NAG CL Interface
f16ubc (zgb_​norm)

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1 Purpose

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×n band matrix stored in banded packed form.

2 Specification

#include <nag.h>
void  f16ubc (Nag_OrderType order, Nag_NormType norm, Integer m, Integer n, Integer kl, Integer ku, const Complex ab[], Integer pdab, double *r, NagError *fail)
The function may be called by the names: f16ubc, nag_blast_zgb_norm or nag_zgb_norm.

3 Description

Given a complex m×n band matrix, A, f16ubc calculates one of the values given by
A1=maxji=1m|aij| (the 1-norm of A),
A=maxij= 1n|aij| (the -norm of A),
AF=(i=1mj=1n |aij|2)1/2 (the Frobenius norm of A),  or
maxi,j|aij| (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: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: norm Nag_NormType Input
On entry: specifies the value to be returned.
The 1-norm.
The Frobenius (or Euclidean) norm.
The -norm.
The value maxi,j|aij| (not a norm).
Constraint: norm=Nag_OneNorm, Nag_FrobeniusNorm, Nag_InfNorm or Nag_MaxNorm.
3: m Integer Input
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4: n Integer Input
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5: kl Integer Input
On entry: kl, the number of subdiagonals within the band of A.
Constraint: kl0.
6: ku Integer Input
On entry: ku, the number of superdiagonals within the band of A.
Constraint: ku0.
7: ab[dim] const Complex Input
Note: the dimension, dim, of the array ab must be at least
  • max(1,pdab×n) when order=Nag_ColMajor;
  • max(1,m×pdab) when order=Nag_RowMajor.
On entry: the m×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=max(1,i-kl),,min(n,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: pdab Integer Input
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: r double * Output
On exit: the value of the norm specified by norm.
10: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

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

Background information to multithreading can be found in the Multithreading documentation.
f16ubc is not threaded in any implementation.

9 Further Comments


10 Example

Reads in a 6×4 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)