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

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_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);

lapack_int LAPACKE_csysv_aa (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, lapack_complex_float * A, lapack_int lda, lapack_int * ipiv, lapack_complex_float * B, lapack_int ldb);

lapack_int LAPACKE_zsysv_aa (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, lapack_complex_double * A, lapack_int lda, lapack_int * ipiv, lapack_complex_double * B, lapack_int ldb);

Description

The ?sysv routine computes the solution to a 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 tri-diagonal. 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
  • = 'U': The upper triangle of A is stored.
  • = 'L': The lower triangle of A is stored.
n

The number of linear equations; that is, the order of the matrix A. n ≥ 0.

nrhs

The number of right-hand sides; that is, the number of columns of the matrix B. nrhs ≥ 0.

A

Array of size max(1, 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.

B

Array of size max(1, ldb*nrhs) for column-major layout and max(1, ldb*n) for row-major layout. On entry, the n-by-nrhs right-hand side matrix B.

ldb

The leading dimension of the array B. ldb ≥ max(1, n) for column-major layout and ldbnrhs for row-major layout.

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; that is, the 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.

Return Values

This function returns a value info.

= 0: Successful exit.

< 0: If info = -i, the ith 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, so the solution could not be computed.

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