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 3.3.1.3 in How to Use the NAG Library and its Documentation 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 n-element vector x.
If incx>0, xi must be stored in x[i-1×incx], for i=1,2,,m.
If incx<0, xi must be stored in x[m-i×incx], for i=1,2,,m.
Intermediate elements of x are not referenced. If m=0, x is not referenced and may be NULL.
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 n-element vector y.
If incy>0, yi must be stored in y[i-1×incy], for i=1,2,,n.
If incy<0, yi must be stored in y[n-i×incy], for i=1,2,,n.
Intermediate elements of y are not referenced. If α=0.0 or n=0, y is not referenced and may be NULL.
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 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation 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

nag_zger (f16smc) is not threaded in any implementation.

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)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017