def det(a, overwrite_a=False):
"""Compute the determinant of a matrix
Parameters
----------
a : array, shape (M, M)
Returns
-------
det : float or complex
Determinant of a
Notes
-----
The determinant is computed via LU factorization, LAPACK routine z/dgetrf.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError('expected square matrix')
overwrite_a = overwrite_a or _datacopied(a1, a)
fdet, = get_flinalg_funcs(('det', ), (a1, ))
a_det, info = fdet(a1, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of internal '
'det.getrf' % -info)
return a_det
def det(a, overwrite_a=0):
"""Compute the determinant of a matrix
Parameters
----------
a : array, shape (M, M)
Returns
-------
det : float or complex
Determinant of a
Notes
-----
The determinant is computed via LU factorization, LAPACK routine z/dgetrf.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError, "expected square matrix"
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a, "__array__"))
fdet, = get_flinalg_funcs(("det",), (a1,))
a_det, info = fdet(a1, overwrite_a=overwrite_a)
if info < 0:
raise ValueError, "illegal value in %-th argument of internal det.getrf" % (-info)
return a_det
def det(a, overwrite_a=False):
"""Compute the determinant of a matrix
Parameters
----------
a : array, shape (M, M)
Returns
-------
det : float or complex
Determinant of a
Notes
-----
The determinant is computed via LU factorization, LAPACK routine z/dgetrf.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError('expected square matrix')
overwrite_a = overwrite_a or _datacopied(a1, a)
fdet, = get_flinalg_funcs(('det',), (a1,))
a_det, info = fdet(a1, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of internal '
'det.getrf' % -info)
return a_det
def lu(a,permute_l=0,overwrite_a=0):
"""Return LU decompostion of a matrix.
Inputs:
a -- An M x N matrix.
permute_l -- Perform matrix multiplication p * l [disabled].
Outputs:
p,l,u -- LU decomposition matrices of a [permute_l=0]
pl,u -- LU decomposition matrices of a [permute_l=1]
Definitions:
a = p * l * u [permute_l=0]
a = pl * u [permute_l=1]
p - An M x M permutation matrix
l - An M x K lower triangular or trapezoidal matrix
with unit-diagonal
u - An K x N upper triangular or trapezoidal matrix
K = min(M,N)
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2:
raise ValueError, 'expected matrix'
overwrite_a = overwrite_a or (_datanotshared(a1,a))
flu, = get_flinalg_funcs(('lu',),(a1,))
p,l,u,info = flu(a1,permute_l=permute_l,overwrite_a = overwrite_a)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal lu.getrf'%(-info)
if permute_l:
return l,u
return p,l,u
def det(a, overwrite_a=False, check_finite=True):
"""
Compute the determinant of a matrix
The determinant of a square matrix is a value derived arithmetically
from the coefficients of the matrix.
The determinant for a 3x3 matrix, for example, is computed as follows::
a b c
d e f = A
g h i
det(A) = a*e*i +b*f*g + c*d*h - c*e*g - b*d*i - a*f*h
Parameters
----------
a : array_like, shape (M, M)
A square matrix.
overwrite_a : bool
Allow overwriting data in a (may enhance performance).
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
-------
det : float or complex
Determinant of `a`.
Notes
-----
The determinant is computed via LU factorization, LAPACK routine z/dgetrf.
Examples
--------
>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> linalg.det(a)
0.0
>>> a = np.array([[0,2,3],[4,5,6],[7,8,9]])
>>> linalg.det(a)
3.0
"""
if check_finite:
a1 = np.asarray_chkfinite(a)
else:
a1 = np.asarray(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError('expected square matrix')
overwrite_a = overwrite_a or _datacopied(a1, a)
fdet, = get_flinalg_funcs(('det',), (a1,))
a_det, info = fdet(a1, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of internal '
'det.getrf' % -info)
return a_det
def det(a, overwrite_a=False, check_finite=True):
"""
Compute the determinant of a matrix
The determinant of a square matrix is a value derived arithmetically
from the coefficients of the matrix.
The determinant for a 3x3 matrix, for example, is computed as follows::
a b c
d e f = A
g h i
det(A) = a*e*i +b*f*g + c*d*h - c*e*g - b*d*i - a*f*h
Parameters
----------
a : array_like, shape (M, M)
A square matrix.
overwrite_a : bool
Allow overwriting data in a (may enhance performance).
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
-------
det : float or complex
Determinant of `a`.
Notes
-----
The determinant is computed via LU factorization, LAPACK routine z/dgetrf.
Examples
--------
>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> linalg.det(a)
0.0
>>> a = np.array([[0,2,3],[4,5,6],[7,8,9]])
>>> linalg.det(a)
3.0
"""
if check_finite:
a1 = np.asarray_chkfinite(a)
else:
a1 = np.asarray(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError('expected square matrix')
overwrite_a = overwrite_a or _datacopied(a1, a)
fdet, = get_flinalg_funcs(('det', ), (a1, ))
a_det, info = fdet(a1, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of internal '
'det.getrf' % -info)
return a_det
def lu(a, permute_l=False, overwrite_a=False):
"""Compute pivoted LU decompostion of a matrix.
The decomposition is::
A = P L U
where P is a permutation matrix, L lower triangular with unit
diagonal elements, and U upper triangular.
Parameters
----------
a : array, shape (M, N)
Array to decompose
permute_l : boolean
Perform the multiplication P*L (Default: do not permute)
overwrite_a : boolean
Whether to overwrite data in a (may improve performance)
Returns
-------
(If permute_l == False)
p : array, shape (M, M)
Permutation matrix
l : array, shape (M, K)
Lower triangular or trapezoidal matrix with unit diagonal.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
(If permute_l == True)
pl : array, shape (M, K)
Permuted L matrix.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
Notes
-----
This is a LU factorization routine written for Scipy.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2:
raise ValueError('expected matrix')
overwrite_a = overwrite_a or (_datanotshared(a1, a))
flu, = get_flinalg_funcs(('lu', ), (a1, ))
p, l, u, info = flu(a1, permute_l=permute_l, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of '
'internal lu.getrf' % -info)
if permute_l:
return l, u
return p, l, u
def lu(a, permute_l=False, overwrite_a=False):
"""Compute pivoted LU decompostion of a matrix.
The decomposition is::
A = P L U
where P is a permutation matrix, L lower triangular with unit
diagonal elements, and U upper triangular.
Parameters
----------
a : array, shape (M, N)
Array to decompose
permute_l : boolean
Perform the multiplication P*L (Default: do not permute)
overwrite_a : boolean
Whether to overwrite data in a (may improve performance)
Returns
-------
(If permute_l == False)
p : array, shape (M, M)
Permutation matrix
l : array, shape (M, K)
Lower triangular or trapezoidal matrix with unit diagonal.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
(If permute_l == True)
pl : array, shape (M, K)
Permuted L matrix.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
Notes
-----
This is a LU factorization routine written for Scipy.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2:
raise ValueError('expected matrix')
overwrite_a = overwrite_a or (_datacopied(a1, a))
flu, = get_flinalg_funcs(('lu',), (a1,))
p, l, u, info = flu(a1, permute_l=permute_l, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of '
'internal lu.getrf' % -info)
if permute_l:
return l, u
return p, l, u
def det(a, overwrite_a=0):
""" det(a, overwrite_a=0) -> d
Return determinant of a square matrix.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError, 'expected square matrix'
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a,'__array__'))
fdet, = get_flinalg_funcs(('det',),(a1,))
a_det,info = fdet(a1,overwrite_a=overwrite_a)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal det.getrf'%(-info)
return a_det
def lu(a, permute_l=False, overwrite_a=False, check_finite=True):
"""Compute pivoted LU decompostion of a matrix.
The decomposition is::
A = P L U
where P is a permutation matrix, L lower triangular with unit
diagonal elements, and U upper triangular.
Parameters
----------
a : array, shape (M, N)
Array to decompose
permute_l : boolean
Perform the multiplication P*L (Default: do not permute)
overwrite_a : boolean
Whether to overwrite data in a (may improve performance)
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
-------
(If permute_l == False)
p : array, shape (M, M)
Permutation matrix
l : array, shape (M, K)
Lower triangular or trapezoidal matrix with unit diagonal.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
(If permute_l == True)
pl : array, shape (M, K)
Permuted L matrix.
K = min(M, N)
u : array, shape (K, N)
Upper triangular or trapezoidal matrix
Notes
-----
This is a LU factorization routine written for Scipy.
"""
if check_finite:
a1 = asarray_chkfinite(a)
else:
a1 = asarray(a)
if len(a1.shape) != 2:
raise ValueError('expected matrix')
overwrite_a = overwrite_a or (_datacopied(a1, a))
flu, = get_flinalg_funcs(('lu', ), (a1, ))
p, l, u, info = flu(a1, permute_l=permute_l, overwrite_a=overwrite_a)
if info < 0:
raise ValueError('illegal value in %d-th argument of '
'internal lu.getrf' % -info)
if permute_l:
return l, u
return p, l, u