def plotgrid_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
p1 = plot(x)
p2 = plot_parametric((sin(x), cos(x)), (x, sin(x)), show=False)
p3 = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500, show=False)
p4 = plot3d_parametric_line(sin(x), cos(x), x, show=False)
# symmetric grid
p = PlotGrid(2, 2, p1, p2, p3, p4)
p.save(tmp_file('%s_grid1' % name))
p._backend.close()
# grid size greater than the number of subplots
p = PlotGrid(3, 4, p1, p2, p3, p4)
p.save(tmp_file('%s_grid2' % name))
p._backend.close()
p5 = plot(cos(x),(x, -pi, pi), show=False)
p5[0].line_color = lambda a: a
p6 = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1), show=False)
p7 = plot_contour((x**2 + y**2, (x, -5, 5), (y, -5, 5)), (x**3 + y**3, (x, -3, 3), (y, -3, 3)), show=False)
# unsymmetric grid (subplots in one line)
p = PlotGrid(1, 3, p5, p6, p7)
p.save(tmp_file('%s_grid3' % name))
p._backend.close()
def plotgrid_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
p1 = plot(x)
p2 = plot_parametric((sin(x), cos(x)), (x, sin(x)), show=False)
p3 = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500, show=False)
p4 = plot3d_parametric_line(sin(x), cos(x), x, show=False)
# symmetric grid
p = PlotGrid(2, 2, p1, p2, p3, p4)
p.save(tmp_file('%s_grid1' % name))
p._backend.close()
# grid size greater than the number of subplots
p = PlotGrid(3, 4, p1, p2, p3, p4)
p.save(tmp_file('%s_grid2' % name))
p._backend.close()
p5 = plot(cos(x),(x, -pi, pi), show=False)
p5[0].line_color = lambda a: a
p6 = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1), show=False)
p7 = plot_contour((x**2 + y**2, (x, -5, 5), (y, -5, 5)), (x**3 + y**3, (x, -3, 3), (y, -3, 3)), show=False)
# unsymmetric grid (subplots in one line)
p = PlotGrid(1, 3, p5, p6, p7)
p.save(tmp_file('%s_grid3' % name))
p._backend.close()
def ball():
# x^2+y^2+z^2=a^2
# plot3d(x**2+y**2+z**2,(x,-2,2),(y,-2,2),(z,-2,z))
plot3d_parametric_surface(cos(u + v), sin(u - v), u - v, (u, -5, 5),
(v, -5, 5))
plot3d_parametric_line((cos(u), sin(u), u, (u, -5, 5)),
(sin(u), u**2, u, (u, -5, 5)))
# 圆
plot_parametric((cos(u), sin(u), (u, -5, 5)), (cos(u), u, (u, -5, 5)))
def plot_circle(L_func, L_value):
''''''
# Cartesian coordinates
# Plots a function of a single variable as a curve
# plot(L_func)
# plot3d(L_func)
# 直角坐标与极坐标互化
# The transformation of Cartesian coordinates and polar coordinates
# x=ρcosθ,y=ρsinθ,x²+y²=ρ²
if str(L_func) == 'x**2 + y**2':
print('polar coordinates')
new_x = sqrt(L_value) * cos(theta)
new_y = sqrt(L_value) * sin(theta)
# 不可以用pi，要用实数
plot_parametric(new_x, new_y, (theta, 0, 7))
def plot_geom(items):
plots = []
#create plots from implicit equations
for item in items:
if isinstance(item,Circle):
cc = Circle(item.center.evalf(), item.radius)
pl = plot_implicit(cc.equation(),show=False)
plots.append(pl)
elif isinstance(item,Segment):
limits = item.plot_interval()
var, a0,a1 = limits
xeq,yeq = item.arbitrary_point().args
#introduce numerical precision
xeq = xeq.evalf()
yeq = yeq.evalf()
new_limits = (xeq.free_symbols.pop(),a0,a1)
pl = plot_parametric(xeq,yeq,new_limits, show=False, line_color='r')
plots.append(pl)
elif isinstance(item,Line):
pl = plot_implicit(item.equation().evalf(),show=False)
plots.append(pl)
elif isinstance(item,Point):
pc = Circle(item.evalf(), .2)
plots.append(plot_geom([pc]))
else:
raise TypeError("item does not have recognized geometry type")
#combine plots
p = plots.pop()
for e in plots:
p.extend(e)
return p
def plot_stuff():
#evalf
xf, yf = F.args
t = xf.free_symbols.pop()
state = {t: 3.3}
#funcified = funcify_all(items, t)
evaluated = eval_all(items, state)
total_plot = plot_geom(evaluated)
#evaluate mechanism at multiple points
mechanism = [b1, b2, b3, b4]
#func_mech = funcify_all(mechanism, t)
steps = 7
t_plot = total_plot
for p in frange(0.0, 2 * np.pi, 2 * np.pi / steps):
p_state = {t: p}
evaluated = eval_all(mechanism, p_state)
p_plot = plot_geom(evaluated)
t_plot.extend(p_plot)
#trace out foot path
path_plot = plot_parametric(xf.evalf(),
yf.evalf(),
(xf.free_symbols.pop(), 0.0, 2 * np.pi),
show=False)
t_plot.extend(path_plot)
t_plot.show()
total_plot.show()
t_plot.save("klann2.png")
def plot_stuff():
#evalf
xf, yf = F.args
t = xf.free_symbols.pop()
state = {t:3.3}
#funcified = funcify_all(items, t)
evaluated = eval_all(items, state)
total_plot = plot_geom(evaluated)
#evaluate mechanism at multiple points
mechanism = [b1,b2,b3,b4]
#func_mech = funcify_all(mechanism, t)
steps = 7
t_plot = total_plot
for p in frange(0.0, 2*np.pi, 2*np.pi/steps):
p_state = {t:p}
evaluated = eval_all(mechanism,p_state)
p_plot = plot_geom(evaluated)
t_plot.extend(p_plot)
#trace out foot path
path_plot = plot_parametric(xf.evalf(),yf.evalf(), (xf.free_symbols.pop(),0.0,2*np.pi),show=False)
t_plot.extend(path_plot)
t_plot.show()
total_plot.show()
t_plot.save("klann2.png")
def test_issue_11764():
matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
if not matplotlib:
skip("Matplotlib not the default backend")
x = Symbol('x')
p = plot_parametric(cos(x), sin(x), (x, 0, 2 * pi), aspect_ratio=(1,1), show=False)
p.aspect_ratio == (1, 1)
# Random number of segments, probably more than 100, but we want to see
# that there are segments generated, as opposed to when the bug was present
assert len(p[0].get_segments()) >= 30
def plot_geom(items):
plots = []
fig = plt.figure()
ax = fig.add_subplot(111)
#create plots from implicit equations
for item in items:
if isinstance(item, Circle):
cc = Circle(item.center.evalf(), item.radius)
pl = plot_implicit(cc.equation(), show=False)
plots.append(pl)
elif isinstance(item, Segment):
limits = item.plot_interval()
var, a0, a1 = limits
xeq, yeq = item.arbitrary_point().args
#introduce numerical precision
xeq = xeq.evalf()
yeq = yeq.evalf()
new_limits = (xeq.free_symbols.pop(), a0, a1)
pl = plot_parametric(xeq,
yeq,
new_limits,
show=False,
line_color='r')
plots.append(pl)
elif isinstance(item, Line):
pl = plot_implicit(item.equation().evalf(), show=False)
plots.append(pl)
elif isinstance(item, Point):
pc = Circle(item.evalf(), .2)
plots.append(plot_geom([pc]))
elif isinstance(item, list):
print("item")
print(item)
mat_pts = [(p.x.evalf(), p.y.evalf()) for p in item]
print("mat_pts")
print(mat_pts)
mat_pts += [mat_pts[0]] #line has to end where it starts
codes = [Path.MOVETO]
for i in range(len(mat_pts) - 2):
codes += [Path.LINETO]
codes += [Path.CLOSEPOLY]
path = Path(mat_pts, codes)
patch = patches.PathPatch(path, facecolor='red', alpha=.5, lw=2)
ax.add_patch(patch)
ax.set_xlim(-200, 200)
ax.set_ylim(-200, 200)
else:
raise TypeError("item does not have recognized geometry type")
#combine plots
plt.show()
p = plots.pop()
for e in plots:
p.extend(e)
return p
def __init__(self):
self.plotters = {
"plot":
lambda args, params: plot(*args, **params),
"plot_parametric":
lambda args, params: plot_parametric(*args, **params),
"plot3d":
lambda args, params: plot3d(*args, **params),
"plot3d_parametric_line":
lambda args, params: plot3d_parametric_line(*args, **params),
"plot3d_parametric_surface":
lambda args, params: plot3d_parametric_surface(*args, **params),
}
def plot_geom(items):
plots = []
fig = plt.figure()
ax = fig.add_subplot(111)
#create plots from implicit equations
for item in items:
if isinstance(item,Circle):
cc = Circle(item.center.evalf(), item.radius)
pl = plot_implicit(cc.equation(),show=False)
plots.append(pl)
elif isinstance(item,Segment):
limits = item.plot_interval()
var, a0,a1 = limits
xeq,yeq = item.arbitrary_point().args
#introduce numerical precision
xeq = xeq.evalf()
yeq = yeq.evalf()
new_limits = (xeq.free_symbols.pop(),a0,a1)
pl = plot_parametric(xeq,yeq,new_limits, show=False, line_color='r')
plots.append(pl)
elif isinstance(item,Line):
pl = plot_implicit(item.equation().evalf(),show=False)
plots.append(pl)
elif isinstance(item,Point):
pc = Circle(item.evalf(), .2)
plots.append(plot_geom([pc]))
elif isinstance(item, list):
print("item")
print(item)
mat_pts = [(p.x.evalf(),p.y.evalf()) for p in item]
print("mat_pts")
print(mat_pts)
mat_pts += [mat_pts[0]] #line has to end where it starts
codes = [Path.MOVETO]
for i in range(len(mat_pts)-2):
codes += [Path.LINETO]
codes += [Path.CLOSEPOLY]
path = Path(mat_pts, codes)
patch = patches.PathPatch(path, facecolor = 'red', alpha= .5,lw=2)
ax.add_patch(patch)
ax.set_xlim(-200,200)
ax.set_ylim(-200,200)
else:
raise TypeError("item does not have recognized geometry type")
#combine plots
plt.show()
p = plots.pop()
for e in plots:
p.extend(e)
return p
def shoot():
g = 9.81
series = []
cpt = 1
for i in range(3):
print
print"*****************"
print"Shoot number", cpt
v=int(raw_input("Choose the velocity of your shoot: ")) # velocity
alpha_deg=int(raw_input("Choose the angle of your shoot: ")) # angle
print
r=(2*v*math.cos(math.radians(alpha_deg))*v*math.sin(math.radians(alpha_deg)))/g # range of the shoot
h=(v*v*(math.sin(math.radians(alpha_deg))*math.sin(math.radians(alpha_deg))))/(2*g) # height of the shoot
print"Range =", math.ceil(r), "meters"
print"Height =", math.ceil(h), "meters"
cpt+=1
print
t = symbols("t")
alpha_rad = S(alpha_deg) * pi / 180
z = v * sin(alpha_rad)*t - 1/2*g*t**2
impact = solve(z,t)
tMax = max(impact)
x = v*cos(alpha_rad)* t
serie = (x,z, (t,0,tMax))
series.append(serie)
p = plot_parametric(*series, show=False)
p[0].line_color = "red"
p[1].line_color = "purple"
p[2].line_color = "black"
#p[3].line_color = "green"
#p[4].line_color = "yellow"
p.show()
r=math.ceil(r)
h=math.ceil(h)
return r
def func_gui():
fun_x = funx.get()
fun_y = funy.get()
l = l_x.get()
u = u_x.get()
'''if Diff.get():
p1 = plot(diff(fun_y,fun_x),('t',l,u),show=false)
p1[0].line_color=result[1]
p1.show()
print diff(fun_x,t)
print diff(fun_y,t)
elif Diff2.get():
p2 = plot(diff(fun_x,fun_y),('t',l,u),show=false)
p2[0].line_color=result[1]
p2.show()
else :'''
p3 = plot_parametric(fun_x,fun_y,('t',l,u),show=false,title=tit.get(),xlabel=x_lab.get(),ylabel=y_lab.get())
p3[0].line_color=result[1]
p3.show()
def decision_boundary(dataset,a_priori_prob,title):
mean=[np.mean(dataset[0],axis=0),np.mean(dataset[1],axis=0)]
cov=[np.cov(dataset[0],rowvar=False),np.cov(dataset[1],rowvar=False)]
x1,x2=symbols('x1 x2')
M=Matrix([x1,x2])
g=gi(M,mean[0].reshape(2,1),cov[0],a_priori_prob[0])-gi(M,mean[1].reshape(2,1),cov[1],a_priori_prob[1])
soln=solve(g,(x1,x2))
p1=plot_parametric(soln[0],label="decision boundary",line_color='black',show=False)
fig,ax=plt.subplots(figsize=(14,8))
ax.set_title(title)
move_sympyplot_to_axes(p1,ax)
plt.scatter(x=dataset[0][:,0],y=dataset[0][:,1],label="class 1")
plt.scatter(x=dataset[1][:,0],y=dataset[1][:,1],label="class 2")
plt.legend(loc='best')
return fig
def plot_geom(items):
plots = []
#create plots from implicit equations
for item in items:
if isinstance(item, Circle):
cc = Circle(item.center.evalf(), item.radius)
pl = plot_implicit(cc.equation(), show=False)
plots.append(pl)
elif isinstance(item, Segment):
limits = item.plot_interval()
var, a0, a1 = limits
xeq, yeq = item.arbitrary_point().args
#introduce numerical precision
xeq = xeq.evalf()
yeq = yeq.evalf()
new_limits = (xeq.free_symbols.pop(), a0, a1)
pl = plot_parametric(xeq,
yeq,
new_limits,
show=False,
line_color='r')
plots.append(pl)
elif isinstance(item, Line):
pl = plot_implicit(item.equation().evalf(), show=False)
plots.append(pl)
elif isinstance(item, Point):
pc = Circle(item.evalf(), .2)
plots.append(plot_geom([pc]))
else:
raise TypeError("item does not have recognized geometry type")
#combine plots
p = plots.pop()
for e in plots:
p.extend(e)
return p
def plot_parametric(*args, **kwargs):
kwargs.pop("show", None)
return plotter.plot_parametric(*plotArgs(args), show=False, **kwargs)
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)),
(2 * x * cos(x), 2 * x * sin(x), x, (x, 0, 15)),
show=False)
param_line_3d[0].line_color = lambda u: u # parametric
param_line_3d[
1].line_color = lambda u, v: u * v # first and second coordinates
param_line_3d[2].line_color = lambda u, v, w: u * v * w # all coordinates
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())
"""
Program that plots the function alpha(t)
According to alpha(t) you can uncomment the code of the plotting section
"""
# Libraries
import sympy as sp
import sympy.plotting as spp
# Symbols to be used, do not change these
t = sp.symbols('t', positive=True)
# Constants
# alpha(t) vector
alpha = sp.Matrix([[t, t**2]])
# Plotting section
# Obtainting the components of alpha(t)
x = alpha[0]
y = alpha[1]
# z=alpha[2]
# 2D
spp.plot_parametric(x, y, (t, 0, 1), title=r"Plot of $\alpha(t)$")
# 3D
#spp.plot3d_parametric_line(x,y,z,(t,-3,3),title=r"Plot of $\alpha(t)$")
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()
nu_frequency = .1
# /(2*pi);
lambda_e1 = 1.0
# sigma = integrate(K_e1*exp(-lambda_e1*( time - s_time ))*Elect_Amp * sin(2*pi*nu_frequency) ,s_time)
# sigma = integrate(K_e1* exp(-lambda_e1*( s_time )) ,s_time)
# sigma = integrate( s_time ,s_time)
# sigma = integrate( sin(2*pi*nu_frequency*s_time) ,s_time)
# sigma= integrate(K_e1*exp(-lambda_e1*( time - s_time )) * Elect_Amp * sin(2*pi*nu_frequency*s_time), s_time)
Elect = sin(2 * pi * nu_frequency * time)
Elect_dot = diff(Elect, time)
sigma = integrate(
exp(-lambda_e1 * (time - s_time)) * Elect_dot.subs(time, s_time), s_time)
# print sigma;
sigma_t = sigma.subs(s_time, time) - sigma.subs(s_time, 0)
# sigma_t_plot=plot(sigma_t,(time,0,10))
hysteresis_plot = plot_parametric(Elect, sigma_t, (time, 0, 10 / nu_frequency))
# plot([cos, sin], [-4, 4])
print sigma_t
# print sigma
from sympy import *
from sympy.plotting import (plot_parametric, plot_implicit, plot3d,
plot3d_parametric_line, plot3d_parametric_surface)
x = symbols('x')
plot(sin(x) / x, (x, -5, 5))
# фигура Лиссажу
t = Symbol('t')
plot_parametric(sin(2 * t),
cos(3 * t), (t, -2 * pi, 2 * pi),
title='Lissajous',
xlabel='x',
ylabel='y')
# тор
u, v = symbols('u v')
a = 0.3
plot3d_parametric_surface((1 + a * cos(u)) * cos(v), (1 + a * cos(u)) * sin(v),
a * sin(u), (u, 0, 2 * pi), (v, 0, 2 * pi))
plot3d_parametric_surface, plot3d_parametric_line,
plot3d)
def sympy_plot():0
x, y, u, v = symbols('x, y, u, v')
# all graphs are not shown when first created
a = plot(x*sin(x**2), (x, 2, 4), show=False) # cartesian plot
b = plot(cos(x-1)*x**2, (x, -5, 5), show=False) # cartesian plot
c = plot3d_parametric_line(sin(x), cos(x), x, (x, 0, 20), show=False) # 3d parametric line plot
d = plot3d(sin(x)*cos(y)*sin(x*y), (x, -3, 3), (y, -3, 3), show=False) # 3d surface cartesian plot3d (multivariable)
e = plot3d_parametric_surface(cos(u)*v, sin(u)*v, sin(0.3*u*v), (u, 0, 10), (v, -2, 2), show=False) # 3d parametric surface plot (multivariable)
param_lines_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) # 2d parametric multiple lines plot
param_lines_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)),
(2*x*cos(x), 2*x*sin(x), x, (x, 0, 15)), show=False) # 3d parametric multiple lines plot
for i in [a, b, c, d, e, param_lines_2d, param_lines_3d]:
i.show()
sympy_plot()
# SymPy real Example (Monte Carlo Simulation)
import random
from sympy import *
def plot_parametric(*args, **kwargs):
if "show" in kwargs:
kwargs.pop("show")
return plotter.plot_parametric(*plotArgs(args), show=False, **kwargs)
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_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):
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())
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)),
(2*x*cos(x), 2*x*sin(x), x, (x, 0, 15)), show=False)
param_line_3d[0].line_color = lambda u: u # parametric
param_line_3d[1].line_color = lambda u, v: u*v # first and second coordinates
param_line_3d[2].line_color = lambda u, v, w: u*v*w # all coordinates
if __name__ == '__main__':
for p in [b, e, f, g, h, param_line_2d, param_line_3d]:
p.show()
# Save the data in a file:
# the information is stored as:
# n, t, Omega(t)
file_name = 'test' +str(i)+'.txt'
with open(os.path.join(dir_path, file_name), 'w') as outfile:
for ind, t in enumerate(tt):
outfile.write("%s, %s, %s \n" % (ind, t, kappa(l_of_t_func(t))))
fig, (ax1, ax2) = plt.subplots(2)
# Convert the functions into numpy functions to be able to plot them with matplotlib
xx = convert_numpy(x, param=l)
yy = convert_numpy(y, param=l)
ax1.plot(xx(ll), yy(ll))
ax2.plot(tt, kappa(l_of_t_func(tt)))
kappa_write[i,:] = kappa(l_of_t_func(tt))
if np.amax(kappa_write[i,:]) > max_val:
max_val = np.amax(kappa_write[i,:])
print(max_val)
# Can also use the sympy plotting option if you want
plot_parametric(x, y, (l, 0, ll_max))
# 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 = 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 main():
phi, phi_top, phi_middle, phi_bottom, ra, ta, za, df_za, ri, ri_top, ri_bottom = symbols(
'phi phi_top phi_middle phi_bottom ra ta za df_za ri ri_top ri_bottom')
zi, zi_top, zi_bottom, fi, h0, h1, zb, rb = symbols(
'zi zi_top zi_bottom fi h0 h1 zb rb')
# Flat surface, Table 1.1
#za = 0
#
#s1 = 1
#n = 1.5
#t = 10
#ta = -70
#tb = 75
# Spherical surface, Table 1.2
#za = 100 - sqrt(100**2 - ra**2)
#
#s1 = 1
#n = 1.5
#t = 8
#ta = -70
#tb = 80
# Parabolic surface, Table 1.3
#za = ra**2 / 200
#
#s1 = 1
#n = 1.5
#t = 10
#ta = -80
#tb = 100
# Cosine surface, Table 1.4
#za = cos(ra/3)
#
#s1 = 1
#n = 1.5
#t = 8
#ta = -70
#tb = 80
# Bessel surface, Figure 4.d
za = besselj(0, ra / 2)
s1 = 1
n = 1.5
t = 5
ta = -30
tb = 75
# Parabolic from "Single Lens Telescope"
#za = -ra**2 / 4
rmax = 50
precision = 50
df_za = diff(za, ra)
phi_top = (ra + (-ta + za) * df_za)**2
phi_middle = n**2 * (ra**2 + (ta - za)**2) * (1 + df_za**2)
phi_bottom = sqrt(1 + df_za**2)
phi = sqrt(1 - (phi_top / phi_middle)) / phi_bottom
#phi = sqrt(1 - ((ra + (-ta + za) * df_za)**2 / (n**2 * (ra**2 + (ta - za)**2) * (1 + df_za**2)))) / sqrt(1 + df_za**2)
ri_top = ra + (-ta + za) * df_za
ri_bottom = n * sqrt(ra**2 + (ta - df_za)**2) * (1 + df_za**2)
ri = (ri_top / ri_bottom) - df_za * phi
#ri = ((ra + (-ta + za) * df_za) / (n * sqrt(ra**2 + (ta - za)**2) * (1 + df_za**2))) - (df_za * phi)
zi_top = df_za * (ra + (-ta + za) * df_za)
zi_bottom = n * sqrt(ra**2 + (ta - za)**2) * (1 + df_za**2)
zi = (zi_top / zi_bottom) + phi
#zi = ((df_za * (ra + (-ta + za) * df_za)) / ((n * sqrt(ra**2 + (ta - za)**2)) * (1 + df_za**2))) + phi
fi = ta - tb - sign(ta) * sqrt(ra**2 + (ta - za)**2)
h0 = ri**2 * za + fi * n * zi - ra * ri * zi + (t + tb) * zi**2 - n**2 * (
za + t * zi)
h1 = ra**2 + 2 * ra * ri * t + (
tb - za)**2 + t**2 * (ri**2 +
(-1 + zi)**2) - 2 * t * (tb - za) * (-1 + zi)
zb = (h0 + s1 * sqrt(zi**2 * (fi**2 - 2 * fi * n *
(ra * ri + ri**2 * t + zi *
(t * (zi - 1) - tb + za)) + h1 * n**2 -
(ra * zi + ri *
(t + tb - za))**2))) / (-n**2 + 1)
rb = ra + (ri * (-za + zb)) / zi
p = plot_parametric((ra, za), (rb, zb), (ra, -rmax, rmax),
xlim=(-30, 30),
ylim=(-30, 30))
#foo = solveset(Eq(ra/za, rb/zb), ra)
#print(foo)
ras = numpy.linspace(0, rmax, precision)
f_za = lambdify(ra, za, "numpy")
f_rb = lambdify(ra, rb, "numpy")
f_zb = lambdify(ra, zb, "numpy")
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())
- Otherwise, prints 'can not be parametrized'
"""
# Print the function explicit in 's'
desp = sp.solve(equa, t)
print("Parameter f(s):%s\n" % (desp))
# Reparametrization of alpha(t)
nalpha = alpha.subs(t, desp[0])
print("alpha(s): %s" % (nalpha))
except:
print("The arc's length function can not be solved")
print("alpha(s) can not be parametrized by arc's length")
except:
# This code is executed if 'lenArc' could not be solved
print("The integral can not be solved\n")
print("alpha(t) can not be parametrized by arc's length")
# Plotting section
x = alpha[0]
y = alpha[1]
#z = alpha[2]
# 2d
spp.plot_parametric(x, y, (t, 0, 1), legend=True)
# 3d
#spp.plot3d_parametric_line(x,y,z,(t,-2*sp.pi,2*sp.pi), label=True)