NAG Library Routine Document

f06ref  (dlansb)

 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

Fortran Interface
Function f06ref ( norm, uplo, n, k, ab, ldab, work)
Real (Kind=nag_wp):: f06ref
Integer, Intent (In):: n, k, ldab
Real (Kind=nag_wp), Intent (In):: ab(ldab,*)
Real (Kind=nag_wp), Intent (Inout):: work(*)
Character (1), Intent (In):: norm, uplo
C Header Interface
#include nagmk26.h
double  f06ref_ ( const char *norm, const char *uplo, const Integer *n, const Integer *k, const double ab[], const Integer *ldab, double work[], const Charlen length_norm, const Charlen length_uplo)

3
Description

None.

4
References

None.

5
Arguments

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

f06ref is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017