def _calc_P_Q(A):
A = jnp.asarray(A)
if A.ndim != 2 or A.shape[0] != A.shape[1]:
raise ValueError('expected A to be a square matrix')
A_L1 = np_linalg.norm(A, 1)
n_squarings = 0
if A.dtype == 'float64' or A.dtype == 'complex128':
maxnorm = 5.371920351148152
n_squarings = jnp.maximum(0, jnp.floor(jnp.log2(A_L1 / maxnorm)))
A = A / 2**n_squarings.astype(A.dtype)
conds = jnp.array([
1.495585217958292e-002, 2.539398330063230e-001,
9.504178996162932e-001, 2.097847961257068e+000
],
dtype=A_L1.dtype)
idx = jnp.digitize(A_L1, conds)
U, V = lax.switch(idx, [_pade3, _pade5, _pade7, _pade9, _pade13], A)
elif A.dtype == 'float32' or A.dtype == 'complex64':
maxnorm = 3.925724783138660
n_squarings = jnp.maximum(0, jnp.floor(jnp.log2(A_L1 / maxnorm)))
A = A / 2**n_squarings.astype(A.dtype)
conds = jnp.array([4.258730016922831e-001, 1.880152677804762e+000],
dtype=A_L1.dtype)
idx = jnp.digitize(A_L1, conds)
U, V = lax.switch(idx, [_pade3, _pade5, _pade7], A)
else:
raise TypeError(f"A.dtype={A.dtype} is not supported.")
P = U + V # p_m(A) : numerator
Q = -U + V # q_m(A) : denominator
return P, Q, n_squarings
def _calc_P_Q(A):
A = jnp.asarray(A)
if A.ndim != 2 or A.shape[0] != A.shape[1]:
raise ValueError('expected A to be a square matrix')
A_L1 = np_linalg.norm(A,1)
n_squarings = 0
if A.dtype == 'float64' or A.dtype == 'complex128':
U3, V3 = _pade3(A)
U5, V5 = _pade5(A)
U7, V7 = _pade7(A)
U9, V9 = _pade9(A)
maxnorm = 5.371920351148152
n_squarings = jnp.maximum(0, jnp.floor(jnp.log2(A_L1 / maxnorm)))
A = A / 2**n_squarings
U13, V13 = _pade13(A)
conds=jnp.array([1.495585217958292e-002, 2.539398330063230e-001,
9.504178996162932e-001, 2.097847961257068e+000])
U = jnp.select((A_L1<conds), (U3, U5, U7, U9), U13)
V = jnp.select((A_L1<conds), (V3, V5, V7, V9), V13)
elif A.dtype == 'float32' or A.dtype == 'complex64':
U3,V3 = _pade3(A)
U5,V5 = _pade5(A)
maxnorm = 3.925724783138660
n_squarings = jnp.maximum(0, jnp.floor(jnp.log2(A_L1 / maxnorm)))
A = A / 2**n_squarings
U7,V7 = _pade7(A)
conds=jnp.array([4.258730016922831e-001, 1.880152677804762e+000])
U = jnp.select((A_L1<conds), (U3, U5), U7)
V = jnp.select((A_L1<conds), (V3, V5), V7)
else:
raise TypeError("A.dtype={} is not supported.".format(A.dtype))
P = U + V # p_m(A) : numerator
Q = -U + V # q_m(A) : denominator
return P, Q, n_squarings
