nag_dsyr2k (f16yrc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dsyr2k (f16yrc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dsyr2k (f16yrc) performs a rank-2k update on a real symmetric matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dsyr2k (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Integer n, Integer k, double alpha, const double a[], Integer pda, const double b[], Integer pdb, double beta, double c[], Integer pdc, NagError *fail)

3  Description

nag_dsyr2k (f16yrc) performs one of the symmetric rank-2k update operations
CαABT + αBAT + βC   or   CαATB + αBTA+βC ,
where A and B are real matrices, C is an n by n real symmetric matrix, and α and β are real 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
CαABT + αBAT + βC .
trans=Nag_Trans or Nag_ConjTrans
CαATB + αBTA + βC .
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
4:     nIntegerInput
On entry: n, the order of the matrix C; the number of rows of A and B if trans=Nag_NoTrans, or the number of columns of A and B otherwise.
Constraint: n0.
5:     kIntegerInput
On entry: k, the number of columns of A and B if trans=Nag_NoTrans, or the number of rows of A and B otherwise.
Constraint: k0.
6:     alphadoubleInput
On entry: the scalar α.
7:     a[dim]const doubleInput
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:     b[dim]const doubleInput
Note: the dimension, dim, of the array b must be at least
  • max1,pdb×k when trans=Nag_NoTrans and order=Nag_ColMajor;
  • max1,n×pdb when trans=Nag_NoTrans and order=Nag_RowMajor;
  • max1,pdb×n when trans=Nag_Trans or Nag_ConjTrans and order=Nag_ColMajor;
  • max1,k×pdb when trans=Nag_Trans or Nag_ConjTrans and 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 matrix B; B is n by k if trans=Nag_NoTrans, or k by n otherwise.
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,
    • if trans=Nag_NoTrans, pdb max1,n ;
    • if trans=Nag_Trans or Nag_ConjTrans, pdb max1,k ;
  • if order=Nag_RowMajor,
    • if trans=Nag_NoTrans, pdbmax1,k;
    • if trans=Nag_Trans or Nag_ConjTrans, pdbmax1,n.
11:   betadoubleInput
On entry: the scalar β.
12:   c[dim]doubleInput/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.
13:   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.
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, 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, k=value, pdb=value.
Constraint: if trans=Nag_NoTrans, pdbmax1,k.
On entry, trans=value, k=value, pdb=value.
Constraint: if trans=Nag_Trans or Nag_ConjTrans, pdb 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.
On entry, trans=value, n=value, pdb=value.
Constraint: if trans=Nag_NoTrans, pdb max1,n .
On entry, trans=value, n=value, pdb=value.
Constraint: if trans=Nag_Trans or Nag_ConjTrans, pdbmax1,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-2k update of real symmetric 4 by 4 matrix C using 4 by 2 matrices A and B, C=C-ABT-BAT, where
C = 4.30 -3.96 0.40 -0.27 -3.96 -4.87 0.31 0.07 0.40 0.31 -8.02 -5.95 -0.27 0.07 -5.95 0.12 ,
A = -3.0 -5.0 -1.0 1.0 2.0 -1.0 1.0 1.0
and
B = 3.0 -2.0 -1.0 1.0 2.0 -1.0 1.0 0.0 .

9.1  Program Text

Program Text (f16yrce.c)

9.2  Program Data

Program Data (f16yrce.d)

9.3  Program Results

Program Results (f16yrce.r)


nag_dsyr2k (f16yrc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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