1DDISNA(1)                LAPACK routine (version 3.1)                DDISNA(1)
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NAME

6       DDISNA  -  the  reciprocal  condition numbers for the eigenvectors of a
7       real symmetric or complex Hermitian matrix or for  the  left  or  right
8       singular vectors of a general m-by-n matrix
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SYNOPSIS

11       SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )
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13           CHARACTER      JOB
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15           INTEGER        INFO, M, N
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17           DOUBLE         PRECISION D( * ), SEP( * )
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PURPOSE

20       DDISNA  computes  the reciprocal condition numbers for the eigenvectors
21       of a real symmetric or complex Hermitian matrix  or  for  the  left  or
22       right  singular vectors of a general m-by-n matrix. The reciprocal con‐
23       dition number is the 'gap' between the corresponding eigenvalue or sin‐
24       gular value and the nearest other one.
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26       The  bound on the error, measured by angle in radians, in the I-th com‐
27       puted vector is given by
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29              DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
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31       where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed to
32       be  smaller  than DLAMCH( 'E' )*ANORM in order to limit the size of the
33       error bound.
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35       DDISNA may also be used to compute error bounds for eigenvectors of the
36       generalized symmetric definite eigenproblem.
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ARGUMENTS

40       JOB     (input) CHARACTER*1
41               Specifies  for  which  problem the reciprocal condition numbers
42               should be computed:
43               = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
44               = 'L':  the left singular vectors of a general matrix;
45               = 'R':  the right singular vectors of a general matrix.
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47       M       (input) INTEGER
48               The number of rows of the matrix. M >= 0.
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50       N       (input) INTEGER
51               If JOB = 'L' or 'R', the number of columns of  the  matrix,  in
52               which case N >= 0. Ignored if JOB = 'E'.
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54       D       (input) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
55               dimension  (min(M,N))  if  JOB = 'L' or 'R' The eigenvalues (if
56               JOB = 'E') or singular values (if JOB =  'L'  or  'R')  of  the
57               matrix,  in  either increasing or decreasing order. If singular
58               values, they must be non-negative.
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60       SEP     (output) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
61               dimension (min(M,N)) if JOB = 'L' or 'R' The reciprocal  condi‐
62               tion numbers of the vectors.
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64       INFO    (output) INTEGER
65               = 0:  successful exit.
66               < 0:  if INFO = -i, the i-th argument had an illegal value.
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70 LAPACK routine (version 3.1)    November 2006                       DDISNA(1)
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