F06REF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06REF

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
    10  Example

1  Purpose

F06REF returns, via the function name, the value of the 1-norm, the -norm, the Frobenius norm, or the maximum absolute value of the elements of a real n by n symmetric band matrix.

2  Specification

FUNCTION F06REF ( NORM, UPLO, N, K, AB, LDAB, WORK)
REAL (KIND=nag_wp) F06REF
INTEGER  N, K, LDAB
REAL (KIND=nag_wp)  AB(LDAB,*), WORK(*)
CHARACTER(1)  NORM, UPLO

3  Description

None.

4  References

None.

5  Parameters

1:     NORM – CHARACTER(1)Input
On entry: specifies the value to be returned.
NORM='1' or 'O'
The 1-norm.
NORM='I'
The -norm (= the 1-norm for a symmetric matrix).
NORM='F' or 'E'
The Frobenius (or Euclidean) norm.
NORM='M'
The value maxi,jaij (not a norm).
Constraint: NORM='1', 'O', 'I', 'F', 'E' or 'M'.
2:     UPLO – CHARACTER(1)Input
On entry: specifies whether the upper or lower triangular part of A is stored.
UPLO='U'
The upper triangular part of A is stored.
UPLO='L'
The lower triangular part of A is stored.
Constraint: UPLO='U' or 'L'.
3:     N – INTEGERInput
On entry: n, the order of the matrix A.
When N=0, F06REF returns zero.
Constraint: N0.
4:     K – INTEGERInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: K0.
5:     ABLDAB* – REAL (KIND=nag_wp) arrayInput
Note: the second dimension of the array AB must be at least N.
On entry: the n by n symmetric band matrix A.
The matrix is stored in rows 1 to k+1, more precisely,
  • if UPLO='U', the elements of the upper triangle of A within the band must be stored with element Aij in ABk+1+i-jj​ for ​max1,j-kij;
  • if UPLO='L', the elements of the lower triangle of A within the band must be stored with element Aij in AB1+i-jj​ for ​jiminn,j+k.
6:     LDAB – INTEGERInput
On entry: the first dimension of the array AB as declared in the (sub)program from which F06REF is called.
Constraint: LDABK+1.
7:     WORK* – REAL (KIND=nag_wp) arrayWorkspace
Note: the dimension of the array WORK must be at least max1,N  if NORM='1', 'O' or 'I', and at least 1 otherwise.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

None.

F06REF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015