NAG CL Interface
f16pec (dspmv)

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1 Purpose

f16pec performs matrix-vector multiplication for a real symmetric matrix stored in packed form.

2 Specification

#include <nag.h>
void  f16pec (Nag_OrderType order, Nag_UploType uplo, Integer n, double alpha, const double ap[], const double x[], Integer incx, double beta, double y[], Integer incy, NagError *fail)
The function may be called by the names: f16pec, nag_blast_dspmv or nag_dspmv.

3 Description

f16pec performs the matrix-vector operation
yαAx + βy ,  
where A is an n×n real symmetric matrix stored in packed form, x and y are n-element real vectors, and 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: ap[dim] const double Input
Note: the dimension, dim, of the array ap must be at least max(1, n × (n+1) / 2 ) .
On entry: the n×n symmetric matrix A, packed by rows or columns.
The storage of elements Aij depends on the order and uplo arguments as follows:
if order=Nag_ColMajor and uplo=Nag_Upper,
Aij is stored in ap[(j-1)×j/2+i-1], for ij;
if order=Nag_ColMajor and uplo=Nag_Lower,
Aij is stored in ap[(2n-j)×(j-1)/2+i-1], for ij;
if order=Nag_RowMajor and uplo=Nag_Upper,
Aij is stored in ap[(2n-i)×(i-1)/2+j-1], for ij;
if order=Nag_RowMajor and uplo=Nag_Lower,
Aij is stored in ap[(i-1)×i/2+j-1], for ij.
6: 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.
7: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
8: beta double Input
On entry: the scalar β.
9: y[dim] double Input/Output
Note: the dimension, dim, of the array y must be at least max(1,1+(n-1)|incy|).
On entry: the vector y. See x for details of storage.
If beta=0, y need not be set.
On exit: the updated vector y.
10: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
11: 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, n=value.
Constraint: n0.
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

f16pec is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example computes the matrix-vector product
y=αAx+βy  
where
A = ( 1.0 2.0 3.0 4.0 2.0 2.0 3.0 4.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 ) ,  
x = ( -1.0 2.0 -3.0 1.0 ) ,  
y = ( 4.0 7.5 8.0 13.0 ) ,  
α= 1.5   and   β= 1.0 .  

10.1 Program Text

Program Text (f16pece.c)

10.2 Program Data

Program Data (f16pece.d)

10.3 Program Results

Program Results (f16pece.r)