Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
F01ZAF unpacks a triangular matrix stored in a vector into a two-dimensional array, or packs a triangular matrix stored in a two-dimensional array into a vector. The matrix is packed by column. This routine is intended for possible use in conjunction with routines from Chapters F06, F07 and F08 where some routines that use triangular matrices store them in the packed form described below.
4 References
None.
5 Parameters
1: JOB – CHARACTER*1Input
On entry: specifies whether the triangular matrix is to be packed or unpacked.
On entry: specifies the type of the matrix to be copied
UPLO='L' (Lower)
The matrix is lower triangular. In this case the packed vector holds, or will hold on exit, the matrix elements in the following order: 1,1,2,1,…,N,1,2,2,3,2,…,N,2, etc..
UPLO='U' (Upper)
The matrix is upper triangular. In this case the packed vector holds, or will hold on exit, the matrix elements in the following order: 1,1, 1,2, 2,2, 1,3, 2,3, 3,3, 1,4, etc..
Constraint:
UPLO must be one of 'L' or 'U'.
3: DIAG – CHARACTER*1Input
On entry: must specify whether the diagonal elements of the matrix are to be copied.
DIAG='B' (Blank)
The diagonal elements of the matrix are not referenced and not copied.
DIAG='U' (Unit diagonal)
The diagonal elements of the matrix are not referenced, but are assumed all to be unity, and are copied as such.
DIAG='N' (Non-unit diagonal)
The diagonal elements of the matrix are referenced and copied.
Constraint:
DIAG must be one of 'B', 'U' or 'N'.
4: N – INTEGERInput
On entry:
n, the number of rows and columns of the triangular matrix.
On entry: if JOB='P', then the leading N by N part of A must contain the matrix to be copied, stored in unpacked form, in the upper or lower triangle depending on parameter UPLO. The opposite triangle of A is not referenced and need not be assigned.
On exit: if JOB='U', then the leading N by N part of array A contains the copied matrix, stored in unpacked form, in the upper or lower triangle depending on parameter UPLO. The opposite triangle of A is not referenced.
6: LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F01ZAF is called.
On entry: if JOB='U', then B must contain the triangular matrix packed by column.
On exit: if JOB='P', then B contains the triangular matrix packed by column.
Note that B must have space for the diagonal elements of the matrix, even if these are not stored.
8: IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to 0, -1 or 1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
On exit: IFAIL=0 unless the routine detects an error (see Section 6).
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of IFAIL on exit.
6 Error Indicators and Warnings
If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
IFAIL=1
On entry,
JOB≠'P' or 'U'.
IFAIL=2
On entry,
UPLO≠'L' or 'U'.
IFAIL=3
On entry,
DIAG≠'N', 'U' or 'B'.
IFAIL=4
On entry,
N<1.
IFAIL=5
On entry,
LDA<N.
7 Accuracy
Not applicable.
8 Further Comments
None.
9 Example
This example reads in a triangular matrix A, and copies it to the packed matrix B.