nag_zgb_norm (f16ubc) (PDF version)
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f16 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_zgb_norm (f16ubc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zgb_norm (f16ubc) calculates the value of the 1-norm, the -norm, the Frobenius norm or the maximum absolute value of the elements of a complex m by n band matrix stored in banded packed form.

2  Specification

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

3  Description

Given a complex m by n band matrix, A, nag_zgb_norm (f16ubc) 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=1n aij21/2 (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 integer codes shown below can be replaced by the equivalent named constants of the form NAG_?_NORM. These named constants are available via the nag_library module and are also used in the example program for clarity.
The 1-norm.
The Frobenius (or Euclidean) norm.
The -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 ComplexInput
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

Reads in a 6 by 4 banded complex matrix A with two subdiagonals and one superdiagonal, and prints the four norms of A.

10.1  Program Text

Program Text (f16ubce.c)

10.2  Program Data

Program Data (f16ubce.d)

10.3  Program Results

Program Results (f16ubce.r)

nag_zgb_norm (f16ubc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

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