Intel® Math Kernel Library 2018 Developer Reference - C

?sysv_aa

Computes the solution to the system of linear equations A * X = B for SY matrices.

LAPACK_DECL lapack_int LAPACKE_ssysv_aa (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, float * a, lapack_int lda, lapack_int * ipiv, float * b, lapack_int ldb );

LAPACK_DECL lapack_int LAPACKE_dsysv_aa (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, double * a, lapack_int lda, lapack_int * ipiv, double * b, lapack_int ldb );

Description

?sysv_aa computes the solution to a real or complex system of linear equations A * X = B, where A is an n-by-n symmetric matrix and X and B are n-by-nrhs matrices. Aasen's algorithm is used to factor A as A = U * T * UT, if uplo = 'U', or A = L * T * LT, if uplo = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

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 number of linear equations or the order of the matrix A. n 0.

nrhs

The number of right hand sides or the number of columns of the matrix B. nrhs 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).

b

Array of size ldb*nrhs. On entry, the n-by-nrhs right hand side matrix B.

ldb

The leading dimension of the array b. ldb max(1,n).

lwork

See Syntax - Workspace. The length of work. lwork max(1, 2*n, 3*n - 2), and for the best performance, lwork max(1, n*nb), where nb is the optimal block size for ?sytrf_aa. 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, if info = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U * T * UT or A = L*T*LT as computed by ?sytrf.

ipiv

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

b

On exit, if info = 0, the n-by-nrhs solution matrix X.

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_ssysv_aa_work (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, float * a, lapack_int lda, lapack_int * ipiv, float * b, lapack_int ldb, float * work, lapack_int lwork );

LAPACK_DECL lapack_int LAPACKE_dsysv_aa_work (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, double * a, lapack_int lda, lapack_int * ipiv, double * b, lapack_int ldb, double * work, lapack_int lwork );