NAG CL Interface
f16smc (zger)

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1 Purpose

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

2 Specification

#include <nag.h>
void  f16smc (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)
The function may be called by the names: f16smc, nag_blast_zger or nag_zger.

3 Description

f16smc performs the rank-1 update operation
AαxyT+βA,  
or
AαxyH+βA,  
where A is an m×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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Arguments

1: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: conj Nag_ConjType Input
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 Integer Input
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4: n Integer Input
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5: alpha Complex Input
On entry: the scalar α.
6: x[dim] const Complex Input
Note: the dimension, dim, of the array x must be at least max(1,1+(n-1)|incx|).
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 Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
8: y[dim] const Complex Input
Note: the dimension, dim, of the array y must be at least max(1,1+(n-1)|incy|).
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 Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
10: beta Complex Input
On entry: the scalar β.
11: a[dim] Complex Input/Output
Note: the dimension, dim, of the array a must be at least
  • max(1,pda×n) when order=Nag_ColMajor;
  • max(1,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×n matrix A.
On exit: the updated matrix A.
12: pda Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax(1,m);
  • if order=Nag_RowMajor, pdan.
13: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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: pdamax(1,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 8 in the Introduction to the NAG Library CL Interface 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

Background information to multithreading can be found in the Multithreading documentation.
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 3×2 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)