?trsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?trsv

Solves a system of linear equations whose coefficients are in a triangular matrix.

Syntax

void cblas_strsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const float *a, const MKL_INT lda, float *x, const MKL_INT incx);

void cblas_dtrsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const double *a, const MKL_INT lda, double *x, const MKL_INT incx);

void cblas_ctrsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const void *a, const MKL_INT lda, void *x, const MKL_INT incx);

void cblas_ztrsv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const void *a, const MKL_INT lda, void *x, const MKL_INT incx);

Include Files

mkl.h

Description

The ?trsv routines solve one of the systems of equations:

A*x = b , or A'*x = b , or conjg(A')*x = b ,

where:

b and x are n -element vectors,

A is an n -by- n unit, or non-unit, upper or lower triangular matrix.

The routine does not test for singularity or near-singularity.

Such tests must be performed before calling this routine.

Input Parameters

Layout: Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).

uplo

Specifies whether the matrix A is upper or lower triangular:

if uplo = CblasLower , then the matrix is low triangular.

trans

Specifies the systems of equations:

if trans = CblasNoTrans , then A*x = b ;

if trans = CblasTrans , then A'*x = b ;

if trans = CblasConjTrans , then oconjg(A')*x = b .

diag

Specifies whether the matrix A is unit triangular:

if diag = CblasUnit then the matrix is unit triangular;

if diag = CblasNonUnit , then the matrix is not unit triangular.

n

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

a

REAL for strsv DOUBLE PRECISION for dtrsv COMPLEX for ctrsv DOUBLE COMPLEX for ztrsv

Array, size (lda, n)lda*n . Before entry with uplo = CblasUpper , the leading n -by- n upper triangular part of the array a must contain the upper triangular matrix and the strictly lower triangular part of a is not referenced. Before entry with uplo = CblasLower , the leading n -by- n lower triangular part of the array a must contain the lower triangular matrix and the strictly upper triangular part of a is not referenced.

When diag = CblasUnit , the diagonal elements of a are not referenced either, but are assumed to be unity.

lda

Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least max(1, n) .

x

REAL for strsv DOUBLE PRECISION for dtrsv COMPLEX for ctrsv DOUBLE COMPLEX for ztrsv Array, size at least (1 + (n - 1)*abs(incx)) . Before entry, the incremented array x must contain the n -element right-hand side vector b .

incx

Specifies the increment for the elements of x .

The value of incx must not be zero.

Output Parameters

x: Overwritten with the solution vector x .

BLAS 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?trsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes