NAG FL Interfacef01vff (ztrttf)

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1Purpose

f01vff copies a complex triangular matrix, stored in a full format array, to a Rectangular Full Packed (RFP) format array.

2Specification

Fortran Interface
 Subroutine f01vff ( uplo, n, a, lda, ar, info)
 Integer, Intent (In) :: n, lda Integer, Intent (Out) :: info Complex (Kind=nag_wp), Intent (In) :: a(lda,*) Complex (Kind=nag_wp), Intent (Out) :: ar(n*(n+1)/2) Character (1), Intent (In) :: transr, uplo
#include <nag.h>
 void f01vff_ (const char *transr, const char *uplo, const Integer *n, const Complex a[], const Integer *lda, Complex ar[], Integer *info, const Charlen length_transr, const Charlen length_uplo)
The routine may be called by the names f01vff, nagf_matop_ztrttf or its LAPACK name ztrttf.

3Description

f01vff packs a complex $n×n$ triangular matrix $A$, stored conventionally in a full format array, into 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.

4References

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

5Arguments

1: $\mathbf{transr}$Character(1) Input
On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.
${\mathbf{transr}}=\text{'N'}$
The RFP representation of the matrix $A$ is stored.
${\mathbf{transr}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{transr}}=\text{'N'}$ or $\text{'C'}$.
2: $\mathbf{uplo}$Character(1) Input
On entry: specifies whether $A$ is upper or lower triangular.
${\mathbf{uplo}}=\text{'U'}$
$A$ is upper triangular.
${\mathbf{uplo}}=\text{'L'}$
$A$ is lower triangular.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
4: $\mathbf{a}\left({\mathbf{lda}},*\right)$Complex (Kind=nag_wp) array Input
Note: the second dimension of the array a must be at least ${\mathbf{n}}$.
On entry: the triangular matrix $A$.
• If ${\mathbf{uplo}}=\text{'U'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
5: $\mathbf{lda}$Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f01vff is called.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
6: $\mathbf{ar}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$Complex (Kind=nag_wp) array Output
On exit: the upper or lower $n×n$ 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.
7: $\mathbf{info}$Integer Output
On exit: ${\mathbf{info}}=0$ unless the routine detects an error (see Section 6).

6Error Indicators and Warnings

${\mathbf{info}}<0$
If ${\mathbf{info}}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

Not applicable.

8Parallelism and Performance

f01vff is not threaded in any implementation.

None.

10Example

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

10.1Program Text

Program Text (f01vffe.f90)

10.2Program Data

Program Data (f01vffe.d)

10.3Program Results

Program Results (f01vffe.r)