if a.shape[-1] != b.shape[common_dim]:
msg = "Incompatible shapes for arguments to triangular_solve: {} and {}."
raise TypeError(msg.format(a.shape, b.shape))
return b.shape
def triangular_solve_transpose_rule(cotangent, a, b, left_side, lower,
transpose_a, conjugate_a):
assert a is not None and b is None
cotangent_b = triangular_solve(a, cotangent, left_side, lower,
not transpose_a, conjugate_a)
return [None, cotangent_b]
triangular_solve_p = standard_primitive(triangular_solve_shape_rule,
triangular_solve_dtype_rule,
'triangular_solve')
ad.defjvp(triangular_solve_p, None,
lambda g_b, a, b, **kwargs: triangular_solve(a, g_b, **kwargs))
ad.primitive_transposes[triangular_solve_p] = triangular_solve_transpose_rule
def qr_impl(operand, full_matrices):
q, r = xla.apply_primitive(qr_p, operand, full_matrices=full_matrices)
return core.pack((q, r))
def qr_translation_rule(c, operand, full_matrices):
return c.QR(operand, full_matrices=full_matrices)
if conjugate_a and not transpose_a:
a = xops.Conj(a)
conjugate_a = False
if not transpose_a:
transpose = xops.TriangularSolveOptions_Transpose.NO_TRANSPOSE
else:
transpose = (xops.TriangularSolveOptions_Transpose.ADJOINT
if conjugate_a else
xops.TriangularSolveOptions_Transpose.TRANSPOSE)
return xops.TriangularSolve(a, b, left_side, lower, unit_diagonal,
transpose)
triangular_solve_p = standard_primitive(
triangular_solve_shape_rule,
triangular_solve_dtype_rule,
'triangular_solve',
translation_rule=_triangular_solve_translation_rule)
ad.defjvp2(triangular_solve_p, triangular_solve_jvp_rule_a,
lambda g_b, _, a, b, **kws: triangular_solve(a, g_b, **kws))
ad.primitive_transposes[triangular_solve_p] = triangular_solve_transpose_rule
batching.primitive_batchers[
triangular_solve_p] = triangular_solve_batching_rule
def _triangular_solve_cpu_translation_rule(c, a, b, left_side, lower,
transpose_a, conjugate_a,
unit_diagonal):
shape = c.GetShape(a)
dtype = shape.element_type().type
def transform_shape_rule(T, v):
return v.shape
def transform_dtype_rule(T, v):
return v.dtype
def transform_translation_rule(c, T, v):
v_dim = len(c.GetShape(v).dimensions()) - 1
return c.DotGeneral(v, T, (((v_dim, ), (0, )), ((), ())))
transform_p = lax.standard_primitive(transform_shape_rule,
transform_dtype_rule, 'transform',
transform_translation_rule)
def transform_batching_rule(operands, batch_dims):
T, v = operands
T_dim, v_dim = batch_dims
assert T_dim is None
assert v_dim == 0
return transform_p.bind(T, v), v_dim
batching.primitive_batchers[transform_p] = transform_batching_rule
