F06RLF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06RLF

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

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

FUNCTION F06RLF ( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
REAL (KIND=nag_wp) F06RLF
INTEGER  N, K, LDAB
REAL (KIND=nag_wp)  AB(LDAB,*), WORK(*)
CHARACTER(1)  NORM, UPLO, DIAG

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:     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:     AB(LDAB,*) – 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  Further Comments

None.

9  Example

None.

F06RLF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

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