def cholesky(a):
"""
Compute the Cholesky decomposition of a matrix.
Returns the Cholesky decomposition, :math:`A = L L^*` of a Hermitian
positive-definite matrix :math:`A`.
Parameters
----------
a : array-like, shape (M, M)
Matrix to be decomposed
Returns
-------
L : array-like, shape (M, M)
Lower-triangular Cholesky factor of A
Raises LinAlgError if decomposition fails
Examples
--------
>>> A = np.array([[1,-2j],[2j,5]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
>>> dot(L, L.T.conj())
array([[ 1.+0.j, 0.-2.j],
[ 0.+2.j, 5.+0.j]])
"""
a, wrap = _makearray(a)
_assertRank2(a)
_assertSquareness(a)
t, result_t = _commonType(a)
a = _fastCopyAndTranspose(t, a)
m = a.shape[0]
n = a.shape[1]
if isComplexType(t):
lapack_routine = lapack_lite.zpotrf
else:
lapack_routine = lapack_lite.dpotrf
results = lapack_routine('L', n, a, m, 0)
if results['info'] > 0:
raise LinAlgError, 'Matrix is not positive definite - \
Cholesky decomposition cannot be computed'
s = triu(a, k=0).transpose()
if (s.dtype != result_t):
s = s.astype(result_t)
return wrap(s)
def cholesky(a):
"""
Compute the Cholesky decomposition of a matrix.
Returns the Cholesky decomposition, :math:`A = L L^*` of a Hermitian
positive-definite matrix :math:`A`.
Parameters
----------
a : array-like, shape (M, M)
Matrix to be decomposed
Returns
-------
L : array-like, shape (M, M)
Lower-triangular Cholesky factor of A
Raises LinAlgError if decomposition fails
Examples
--------
>>> A = np.array([[1,-2j],[2j,5]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
>>> dot(L, L.T.conj())
array([[ 1.+0.j, 0.-2.j],
[ 0.+2.j, 5.+0.j]])
"""
a, wrap = _makearray(a)
_assertRank2(a)
_assertSquareness(a)
t, result_t = _commonType(a)
a = _fastCopyAndTranspose(t, a)
m = a.shape[0]
n = a.shape[1]
if isComplexType(t):
lapack_routine = lapack_lite.zpotrf
else:
lapack_routine = lapack_lite.dpotrf
results = lapack_routine('L', n, a, m, 0)
if results['info'] > 0:
raise LinAlgError, 'Matrix is not positive definite - \
Cholesky decomposition cannot be computed'
s = triu(a, k=0).transpose()
if (s.dtype != result_t):
s = s.astype(result_t)
return wrap(s)
def cholesky(a):
_assertRank2(a)
_assertSquareness(a)
t, result_t = _commonType(a)
a = _fastCopyAndTranspose(t, a)
m = a.shape[0]
n = a.shape[1]
if isComplexType(t):
lapack_routine = lapack_lite.zpotrf
else:
lapack_routine = lapack_lite.dpotrf
results = lapack_routine('L', n, a, m, 0)
if results['info'] > 0:
raise LinAlgError, 'Matrix is not positive definite - \
Cholesky decomposition cannot be computed'
s = triu(a, k=0).transpose()
if (s.dtype != result_t):
return s.astype(result_t)
return s
def cholesky(a):
"""
Cholesky decomposition.
Return the Cholesky decomposition, :math:`A = L L^*` of a Hermitian
positive-definite matrix :math:`A`.
Parameters
----------
a : array_like, shape (M, M)
Hermitian (symmetric, if it is real) and positive definite
input matrix.
Returns
-------
L : array_like, shape (M, M)
Lower-triangular Cholesky factor of A.
Raises
------
LinAlgError
If the decomposition fails.
Notes
-----
The Cholesky decomposition is often used as a fast way of solving
.. math:: A \\mathbf{x} = \\mathbf{b}.
First, we solve for :math:`\\mathbf{y}` in
.. math:: L \\mathbf{y} = \\mathbf{b},
and then for :math:`\\mathbf{x}` in
.. math:: L^* \\mathbf{x} = \\mathbf{y}.
Examples
--------
>>> A = np.array([[1,-2j],[2j,5]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
>>> np.dot(L, L.T.conj())
array([[ 1.+0.j, 0.-2.j],
[ 0.+2.j, 5.+0.j]])
"""
a, wrap = _makearray(a)
_assertRank2(a)
_assertSquareness(a)
t, result_t = _commonType(a)
a = _fastCopyAndTranspose(t, a)
m = a.shape[0]
n = a.shape[1]
if isComplexType(t):
lapack_routine = lapack_lite.zpotrf
else:
lapack_routine = lapack_lite.dpotrf
results = lapack_routine('L', n, a, m, 0)
if results['info'] > 0:
raise LinAlgError, 'Matrix is not positive definite - \
Cholesky decomposition cannot be computed'
s = triu(a, k=0).transpose()
if (s.dtype != result_t):
s = s.astype(result_t)
return wrap(s)
def cholesky(a):
"""
Cholesky decomposition.
Return the Cholesky decomposition, :math:`A = L L^*` of a Hermitian
positive-definite matrix :math:`A`.
Parameters
----------
a : array_like, shape (M, M)
Hermitian (symmetric, if it is real) and positive definite
input matrix.
Returns
-------
L : array_like, shape (M, M)
Lower-triangular Cholesky factor of A.
Raises
------
LinAlgError
If the decomposition fails.
Notes
-----
The Cholesky decomposition is often used as a fast way of solving
.. math:: A \\mathbf{x} = \\mathbf{b}.
First, we solve for :math:`\\mathbf{y}` in
.. math:: L \\mathbf{y} = \\mathbf{b},
and then for :math:`\\mathbf{x}` in
.. math:: L^* \\mathbf{x} = \\mathbf{y}.
Examples
--------
>>> A = np.array([[1,-2j],[2j,5]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
>>> np.dot(L, L.T.conj())
array([[ 1.+0.j, 0.-2.j],
[ 0.+2.j, 5.+0.j]])
"""
a, wrap = _makearray(a)
_assertRank2(a)
_assertSquareness(a)
t, result_t = _commonType(a)
a = _fastCopyAndTranspose(t, a)
m = a.shape[0]
n = a.shape[1]
if isComplexType(t):
lapack_routine = lapack_lite.zpotrf
else:
lapack_routine = lapack_lite.dpotrf
results = lapack_routine('L', n, a, m, 0)
if results['info'] > 0:
raise LinAlgError, 'Matrix is not positive definite - \
Cholesky decomposition cannot be computed'
s = triu(a, k=0).transpose()
if (s.dtype != result_t):
s = s.astype(result_t)
return wrap(s)
