def unary_nd(f, x, eps=EPS):
if isinstance(x, array_types):
if np.iscomplexobj(x):
nd_grad = np.zeros(x.shape) + 0j
elif isinstance(x, garray_obj):
nd_grad = np.array(np.zeros(x.shape), dtype=np.gpu_float32)
else:
nd_grad = np.zeros(x.shape)
for dims in it.product(*list(map(range, x.shape))):
nd_grad[dims] = unary_nd(indexed_function(f, x, dims), x[dims])
return nd_grad
elif isinstance(x, tuple):
return tuple([
unary_nd(indexed_function(f, tuple(x), i), x[i])
for i in range(len(x))
])
elif isinstance(x, dict):
return {
k: unary_nd(indexed_function(f, x, k), v)
for k, v in six.iteritems(x)
}
elif isinstance(x, list):
return [
unary_nd(indexed_function(f, x, i), v) for i, v in enumerate(x)
]
elif np.iscomplexobj(x):
result = (f(x + eps/2) - f(x - eps/2)) / eps \
- 1j*(f(x + 1j*eps/2) - f(x - 1j*eps/2)) / eps
return type(safe_type(x))(result)
else:
return type(safe_type(x))((f(x + eps / 2) - f(x - eps / 2)) / eps)
def vjp(g):
ge, gu = g
ge = _matrix_diag(ge)
f = 1/(e[..., anp.newaxis, :] - e[..., :, anp.newaxis] + 1.e-20)
f -= _diag(f)
ut = anp.swapaxes(u, -1, -2)
r1 = f * _dot(ut, gu)
r2 = -f * (_dot(_dot(ut, anp.conj(u)), anp.real(_dot(ut, gu)) * anp.eye(n)))
r = _dot(_dot(anp.linalg.inv(ut), ge + r1 + r2), ut)
if not anp.iscomplexobj(x):
r = anp.real(r)
# the derivative is still complex for real input (imaginary delta is allowed), real output
# but the derivative should be real in real input case when imaginary delta is forbidden
return r
def unary_nd(f, x, eps=EPS):
if isinstance(x, array_types):
if np.iscomplexobj(x):
nd_grad = np.zeros(x.shape) + 0j
elif isinstance(x, garray_obj):
nd_grad = np.array(np.zeros(x.shape), dtype=np.gpu_float32)
else:
nd_grad = np.zeros(x.shape)
for dims in it.product(*list(map(range, x.shape))):
nd_grad[dims] = unary_nd(indexed_function(f, x, dims), x[dims])
return nd_grad
elif isinstance(x, tuple):
return tuple([unary_nd(indexed_function(f, tuple(x), i), x[i])
for i in range(len(x))])
elif isinstance(x, dict):
return {k : unary_nd(indexed_function(f, x, k), v) for k, v in six.iteritems(x)}
elif isinstance(x, list):
return [unary_nd(indexed_function(f, x, i), v) for i, v in enumerate(x)]
elif np.iscomplexobj(x):
result = (f(x + eps/2) - f(x - eps/2)) / eps \
- 1j*(f(x + 1j*eps/2) - f(x - 1j*eps/2)) / eps
return type(safe_type(x))(result)
else:
return type(safe_type(x))((f(x + eps/2) - f(x - eps/2)) / eps)
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 _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 _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 test_real_type():
fun = lambda x: np.sum(np.real(x))
df = grad(fun)
assert np.isrealobj(df(2.0))
assert np.iscomplexobj(df(1.0j))
def test_real_type():
fun = lambda x: np.sum(np.real(x))
df = grad(fun)
assert np.isrealobj(df(2.0))
assert np.iscomplexobj(df(1.0j))