NAG FL Interface
f06plf (dtpsv)

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FL Specification Language:

1 Purpose

f06plf solves a real triangular system of equations, stored in packed form, with a single right-hand side.

2 Specification

Fortran Interface
Subroutine f06plf ( uplo, trans, diag, n, ap, x, incx)
Integer, Intent (In) :: n, incx
Real (Kind=nag_wp), Intent (In) :: ap(*)
Real (Kind=nag_wp), Intent (Inout) :: x(*)
Character (1), Intent (In) :: uplo, trans, diag
C Header Interface
#include <nag.h>
void  f06plf_ (const char *uplo, const char *trans, const char *diag, const Integer *n, const double ap[], double x[], const Integer *incx, const Charlen length_uplo, const Charlen length_trans, const Charlen length_diag)
The routine may be called by the names f06plf, nagf_blas_dtpsv or its BLAS name dtpsv.

3 Description

f06plf performs one of the matrix-vector operations
xA-1x   or   xA-Tx ,  
where A is an n×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


5 Arguments

1: uplo Character(1) Input
On entry: specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: uplo='U' or 'L'.
2: trans Character(1) Input
On entry: specifies the operation to be performed.
trans='T' or 'C'
Constraint: trans='N', 'T' or 'C'.
3: diag Character(1) Input
On entry: specifies whether A has nonunit or unit diagonal elements.
The diagonal elements are stored explicitly.
The diagonal elements are assumed to be 1, and are not referenced.
Constraint: diag='N' or 'U'.
4: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
5: ap(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array ap must be at least n× (n+1)/2 .
On entry: the n×n triangular matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A must be stored with element Aij in ap(i+j(j-1)/2) for ij;
  • if uplo='L', the lower triangle of A must be stored with element Aij in ap(i+(2n-j)(j-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) array Input/Output
Note: the dimension of the array x must be at least max(1, 1+(n-1) ×|incx| ) .
On entry: the n-element vector x.
If incx>0, xi must be stored in x(1+(i1)×incx) , for i=1,2,,n.
If incx<0, xi must be stored in x(1(ni)×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 Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.

6 Error Indicators and Warnings


7 Accuracy

Not applicable.

8 Parallelism and Performance

f06plf is not threaded in any implementation.

9 Further Comments


10 Example