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.- The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. - 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