def psd_solve_with_chol(node):
if node.op == solve:
A, b = node.inputs # result is solution Ax=b
if is_psd(A):
L = cholesky(A)
# N.B. this can be further reduced to a yet-unwritten cho_solve Op
# __if__ no other Op makes use of the the L matrix during the
# stabilization
Li_b = Solve('lower_triangular')(L, b)
x = Solve('upper_triangular')(L.T, Li_b)
return [x]
def tag_solve_triangular(node):
"""
If a general solve() is applied to the output of a cholesky op, then
replace it with a triangular solve.
"""
if node.op == solve:
if node.op.A_structure == 'general':
A, b = node.inputs # result is solution Ax=b
if A.owner and isinstance(A.owner.op, type(cholesky)):
if A.owner.op.lower:
return [Solve('lower_triangular')(A, b)]
else:
return [Solve('upper_triangular')(A, b)]
if (A.owner and isinstance(A.owner.op, DimShuffle)
and A.owner.op.new_order == (1, 0)):
A_T, = A.owner.inputs
if A_T.owner and isinstance(A_T.owner.op, type(cholesky)):
if A_T.owner.op.lower:
return [Solve('upper_triangular')(A, b)]
else:
return [Solve('lower_triangular')(A, b)]
def verify_solve_grad(self, m, n, A_structure, lower, rng):
# ensure diagonal elements of A relatively large to avoid numerical
# precision issues
A_val = (rng.normal(size=(m, m)) * 0.5 + np.eye(m)).astype(config.floatX)
if A_structure == "lower_triangular":
A_val = np.tril(A_val)
elif A_structure == "upper_triangular":
A_val = np.triu(A_val)
if n is None:
b_val = rng.normal(size=m).astype(config.floatX)
else:
b_val = rng.normal(size=(m, n)).astype(config.floatX)
eps = None
if config.floatX == "float64":
eps = 2e-8
solve_op = Solve(A_structure=A_structure, lower=lower)
utt.verify_grad(solve_op, [A_val, b_val], 3, rng, eps=eps)
def setUp(self):
super(test_Solve, self).setUp()
self.op_class = Solve
self.op = Solve()
import numpy as np
try:
import scipy.linalg
imported_scipy = True
except ImportError:
# some ops (e.g. Cholesky, Solve, A_Xinv_b) won't work
imported_scipy = False
from theano import tensor
import theano.tensor
from theano.tensor import as_tensor_variable
from theano.gof import Op, Apply
from theano.tensor.slinalg import Solve
solve_upper_triangular = Solve(A_structure='upper_triangular', lower=False)
class QR_Chol(Op):
"""
(mostly) Copy from theano:
Incomplete QR Decomposition.
Computes the QR decomposition of a matrix.
Factor the matrix a as qr and return a single matrix.
"""
__props__ = ('mode', )
def __init__(self, mode):
self.mode = mode
def setup_method(self):
self.op_class = Solve
self.op = Solve()
super().setup_method()
def __init__(self, driver='gelsy'):
self.driver = driver
Solve.__init__(self)
def __init__(self, lambda_=None):
Solve.__init__(self)
self.lambda_ = lambda_ if lambda_ is not None else 0.
