?sytrs

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?sytrs_3

Solves a system of linear equations A * X = B with a real or complex symmetric matrix.

lapack_int LAPACKE_ssytrs_3 (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const float * A, lapack_int lda, const float * e, const lapack_int * ipiv, float * B, lapack_int ldb);

lapack_int LAPACKE_dsytrs_3 (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const double * A, lapack_int lda, const double * e, const lapack_int * ipiv, double * B, lapack_int ldb);

lapack_int LAPACKE_csytrs_3 (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const lapack_complex_float * A, lapack_int lda, const lapack_complex_float * e, const lapack_int * ipiv, lapack_complex_float * B, lapack_int ldb);

lapack_int LAPACKE_zsytrs_3 (int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const lapack_complex_double * A, lapack_int lda, const lapack_complex_double * e, const lapack_int * ipiv, lapack_complex_double * B, lapack_int ldb);

Description

?sytrs_3 solves a system of linear equations A * X = B with a real or complex symmetric matrix A using the factorization computed by ?sytrf_rk: A = P*U*D*(U^T)*(P^T) or A = P*L*D*(L^T)*(P^T), where U (or L) is unit upper (or lower) triangular matrix, U^T (or L^T) is the transpose of U (or L), P is a permutation matrix, P^T is the transpose of P, and D is a symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm uses 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

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

= 'U': Upper triangular; the form is A= P*U*D*(U^T)*(P^T).
= 'L': Lower triangular; the form is A = P*L*D*(L^T)*(P^T).

n

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). Diagonal of the block diagonal matrix D and factors U or L as computed by ?sytrf_rk:

Only diagonal elements of the symmetric block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in array e.

—and—
If uplo = 'U', factor U in the superdiagonal part of A. If uplo = 'L', factor L in the subdiagonal part of A.

lda

The leading dimension of the array A.

e

Array of size n. On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If uplo = 'U', e(i) = D(i-1,i),i=2:N, and e(1) is not referenced. If uplo = 'L', e(i) = D(i+1,i), i=1:N-1, and e(n) is not referenced.

NOTE:

For 1-by-1 diagonal block D(k), where 1 ≤ k ≤ n, the element e[k-1] is not referenced in both the uplo = 'U' and uplo = 'L' cases.

ipiv

Array of size n. Details of the interchanges and the block structure of D as determined by ?sytrf_rk.

B

On entry, the right-hand side matrix B.

The size of B is at least max(1, ldb*nrhs) for column-major layout and max(1, ldb*n) for row-major layout.

ldb

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

Output Parameters

B: On exit, the solution matrix X.

Return Values

This function returns a value info.

= 0: Successful exit.

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

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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