?sytrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?sytrs_3

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

Syntax

call ssytrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)
call dsytrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)
call csytrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)
call zsytrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)

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

uplo: CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

n: INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

nrhs

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

A

REAL for ssytrs_3 DOUBLE PRECISION for dsytrs_3 COMPLEX for csytrs_3 COMPLEX*16 for zsytrs_3

Array, dimension ( lda , n ). Diagonal of the block diagonal matrix D and factors U or L as computed by ?sytrf_rk :

lda

INTEGER

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

e

REAL for ssytrs_3 DOUBLE PRECISION for dsytrs_3 COMPLEX for csytrs_3 COMPLEX*16 for zsytrs_3

Array, dimension ( 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.

ipiv

INTEGER

Array, dimension ( n ). Details of the interchanges and the block structure of D as determined by ?sytrf_rk .

B

REAL for ssytrs_3 DOUBLE PRECISION for dsytrs_3 COMPLEX for csytrs_3 COMPLEX*16 for zsytrs_3 On entry, the right-hand side matrix B. The second dimension of B must be at least max(1, nrhs ). 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

INTEGER

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

Output Parameters

B: REAL for ssytrs_3 DOUBLE PRECISION for dsytrs_3 COMPLEX for csytrs_3 COMPLEX*16 for zsytrs_3 On exit, the solution matrix X.

info

INTEGER .

If info = 0, the execution is successful.
If info = -i , the i^th argument had an illegal value.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytrs_3

Syntax

Description

Input Parameters

Output Parameters

Return Values