?tpsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?tpsv

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

Syntax

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

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

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

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

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

Include Files

mkl.fi, blas.f90

Description

The ?tpsv routines solve one of the following 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, supplied in packed form.

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

Such tests must be performed before calling this routine.

Input Parameters

uplo

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

uplo = 'U' or 'u'

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

trans

CHARACTER*1. Specifies the system of equations:

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

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

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

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 stpsv

DOUBLE PRECISION for dtpsv

COMPLEX for ctpsv

DOUBLE COMPLEX for ztpsv

Array, size at least ((n*(n + 1))/2).

Before entry with uplo = 'U' or 'u', the array ap must contain the upper triangular part of the 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 part of the 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.

x

REAL for stpsv

DOUBLE PRECISION for dtpsv

COMPLEX for ctpsv

DOUBLE COMPLEX for ztpsv

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

INTEGER. 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

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 tpsv 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'.

Parent topic: BLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?tpsv