "1"):
plot3d(f1, (x, -1, 1), (y, -1, 1), title = "f1")
elif(cmd == "2"):
plot3d(T1f1, (x, -1, 1), (y, -1, 1), title ="T1(x,y) of f1")
elif(cmd == "3"):
plot3d(T2f1, (x, -1, 1), (y, -1, 1), title ="T2(x,y) of f1")
elif(cmd == "4"):
plot3d(f1, T1f1, T2f1, (x, -1, 1), (y, -1, 1), title = "f1, T1(x,y) and T2(x,y)")
elif(cmd == "5"):
plot3d(f2, (x, -1, 1), (y, -1, 1), title = "f2")
elif(cmd == "6"):
plot3d(T1f2, (x, -1, 1), (y, -1, 1), title ="T1(x,y) of f2")
elif(cmd == "7"):
plot3d(T2f2, (x, -1, 1), (y, -1, 1), title ="T2(x,y) of f2")
elif(cmd == "8"):
plot3d(f2, T1f2, T2f2, (x, -1, 1), (y, -1, 1), title = "f2, T1(x,y) and T2(x,y)")
elif(cmd == "0"):
lx = range(5)
ly = [i**2 for i in lx]
x = Symbol('x')
y = Symbol('y')
u = Symbol('u')
v = Symbol('v')
expr = x**2 - 1
b = plot(expr, (x, 2, 4), show=False) # cartesian plot
e = plot(exp(-x), (x, 0, 4),
show=False) # cartesian plot (and coloring, see below)
f = plot3d_parametric_line(sin(x), cos(x), x, (x, 0, 10),
show=False) # 3d parametric line plot
g = plot3d(sin(x) * cos(y), (x, -5, 5), (y, -10, 10),
show=False) # 3d surface cartesian plot
h = plot3d_parametric_surface(cos(u) * v,
sin(u) * v,
u, (u, 0, 10), (v, -2, 2),
show=False) # 3d parametric surface plot
# Some aesthetics
e[0].line_color = lambda x: x / 4
f[0].line_color = lambda x, y, z: z / 10
g[0].surface_color = lambda x, y: sin(x)
# Some more stuff on aesthetics - coloring wrt coordinates or parameters
param_line_2d = plot_parametric(
(x * cos(x), x * sin(x), (x, 0, 15)),
(1.1 * x * cos(x), 1.1 * x * sin(x), (x, 0, 15)),
show=False)
def plot_and_save_2(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
# parametric 2d plots.
# Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
# Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file("%s_parametric_range" % name))
p._backend.close()
# Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file("%s_parametric_multiple" % name))
p._backend.close()
# Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file("%s_parametric_multiple_ranges" % name))
p._backend.close()
# depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file("%s_recursion_depth" % name))
p._backend.close()
# No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file("%s_adaptive" % name))
p._backend.close()
# 3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file("%s_3d_line" % name))
p._backend.close()
p = plot3d_parametric_line((sin(x), cos(x), x, (x, -5, 5)),
(cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file("%s_3d_line_multiple" % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file("%s_3d_line_points" % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file("%s_surface" % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file("%s_surface_multiple" % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d((x * y, (x, -3, 3), (y, -3, 3)),
(-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file("%s_surface_multiple_ranges" % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file("%s_parametric_surface" % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x * sin(z), x * cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)),
)
p.save(tmp_file("%s_parametric_surface" % name))
p._backend.close()
# Single Contour plot.
p = plot_contour(sin(x) * sin(y), (x, -5, 5), (y, -5, 5))
p.save(tmp_file("%s_contour_plot" % name))
p._backend.close()
# Multiple Contour plots with same range.
p = plot_contour(x**2 + y**2, x**3 + y**3, (x, -5, 5), (y, -5, 5))
p.save(tmp_file("%s_contour_plot" % name))
p._backend.close()
# Multiple Contour plots with different range.
p = plot_contour(
(x**2 + y**2, (x, -5, 5), (y, -5, 5)),
(x**3 + y**3, (x, -3, 3), (y, -3, 3)),
)
p.save(tmp_file("%s_contour_plot" % name))
p._backend.close()
def plot_and_save_3(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file("%s_colors_line_arity1" % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file("%s_colors_line_arity2" % name))
p._backend.close()
p = plot(x * sin(x), x * cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file("%s_colors_param_line_arity1" % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file("%s_colors_param_line_arity2a" % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file("%s_colors_param_line_arity2b" % name))
p._backend.close()
p = plot3d_parametric_line(
sin(x) + 0.1 * sin(x) * cos(7 * x),
cos(x) + 0.1 * cos(x) * cos(7 * x),
0.1 * sin(7 * x),
(x, 0, 2 * pi),
)
p[0].line_color = lambdify_(x, sin(4 * x))
p.save(tmp_file("%s_colors_3d_line_arity1" % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file("%s_colors_3d_line_arity2" % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file("%s_colors_3d_line_arity3" % name))
p._backend.close()
p = plot3d(sin(x) * y, (x, 0, 6 * pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file("%s_colors_surface_arity1" % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file("%s_colors_surface_arity2" % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file("%s_colors_surface_arity3a" % name))
p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3 * pi)**2 + y**2))
p.save(tmp_file("%s_colors_surface_arity3b" % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file("%s_colors_param_surf_arity1" % name))
p[0].surface_color = lambda a, b: a * b
p.save(tmp_file("%s_colors_param_surf_arity2" % name))
p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
p.save(tmp_file("%s_colors_param_surf_arity3" % name))
p._backend.close()
# -*- coding: utf-8 -*-
from sympy import Matrix, solve, det, latex
from sympy.abc import x,y,z
from sympy.plotting import plot3d
P1 = (1,2,3)
P2 = (0,-1,1)
P3 = (-2,1,-2)
M = Matrix([[x-P1[0] , y-P1[1] , z-P1[2]] ,
[P2[0]-P1[0] , P2[1]-P1[1] , P2[2]-P1[2]],
[P3[0]-P1[0] , P3[1]-P1[1] , P3[2]-P1[2]]])
sol = solve(det(M), z)
print(u"Ecuación implícita: %s = 0"%det(M))
print(u"Ecuación explícita: z=%s"%(sol[0]))
h = plot3d(sol[0], (x,0,5), (y,0,5), title="$z = %s$"%(latex(sol[0])))
h.save("img_01.png")
h.show()
x3_2_plot = sym.plot(x3[1], (t, 0, 6),
label='om=2',
line_color='r',
legend=True,
show=False)
x3_1_plot.extend(x3_2_plot)
x3_3_plot = sym.plot(x3[2], (t, 0, 6),
label='om=3',
line_color='g',
legend=True,
show=False)
x3_1_plot.extend(x3_3_plot)
x3_1_plot.title = 'Зависимость координаты материальной точки x от времени t'
x3_1_plot.xlabel = 't, с'
x3_1_plot.ylabel = 'x, м'
x3_1_plot.show()
A_expr = 1 / (sym.sqrt((omega0**2 - om**2)**2 + 4 * delta0**2 * om**2))
fi_expr = sym.atan(2 * delta0 * om / (omega0**2 - om**2))
x3_expr = A_expr * sym.cos(t * om + fi_expr)
x3_plot3d = symplot.plot3d(x3_expr, (t, 0, 6),
(om, om_val[0], om_val[len(om_val) - 1]),
show=False)
x3_plot3d.title = ('Зависимость коорд. мат. точки x '
'от времени t и вынуждающей силы omega')
x3_plot3d.xlabel = 't, с'
x3_plot3d.ylabel = 'omega'
x3_plot3d.show()
def plot_and_save_2(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line(
(sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d(
(x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x*sin(z), x*cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Single Contour plot.
p = plot_contour(sin(x)*sin(y), (x, -5, 5), (y, -5, 5))
p.save(tmp_file('%s_contour_plot' % name))
p._backend.close()
# Multiple Contour plots with same range.
p = plot_contour(x**2 + y**2, x**3 + y**3, (x, -5, 5), (y, -5, 5))
p.save(tmp_file('%s_contour_plot' % name))
p._backend.close()
# Multiple Contour plots with different range.
p = plot_contour((x**2 + y**2, (x, -5, 5), (y, -5, 5)), (x**3 + y**3, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_contour_plot' % name))
p._backend.close()
def plot_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x * sin(x), x * cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors' % name))
p._backend.close()
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem' % name))
p._backend.close()
p = plot(sin(x), (x, -2 * pi, 4 * pi))
p.save(tmp_file('%s_line_explicit' % name))
p._backend.close()
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range' % name))
p._backend.close()
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range' % name))
p._backend.close()
raises(ValueError, lambda: plot(x, y))
p = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1))
p.save(tmp_file('%s_plot_piecewise' % name))
p._backend.close()
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line((sin(x), cos(x), x, (x, -5, 5)),
(cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d((x * y, (x, -3, 3), (y, -3, 3)),
(-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x * sin(z), x * cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x * sin(x), x * cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(
sin(x) + 0.1 * sin(x) * cos(7 * x),
cos(x) + 0.1 * cos(x) * cos(7 * x), 0.1 * sin(7 * x), (x, 0, 2 * pi))
p[0].line_color = lambda a: sin(4 * a)
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x) * y, (x, 0, 6 * pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambda a, b, c: sqrt((a - 3 * pi)**2 + b**2)
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a * b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambda a, b, c: sqrt(a**2 + b**2 + c**2)
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
###
# Examples from the 'advanced' notebook
###
i = Integral(log((sin(x)**2 + 1) * sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral' % name))
p._backend.close()
s = Sum(1 / x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum' % name))
p._backend.close()
p = plot(Sum(1 / x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum' % name))
p._backend.close()
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I * cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
#Characteristic function of a StudentT distribution with nu=10
plot((meijerg(
((1 / 2, ), ()),
((5, 0, 1 / 2), ()), 5 * x**2 * exp_polar(-I * pi) / 2) + meijerg(
((1 / 2, ), ()),
((5, 0, 1 / 2),
()), 5 * x**2 * exp_polar(I * pi) / 2)) / (48 * pi),
(x, 1e-6, 1e-2)).save(tmp_file())
def plot_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x*sin(x), x*cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors' % name))
p._backend.close()
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem' % name))
p._backend.close()
p = plot(sin(x), (x, -2*pi, 4*pi))
p.save(tmp_file('%s_line_explicit' % name))
p._backend.close()
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range' % name))
p._backend.close()
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range' % name))
p._backend.close()
raises(ValueError, lambda: plot(x, y))
#Piecewise plots
p = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1))
p.save(tmp_file('%s_plot_piecewise' % name))
p._backend.close()
p = plot(Piecewise((x, x < 1), (x**2, True)), (x, -3, 3))
p.save(tmp_file('%s_plot_piecewise_2' % name))
p._backend.close()
# test issue 7471
p1 = plot(x)
p2 = plot(3)
p1.extend(p2)
p.save(tmp_file('%s_horizontal_line' % name))
p._backend.close()
# test issue 10925
f = Piecewise((-1, x < -1), (x, And(-1 <= x, x < 0)), \
(x**2, And(0 <= x, x < 1)), (x**3, x >= 1))
p = plot(f, (x, -3, 3))
p.save(tmp_file('%s_plot_piecewise_3' % name))
p._backend.close()
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line(
(sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d(
(x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x*sin(z), x*cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x*sin(x), x*cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x) + 0.1*sin(x)*cos(7*x),
cos(x) + 0.1*cos(x)*cos(7*x),
0.1*sin(7*x),
(x, 0, 2*pi))
p[0].line_color = lambdify_(x, sin(4*x))
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3*pi)**2 + y**2))
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a*b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
###
# Examples from the 'advanced' notebook
###
# XXX: This raises the warning "The evaluation of the expression is
# problematic. We are trying a failback method that may still work. Please
# report this as a bug." It has to use the fallback because using evalf()
# is the only way to evaluate the integral. We should perhaps just remove
# that warning.
with warnings.catch_warnings(record=True) as w:
i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral' % name))
p._backend.close()
# Make sure no other warnings were raised
for i in w:
assert issubclass(i.category, UserWarning)
assert "The evaluation of the expression is problematic" in str(i.message)
s = Sum(1/x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum' % name))
p._backend.close()
p = plot(Sum(1/x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum' % name))
p._backend.close()
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I*cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
#Characteristic function of a StudentT distribution with nu=10
plot((meijerg(((1 / 2,), ()), ((5, 0, 1 / 2), ()), 5 * x**2 * exp_polar(-I*pi)/2)
+ meijerg(((1/2,), ()), ((5, 0, 1/2), ()),
5*x**2 * exp_polar(I*pi)/2)) / (48 * pi), (x, 1e-6, 1e-2)).save(tmp_file())
for i in range(0, len(delta)):
x2.append(A * sym.cos(t * omega0) * sym.exp(-t * delta[i]))
x2_plot = sym.plot(legend=True, show=False)
for j in range(0, len(delta)):
label = 'r=' + str(r_val[j])
x2_ext_plot = sym.plot(x2[j], (t, 0, 6),
label=label,
line_color=line_colors[j],
legend=True,
show=False)
x2_plot.extend(x2_ext_plot)
x2_plot.title = 'Зависимость координаты материальной точки x от времени t'
x2_plot.xlabel = 't, с'
x2_plot.ylabel = 'x, м'
x2_plot.show()
x2_expr = A * sym.cos(t * omega0) * sym.exp(-t * (r / (2 * m0)))
x2_plot3d = symplot.plot3d(x2_expr, (t, 0, 6),
(r, r_val[0], r_val[len(r_val) - 1]),
show=False)
x2_plot3d.title = ('Зависимость коорд. мат. точки x '
'от времени t и коэфф. вязкого трения r')
x2_plot3d.xlabel = 't, с'
x2_plot3d.ylabel = 'r'
x2_plot3d.show()