nag_zger (f16smc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zger (f16smc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zger (f16smc) performs a rank-1 update on a complex general matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zger (Nag_OrderType order, Nag_ConjType conj, Integer m, Integer n, Complex alpha, const Complex x[], Integer incx, const Complex y[], Integer incy, Complex beta, Complex a[], Integer pda, NagError *fail)

3  Description

nag_zger (f16smc) performs the rank-1 update operation
AαxyT+βA,
or
AαxyH+βA,
where A is an m by n complex matrix, x is an m element complex vector, y is an n-element complex vector, 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:     conjNag_ConjTypeInput
On entry: the argument conj specifies whether the elements yi are used unconjugated or conjugated, as follows:
conj=Nag_NoConj
The elements yi are not conjugated.
conj=Nag_Conj
The complex conjugate of the elements yi are used.
Constraint: conj=Nag_NoConj or Nag_Conj.
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:     alphaComplexInput
On entry: the scalar α.
6:     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.
7:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
8:     y[dim]const ComplexInput
Note: the dimension, dim, of the array y must be at least max1,1+n-1incy.
On entry: the vector y.
9:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
10:   betaComplexInput
On entry: the scalar β.
11:   a[dim]ComplexInput/Output
Note: the dimension, dim, of the array a must be at least
  • max1,pda×n when order=Nag_ColMajor;
  • max1,m×pda when order=Nag_RowMajor.
If order=Nag_ColMajor, Aij is stored in a[j-1×pda+i-1].
If order=Nag_RowMajor, Aij is stored in a[i-1×pda+j-1].
On entry: the m by n matrix A.
On exit: the updated matrix A.
12:   pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax1,m;
  • if order=Nag_RowMajor, pdan.
13:   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, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, m=value.
Constraint: pdamax1,m.
On entry, pda=value and n=value.
Constraint: pdan.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

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

Perform rank-1 update of complex matrix A using vectors x and y:
A A - x yH ,
where A is the 3 by 2 complex matrix given by
A = 4.0+4.0i 2.0+2.0i 4.0+7.0i 4.0+3.0i 11.0+3.0i 9.0+7.0i ,
and the vectors x and y are
x = 2.0+1.0i 3.0+2.0i 5.0-1.0i
and
y = 2.0+1.0i 1.0-2.0i .
The vector y is stored in every second element of array y (incy=2).

9.1  Program Text

Program Text (f16smce.c)

9.2  Program Data

Program Data (f16smce.d)

9.3  Program Results

Program Results (f16smce.r)


nag_zger (f16smc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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