NAG CL Interface
f08flc (ddisna)

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1 Purpose

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

2 Specification

#include <nag.h>
void  f08flc (Nag_JobType job, Integer m, Integer n, const double d[], double sep[], NagError *fail)
The function may be called by the names: f08flc, nag_lapackeig_ddisna or nag_ddisna.

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: job Nag_JobType Input
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: m Integer Input
On entry: m, the number of rows of the matrix A.
Constraint: m0.
3: n Integer Input
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 double Input
Note: the dimension, dim, of the array d must be at least
  • max(1,m) when job=Nag_EigVecs;
  • max(1,min(m,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] double Output
Note: the dimension, dim, of the array sep must be at least
  • max(1,m) when job=Nag_EigVecs;
  • max(1,min(m,n)) when job=Nag_LeftSingVecs or Nag_RightSingVecs.
On exit: the reciprocal condition numbers of the vectors.
6: 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_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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
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.
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 Parallelism and Performance

f08flc is not threaded in any implementation.

9 Further Comments

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.

10 Example

The use of f08flc in computing error bounds for eigenvectors of the symmetric eigenvalue problem is illustrated in f08fac; its use in computing error bounds for singular vectors is illustrated in f08kbc; and its use in computing error bounds for eigenvectors of the generalized symmetric definite eigenvalue problem is illustrated in f08sac.