F11MLF (PDF version)
F11 Chapter Contents
F11 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F11MLF

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.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

F11MLF computes the 1-norm, the -norm or the maximum absolute value of the elements of a real, square, sparse matrix which is held in compressed column (Harwell–Boeing) format.

2  Specification

SUBROUTINE F11MLF ( NORM, ANORM, N, ICOLZP, IROWIX, A, IFAIL)
INTEGER  N, ICOLZP(*), IROWIX(*), IFAIL
REAL (KIND=nag_wp)  ANORM, A(*)
CHARACTER(1)  NORM

3  Description

F11MLF computes various quantities relating to norms of a real, sparse n by n matrix A presented in compressed column (Harwell–Boeing) format.

4  References

None.

5  Parameters

1:     NORM – CHARACTER(1)Input
On entry: specifies the value to be returned in ANORM.
NORM='1' or 'O'
The 1-norm A1 of the matrix is computed, that is max1jni=1nAij.
NORM='I'
The -norm A of the matrix is computed, that is max1in j=1n Aij.
NORM='M'
The value max1i,jnAij  (not a norm).
Constraint: NORM='1', 'O', 'I' or 'M'.
2:     ANORM – REAL (KIND=nag_wp)Output
On exit: the computed quantity relating the matrix.
3:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
4:     ICOLZP(*) – INTEGER arrayInput
Note: the dimension of the array ICOLZP must be at least N+1.
On entry: ICOLZPi contains the index in A of the start of a new column. See Section 2.1.3 in the F11 Chapter Introduction.
5:     IROWIX(*) – INTEGER arrayInput
Note: the dimension of the array IROWIX must be at least ICOLZPN+1-1, the number of nonzeros of the sparse matrix A.
On entry: the row index array of sparse matrix A.
6:     A(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array A must be at least ICOLZPN+1-1, the number of nonzeros of the sparse matrix A.
On entry: the array of nonzero values in the sparse matrix A.
7:     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.
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.
On exit: IFAIL=0 unless the routine detects an error or a warning has been flagged (see Section 6).

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,NORM'1', 'O', 'I' or 'M',
orN<0.
IFAIL=301
Unable to allocate required internal workspace.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example computes norms and maximum absolute value of the matrix A, where
A= 2.00 1.00 0 0 0 0 0 1.00 -1.00 0 4.00 0 1.00 0 1.00 0 0 0 1.00 2.00 0 -2.00 0 0 3.00 .

9.1  Program Text

Program Text (f11mlfe.f90)

9.2  Program Data

Program Data (f11mlfe.d)

9.3  Program Results

Program Results (f11mlfe.r)


F11MLF (PDF version)
F11 Chapter Contents
F11 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012