nag_ddisna (f08flc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_ddisna (f08flc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_ddisna (f08flc) computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian m by m matrix A, or for the left or right singular vectors of a general m by n matrix A.

2  Specification

#include <nag.h>
#include <nagf08.h>
void  nag_ddisna (Nag_JobType job, Integer m, Integer n, const double d[], double sep[], NagError *fail)

3  Description

The bound on the error, measured by the angle in radians, for the ith computed vector is given by ε A2 / sepi , where ε is the machine precision and sepi  is the reciprocal condition number for the vectors, returned in the array element sep[i-1] . sep[i-1]  is restricted to be at least ε A2  in order to limit the size of the error bound.

4  References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5  Arguments

1:     jobNag_JobTypeInput
On entry: specifies for which problem the reciprocal condition number should be computed.
job=Nag_EigVecs
The eigenvectors of a symmetric or Hermitian matrix.
job=Nag_LeftSingVecs
The left singular vectors of a general matrix.
job=Nag_RightSingVecs
The right singular vectors of a general matrix.
Constraint: job=Nag_EigVecs, Nag_LeftSingVecs or Nag_RightSingVecs.
2:     mIntegerInput
On entry: m, the number of rows of the matrix A.
Constraint: m0.
3:     nIntegerInput
On entry: n, the number of columns of the matrix when job=Nag_LeftSingVecs or Nag_RightSingVecs.
If job=Nag_EigVecs, n is not referenced.
Constraint: if job=Nag_LeftSingVecs or Nag_RightSingVecs, n0.
4:     d[dim]const doubleInput
Note: the dimension, dim, of the array d must be at least
  • max1,m when job=Nag_EigVecs;
  • max1,minm,n when job=Nag_LeftSingVecs or Nag_RightSingVecs.
On entry: the eigenvalues if job=Nag_EigVecs, or singular values if job=Nag_LeftSingVecs or Nag_RightSingVecs of the matrix A.
Constraints:
  • the elements of the array d must be in either increasing or decreasing order;
  • if job=Nag_LeftSingVecs or Nag_RightSingVecs the elements of d must be non-negative.
5:     sep[dim]doubleOutput
Note: the dimension, dim, of the array sep must be at least
  • max1,m when job=Nag_EigVecs;
  • max1,minm,n when job=Nag_LeftSingVecs or Nag_RightSingVecs.
On exit: the reciprocal condition numbers of the vectors.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_ENUM_INT
On entry, job=value and n=value.
Constraint: if job=Nag_LeftSingVecs or Nag_RightSingVecs, n0.
NE_INT
On entry, m=value.
Constraint: m0.
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.
NE_NOT_MONOTONIC
Constraint: the elements of the array d must be in either increasing or decreasing order.
if job=Nag_LeftSingVecs or Nag_RightSingVecs the elements of d must be non-negative.

7  Accuracy

The reciprocal condition numbers are computed to machine precision relative to the size of the eigenvalues, or singular values.

8  Further Comments

nag_ddisna (f08flc) may also be used towards computing error bounds for the eigenvectors of the generalized symmetric or Hermitian definite eigenproblem. See Golub and Van Loan (1996) for further details on the error bounds.

9  Example

The use of nag_ddisna (f08flc) in computing error bounds for eigenvectors of the symmetric eigenvalue problem is illustrated in Section 9 in nag_dsyev (f08fac); its use in computing error bounds for singular vectors is illustrated in Section 9 in nag_dgesvd (f08kbc); and its use in computing error bounds for eigenvectors of the generalized symmetric definite eigenvalue problem is illustrated in Section 9 in nag_dsygv (f08sac).

nag_ddisna (f08flc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG C Library Manual

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