F06UBF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06UBF

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
    9  Example

1  Purpose

F06UBF 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 complex n by n band matrix.

2  Specification

FUNCTION F06UBF ( NORM, N, KL, KU, AB, LDAB, WORK)
REAL (KIND=nag_wp) F06UBF
INTEGER  N, KL, KU, LDAB
REAL (KIND=nag_wp)  WORK(*)
COMPLEX (KIND=nag_wp)  AB(LDAB,*)
CHARACTER(1)  NORM

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.
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:     N – INTEGERInput
On entry: n, the order of the matrix A.
When N=0, F06UBF returns zero.
Constraint: N0.
3:     KL – INTEGERInput
On entry: kl, the number of subdiagonals within the band of A.
Constraint: KL0.
4:     KU – INTEGERInput
On entry: ku, the number of superdiagonals within the band of A.
Constraint: KU0.
5:     AB(LDAB,*) – COMPLEX (KIND=nag_wp) arrayInput
Note: the second dimension of the array AB must be at least N.
On entry: the n by n band matrix A.
The matrix is stored in rows 1 to kl+ku+1, more precisely, the element Aij must be stored in
ABku+1+i-jj  for ​max1,j-kuiminn,j+kl.
6:     LDAB – INTEGERInput
On entry: the first dimension of the array AB as declared in the (sub)program from which F06UBF is called.
Constraint: LDABKL+KU+1.
7:     WORK(*) – REAL (KIND=nag_wp) arrayWorkspace
Note: the dimension of the array WORK must be at least max1,N  if NORM='I', and at least 1 otherwise.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06UBF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

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