NAG Library Routine Document

f06ubf (zlangb)

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

Fortran Interface
Function f06ubf ( norm, n, kl, ku, ab, ldab, work)
Real (Kind=nag_wp):: f06ubf
Integer, Intent (In):: n, kl, ku, ldab
Real (Kind=nag_wp), Intent (Inout):: work(*)
Complex (Kind=nag_wp), Intent (In):: ab(ldab,*)
Character (1), Intent (In):: norm
C Header Interface
#include <nagmk26.h>
double  f06ubf_ (const char *norm, const Integer *n, const Integer *kl, const Integer *ku, const Complex ab[], const Integer *ldab, double work[], const Charlen length_norm)

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.
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:     abldab* – 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
Parallelism and Performance

f06ubf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.