F06PLF (DTPSV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06PLF (DTPSV)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06PLF (DTPSV) solves a real triangular system of equations, stored in packed form, with a single right hand side.

2  Specification

SUBROUTINE F06PLF ( UPLO, TRANS, DIAG, N, AP, X, INCX)
INTEGER  N, INCX
REAL (KIND=nag_wp)  AP(*), X(*)
CHARACTER(1)  UPLO, TRANS, DIAG
The routine may be called by its BLAS name dtpsv.

3  Description

F06PLF (DTPSV) performs one of the matrix-vector operations
xA-1x   or   xA-Tx ,
where A is an n by n real triangular matrix, stored in packed form, and x is an n element real vector. A-T denotes A-T or equivalently A-T.
No test for singularity or near-singularity of A is included in this routine. Such tests must be performed before calling this routine.

4  References

None.

5  Parameters

1:     UPLO – CHARACTER(1)Input
On entry: specifies whether A is upper or lower triangular.
UPLO='U'
A is upper triangular.
UPLO='L'
A is lower triangular.
Constraint: UPLO='U' or 'L'.
2:     TRANS – CHARACTER(1)Input
On entry: specifies the operation to be performed.
TRANS='N'
xA-1x.
TRANS='T' or 'C'
xA-Tx.
Constraint: TRANS='N', 'T' or 'C'.
3:     DIAG – CHARACTER(1)Input
On entry: specifies whether A has nonunit or unit diagonal elements.
DIAG='N'
The diagonal elements are stored explicitly.
DIAG='U'
The diagonal elements are assumed to be 1, and are not referenced.
Constraint: DIAG='N' or 'U'.
4:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
5:     AP(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array AP must be at least N× N+1/2 .
On entry: the n by n triangular matrix A, packed by columns.
More precisely,
  • if UPLO='U', the upper triangle of A must be stored with element Aij in APi+jj-1/2 for ij;
  • if UPLO='L', the lower triangle of A must be stored with element Aij in APi+2n-jj-1/2 for ij.
If DIAG='U', the diagonal elements of A are assumed to be 1, and are not referenced; the same storage scheme is used whether DIAG='N' or ‘U’.
6:     X(*) – REAL (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array X must be at least max1, 1+N-1 ×INCX .
On entry: the n element vector x.
If INCX>0, xi must be stored in X1+i1×INCX, for i=1,2,,N.
If INCX<0, xi must be stored in X1Ni×INCX, for i=1,2,,N.
On exit: the updated vector x stored in the array elements used to supply the original vector x.
7:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of x.
Constraint: INCX0.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06PLF (DTPSV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011