NAG Library Routine Document

f01vmf (ztfttp)

1
Purpose

f01vmf (ztfttp) copies a complex triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a standard packed format array.

2
Specification

Fortran Interface
Subroutine f01vmf ( transr, uplo, n, ar, ap, info)
Integer, Intent (In):: n
Integer, Intent (Out):: info
Complex (Kind=nag_wp), Intent (In):: ar(n*(n+1)/2)
Complex (Kind=nag_wp), Intent (Out):: ap(n*(n+1)/2)
Character (1), Intent (In):: transr, uplo
C Header Interface
#include <nagmk26.h>
void  f01vmf_ (const char *transr, const char *uplo, const Integer *n, const Complex ar[], Complex ap[], Integer *info, const Charlen length_transr, const Charlen length_uplo)
The routine may be called by its LAPACK name ztfttp.

3
Description

f01vmf (ztfttp) packs a complex n by n triangular matrix A, stored in RFP format, to packed 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:     arn×n+1/2 – Complex (Kind=nag_wp) arrayInput
On entry: 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.
5:     apn×n+1/2 – Complex (Kind=nag_wp) arrayOutput
On exit: the n by n triangular matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A is stored with element Aij in api+jj-1/2 for ij;
  • if uplo='L', the lower triangle of A is stored with element Aij in api+2n-jj-1/2 for ij.
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

f01vmf (ztfttp) is not threaded in any implementation.

9
Further Comments

None.

10
Example

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

10.1
Program Text

Program Text (f01vmfe.f90)

10.2
Program Data

Program Data (f01vmfe.d)

10.3
Program Results

Program Results (f01vmfe.r)