def gradients_univariate():
# Parameters!
pt = 8
x1 = Parameter(param_type="Uniform", lower=-1.0, upper=1.0, points=pt, derivative_flag=1)
x2 = Parameter(param_type="Uniform", lower=-1.0, upper=1.0, points=pt, derivative_flag=1)
parameters = [x1, x2]
dims = len(parameters)
# Basis selection!
hyperbolic_cross = IndexSet("Total order", orders=[pt-1,pt-1])
esq = EffectiveSubsampling(parameters, hyperbolic_cross)
A , p, w = esq.getAmatrix()
C = esq.getCmatrix()
# Matrix sizes
m, n = A.shape
print m, n
print '*****************'
m, n = C.shape
print m, n
# Now perform least squares!
W = np.mat(np.diag(np.sqrt(w)))
b = W.T * evalfunction(p, fun)
d = evalgradients(p, fungrad, 'vector')
x = qr.solveLSQ(np.vstack([A, C]), np.vstack([b, d]) )
print x
def nogradients_univariate():
# Parameters!
pt = 6
x1 = Parameter(param_type="Uniform", lower=-1.0, upper=1.0, points=pt)
parameters = [x1, x1]
# Effective subsampling object!
esq = EffectiveSubsampling(parameters)
# Solve the least squares problem
A, p, w = esq.getAmatrix() # Is this always square??
W = np.mat(np.diag(np.sqrt(w) ) )
b = W.T * evalfunction(p, fun)
x = qr.solveLSQ(A,b)
print x
def gradients_multivariate_subsampled():
# Parameters!
pt = 3
x1 = Parameter(param_type="Uniform", lower=-1.0, upper=1.0, points=pt, derivative_flag=1)
x2 = Parameter(param_type="Uniform", lower=-1.0, upper=1.0, points=pt, derivative_flag=1)
parameters = [x1, x2]
dims = len(parameters)
# Basis selection!
basis = IndexSet("Total order", orders=[pt-1,pt-1])
esq = EffectiveSubsampling(parameters, basis)
A , p, w = esq.getAmatrix()
C = esq.getCmatrix()
# QR column pivotings
P = qr.mgs_pivoting(A.T)
# Now perform least squares!
basis_terms_required = basis.getCardinality()
minimum_points = np.int( (basis_terms_required + dims)/(dims + 1.) ) + 5
nodes = P[0:minimum_points]
A = getRows(A, nodes)
C = getRowsC(C, nodes, dims)
m, n = A.shape
#print m , n
m, n = C.shape
#print m, n
w = w[nodes]
p = p[nodes,:]
#print p, w
W = np.mat(np.diag(np.sqrt(w)))
b = W.T * evalfunction(p, fun)
d = evalgradients(p, fungrad, 'vector')
R = np.vstack([A, C])
print np.linalg.cond(R)
print R
print np.vstack([b, d])
x = qr.solveLSQ(np.vstack([A, C]), np.vstack([b, d]) )
print '\n'
print x
"""
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:
raise (RuntimeError, 'QR testing failed')