def test_qr_factorization_fat_matrix(self):
A = [[
0.549723608291140, 0.380445846975357, 0.779167230102011,
0.011902069501241, 0.528533135506213, 0.689214503140008,
0.913337361501670, 0.078175528753184, 0.774910464711502
],
[
0.917193663829810, 0.567821640725221, 0.934010684229183,
0.337122644398882, 0.165648729499781, 0.748151592823709,
0.152378018969223, 0.442678269775446, 0.817303220653433
],
[
0.285839018820374, 0.075854289563064, 0.129906208473730,
0.162182308193243, 0.601981941401637, 0.450541598502498,
0.825816977489547, 0.106652770180584, 0.868694705363510
],
[
0.757200229110721, 0.053950118666607, 0.568823660872193,
0.794284540683907, 0.262971284540144, 0.083821377996933,
0.538342435260057, 0.961898080855054, 0.084435845510910
],
[
0.753729094278495, 0.530797553008973, 0.469390641058206,
0.311215042044805, 0.654079098476782, 0.228976968716819,
0.996134716626885, 0.004634224134067, 0.399782649098896
]]
Q, R = qr.qr_Householder(A)
Q1, R1 = qr.qr_Householder(A, 1)
if np.linalg.norm(A - (Q * R), 2) < 2e-15 and np.linalg.norm(
A - (Q1 * R1), 2) < 2e-15:
print 'Success!'
else:
error_function('ERROR: QR Householder not working!')
def test_gaussian_tensorgrid(self):
# 4D function for testing!
def fun(x):
return np.cos(x[0]) + x[1]**2 + x[2] * x[3]
x1 = Parameter(param_type='Gaussian',
shape_parameter_A=0,
shape_parameter_B=1,
points=4)
x2 = Parameter(param_type='Gaussian',
shape_parameter_A=0,
shape_parameter_B=1,
points=4)
x3 = Parameter(param_type='Gaussian',
shape_parameter_A=0,
shape_parameter_B=1,
points=4)
x4 = Parameter(param_type='Gaussian',
shape_parameter_A=0,
shape_parameter_B=1,
points=4)
parameters = [x1, x2, x3, x4]
result, points = integrals.tensorgrid(parameters, fun)
print result
if np.linalg.norm(result - 1.606, 2) < 1e-4:
print np.linalg.norm(result - 1.606, 2)
print 'Success!'
else:
error_function('ERROR: Normal integration routine not working!')
# Test to see if we get points and weights when function is not callable!
points, weights = integrals.tensorgrid(parameters)
def test_qr_factorization(self):
A = [[0.8147, 0.0975, 0.1576,
0.1419], [0.9058, 0.2785, 0.9706, 0.4218],
[0.1270, 0.5469, 0.9572,
0.9157], [0.9134, 0.9575, 0.4854, 0.7922],
[0.6324, 0.9649, 0.8003, 0.9595]]
Q, R = qr.qr_Householder(A)
Q1, R1 = qr.qr_Householder(A, 1)
if np.linalg.norm(A - (Q * R), 2) < 1e-15 and np.linalg.norm(
A - (Q1 * R1), 2) < 1e-15:
print 'Success!'
else:
error_function('ERROR: QR Householder not working!')
def test_householder_vector(self):
x = [4., 2., 1., -2., 4., 1.]
x = np.mat(x)
v, beta = qr.house(x.T)
# Know solution
real_v = [
1.0000, -0.80621082, -0.4031054, 0.80621082, -1.61242164,
-0.4031054
]
real_v = np.mat(real_v)
real_v = real_v.T
if np.linalg.norm(real_v - v, 2) < 1e-07:
print 'Success!'
else:
error_function('ERROR: Householder vector incorrect!')
def test_uniform_tensorgrid(self):
# 4D function for testing!
def fun(x):
return np.cos(x[0]) + x[1]**2 + x[2] * x[3]
x1 = Parameter(lower=-0.5, upper=0.5, points=4)
x2 = Parameter(lower=-1, upper=2, points=4)
x3 = Parameter(lower=-3, upper=2, points=4)
x4 = Parameter(lower=-2, upper=1, points=4)
parameters = [x1, x2, x3, x4]
result, points = integrals.tensorgrid(parameters, fun)
print result
if np.linalg.norm(result - 99.39829845, 2) < 1e-9:
print np.linalg.norm(result - 99.39829845, 2)
print 'Success!'
else:
error_function('ERROR: Uniform integration routine not working!')
def test_constrained_least_squares(self):
A = [[0.8147, 0.0975, 0.1576], [0.9058, 0.2785, 0.9706],
[0.1270, 0.5469, 0.9572], [0.9134, 0.9575, 0.4854],
[0.6324, 0.9649, 0.8003]]
b = [0.1419, 0.4218, 0.9157, 0.7922, 0.9595]
b = np.mat(b)
b = b.T
C = [[0.7060, 0.0462, 0.6948], [0.0318, 0.0971, 0.3171],
[0.2769, 0.8235, 0.9502]]
d = [0.0344, 0.4387, 0.3816]
d = np.mat(d)
d = d.T
x = qr.solve_constrainedLSQ(A, b, C, d)
x_MATLAB = [-1.7588, -1.1531, 1.9134]
x_MATLAB = np.mat(x_MATLAB)
x_MATLAB = x_MATLAB.T
residual = x - x_MATLAB
if np.linalg.norm(residual, 2) < 2e-3:
print 'Success!'
else:
error_function('ERROR: Least squares routine not working!')
def test_least_squares(self):
A = [[0.129783563321146, 0.693035803160460, 0.542987352374312],
[0.971602452337381, 0.702475484644310, 0.540162073918995],
[0.940153258292462, 0.371312184808707, 0.786284036629558],
[0.933119647195370, 0.064105941014906, 0.601409398329654],
[0.983758270635912, 0.443451755787831, 0.947013554266040]]
b = [
0.631218455441575, 0.878837482885143, 0.122686301726737,
0.813548224731922, 0.977604352516636
]
b = np.mat(b)
b = b.T
x = qr.solveLSQ(A, b)
x_MATLAB = [0.356346872539370, 0.515012358852366, 0.221551548589301]
x_MATLAB = np.mat(x_MATLAB)
x_MATLAB = x_MATLAB.T
residual = x - x_MATLAB
if np.linalg.norm(residual, 2) < 4e-15:
print 'Success!'
else:
error_function('ERROR: Least squares routine not working!')
def test_effective_quadratures_rule(self):
# 4D function for testing!
def fun(x):
return np.cos(x[0]) + x[1]**2 + x[2] * x[3]
x1 = Parameter(lower=-0.5, upper=0.5, points=4)
x2 = Parameter(lower=-1, upper=2, points=4)
x3 = Parameter(lower=-3, upper=2, points=4)
x4 = Parameter(lower=-2, upper=1, points=4)
parameters = [x1, x2, x3, x4]
result, points = integrals.effectivequadratures(parameters,
q_parameter=0.8,
function=fun)
print result
if np.abs(result - 99.3982) < 1e-4:
print np.abs(result - 99.3982)
print 'Success!'
else:
error_function(
'ERROR: Effective-Quadratures integration routine not working!'
)
def test_uniform_sparsegrid(self):
# 4D function for testing!
def fun(x):
return np.cos(x[0]) + x[1]**2 + x[2] * x[3]
x1 = Parameter(lower=-0.5, upper=0.5, points=4)
x2 = Parameter(lower=-1, upper=2, points=4)
x3 = Parameter(lower=-3, upper=2, points=4)
x4 = Parameter(lower=-2, upper=1, points=4)
parameters = [x1, x2, x3, x4]
result, points = integrals.sparsegrid(parameters,
level=5,
growth_rule='exponential',
function=fun)
print result
if np.linalg.norm(result - 99.3982, 2) < 1e-4:
print np.linalg.norm(result - 99.3982, 2)
print 'Success!'
else:
error_function(
'ERROR: Sparse grid integration routine not working!')