Visible to Intel only — GUID: GUID-16F92449-D99E-4813-8F65-4599EC1B18BD
Visible to Intel only — GUID: GUID-16F92449-D99E-4813-8F65-4599EC1B18BD
?disna
Computes the reciprocal condition numbers for the eigenvectors of a symmetric/ Hermitian matrix or for the left or right singular vectors of a general matrix.
Syntax
call sdisna(job, m, n, d, sep, info)
call ddisna(job, m, n, d, sep, info)
call disna(d, sep [,job] [,minmn] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix.
The reciprocal condition number is the 'gap' between the corresponding eigenvalue or singular value and the nearest other one.
The bound on the error, measured by angle in radians, in the i-th computed vector is given by
?lamch('E')*(anorm/sep(i))
where anorm = ||A||2 = max( |d(j)| ). sep(i) is not allowed to be smaller than slamch('E')*anorm in order to limit the size of the error bound.
?disna may also be used to compute error bounds for eigenvectors of the generalized symmetric definite eigenproblem.
Input Parameters
- job
-
CHARACTER*1. Must be 'E','L', or 'R'. Specifies for which problem the reciprocal condition numbers should be computed:
job = 'E': for the eigenvectors of a symmetric/Hermitian matrix;
job = 'L': for the left singular vectors of a general matrix;
job = 'R': for the right singular vectors of a general matrix.
- m
-
INTEGER. The number of rows of the matrix (m≥ 0).
- n
-
INTEGER.
If job = 'L', or 'R', the number of columns of the matrix (n≥ 0). Ignored if job = 'E'.
- d
-
REAL for sdisna
DOUBLE PRECISION for ddisna.
Array, dimension at least max(1,m) if job = 'E', and at least max(1, min(m,n)) if job = 'L' or 'R'.
This array must contain the eigenvalues (if job = 'E') or singular values (if job = 'L' or 'R') of the matrix, in either increasing or decreasing order.
If singular values, they must be non-negative.
Output Parameters
- sep
-
REAL for sdisna
DOUBLE PRECISION for ddisna.
Array, dimension at least max(1,m) if job = 'E', and at least max(1, min(m,n)) if job = 'L' or 'R'. The reciprocal condition numbers of the vectors.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine disna interface are the following:
- d
-
Holds the vector of length min(m,n).
- sep
-
Holds the vector of length min(m,n).
- job
-
Must be 'E', 'L', or 'R'. The default value is 'E'.
- minmn
-
Indicates which of the values m or n is smaller. Must be either 'M' or 'N', the default is 'M'.
If job = 'E', this argument is superfluous, If job = 'L' or 'R', this argument is used by the routine.