NAG Library Routine Document

f06rlf (dlantb)

1
Purpose

f06rlf 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 triangular band matrix.

2
Specification

Fortran Interface
Function f06rlf ( norm, uplo, diag, n, k, ab, ldab, work)
Real (Kind=nag_wp):: f06rlf
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, diag
C Header Interface
#include <nagmk26.h>
double  f06rlf_ (const char *norm, const char *uplo, const char *diag, const Integer *n, const Integer *k, const double ab[], const Integer *ldab, double work[], const Charlen length_norm, const Charlen length_uplo, const Charlen length_diag)

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:     uplo – Character(1)Input
On entry: specifies whether A is upper or lower triangular.
uplo='U'
A is upper triangular.
uplo='L'
A is lower triangular.
Constraint: uplo='U' or 'L'.
3:     diag – Character(1)Input
On entry: specifies whether A has nonunit or unit diagonal elements.
diag='N'
The diagonal elements are stored explicitly.
diag='U'
The diagonal elements are assumed to be 1, and are not referenced.
Constraint: diag='N' or 'U'.
4:     n – IntegerInput
On entry: n, the order of the matrix A.
When n=0, f06rlf returns zero.
Constraint: n0.
5:     k – IntegerInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
6:     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 triangular 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.
If diag='U', the diagonal elements of A are assumed to be 1, and are not referenced.
7:     ldab – IntegerInput
On entry: the first dimension of the array ab as declared in the (sub)program from which f06rlf is called.
Constraint: ldabk+1.
8:     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

f06rlf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.