1DDISNA(1)                LAPACK routine (version 3.2)                DDISNA(1)
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NAME

6       DDISNA - computes the reciprocal condition numbers for the eigenvectors
7       of a real symmetric or complex Hermitian matrix  or  for  the  left  or
8       right 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.
25       The  bound on the error, measured by angle in radians, in the I-th com‐
26       puted vector is given by
27              DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
28       where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed to
29       be  smaller  than DLAMCH( 'E' )*ANORM in order to limit the size of the
30       error bound.
31       DDISNA may also be used to compute error bounds for eigenvectors of the
32       generalized symmetric definite eigenproblem.
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ARGUMENTS

35       JOB     (input) CHARACTER*1
36               Specifies  for  which  problem the reciprocal condition numbers
37               should be computed:
38               = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
39               = 'L':  the left singular vectors of a general matrix;
40               = 'R':  the right singular vectors of a general matrix.
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42       M       (input) INTEGER
43               The number of rows of the matrix. M >= 0.
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45       N       (input) INTEGER
46               If JOB = 'L' or 'R', the number of columns of  the  matrix,  in
47               which case N >= 0. Ignored if JOB = 'E'.
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49       D       (input) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
50               dimension  (min(M,N))  if  JOB = 'L' or 'R' The eigenvalues (if
51               JOB = 'E') or singular values (if JOB =  'L'  or  'R')  of  the
52               matrix,  in  either increasing or decreasing order. If singular
53               values, they must be non-negative.
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55       SEP     (output) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
56               dimension (min(M,N)) if JOB = 'L' or 'R' The reciprocal  condi‐
57               tion numbers of the vectors.
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59       INFO    (output) INTEGER
60               = 0:  successful exit.
61               < 0:  if INFO = -i, the i-th argument had an illegal value.
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65 LAPACK routine (version 3.2)    November 2008                       DDISNA(1)
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