?tpmv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?tpmv

Computes a matrix-vector product using a triangular packed matrix.

Syntax

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

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

void cblas_ctpmv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const void *ap, void *x, const MKL_INT incx);

void cblas_ztpmv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
                 const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n,
                 const void *ap, void *x, const MKL_INT incx);

Include Files

mkl.h

Description

The ?tpmv routines perform one of the matrix-vector operations defined as

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

where:

x is an n -element vector,

A is an n -by- n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

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 operation:

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

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

if trans = CblasConjTrans , then x := conjg(A')*x .

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.

ap

REAL for stpmv DOUBLE PRECISION for dtpmv COMPLEX for ctpmv DOUBLE COMPLEX for ztpmv Array, size at least ((n*(n + 1))/2) . For Layout = CblasColMajor :

Before entry with uplo = CblasUpper , the array ap must contain the upper triangular matrix packed sequentially, column-by-column, so that respectively, and so on. Before entry with uplo = CblasLower ap[0] contains A_{1, 1} , ap[1] and ap[2] contain A_{1, 2} and A_{2, 2} , the array ap must contain the lower triangular matrix packed sequentially, column-by-column, so that ap[0] contains A_{1, 1} , ap[1] and ap[2] contain A_{2, 1} and A_{3, 1} respectively, and so on. When diag = CblasUnit , the diagonal elements of a are not referenced, but are assumed to be unity.

For Layout = CblasRowMajor : Before entry with uplo = CblasUpper , the array ap must contain the upper triangular matrix packed sequentially, row-by-row, ap[0] contains A_{1, 1} , ap[1] and ap[2] contain A_{1, 2} and A_{1, 3} respectively, and so on. Before entry with uplo = CblasLower , the array ap must contain the lower triangular matrix packed sequentially, row-by-row, so that ap[0] contains A_{1, 1} , ap[1] and ap[2] contain A_{2, 1} and A_{2, 2} respectively, and so on.

x

REAL for stpmv DOUBLE PRECISION for dtpmv COMPLEX for ctpmv DOUBLE COMPLEX for ztpmv Array, size at least (1 + (n - 1)*abs(incx)) . Before entry, the incremented array x must contain the n -element vector x .

incx

Specifies the increment for the elements of x .

The value of incx must not be zero.

Output Parameters

x: Overwritten with the transformed 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

?tpmv

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes