The routine may be called by the names f08flf, nagf_lapackeig_ddisna or its LAPACK name ddisna.
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
On entry: 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
On entry: , the number of columns of the matrix when or .
Note: the dimension of the array sep
must be at least
if and at least if or .
On exit: the reciprocal condition numbers of the vectors.
6: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error 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.
8Parallelism and Performance
f08flf is not threaded in any implementation.
f08flf 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 in computing error bounds for eigenvectors of the symmetric eigenvalue problem is illustrated in f08faf; its use in computing error bounds for singular vectors is illustrated in f08kbf; and its use in computing error bounds for eigenvectors of the generalized symmetric definite eigenvalue problem is illustrated in f08saf.