?trsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?trsv

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

Syntax

call strsv(uplo, trans, diag, n, a, lda, x, incx)

call dtrsv(uplo, trans, diag, n, a, lda, x, incx)

call ctrsv(uplo, trans, diag, n, a, lda, x, incx)

call ztrsv(uplo, trans, diag, n, a, lda, x, incx)

call trsv(a, x [,uplo] [, trans] [,diag])

Include Files

mkl.fi, blas.f90

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

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 systems 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 oconjg(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.

a

REAL for strsv

DOUBLE PRECISION for dtrsv

COMPLEX for ctrsv

DOUBLE COMPLEX for ztrsv

Array, size (lda, n) . Before entry with uplo = 'U' or 'u', 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 = 'L' or 'l', 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 = 'U' or 'u', the diagonal elements of a are not referenced either, but are assumed to be unity.

lda

INTEGER. 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

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 trsv interface are the following:

a

Holds the matrix a of size (n,n).

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

?trsv