nag_zgbmv (f16sbc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_zgbmv (f16sbc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zgbmv (f16sbc) performs matrix-vector multiplication for a complex band matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zgbmv (Nag_OrderType order, Nag_TransType trans, Integer m, Integer n, Integer kl, Integer ku, Complex alpha, const Complex ab[], Integer pdab, const Complex x[], Integer incx, Complex beta, Complex y[], Integer incy, NagError *fail)

3  Description

nag_zgbmv (f16sbc) performs one of the matrix-vector operations
yαAx+βy,  yαATx+βy  or  yαAHx+βy
where A is an m by n complex band matrix with kl subdiagonals and ku superdiagonals, x and y are complex vectors, and α and β are complex scalars.
If m=0 or n=0, no operation is performed.

4  References

The BLAS Technical Forum Standard (2001) http://www.netlib.org/blas/blast-forum

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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_NoTrans
yαAx+βy.
trans=Nag_Trans
yαATx+βy.
trans=Nag_ConjTrans
yαAHx+βy.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
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:     alphaComplexInput
On entry: the scalar α.
8:     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].
9:     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.
10:   x[dim]const ComplexInput
Note: the dimension, dim, of the array x must be at least
  • max1,1+n-1incx when trans=Nag_NoTrans;
  • max1,1+m-1incx when trans=Nag_Trans or Nag_ConjTrans.
On entry: the vector x.
11:   incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
12:   betaComplexInput
On entry: the scalar β.
13:   y[dim]ComplexInput/Output
Note: the dimension, dim, of the array y must be at least
  • max1,1+m-1incy when trans=Nag_NoTrans;
  • max1,1+n-1incy when trans=Nag_Trans or Nag_ConjTrans.
On entry: the vector y.
If beta=0, y need not be set.
On exit: the updated vector y.
14:   incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
15:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, kl=value.
Constraint: kl0.
On entry, ku=value.
Constraint: ku0.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_3
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 The BLAS Technical Forum Standard (2001)).

8  Further Comments

None.

9  Example

This example computes the matrix-vector product
y=αAx+βy
where
A = 1.0+1.0i 1.0+2.0i 0.0+0.0i 0.0+0.0i 2.0+1.0i 2.0+2.0i 2.0+3.0i 0.0+0.0i 3.0+1.0i 3.0+2.0i 3.0+3.0i 3.0+4.0i 0.0+0.0i 4.0+2.0i 4.0+3.0i 4.0+4.0i 0.0+0.0i 0.0+0.0i 5.0+3.0i 5.0+4.0i 0.0+0.0i 0.0+0.0i 0.0+0.0i 6.0+4.0i ,
x = 1.0-1.0i 2.0-2.0i 3.0-3.0i 4.0-4.0i ,
y = -3.5+00.0i -11.5+01.0i -27.5+03.0i -29.0+07.5i -25.5+10.0i -14.5+10.0i ,
α=1.0+0.0i   and   β=2.0+0.0i .

9.1  Program Text

Program Text (f16sbce.c)

9.2  Program Data

Program Data (f16sbce.d)

9.3  Program Results

Program Results (f16sbce.r)


nag_zgbmv (f16sbc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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