cblas_?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:

uplo = CblasUpper

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

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 = CblasLowerap[0] contains A1, 1, ap[1] and ap[2] contain A1, 2 and A2, 2, the array ap must contain the lower triangular matrix packed sequentially, column-by-column, so thatap[0] contains A1, 1, ap[1] and ap[2] contain A2, 1 and A3, 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 A1, 1, ap[1] and ap[2] contain A1, 2 and A1, 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 A1, 1, ap[1] and ap[2] contain A2, 1 and A2, 2 respectively, and so on.

x

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.

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