nag_dspr (f16pqc) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_dspr (f16pqc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dspr (f16pqc) performs a rank-1 update on a real symmetric matrix stored in packed form.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dspr (Nag_OrderType order, Nag_UploType uplo, Integer n, double alpha, const double x[], Integer incx, double beta, double ap[], NagError *fail)

3  Description

nag_dspr (f16pqc) performs the symmetric rank-1 update operation
where A is an n by n real symmetric matrix, stored in packed form, 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

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 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 A is stored.
The upper triangular part of A is stored.
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     alphadoubleInput
On entry: the scalar α.
5:     x[dim]const doubleInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1incx.
On entry: the vector x.
6:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
7:     betadoubleInput
On entry: the scalar β.
8:     ap[dim]doubleInput/Output
Note: the dimension, dim, of the array ap must be at least max1, n × n+1 / 2 .
On entry: the n by 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.
On exit: the updated matrix A.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, incx=value.
Constraint: incx0.
On entry, n=value.
Constraint: n0.

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

Not applicable.

9  Further Comments

No test for singularity or near-singularity of A is included in nag_dspr (f16pqc). Such tests must be performed before calling this function.

10  Example

Perform rank-1 update of real symmetric matrix A, stored in packed storage format, using vector x:
A A-xxT ,
where A is the 4 by 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
x = 2.0,2.0,0.2,-0.14T .

10.1  Program Text

Program Text (f16pqce.c)

10.2  Program Data

Program Data (f16pqce.d)

10.3  Program Results

Program Results (f16pqce.r)

nag_dspr (f16pqc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014