def cond(x, p=None):
_assertNoEmpty2d(x)
if p in (None, 2):
s = la.svd(x, compute_uv=False)
return s[..., 0] / s[..., -1]
elif p == -2:
s = la.svd(x, compute_uv=False)
r = s[..., -1] / s[..., 0]
else:
_assertRankAtLeast2(x)
_assertNdSquareness(x)
invx = la.inv(x)
r = la.norm(x, ord=p, axis=(-2, -1)) * la.norm(invx, ord=p, axis=(-2, -1))
# Convert nans to infs unless the original array had nan entries
orig_nan_check = np.full_like(r, ~np.isnan(r).any())
nan_mask = np.logical_and(np.isnan(r), ~np.isnan(x).any(axis=(-2, -1)))
r = np.where(orig_nan_check, np.where(nan_mask, np.inf, r), r)
return r
def construct_uv(Atemp, chiM):
chiA = Atemp.shape[0]
chitemp = min(chiA**2, chiM)
utemp, stemp, vtemp = LA.svd(Atemp.reshape(chiA**2, chiA**2),
full_matrices=False)
U1 = utemp[:, :chitemp] @ np.diag(np.sqrt(stemp[:chitemp]))
U1 = U1.reshape(chiA, chiA, chitemp)
V1 = np.diag(np.sqrt(stemp[:chitemp])) @ vtemp[:chitemp, :]
V1 = np.transpose(V1.reshape(chitemp, chiA, chiA), (1, 2, 0))
return U1, V1
n = A.shape
eps = 1e-12 # accuracy
delta = (eps/math.sqrt(d-1)) * la.norm(A) # cutting param
C = A # tmp tensor
G = [] # tt-cores
r = [] # tt-ranks
r.append(1)
for k in range(1, d):
C = np.reshape(C, (r[k-1] * n[k-1], int(N / (r[k-1] * n[k-1]))))
# calc low-rank approximation
u, s, v = la.svd(C)
sum = 0
nsize = np.size(s)
rres = np.size(s)
for rk in range(0, nsize):
for m in range(rk+1, nsize):
sum = sum + (s[m] ** 2)
if (sum <= (eps ** 2) * la.norm(A)) and (rres > rk):
rres = rk + 1
sum = 0
r.append(rres)
G.append(np.reshape(u[:, :r[k]], (r[k-1], n[k-1], r[k])))
s = np.diag(s)
C = np.dot(s[:r[k], :r[k]], v[:r[k], :])
N = (N * r[k]) / (n[k-1] * r[k-1])
def svd(a, full_matrices=True, compute_uv=True):
if isinstance(a, JaxArray): a = a.value
u, s, vh = linalg.svd(a,
full_matrices=full_matrices,
compute_uv=compute_uv)
return JaxArray(u), JaxArray(s), JaxArray(vh)