nag_zsyrk (f16zuc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zsyrk (f16zuc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zsyrk (f16zuc) performs a rank-k update on a complex symmetric matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zsyrk (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Integer n, Integer k, Complex alpha, const Complex a[], Integer pda, Complex beta, Complex c[], Integer pdc, NagError *fail)

3  Description

nag_zsyrk (f16zuc) performs one of the symmetric rank-k update operations
CαAAT + βC   or   CαATA + βC ,
where A is a complex matrix, C is an n by n complex symmetric matrix, 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 C is stored.
uplo=Nag_Upper
The upper triangular part of C is stored.
uplo=Nag_Lower
The lower triangular part of C is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
trans=Nag_NoTrans
CαAAT+βC.
trans=Nag_Trans
CαATA+βC.
Constraint: trans=Nag_NoTrans or Nag_Trans.
4:     nIntegerInput
On entry: n, the order of the matrix C; the number of rows of A if trans=Nag_NoTrans, or the number of columns of A otherwise.
Constraint: n0.
5:     kIntegerInput
On entry: k, the number of columns of A if trans=Nag_NoTrans, or the number of rows of A otherwise.
Constraint: k0.
6:     alphaComplexInput
On entry: the scalar α.
7:     a[dim]const ComplexInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×k when trans=Nag_NoTrans and order=Nag_ColMajor;
  • max1,n×pda when trans=Nag_NoTrans and order=Nag_RowMajor;
  • max1,pda×n when trans=Nag_Trans or Nag_ConjTrans and order=Nag_ColMajor;
  • max1,k×pda when trans=Nag_Trans or Nag_ConjTrans and 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 matrix A; A is n by k if trans=Nag_NoTrans, or k by n otherwise.
8:     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,
    • if trans=Nag_NoTrans, pda max1,n ;
    • if trans=Nag_Trans or Nag_ConjTrans, pda max1,k ;
  • if order=Nag_RowMajor,
    • if trans=Nag_NoTrans, pdamax1,k;
    • if trans=Nag_Trans or Nag_ConjTrans, pdamax1,n.
9:     betaComplexInput
On entry: the scalar β.
10:   c[dim]ComplexInput/Output
Note: the dimension, dim, of the array c must be at least max1,pdc×n.
On entry: the n by n symmetric matrix C.
If order=Nag_ColMajor, Cij is stored in c[j-1×pdc+i-1].
If order=Nag_RowMajor, Cij is stored in c[i-1×pdc+j-1].
If uplo=Nag_Upper, the upper triangular part of C must be stored and the elements of the array below the diagonal are not referenced.
If uplo=Nag_Lower, the lower triangular part of C must be stored and the elements of the array above the diagonal are not referenced.
On exit: the updated matrix C.
11:   pdcIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix C in the array c.
Constraint: pdcmax1,n.
12:   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_ENUM_INT_2
On entry, trans=value, k=value, pda=value.
Constraint: if trans=Nag_NoTrans, pdamax1,k.
On entry, trans=value, k=value, pda=value.
Constraint: if trans=Nag_Trans or Nag_ConjTrans, pda max1,k .
On entry, trans=value, n=value, pda=value.
Constraint: if trans=Nag_NoTrans, pda max1,n .
On entry, trans=value, n=value, pda=value.
Constraint: if trans=Nag_Trans or Nag_ConjTrans, pdamax1,n.
NE_INT
On entry, k=value.
Constraint: k0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdc=value, n=value.
Constraint: pdcmax1,n.
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-k update of complex symmetric 4 by 4 matrix C using 4 by 2 matrix A (k=2), C=C-1.0-1.0iAAT, where
C = 4.78+1.03i 2.00-0.30i 2.89-1.34i -1.89+1.15i 2.00-0.30i -4.11-2.30i 2.36-4.25i 0.04-3.69i 2.89-1.34i 2.36-4.25i 4.15+0.57i -0.02+0.46i -1.89+1.15i 0.04-3.69i -0.02+0.46i 0.33-1.91i
and
A = 1.7-2.3i -1.8+2.4i 2.9-2.1i 1.2+1.4i -2.9+1.0i 0.6+0.8i 1.5+0.9i -1.4-1.7i .

9.1  Program Text

Program Text (f16zuce.c)

9.2  Program Data

Program Data (f16zuce.d)

9.3  Program Results

Program Results (f16zuce.r)


nag_zsyrk (f16zuc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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