nag_dgb_norm (f16rbc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_dgb_norm (f16rbc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dgb_norm (f16rbc) calculates the value of the 1-norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a real m by n band matrix, stored in banded form.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dgb_norm (Nag_OrderType order, Nag_NormType norm, Integer m, Integer n, Integer kl, Integer ku, const double ab[], Integer pdab, double *r, NagError *fail)

3  Description

Given a real m by n banded matrix, A, nag_dgb_norm (f16rbc) calculates one of the values given by
A1=maxji=1maij (the 1-norm of A),
A=maxij= 1naij (the -norm of A),
AF=i=1mj=1naij21/2 (the Frobenius norm of A),   or
maxi,jaij (the maximum absolute element value of A).

4  References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     normNag_NormTypeInput
On entry: specifies the value to be returned.
The 1-norm.
The -norm.
The Frobenius (or Euclidean) norm.
The value maxi,jaij (not a norm).
Constraint: norm=Nag_OneNorm, Nag_TwoNorm, Nag_FrobeniusNorm, Nag_InfNorm or Nag_MaxNorm.
3:     mIntegerInput
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4:     nIntegerInput
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5:     klIntegerInput
On entry: kl, the number of subdiagonals within the band of A.
Constraint: kl0.
6:     kuIntegerInput
On entry: ku, the number of superdiagonals within the band of A.
Constraint: ku0.
7:     ab[dim]const doubleInput
Note: the dimension, dim, of the array ab must be at least
  • max1,pdab×n when order=Nag_ColMajor;
  • max1,m×pdab when order=Nag_RowMajor.
On entry: the m by n band matrix A.
This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements Aij, for row i=1,,m and column j=max1,i-kl,,minn,i+ku, depends on the order argument as follows:
  • if order=Nag_ColMajor, Aij is stored as ab[j-1×pdab+ku+i-j];
  • if order=Nag_RowMajor, Aij is stored as ab[i-1×pdab+kl+j-i].
8:     pdabIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array ab.
Constraint: pdabkl+ku+1.
9:     rdouble *Output
On exit: the value of the norm specified by norm.
10:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, kl=value.
Constraint: kl0.
On entry, ku=value.
Constraint: ku0.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pdab=value, kl=value, ku=value.
Constraint: pdabkl+ku+1.

7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8  Parallelism and Performance

Not applicable.

9  Further Comments


10  Example

Calculates the various norms of a 6 by 4 banded matrix with two subdiagonals and one superdiagonal.

10.1  Program Text

Program Text (f16rbce.c)

10.2  Program Data

Program Data (f16rbce.d)

10.3  Program Results

Program Results (f16rbce.r)

nag_dgb_norm (f16rbc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014