def run_eigsy(A, verbose=False):
if verbose:
print("original matrix:\n", str(A))
D, Q = mp.eigsy(A)
B = Q * mp.diag(D) * Q.transpose()
C = A - B
E = Q * Q.transpose() - mp.eye(A.rows)
if verbose:
print("eigenvalues:\n", D)
print("eigenvectors:\n", Q)
NC = mp.mnorm(C)
NE = mp.mnorm(E)
if verbose:
print("difference:", NC, "\n", C, "\n")
print("difference:", NE, "\n", E, "\n")
eps = mp.exp(0.8 * mp.log(mp.eps))
assert NC < eps
assert NE < eps
return NC
def run_eigsy(A, verbose = False):
if verbose:
print("original matrix:\n", str(A))
D, Q = mp.eigsy(A)
B = Q * mp.diag(D) * Q.transpose()
C = A - B
E = Q * Q.transpose() - mp.eye(A.rows)
if verbose:
print("eigenvalues:\n", D)
print("eigenvectors:\n", Q)
NC = mp.mnorm(C)
NE = mp.mnorm(E)
if verbose:
print("difference:", NC, "\n", C, "\n")
print("difference:", NE, "\n", E, "\n")
eps = mp.exp( 0.8 * mp.log(mp.eps))
assert NC < eps
assert NE < eps
return NC
def run_svd_r(A, full_matrices=False, verbose=True):
m, n = A.rows, A.cols
eps = mp.exp(0.8 * mp.log(mp.eps))
if verbose:
print("original matrix:\n", str(A))
print("full", full_matrices)
U, S0, V = mp.svd_r(A, full_matrices=full_matrices)
S = mp.zeros(U.cols, V.rows)
for j in xrange(min(m, n)):
S[j, j] = S0[j]
if verbose:
print("U:\n", str(U))
print("S:\n", str(S0))
print("V:\n", str(V))
C = U * S * V - A
err = mp.mnorm(C)
if verbose:
print("C\n", str(C), "\n", err)
assert err < eps
D = V * V.transpose() - mp.eye(V.rows)
err = mp.mnorm(D)
if verbose:
print("D:\n", str(D), "\n", err)
assert err < eps
E = U.transpose() * U - mp.eye(U.cols)
err = mp.mnorm(E)
if verbose:
print("E:\n", str(E), "\n", err)
assert err < eps
def run_svd_r(A, full_matrices = False, verbose = True):
m, n = A.rows, A.cols
eps = mp.exp(0.8 * mp.log(mp.eps))
if verbose:
print("original matrix:\n", str(A))
print("full", full_matrices)
U, S0, V = mp.svd_r(A, full_matrices = full_matrices)
S = mp.zeros(U.cols, V.rows)
for j in xrange(min(m, n)):
S[j,j] = S0[j]
if verbose:
print("U:\n", str(U))
print("S:\n", str(S0))
print("V:\n", str(V))
C = U * S * V - A
err = mp.mnorm(C)
if verbose:
print("C\n", str(C), "\n", err)
assert err < eps
D = V * V.transpose() - mp.eye(V.rows)
err = mp.mnorm(D)
if verbose:
print("D:\n", str(D), "\n", err)
assert err < eps
E = U.transpose() * U - mp.eye(U.cols)
err = mp.mnorm(E)
if verbose:
print("E:\n", str(E), "\n", err)
assert err < eps