nag_zhbmv (f16sdc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_zhbmv (f16sdc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zhbmv (f16sdc) performs matrix-vector multiplication for a complex Hermitian band matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zhbmv (Nag_OrderType order, Nag_UploType uplo, Integer n, Integer k, Complex alpha, const Complex ab[], Integer pdab, const Complex x[], Integer incx, Complex beta, Complex y[], Integer incy, NagError *fail)

3  Description

nag_zhbmv (f16sdc) performs the matrix-vector operation
yαAx+βy,
where A is an n by n complex Hermitian band matrix with k subdiagonals and k superdiagonals, x and y are n-element complex vectors, and α and β are complex scalars.

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:     uploNag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of A is stored.
uplo=Nag_Upper
The upper triangular part of A is stored.
uplo=Nag_Lower
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     kIntegerInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
5:     alphaComplexInput
On entry: the scalar α.
6:     ab[dim]const ComplexInput
Note: the dimension, dim, of the array ab must be at least max1,pdab×n.
On entry: the n by n Hermitian band matrix A.
This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements of Aij, depends on the order and uplo arguments as follows:
  • if order=Nag_ColMajor and uplo=Nag_Upper,
              Aij is stored in ab[k+i-j+j-1×pdab], for j=1,,n and i=max1,j-k,,j;
  • if order=Nag_ColMajor and uplo=Nag_Lower,
              Aij is stored in ab[i-j+j-1×pdab], for j=1,,n and i=j,,minn,j+k;
  • if order=Nag_RowMajor and uplo=Nag_Upper,
              Aij is stored in ab[j-i+i-1×pdab], for i=1,,n and j=i,,minn,i+k;
  • if order=Nag_RowMajor and uplo=Nag_Lower,
              Aij is stored in ab[k+j-i+i-1×pdab], for i=1,,n and j=max1,i-k,,i.
7:     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: pdabk+1.
8:     x[dim]const ComplexInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1incx.
On entry: the vector x.
9:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
10:   betaComplexInput
On entry: the scalar β.
11:   y[dim]ComplexInput/Output
Note: the dimension, dim, of the array y must be at least max1,1+n-1incy.
On entry: the vector y.
If beta=0, y need not be set.
On exit: the updated vector y.
12:   incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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, k=value.
Constraint: k0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdab=value, k=value.
Constraint: pdabk+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+0.0i 2.0-1.0i 3.0-1.0i 0.0+0.0i 0.0+0.0i 2.0+1.0i 2.0+0.0i 3.0-2.0i 4.0-2.0i 0.0+0.0i 3.0+1.0i 3.0+2.0i 3.0+0.0i 4.0-3.0i 5.0-3.0i 0.0+0.0i 4.0+2.0i 4.0+3.0i 4.0+0.0i 5.0-4.0i 0.0+0.0i 0.0+0.0i 5.0+3.0i 5.0+4.0i 5.0+0.0i ,
x = -1.0+1.0i 2.0+2.0i -3.0-1.0i 2.0+3.0i -1.0+1.0i ,
y = 3.0-0.5i -0.5-6.0i 0.5-8.5i 2.5-6.0i 14.0-2.0i ,
α=1.0+0.0i   and   β=2.0+0.0i .

9.1  Program Text

Program Text (f16sdce.c)

9.2  Program Data

Program Data (f16sdce.d)

9.3  Program Results

Program Results (f16sdce.r)


nag_zhbmv (f16sdc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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