def f(r, y):
PD = r.dot(r.T)
L = gpu_cholesky(PD)
A = gpu_solve_lower_triangular(L, y)
AAT = aesara.tensor.dot(A, A.T)
B = AAT + aesara.tensor.eye(N)
LB = gpu_cholesky(B)
return aesara.tensor.sum(aesara.tensor.log(aesara.tensor.diag(LB)))
def test_cholesky_grad():
rng = np.random.RandomState(utt.fetch_seed())
r = rng.randn(5, 5).astype(config.floatX)
# The dots are inside the graph since Cholesky needs separable matrices
# Check the default.
utt.verify_grad(lambda r: gpu_cholesky(r.dot(r.T)), [r], 3, rng)
# Explicit lower-triangular.
utt.verify_grad(lambda r: GpuCholesky(lower=True)(r.dot(r.T)), [r], 3, rng)
# Explicit upper-triangular.
utt.verify_grad(lambda r: GpuCholesky(lower=False)(r.dot(r.T)), [r], 3, rng)