cho_factor#
- scipy.linalg.cho_factor(a, lower=False, overwrite_a=False, check_finite=True)[source]#
- Compute the Cholesky decomposition of a matrix, to use in cho_solve - Returns a matrix containing the Cholesky decomposition, - A = L L*or- A = U* Uof a Hermitian positive-definite matrix a. The return value can be directly used as the first parameter to cho_solve.- Warning - The returned matrix also contains random data in the entries not used by the Cholesky decomposition. If you need to zero these entries, use the function - choleskyinstead.- Parameters:
- a(M, M) array_like
- Matrix to be decomposed 
- lowerbool, optional
- Whether to compute the upper or lower triangular Cholesky factorization. During decomposition, only the selected half of the matrix is referenced. (Default: upper-triangular) 
- overwrite_abool, optional
- Whether to overwrite data in a (may improve performance) 
- check_finitebool, optional
- Whether to check that the entire input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. 
 
- Returns:
- c(M, M) ndarray
- Matrix whose upper or lower triangle contains the Cholesky factor of a. Other parts of the matrix contain random data. 
- lowerbool
- Flag indicating whether the factor is in the lower or upper triangle 
 
- Raises:
- LinAlgError
- Raised if decomposition fails. 
 
 - See also - cho_solve
- Solve a linear set equations using the Cholesky factorization of a matrix. 
 - Notes - During the finiteness check (if selected), the entire matrix a is checked. During decomposition, a is assumed to be symmetric or Hermitian (as applicable), and only the half selected by option lower is referenced. Consequently, if a is asymmetric/non-Hermitian, - choleskymay still succeed if the symmetric/Hermitian matrix represented by the selected half is positive definite, yet it may fail if an element in the other half is non-finite.- Examples - >>> import numpy as np >>> from scipy.linalg import cho_factor >>> A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]]) >>> c, low = cho_factor(A) >>> c array([[3. , 1. , 0.33333333, 1.66666667], [3. , 2.44948974, 1.90515869, -0.27216553], [1. , 5. , 2.29330749, 0.8559528 ], [5. , 1. , 2. , 1.55418563]]) >>> np.allclose(np.triu(c).T @ np. triu(c) - A, np.zeros((4, 4))) True