nag_zger (f16smc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG 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

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

5  Arguments

1:     order Nag_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:     conj Nag_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:     m IntegerInput
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4:     n IntegerInput
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5:     alpha ComplexInput
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:     incx IntegerInput
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:     incy IntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
10:   beta ComplexInput
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:   pda IntegerInput
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:   fail NagError *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.
See Section 3.2.1.2 in the Essential Introduction for further information.
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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction 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

Not applicable.

9  Further Comments

None.

10  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).

10.1  Program Text

Program Text (f16smce.c)

10.2  Program Data

Program Data (f16smce.d)

10.3  Program Results

Program Results (f16smce.r)


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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015