The function may be called by the names: f08flc, nag_lapackeig_ddisna or nag_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: – Nag_JobTypeInput
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, dim, of the array sep
must be at least
when or .
On exit: the reciprocal condition numbers of the vectors.
6: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, and .
Constraint: if or , .
On entry, .
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.
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.
Constraint: the elements of the array d must be in either increasing or decreasing order. if or the elements of d must be non-negative.
The reciprocal condition numbers are computed to machine precision relative to the size of the eigenvalues, or singular values.
8Parallelism and Performance
f08flc is not threaded in any implementation.
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.
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.