NAG CL Interface
f16ppc (dsyr)

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1 Purpose

f16ppc performs a rank-1 update on a real symmetric matrix.

2 Specification

#include <nag.h>
void  f16ppc (Nag_OrderType order, Nag_UploType uplo, Integer n, double alpha, const double x[], Integer incx, double beta, double a[], Integer pda, NagError *fail)
The function may be called by the names: f16ppc, nag_blast_dsyr or nag_dsyr.

3 Description

f16ppc performs the symmetric rank-1 update operation
AαxxT+βA,  
where A is an n×n real symmetric matrix, x is an n-element real vector, while α and β are real 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: uplo Nag_UploType Input
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.
3: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
4: alpha double Input
On entry: the scalar α.
5: x[dim] const double 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,,n.
If incx<0, xi must be stored in x[(n-i)×|incx|], for i=1,2,,n.
Intermediate elements of x are not referenced. If n=0, x is not referenced and may be NULL.
6: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
7: beta double Input
On entry: the scalar β.
8: a[dim] double Input/Output
Note: the dimension, dim, of the array a must be at least max(1,pda×n).
On entry: the n×n symmetric matrix A.
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.
On exit: the updated matrix A.
9: pda Integer Input
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraint: pdamax(1,n).
10: 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, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, n=value.
Constraint: pdamax(1,n).
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

f16ppc is not threaded in any implementation.

9 Further Comments

None.

10 Example

Perform rank-1 update of real symmetric matrix A using vector x:
A A - x xT ,  
where A is the 4×4 matrix given by
A = ( 4.30 4.00 0.40 -0.28 4.00 -4.87 0.31 0.07 0.40 0.31 -8.02 -5.95 -0.28 0.07 -5.95 0.12 )  
and
x = (2.0,2.0,0.2,-0.14) T .  

10.1 Program Text

Program Text (f16ppce.c)

10.2 Program Data

Program Data (f16ppce.d)

10.3 Program Results

Program Results (f16ppce.r)