Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
lapack_int LAPACKE_spotrf (int matrix_layout , char uplo , lapack_int n , float * a , lapack_int lda );
lapack_int LAPACKE_dpotrf (int matrix_layout , char uplo , lapack_int n , double * a , lapack_int lda );
lapack_int LAPACKE_cpotrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * a , lapack_int lda );
lapack_int LAPACKE_zpotrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * a , lapack_int lda );
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix A:
|A = UT* U for real data, A = UH* U for complex data||if uplo='U'|
|A = L*LT for real data, A = L*LH for complex data||if uplo='L'|
where L is a lower triangular matrix and U is upper triangular.
This routine supports the Progress Routine feature. See Progress Function for details.
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
Must be 'U' or 'L'.
Indicates whether the upper or lower triangular part of A is stored and how A is factored:
If uplo = 'U', the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.
If uplo = 'L', the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.
Specifies the order of the matrix A. The value of n must be at least zero.
Array, size max(1, lda*n. The array a contains either the upper or the lower triangular part of the matrix A (see uplo).
The leading dimension of a. Must be at least max(1, n).
The upper or lower triangular part of a is overwritten by the Cholesky factor U or L, as specified by uplo.
This function returns a value info.
If info=0, the execution is successful.
If info = -i, parameter i had an illegal value.
If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.
If uplo = 'U', the computed factor U is the exact factor of a perturbed matrix A + E, where
c(n) is a modest linear function of n, and ε is the machine precision.
A similar estimate holds for uplo = 'L'.
The total number of floating-point operations is approximately (1/3)n3 for real flavors or (4/3)n3 for complex flavors.
After calling this routine, you can call the following routines:
to solve A*X = B
to estimate the condition number of A
to compute the inverse of A.