def plot_eigs_cover(obj, la):
r"""
:param obj: object of the class ``BrakeClass``
:param la: eigenavlues
:return: radius of the disc covering all the eigenvalues
"""
x1 = obj.target[0]
x2 = obj.target[1]
y1 = obj.target[2]
y2 = obj.target[3]
# calculate center of the obj.target rectangular region
tau = complex((x1 + x2) / 2, (y1 + y2) / 2)
radius = max(abs(la - tau))
#fig = plt.gcf()
fig = plt.figure(figsize=(24.0, 15.0))
circle = plt.Circle((tau.real, tau.imag), radius, color='g', fill=False)
react = plt.Rectangle((x1, y1),
abs(x2 - x1),
abs(y2 - y1),
color='black',
fill=False)
ax = plt.gca()
ax.cla() # clear things for fresh plot
ax.set_xlim((tau.real - 1.1 * radius, tau.real + 1.1 * radius))
ax.set_ylim((tau.imag - 1.1 * radius, tau.imag + 1.1 * radius))
plt.axhline(0, color='blue')
plt.axvline(0, color='blue')
x = la.real
y = la.imag
for i in range(0, len(x)):
if x[i] >= 0:
ax.plot(x[i], y[i], 'o', color='red')
else:
ax.plot(x[i], y[i], 'o', color='green')
ax.plot((tau.real), (tau.imag), '+', color='r')
fig.gca().add_artist(circle)
fig.gca().add_artist(react)
#fig.savefig(obj.output_path+'plotcover.png')
brake.save(obj.output_path + 'plotEigsCover',
ext="png",
close=True,
verbose=False)
return radius
rank = estimate_rank(aslinearoperator(componentMatrix), eps)
#print 'Approximate rank with relative error of(', eps, ')for numerical rank definition = ',rank
print obj.data_file_list[i], obj.data_file_name[
i], componentMatrix.shape, ' NonZeros = ', componentMatrix.nnz, ' 1-Norm = ', normMatrix, ' rank ', rank
obj.logger_i.info(obj.data_file_list[i] + ' ' + obj.data_file_name[i] +
str(componentMatrix.shape) + ' NonZeros = ' +
str(componentMatrix.nnz) + ' 1-Norm = ' +
str(normMatrix) + ' rank ' + str(rank))
#saving the sparsity pattern
fig = plt.figure(figsize=(24.0, 15.0))
fig.clf()
fig.gca().add_artist(plt.spy(componentMatrix))
brake.save(obj.output_path + 'dataAnalysis/' + obj.data_file_name[i],
ext="png",
close=True,
verbose=False)
end_program = timeit.default_timer()
print "\n", "\n", "\n", 'Total Run Time = : ' + "%.2f" % (
end_program - begin_program) + ' sec'
if (obj.log_level):
obj.logger_i.info(
'\nNote: The rank obtained using python estimate_rank utility')
obj.logger_i.info(
'is observed to be lower than the rank obtained using MATLAB')
obj.logger_i.info(
'\nNote: The norm computed is a lower bound of the 1-norm of the sparse matrix.'
)
plt.subplot(223)
plt.plot(xDim, yTheta2List[0], '-ro', label='Traditional')
plt.plot(xDim, yTheta2List[1], '-kD', label='wset1')
plt.plot(xDim, yTheta2List[2], '-bs', label='wset2')
plt.plot(xDim, yTheta2List[3], '-go', label='wset3')
plt.legend(loc='lower left', shadow=True)
plt.yscale('log')
plt.xlabel('dimension')
plt.ylabel('theta2')
#plt.title('maximum angle between exact eigenvector and the computed eigenvector')
plt.grid(True)
plt.subplot(224)
#plt.plot(xDim, ySingularList[0], '-ro', label='Traditional')
plt.plot(xDim, ySingularList[1], '-kD', label='wset1')
plt.plot(xDim, ySingularList[2], '-bs', label='wset2')
plt.plot(xDim, ySingularList[3], '-go', label='wset3')
plt.legend(loc='lower left', shadow=True)
plt.yscale('log')
plt.xlabel('dimension')
plt.ylabel('singular values')
plt.title('Decay of singular values')
plt.grid(True)
brake.save(obj.output_path + 'traditionalVsPOD' + str(obj.omegaTest /
(2 * math.pi)),
ext="png",
close=False,
verbose=True)
plt.show()
def draw_circles(obj, next_shift, next_radius):
r"""
:param obj: object of the class ``BrakeClass``
:param next_shift: the shift point to be shown on the plot
:param next_radius: the radius of the shift point to be shown
:return: plots a circle corresponding to the next shift point and appends it to the existing plot.
:raises: ``Cover_BadInputError``, When the provided input is not as expected
"""
target = obj.target
# Exceptions
#------------------------------------------------------------
if len(target) == 0:
raise Cover_BadInputError('The target is not specified')
elif len(target) < 4:
raise Cover_BadInputError('target region does not define a reactangle')
elif target[1] <= target[0] or target[3] <= target[2]:
raise Cover_BadInputError('the target reactangle is not defined')
if not next_radius:
raise Cover_BadInputError('The previous_radius is not specified')
elif next_radius <= 0:
raise Cover_BadInputError('The radius is nonpositive')
x1 = target[0]
x2 = target[1]
y1 = target[2]
y2 = target[3]
if not next_shift:
raise Cover_BadInputError('The next_shift array is not length 1')
elif next_shift.real < x1 \
or next_shift.real > x2 \
or next_shift.imag < y1 \
or next_shift.imag > y2:
raise Cover_BadInputError('shift point not in target region')
#------------------------------------------------------------
x1 = target[0]
x2 = target[1]
y1 = target[2]
y2 = target[3]
fig = plt.gcf()
circle = plt.Circle((next_shift.real, next_shift.imag),
next_radius,
color='b',
fill=False)
react = plt.Rectangle((x1, y1),
abs(x2 - x1),
abs(y2 - y1),
color='black',
fill=False)
ax = plt.gca()
#ax.cla() # clear things for fresh plot
ax.set_xlim((y1 - 1000, y2 + 1000))
ax.set_ylim((y1 - 1000, y2 + 1000))
plt.axhline(0, color='blue')
plt.axvline(0, color='blue')
fig.gca().add_artist(circle)
fig.gca().add_artist(react)
brake.save(obj.output_path + 'drawCircles',
ext="png",
close=True,
verbose=False)
return
plt.title('relative error between computed and exact eigenvalues')
plt.grid(True)
plt.subplot(222)
plt.plot(x, y, '-kD')
plt.yscale('log')
plt.xlabel('dimension')
plt.title('maximum angle between exact eigenvector and the projection space')
plt.grid(True)
plt.subplot(223)
plt.plot(x, y, '-bs')
plt.yscale('log')
plt.xlabel('dimension')
plt.title(
'maximum angle between exact eigenvector and the computed eigenvector')
plt.grid(True)
plt.subplot(224)
plt.plot(x, y, '-go')
plt.yscale('log')
plt.xlabel('dimension')
plt.title('decay of singular values')
plt.grid(True)
#plt.subplot_tool()
#plt.show()
brake.save(obj.output_path + 'testBrake', ext="png", close=False, verbose=True)
plt.show()