?sytrf

Computes the factorization of a symmetric matrix using Aasen's algorithm.

lapack_int LAPACKE_ssytrf_aa (int matrix_layout, char uplo, lapack_int n, float * A, lapack_int lda, lapack_int * ipiv);

lapack_int LAPACKE_dsytrf_aa (int matrix_layout, char uplo, lapack_int n, double * A, lapack_int lda, lapack_int * ipiv);

lapack_int LAPACKE_csytrf_aa (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * A, lapack_int lda, lapack_int * ipiv);

lapack_int LAPACKE_zsytrf_aa (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * A, lapack_int lda, lapack_int * ipiv);

Description

?sytrf_aa computes the factorization of a symmetric matrix A using Aasen's algorithm. The form of the factorization is A = U*T*U^T or A = L*T*L^T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric tridiagonal matrix.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

= 'U': The upper triangle of A is stored.
= 'L': The lower triangle of A is stored.

n

The order of the matrix A. n ≥ 0.

A

Array of size max(1, lda*n). The array A contains either the upper or the lower triangular part of the matrix A (see uplo).

lda

The leading dimension of the array A.

Output Parameters

A: On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo is 'L' (or 'U').
ipiv: Array of size n. On exit, it contains the details of the interchanges; that is, the row and column k of A were interchanged with the row and column ipiv(k).

Return Values

This function returns a value info.

= 0: Successful exit.

< 0: If info = -i, the i^th argument had an illegal value.

> 0: If info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.