--- rpl/lapack/lapack/ddisna.f 2010/12/21 13:53:24 1.7 +++ rpl/lapack/lapack/ddisna.f 2011/11/21 20:42:49 1.8 @@ -1,9 +1,126 @@ +*> \brief \b DDISNA +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DDISNA + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOB +* INTEGER INFO, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), SEP( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DDISNA 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 +*> +*> DLAMCH( 'E' ) * ( ANORM / SEP( I ) ) +*> +*> where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed +*> to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of +*> the error bound. +*> +*> DDISNA may also be used to compute error bounds for eigenvectors of +*> the generalized symmetric definite eigenproblem. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOB +*> \verbatim +*> JOB is CHARACTER*1 +*> Specifies for which problem the reciprocal condition numbers +*> should be computed: +*> = 'E': the eigenvectors of a symmetric/Hermitian matrix; +*> = 'L': the left singular vectors of a general matrix; +*> = 'R': the right singular vectors of a general matrix. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> If JOB = 'L' or 'R', the number of columns of the matrix, +*> in which case N >= 0. Ignored if JOB = 'E'. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (M) if JOB = 'E' +*> dimension (min(M,N)) if JOB = 'L' or 'R' +*> 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. +*> \endverbatim +*> +*> \param[out] SEP +*> \verbatim +*> SEP is DOUBLE PRECISION array, dimension (M) if JOB = 'E' +*> dimension (min(M,N)) if JOB = 'L' or 'R' +*> The reciprocal condition numbers of the vectors. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit. +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER JOB @@ -13,58 +130,6 @@ DOUBLE PRECISION D( * ), SEP( * ) * .. * -* Purpose -* ======= -* -* DDISNA 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 -* -* DLAMCH( 'E' ) * ( ANORM / SEP( I ) ) -* -* where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed -* to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of -* the error bound. -* -* DDISNA may also be used to compute error bounds for eigenvectors of -* the generalized symmetric definite eigenproblem. -* -* Arguments -* ========= -* -* JOB (input) CHARACTER*1 -* Specifies for which problem the reciprocal condition numbers -* should be computed: -* = 'E': the eigenvectors of a symmetric/Hermitian matrix; -* = 'L': the left singular vectors of a general matrix; -* = 'R': the right singular vectors of a general matrix. -* -* M (input) INTEGER -* The number of rows of the matrix. M >= 0. -* -* N (input) INTEGER -* If JOB = 'L' or 'R', the number of columns of the matrix, -* in which case N >= 0. Ignored if JOB = 'E'. -* -* D (input) DOUBLE PRECISION array, dimension (M) if JOB = 'E' -* dimension (min(M,N)) if JOB = 'L' or 'R' -* 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. -* -* SEP (output) DOUBLE PRECISION array, dimension (M) if JOB = 'E' -* dimension (min(M,N)) if JOB = 'L' or 'R' -* The reciprocal condition numbers of the vectors. -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value. -* * ===================================================================== * * .. Parameters ..