NAG Library Routine Document
f08flf (ddisna) computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian by matrix , or for the left or right singular vectors of a general by matrix .
|Integer, Intent (In)||:: ||m, n|
|Integer, Intent (Out)||:: ||info|
|Real (Kind=nag_wp), Intent (In)||:: ||d(*)|
|Real (Kind=nag_wp), Intent (Inout)||:: ||sep(*)|
|Character (1), Intent (In)||:: ||job|C Header Interface
f08flf_ (const char *job, const Integer *m, const Integer *n, const double d, double sep, Integer *info, const Charlen length_job)|
The routine may be called by its
The bound on the error, measured by the angle in radians, for the th computed vector is given by , where is the machine precision and is the reciprocal condition number for the vectors, returned in the array element . is restricted to be at least in order to limit the size of the error bound.
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
- 1: – Character(1)Input
: specifies for which problem the reciprocal condition number should be computed.
- The eigenvectors of a symmetric or Hermitian matrix.
- The left singular vectors of a general matrix.
- The right singular vectors of a general matrix.
, or .
- 2: – IntegerInput
On entry: , the number of rows of the matrix .
- 3: – IntegerInput
, the number of columns of the matrix when
is not referenced.
if or , .
- 4: – Real (Kind=nag_wp) arrayInput
the dimension of the array d
must be at least
and at least
On entry: the eigenvalues if , or singular values if or of the matrix .
- the elements of the array d must be in either increasing or decreasing order;
- if or the elements of d must be non-negative.
- 5: – Real (Kind=nag_wp) arrayOutput
the dimension of the array sep
must be at least
and at least
On exit: the reciprocal condition numbers of the vectors.
- 6: – IntegerOutput
unless the routine detects an error (see Section 6
Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The reciprocal condition numbers are computed to machine precision relative to the size of the eigenvalues, or singular values.
Parallelism and Performance
f08flf (ddisna) is not threaded in any implementation.
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.
The use of f08flf (ddisna)
in computing error bounds for eigenvectors of the symmetric eigenvalue problem is illustrated in Section 10
in f08faf (dsyev)
; its use in computing error bounds for singular vectors is illustrated in Section 10
in f08kbf (dgesvd)
; and its use in computing error bounds for eigenvectors of the generalized symmetric definite eigenvalue problem is illustrated in Section 10
in f08saf (dsygv)