NAG C Library Function Document

nag_dtfttp (f01vlc)

1
Purpose

nag_dtfttp (f01vlc) copies a real triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a standard packed format array.

2
Specification

#include <nag.h>
#include <nagf01.h>
void  nag_dtfttp (Nag_OrderType order, Nag_RFP_Store transr, Nag_UploType uplo, Integer n, const double ar[], double ap[], NagError *fail)

3
Description

nag_dtfttp (f01vlc) packs a real n by n triangular matrix A, stored in RFP format, to packed format. This function is intended for possible use in conjunction with functions from Chapters f06, f07 and f16 where some functions 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:     order Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     transr Nag_RFP_StoreInput
On entry: specifies whether the normal RFP representation of A or its transpose is stored.
transr=Nag_RFP_Normal
The RFP representation of the matrix A is stored.
transr=Nag_RFP_Trans
The transpose of the RFP representation of the matrix A is stored.
Constraint: transr=Nag_RFP_Normal or Nag_RFP_Trans.
3:     uplo Nag_UploTypeInput
On entry: specifies whether A is upper or lower triangular.
uplo=Nag_Upper
A is upper triangular.
uplo=Nag_Lower
A is lower triangular.
Constraint: uplo=Nag_Upper or Nag_Lower.
4:     n IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
5:     ar[n×n+1/2] const doubleInput
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.
6:     ap[dim] doubleOutput
Note: the dimension, dim, of the array ap must be at least n×n+1/2.
On exit: the n by n triangular matrix A, packed by rows or columns depending on order.
The storage of elements Aij depends on the order and uplo arguments as follows:
  • if order=Nag_ColMajor and uplo=Nag_Upper,
              Aij is stored in ap[j-1×j/2+i-1], for ij;
  • if order=Nag_ColMajor and uplo=Nag_Lower,
              Aij is stored in ap[2n-j×j-1/2+i-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Upper,
              Aij is stored in ap[2n-i×i-1/2+j-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Lower,
              Aij is stored in ap[i-1×i/2+j-1], for ij.
7:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

Not applicable.

8
Parallelism and Performance

nag_dtfttp (f01vlc) 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 (f01vlce.c)

10.2
Program Data

Program Data (f01vlce.d)

10.3
Program Results

Program Results (f01vlce.r)