def test_linear_algebra( self ):
M = 3; N = 20
A = numpy.random.normal( 0., 1., ( M, N ) )
b = numpy.random.normal( 0., 1., ( M ) )
out = numpy.linalg.lstsq( A , b )
x_true = out[0]
x = svd_solve( A, b.reshape(b.shape[0],1))[0].squeeze()
assert numpy.allclose( x, x_true )
M = 10; N = 5
A = numpy.random.normal( 0., 1., ( M, N ) )
b = numpy.random.normal( 0., 1., ( M ) )
AtA = numpy.dot( A.T, A )
assert numpy.allclose( numpy.linalg.cholesky( AtA ), cholesky( AtA ) )
out = numpy.linalg.lstsq( A , b )
x_true = out[0]
x = cholesky_solve( AtA, numpy.dot( A.T, b ) ).squeeze()
assert numpy.allclose( x, x_true )
x = solve_using_cholesky_factor( numpy.linalg.cholesky( AtA ),
numpy.dot( A.T, b ).reshape(A.shape[1],1), 1 )[1].squeeze()
assert numpy.allclose( x, x_true )
x = qr_solve( numpy.dot( A.T, A ), numpy.dot( A.T, b ).reshape(A.shape[1],1), 1 ).squeeze()
assert numpy.allclose( x, x_true )
def OMP_fast_cv( pts, vals, pce, test_pts = None, test_vals = None ):
i = 0
indices = PolyIndexVector()
pce.get_basis_indices( indices )
for index in indices:
index.set_array_index( i )
i += 1
all_train_indices = []
all_validation_indices = []
#cv_iterator = LeaveOneOutCrossValidationIterator( pts.shape[1] )
cv_iterator = KFoldCrossValidationIterator( 10, pts.shape[1] )
for train_indices, validation_indices in cv_iterator:
all_train_indices.append( train_indices )
all_validation_indices.append( validation_indices )
A = pce.build_vandermonde( pts )
out = orthogonal_matching_pursuit_cholesky( A, vals.squeeze(),
all_train_indices,
all_validation_indices,
0.,
numpy.iinfo(numpy.int32).max,
0 )
"""
# check cholesky omp is producing correct one at a time estimates
new_indices = PolyIndexVector()
new_indices.resize( 20 )
pce.get_basis_indices( indices )
for i in xrange( 20 ):
new_indices[int(i)] = indices[int(out[1][1,i])]
new_indices[int(i)].set_array_index( i )
pce.set_basis_indices( new_indices )
i = 0
error = numpy.empty( (len(all_validation_indices)), numpy.double )
for train_indices, validation_indices in cv_iterator:
A = pce.build_vandermonde( pts[:,train_indices] )
coeff = svd_solve_default( A, vals[train_indices] )
pce.set_coefficients( coeff[0] );
pred_vals = pce.evaluate_set( pts[:,validation_indices] )
print pred_vals, pts[:,validation_indices], i
error[i] = vals[validation_indices,0] - pred_vals.squeeze()
i += 1
print error
print numpy.asarray( out[2][19] )[:,0]
assert False
"""
solutions = out[0] #num_folds x num_steps x num_pts_per_fold
metrics = out[1]
cv_residuals = out[2]
print len( cv_residuals ), len( cv_residuals[0] ), len( cv_residuals[0][0] )
num_steps = len( cv_residuals )
num_folds = len( cv_residuals[0] )
scores = numpy.zeros( ( num_steps ), numpy.double )
for i in xrange( num_folds ):
for j in xrange( num_steps ):
scores[j] += numpy.sqrt( numpy.mean( cv_residuals[j][i]**2, axis = 0 ) )
scores /= num_folds
argmin = int( numpy.argmin( scores ) )
# plot true error vs cross validation error
if test_pts is not None:
# plot cv errors
tau = numpy.sum( numpy.absolute( out[0] ), axis = 0 )
pylab.semilogy( tau, scores, 'bh-' )
pylab.semilogy( tau[argmin], scores[argmin], 'gd', )
# plot true errors
pce.set_coefficients( out[0] )
pred_vals = pce.evaluate_set( test_pts )
print numpy.linalg.norm( pred_vals[:,30] - test_vals )
errors = pred_vals - numpy.tile( test_vals.reshape(test_vals.shape[0], 1 ), ( 1, pred_vals.shape[1] ) )
error_norms = numpy.sqrt( numpy.sum( errors**2, axis = 0 ) /
test_vals.shape[0] )
error_argmin = numpy.argmin( error_norms )
omp_tau, cv_error = OMP_brute_cv( pts, vals, pce, True )
omp_argmin = numpy.argmin( cv_error )
pylab.semilogy( omp_tau[::-1], cv_error[::-1], 'o-' )
pylab.semilogy( [omp_tau[omp_argmin]], [cv_error[omp_argmin]], 'go' )
print [omp_tau[omp_argmin]], [cv_error[omp_argmin]]
print cv_error, omp_argmin
#pylab.loglog( tau, out[1][0,:], 'o-' )
pylab.semilogy( tau, error_norms, 'ks-' )
pylab.semilogy( [tau[error_argmin]], [error_norms[error_argmin]], 'rd' )
pylab.semilogy( [tau[argmin]], [error_norms[argmin]], 'gd' )
print error_norms[error_argmin]
pylab.show()
best_indices = PolyIndexVector()
best_indices.resize( argmin )
for i in xrange( argmin ):
best_indices[i] = indices[int(metrics[1,i])]
best_indices[i].set_array_index( i )
pce.set_basis_indices( best_indices )
A = pce.build_vandermonde( pts )
coeff = svd_solve( A, vals )
pce.set_coefficients( coeff[0] )
