?sytrs_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?sytrs_rook

Solves a system of linear equations with a UDU- or LDL-factored symmetric coefficient matrix.

Syntax

call ssytrs_rook ( uplo , n , nrhs , a , lda , ipiv , b , ldb , info )

call dsytrs_rook ( uplo , n , nrhs , a , lda , ipiv , b , ldb , info )

call csytrs_rook ( uplo , n , nrhs , a , lda , ipiv , b , ldb , info )

call zsytrs_rook ( uplo , n , nrhs , a , lda , ipiv , b , ldb , info )

call sytrs_rook ( a , b , ipiv [ , uplo ] [ , info ] )

Include Files

mkl.fi , mkl_lapack.f90

Description

ssytrs_rook dsytrs_rook csytrs_rook zsytrs_rook sytrs_rook

The routine solves a system of linear equations A*X = B with a symmetric matrix A , using the factorization A = U*D*U^{T} or A = L*D*L^{T} computed by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) .

Input Parameters

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Indicates how the input matrix A has been factored:

If uplo = 'U' , the factorization is of the form A = U*D*U^{T} .

If uplo = 'L' , the factorization is of the form A = L*D*L^{T} .

n

INTEGER . The order of matrix A ; n ≥ 0.

nrhs

INTEGER . The number of right-hand sides; nrhs ≥ 0.

ipiv

INTEGER . Array, size at least max(1, n) . The ipiv array, as returned by GUID-E4F0C583-4A62-4B8C-8035-580C08F2F9BC.xml#GUID-E4F0C583-4A62-4B8C-8035-580C08F2F9BC .

a , b

REAL for ssytrs_rook

DOUBLE PRECISION for dsytrs_rook

COMPLEX for csytrs_rook

DOUBLE COMPLEX for zsytrs_rook .

Arrays: a(lda,n) , b(ldb,nrhs) .

The array a contains the block diagonal matrix D and the multipliers used to obtain U or L as computed by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) (see uplo ).

The array b contains the matrix B whose columns are the right-hand sides for the system of equations.

lda

INTEGER . The leading dimension of a ; lda≥ max(1, n) .

ldb

INTEGER . The leading dimension of b ; ldb≥ max(1, n) .

Output Parameters

b

Overwritten by the solution matrix X .

info

INTEGER .

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

Return Values

No return value, info is an Output Parameter.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions .

Specific details for the routine sytrs_rook interface are as follows:

a

Holds the matrix A of size ( n , n ).

b

Holds the matrix B of size ( n , nrhs ).

ipiv

Holds the vector of length n .

uplo

Must be ‘U’ or ‘L’ . The default value is ‘U’ .

Application Notes

The total number of floating-point operations for one right-hand side vector is approximately \(2n^{2}\) for real flavors or \(8n^{2}\) for complex flavors.

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytrs_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes