from __future__ import division
import scipy.linalg
import autograd.numpy as anp
from autograd.numpy.numpy_wrapper import wrap_namespace
from autograd.extend import defvjp
wrap_namespace(scipy.linalg.__dict__, globals()) # populates module namespace
defvjp(sqrtm, lambda ans, A, **kwargs: lambda g: solve_lyapunov(ans, g))
def _flip(a, trans):
if anp.iscomplexobj(a):
return 'H' if trans in ('N', 0) else 'N'
else:
return 'T' if trans in ('N', 0) else 'N'
def grad_solve_triangular(ans, a, b, trans=0, lower=False, **kwargs):
tri = anp.tril if (lower ^ (_flip(a, trans) == 'N')) else anp.triu
transpose = lambda x: x if _flip(a, trans) != 'N' else x.T
al2d = lambda x: x if x.ndim > 1 else x[..., None]
def vjp(g):
v = al2d(solve_triangular(a, g, trans=_flip(a, trans), lower=lower))
return -transpose(tri(anp.dot(v, al2d(ans).T)))
return vjp
from __future__ import division
import scipy.linalg
import autograd.numpy as anp
from autograd.numpy.numpy_wrapper import wrap_namespace
from autograd.numpy.linalg import atleast_2d_col as al2d
wrap_namespace(scipy.linalg.__dict__, globals()) # populates module namespace
sqrtm.defgrad(lambda ans, A, **kwargs: lambda g: solve_lyapunov(ans, g))
def _flip(a, trans):
if anp.iscomplexobj(a):
return "H" if trans in ("N", 0) else "N"
else:
return "T" if trans in ("N", 0) else "N"
def make_grad_solve_triangular(ans, a, b, trans=0, lower=False, **kwargs):
tri = anp.tril if (lower ^ (_flip(a, trans) == "N")) else anp.triu
transpose = lambda x: x if _flip(a, trans) != "N" else x.T
def solve_triangular_grad(g):
v = al2d(solve_triangular(a, g, trans=_flip(a, trans), lower=lower))
return -transpose(tri(anp.dot(v, al2d(ans).T)))
return solve_triangular_grad
solve_triangular.defgrad(make_grad_solve_triangular)