def rsf2csf(T, Z):
"""Convert real Schur form to complex Schur form.
Convert a quasi-diagonal real-valued Schur form to the upper triangular
complex-valued Schur form.
Parameters
----------
T : array, shape (M, M)
Real Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix
Returns
-------
T : array, shape (M, M)
Complex Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix corresponding to the complex form
See also
--------
schur : Schur decompose a matrix
"""
Z, T = map(asarray_chkfinite, (Z, T))
if len(Z.shape) != 2 or Z.shape[0] != Z.shape[1]:
raise ValueError("matrix must be square.")
if len(T.shape) != 2 or T.shape[0] != T.shape[1]:
raise ValueError("matrix must be square.")
if T.shape[0] != Z.shape[0]:
raise ValueError("matrices must be same dimension.")
N = T.shape[0]
arr = numpy.array
t = _commonType(Z, T, arr([3.0],'F'))
Z, T = _castCopy(t, Z, T)
conj = numpy.conj
dot = numpy.dot
r_ = numpy.r_
transp = numpy.transpose
for m in range(N-1, 0, -1):
if abs(T[m,m-1]) > eps*(abs(T[m-1,m-1]) + abs(T[m,m])):
k = slice(m-1, m+1)
mu = eigvals(T[k,k]) - T[m,m]
r = misc.norm([mu[0], T[m,m-1]])
c = mu[0] / r
s = T[m,m-1] / r
G = r_[arr([[conj(c), s]], dtype=t), arr([[-s, c]], dtype=t)]
Gc = conj(transp(G))
j = slice(m-1, N)
T[k,j] = dot(G, T[k,j])
i = slice(0, m+1)
T[i,k] = dot(T[i,k], Gc)
i = slice(0, N)
Z[i,k] = dot(Z[i,k], Gc)
T[m,m-1] = 0.0;
return T, Z
def rsf2csf(T, Z):
"""Convert real Schur form to complex Schur form.
Convert a quasi-diagonal real-valued Schur form to the upper triangular
complex-valued Schur form.
Parameters
----------
T : array, shape (M, M)
Real Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix
Returns
-------
T : array, shape (M, M)
Complex Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix corresponding to the complex form
See also
--------
schur : Schur decompose a matrix
"""
Z, T = map(asarray_chkfinite, (Z, T))
if len(Z.shape) != 2 or Z.shape[0] != Z.shape[1]:
raise ValueError("matrix must be square.")
if len(T.shape) != 2 or T.shape[0] != T.shape[1]:
raise ValueError("matrix must be square.")
if T.shape[0] != Z.shape[0]:
raise ValueError("matrices must be same dimension.")
N = T.shape[0]
arr = numpy.array
t = _commonType(Z, T, arr([3.0], 'F'))
Z, T = _castCopy(t, Z, T)
conj = numpy.conj
dot = numpy.dot
r_ = numpy.r_
transp = numpy.transpose
for m in range(N - 1, 0, -1):
if abs(T[m, m - 1]) > eps * (abs(T[m - 1, m - 1]) + abs(T[m, m])):
k = slice(m - 1, m + 1)
mu = eigvals(T[k, k]) - T[m, m]
r = misc.norm([mu[0], T[m, m - 1]])
c = mu[0] / r
s = T[m, m - 1] / r
G = r_[arr([[conj(c), s]], dtype=t), arr([[-s, c]], dtype=t)]
Gc = conj(transp(G))
j = slice(m - 1, N)
T[k, j] = dot(G, T[k, j])
i = slice(0, m + 1)
T[i, k] = dot(T[i, k], Gc)
i = slice(0, N)
Z[i, k] = dot(Z[i, k], Gc)
T[m, m - 1] = 0.0
return T, Z
def rsf2csf(T, Z, check_finite=True):
"""Convert real Schur form to complex Schur form.
Convert a quasi-diagonal real-valued Schur form to the upper triangular
complex-valued Schur form.
Parameters
----------
T : array, shape (M, M)
Real Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix
check_finite : boolean, optional
Whether to check the input matrixes contain only finite numbers.
Disabling may give a performance gain, but may result to problems
(crashes, non-termination) if the inputs do contain infinities or NaNs.
Returns
-------
T : array, shape (M, M)
Complex Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix corresponding to the complex form
See also
--------
schur : Schur decompose a matrix
"""
if check_finite:
Z, T = map(asarray_chkfinite, (Z, T))
else:
Z, T = map(asarray, (Z, T))
if len(Z.shape) != 2 or Z.shape[0] != Z.shape[1]:
raise ValueError("matrix must be square.")
if len(T.shape) != 2 or T.shape[0] != T.shape[1]:
raise ValueError("matrix must be square.")
if T.shape[0] != Z.shape[0]:
raise ValueError("matrices must be same dimension.")
N = T.shape[0]
arr = numpy.array
t = _commonType(Z, T, arr([3.0], 'F'))
Z, T = _castCopy(t, Z, T)
conj = numpy.conj
dot = numpy.dot
r_ = numpy.r_
transp = numpy.transpose
for m in range(N - 1, 0, -1):
if abs(T[m, m - 1]) > eps * (abs(T[m - 1, m - 1]) + abs(T[m, m])):
k = slice(m - 1, m + 1)
mu = eigvals(T[k, k]) - T[m, m]
r = misc.norm([mu[0], T[m, m - 1]])
c = mu[0] / r
s = T[m, m - 1] / r
G = r_[arr([[conj(c), s]], dtype=t), arr([[-s, c]], dtype=t)]
Gc = conj(transp(G))
j = slice(m - 1, N)
T[k, j] = dot(G, T[k, j])
i = slice(0, m + 1)
T[i, k] = dot(T[i, k], Gc)
i = slice(0, N)
Z[i, k] = dot(Z[i, k], Gc)
T[m, m - 1] = 0.0
return T, Z
def rsf2csf(T, Z, check_finite=True):
"""Convert real Schur form to complex Schur form.
Convert a quasi-diagonal real-valued Schur form to the upper triangular
complex-valued Schur form.
Parameters
----------
T : array, shape (M, M)
Real Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix
check_finite : boolean, optional
Whether to check the input matrixes contain only finite numbers.
Disabling may give a performance gain, but may result to problems
(crashes, non-termination) if the inputs do contain infinities or NaNs.
Returns
-------
T : array, shape (M, M)
Complex Schur form of the original matrix
Z : array, shape (M, M)
Schur transformation matrix corresponding to the complex form
See also
--------
schur : Schur decompose a matrix
"""
if check_finite:
Z, T = map(asarray_chkfinite, (Z, T))
else:
Z,T = map(asarray, (Z,T))
if len(Z.shape) != 2 or Z.shape[0] != Z.shape[1]:
raise ValueError("matrix must be square.")
if len(T.shape) != 2 or T.shape[0] != T.shape[1]:
raise ValueError("matrix must be square.")
if T.shape[0] != Z.shape[0]:
raise ValueError("matrices must be same dimension.")
N = T.shape[0]
arr = numpy.array
t = _commonType(Z, T, arr([3.0],'F'))
Z, T = _castCopy(t, Z, T)
conj = numpy.conj
dot = numpy.dot
r_ = numpy.r_
transp = numpy.transpose
for m in range(N-1, 0, -1):
if abs(T[m,m-1]) > eps*(abs(T[m-1,m-1]) + abs(T[m,m])):
k = slice(m-1, m+1)
mu = eigvals(T[k,k]) - T[m,m]
r = misc.norm([mu[0], T[m,m-1]])
c = mu[0] / r
s = T[m,m-1] / r
G = r_[arr([[conj(c), s]], dtype=t), arr([[-s, c]], dtype=t)]
Gc = conj(transp(G))
j = slice(m-1, N)
T[k,j] = dot(G, T[k,j])
i = slice(0, m+1)
T[i,k] = dot(T[i,k], Gc)
i = slice(0, N)
Z[i,k] = dot(Z[i,k], Gc)
T[m,m-1] = 0.0;
return T, Z