NAG Library Routine Document

f01vkf  (ztpttf)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

f01vkf (ztpttf) copies a complex triangular matrix, stored in a standard packed format array, to a Rectangular Full Packed (RFP) format array.

2
Specification

Fortran Interface
Subroutine f01vkf ( transr, uplo, n, ap, ar, info)
Integer, Intent (In):: n
Integer, Intent (Out):: info
Complex (Kind=nag_wp), Intent (In):: ap(n*(n+1)/2)
Complex (Kind=nag_wp), Intent (Out):: ar(n*(n+1)/2)
Character (1), Intent (In):: transr, uplo
C Header Interface
#include nagmk26.h
void  f01vkf_ ( const char *transr, const char *uplo, const Integer *n, const Complex ap[], Complex ar[], Integer *info, const Charlen length_transr, const Charlen length_uplo)
The routine may be called by its LAPACK name ztpttf.

3
Description

f01vkf (ztpttf) copies a complex n by n triangular matrix, A, stored in packed format, to RFP format. This routine is intended for possible use in conjunction with routines from Chapters F06, F07 and F16 where some routines that use triangular matrices store them in RFP format. The RFP storage format is described in Section 3.3.3 in the F07 Chapter Introduction and the packed storage format is described in Section 3.3.2 in the F07 Chapter Introduction.

4
References

Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

5
Arguments

1:     transr – Character(1)Input
On entry: specifies whether the normal RFP representation of A or its conjugate transpose is stored.
transr='N'
The RFP representation of the matrix A is stored.
transr='C'
The conjugate transpose of the RFP representation of the matrix A is stored.
Constraint: transr='N' or 'C'.
2:     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'.
3:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     apn×n+1/2 – Complex (Kind=nag_wp) arrayInput
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.
5:     arn×n+1/2 – Complex (Kind=nag_wp) arrayOutput
On exit: the upper or lower n by n triangular matrix A (as specified by uplo) in either normal or transposed RFP format (as specified by transr). The storage format is described in Section 3.3.3 in the F07 Chapter Introduction.
6:     info – IntegerOutput
On exit: info=0 unless the routine detects an error (see Section 6).

6
Error Indicators and Warnings

-999<info<0
If info=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.
info=-999
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f01vkf (ztpttf) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example reads in a triangular matrix in packed format and copies it to RFP format.

10.1
Program Text

Program Text (f01vkfe.f90)

10.2
Program Data

Program Data (f01vkfe.d)

10.3
Program Results

Program Results (f01vkfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017