nag_zsymm (f16ztc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zsymm (f16ztc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zsymm (f16ztc) performs matrix-matrix multiplication for a complex symmetric matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zsymm (Nag_OrderType order, Nag_SideType side, Nag_UploType uplo, Integer m, Integer n, Complex alpha, const Complex a[], Integer pda, const Complex b[], Integer pdb, Complex beta, Complex c[], Integer pdc, NagError *fail)

3  Description

nag_zsymm (f16ztc) performs one of the matrix-matrix operations
CαAB + βC   or   CαBA + βC ,
where A is a complex symmetric matrix, B and C are m by n complex matrices, 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:     sideNag_SideTypeInput
On entry: specifies whether B is operated on from the left or the right.
side=Nag_LeftSide
B is pre-multiplied from the left.
side=Nag_RightSide
B is post-multiplied from the right.
Constraint: side=Nag_LeftSide or Nag_RightSide.
3:     uploNag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of A is stored.
uplo=Nag_Upper
The upper triangular part of A is stored.
uplo=Nag_Lower
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
4:     mIntegerInput
On entry: m, the number of rows of the matrices B and C; the order of A if side=Nag_LeftSide.
Constraint: m0.
5:     nIntegerInput
On entry: n, the number of columns of the matrices B and C; the order of A if side=Nag_RightSide.
Constraint: n0.
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×m when side=Nag_LeftSide;
  • max1,pda×n when side=Nag_RightSide.
On entry: the symmetric matrix A; A is m by m if side=Nag_LeftSide, or n by n if side=Nag_RightSide.
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].
If uplo=Nag_Upper, the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
If uplo=Nag_Lower, the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
8:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraints:
  • if side=Nag_LeftSide, pda max1,m ;
  • if side=Nag_RightSide, pda max1,n .
9:     b[dim]const ComplexInput
Note: the dimension, dim, of the array b must be at least
  • max1,pdb×n when order=Nag_ColMajor;
  • max1,m×pdb when order=Nag_RowMajor.
If order=Nag_ColMajor, Bij is stored in b[j-1×pdb+i-1].
If order=Nag_RowMajor, Bij is stored in b[i-1×pdb+j-1].
On entry: the m by n matrix B.
10:   pdbIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array b.
Constraints:
  • if order=Nag_ColMajor, pdbmax1,m;
  • if order=Nag_RowMajor, pdbmax1,n.
11:   betaComplexInput
On entry: the scalar β.
12:   c[dim]ComplexInput/Output
Note: the dimension, dim, of the array c must be at least
  • max1,pdc×n when order=Nag_ColMajor;
  • max1,m×pdc when order=Nag_RowMajor.
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].
On entry: the m by n matrix C.
If beta=0, c need not be set.
On exit: the updated matrix C.
13:   pdcIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array c.
Constraints:
  • if order=Nag_ColMajor, pdcmax1,m;
  • if order=Nag_RowMajor, pdcmax1,n.
14:   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, side=value, m=value, pda=value.
Constraint: if side=Nag_LeftSide, pda max1,m .
On entry, side=value, n=value, pda=value.
Constraint: if side=Nag_RightSide, pda max1,n .
NE_INT
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdb=value, m=value.
Constraint: pdbmax1,m.
On entry, pdb=value and n=value.
Constraint: pdbmax1,n.
On entry, pdc=value, m=value.
Constraint: pdcmax1,m.
On entry, pdc=value and 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

This example computes the matrix-matrix product
C=αAB+βC
where
A = 1.0+0.0i 1.0+2.0i -2.0+3.0i 1.0-2.0i 2.0+0.0i 1.0+2.0i -2.0-3.0i 1.0-2.0i 3.0+0.0i ,
B = 1.0-1.0i 1.0+2.0i -2.0+1.0i 2.0-2.0i 3.0-1.0i -3.0+1.0i ,
C = -3.5-0.5i 1.5+2.0i -4.5+1.5i -2.0+3.5i -5.5+3.5i 3.0-1.5i ,
α=1.0+0.0i   and   β=2.0+0.0i .

9.1  Program Text

Program Text (f16ztce.c)

9.2  Program Data

Program Data (f16ztce.d)

9.3  Program Results

Program Results (f16ztce.r)


nag_zsymm (f16ztc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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