Intel® Math Kernel Library 2018 Developer Reference - C

?sytrf_aa

Computes the factorization of a real or complex symmetric matrix A using Aasen's algorithm.

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

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

Description

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

If uplo = 'U': The upper triangle of A is stored.

If uplo = 'L': The lower triangle of A is stored.

n

The order of the matrix a. n 0.

a

Array of size lda*n. On entry, the symmetric matrix A. If uplo = 'U', the leading n-by-n upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.

lda

The leading dimension of the array a. lda max(1,n).

lwork

See Syntax - Workspace. The length of work. lwork max(1, 2*n). For optimum performance lworkn*(1 + nb), where nb is the optimal block size. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

Output Parameters

a

On exit, the tridiagonal matrix is stored in the diagonals.

If uplo = 'U', the subdiagonals of A are stored just above the diagonals and L is stored above the subdiagonals.

If uplo = 'L', the subdiagonals of A are stored just below the diagonals and L is stored below the subdiagonals.

ipiv

Array of size (n) On exit, it contains the details of the interchanges, i.e., the row and column k of a were interchanged with the row and column ipiv[k].

work

See Syntax - Workspace. Array of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

Return Values

This function returns a value info.

If info = 0: successful exit.

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

If info > 0: if info = i, Di, i is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

Syntax - Workspace

Use this interface if you want to explicitly provide the workspace array.

LAPACK_DECL lapack_int LAPACKE_ssytrf_aa_work (int matrix_layout, char uplo, lapack_int n, float * a, lapack_int lda, lapack_int * ipiv, float * work, lapack_int lwork );

LAPACK_DECL lapack_int LAPACKE_dsytrf_aa_work (int matrix_layout, char uplo, lapack_int n, double * a, lapack_int lda, lapack_int * ipiv, double * work, lapack_int lwork );