?tpmv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?tpmv

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

Syntax

call stpmv(uplo, trans, diag, n, ap, x, incx)

call dtpmv(uplo, trans, diag, n, ap, x, incx)

call ctpmv(uplo, trans, diag, n, ap, x, incx)

call ztpmv(uplo, trans, diag, n, ap, x, incx)

call tpmv(ap, x [, uplo] [, trans] [, diag])

Include Files

mkl.fi, mkl_blas.f90

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

CHARACTER*1 . Specifies whether the matrix A is upper or lower triangular:

if uplo = 'L' or ‘l’ , then the matrix is low triangular.

trans

CHARACTER*1 . Specifies the operation:

if trans= 'N' or 'n' , then x := A*x ;

if trans= 'T' or 't' , then x := A'*x ;

if trans= 'C' or 'c' , then x := conjg(A')*x .

diag

CHARACTER*1 . Specifies whether the matrix A is unit triangular:

if diag = 'U' or ‘u’ then the matrix is unit triangular;

if diag = 'N' or ‘n’ , then the matrix is not unit triangular.

n

INTEGER . 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 = 'U' or ‘u’ uplo = CblasUpper , the array ap must contain the upper triangular matrix packed sequentially, column-by-column, so that ap(1) contains a(1,1) , ap(2) and ap(3) contain a(1,2) and a(2,2) respectively, and so on. Before entry with uplo = 'L' or ‘l’ , the array ap must contain the lower triangular matrix packed sequentially, column-by-column, so that ap(1) contains a(1,1) , ap(2) and ap(3) contain a(2,1) and a(3,1) respectively, and so on. When diag = 'U' or ‘u’ , 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

INTEGER . 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

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 BLAS 95 Interface Conventions .

Specific details for the routine tpmv interface are the following:

ap: Holds the array ap of size ( n*(n+1)/2 ).
x: Holds the vector with the number of elements n .
uplo: Must be ‘U’ or ‘L’ . The default value is ‘U’ .
trans: Must be ‘N’ , ‘C’ , or ‘T’ . The default value is ‘N’ .
diag: Must be ‘N’ or ‘U’ . The default value is ‘N’ .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?tpmv

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes