--- rpl/lapack/lapack/dstein.f 2010/12/21 13:53:38 1.7 +++ rpl/lapack/lapack/dstein.f 2011/11/21 20:43:04 1.8 @@ -1,10 +1,183 @@ +*> \brief \b DSTEIN +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSTEIN + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, +* IWORK, IFAIL, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDZ, M, N +* .. +* .. Array Arguments .. +* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), +* $ IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSTEIN computes the eigenvectors of a real symmetric tridiagonal +*> matrix T corresponding to specified eigenvalues, using inverse +*> iteration. +*> +*> The maximum number of iterations allowed for each eigenvector is +*> specified by an internal parameter MAXITS (currently set to 5). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The n diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) subdiagonal elements of the tridiagonal matrix +*> T, in elements 1 to N-1. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of eigenvectors to be found. 0 <= M <= N. +*> \endverbatim +*> +*> \param[in] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements of W contain the eigenvalues for +*> which eigenvectors are to be computed. The eigenvalues +*> should be grouped by split-off block and ordered from +*> smallest to largest within the block. ( The output array +*> W from DSTEBZ with ORDER = 'B' is expected here. ) +*> \endverbatim +*> +*> \param[in] IBLOCK +*> \verbatim +*> IBLOCK is INTEGER array, dimension (N) +*> The submatrix indices associated with the corresponding +*> eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to +*> the first submatrix from the top, =2 if W(i) belongs to +*> the second submatrix, etc. ( The output array IBLOCK +*> from DSTEBZ is expected here. ) +*> \endverbatim +*> +*> \param[in] ISPLIT +*> \verbatim +*> ISPLIT is INTEGER array, dimension (N) +*> The splitting points, at which T breaks up into submatrices. +*> The first submatrix consists of rows/columns 1 to +*> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 +*> through ISPLIT( 2 ), etc. +*> ( The output array ISPLIT from DSTEBZ is expected here. ) +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (LDZ, M) +*> The computed eigenvectors. The eigenvector associated +*> with the eigenvalue W(i) is stored in the i-th column of +*> Z. Any vector which fails to converge is set to its current +*> iterate after MAXITS iterations. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (5*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (N) +*> \endverbatim +*> +*> \param[out] IFAIL +*> \verbatim +*> IFAIL is INTEGER array, dimension (M) +*> On normal exit, all elements of IFAIL are zero. +*> If one or more eigenvectors fail to converge after +*> MAXITS iterations, then their indices are stored in +*> array IFAIL. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit. +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, then i eigenvectors failed to converge +*> in MAXITS iterations. Their indices are stored in +*> array IFAIL. +*> \endverbatim +* +*> \par Internal Parameters: +* ========================= +*> +*> \verbatim +*> MAXITS INTEGER, default = 5 +*> The maximum number of iterations performed. +*> +*> EXTRA INTEGER, default = 2 +*> The number of iterations performed after norm growth +*> criterion is satisfied, should be at least 1. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERcomputational +* +* ===================================================================== SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, $ IWORK, IFAIL, 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 .. INTEGER INFO, LDZ, M, N @@ -15,89 +188,6 @@ DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* DSTEIN computes the eigenvectors of a real symmetric tridiagonal -* matrix T corresponding to specified eigenvalues, using inverse -* iteration. -* -* The maximum number of iterations allowed for each eigenvector is -* specified by an internal parameter MAXITS (currently set to 5). -* -* Arguments -* ========= -* -* N (input) INTEGER -* The order of the matrix. N >= 0. -* -* D (input) DOUBLE PRECISION array, dimension (N) -* The n diagonal elements of the tridiagonal matrix T. -* -* E (input) DOUBLE PRECISION array, dimension (N-1) -* The (n-1) subdiagonal elements of the tridiagonal matrix -* T, in elements 1 to N-1. -* -* M (input) INTEGER -* The number of eigenvectors to be found. 0 <= M <= N. -* -* W (input) DOUBLE PRECISION array, dimension (N) -* The first M elements of W contain the eigenvalues for -* which eigenvectors are to be computed. The eigenvalues -* should be grouped by split-off block and ordered from -* smallest to largest within the block. ( The output array -* W from DSTEBZ with ORDER = 'B' is expected here. ) -* -* IBLOCK (input) INTEGER array, dimension (N) -* The submatrix indices associated with the corresponding -* eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to -* the first submatrix from the top, =2 if W(i) belongs to -* the second submatrix, etc. ( The output array IBLOCK -* from DSTEBZ is expected here. ) -* -* ISPLIT (input) INTEGER array, dimension (N) -* The splitting points, at which T breaks up into submatrices. -* The first submatrix consists of rows/columns 1 to -* ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 -* through ISPLIT( 2 ), etc. -* ( The output array ISPLIT from DSTEBZ is expected here. ) -* -* Z (output) DOUBLE PRECISION array, dimension (LDZ, M) -* The computed eigenvectors. The eigenvector associated -* with the eigenvalue W(i) is stored in the i-th column of -* Z. Any vector which fails to converge is set to its current -* iterate after MAXITS iterations. -* -* LDZ (input) INTEGER -* The leading dimension of the array Z. LDZ >= max(1,N). -* -* WORK (workspace) DOUBLE PRECISION array, dimension (5*N) -* -* IWORK (workspace) INTEGER array, dimension (N) -* -* IFAIL (output) INTEGER array, dimension (M) -* On normal exit, all elements of IFAIL are zero. -* If one or more eigenvectors fail to converge after -* MAXITS iterations, then their indices are stored in -* array IFAIL. -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = i, then i eigenvectors failed to converge -* in MAXITS iterations. Their indices are stored in -* array IFAIL. -* -* Internal Parameters -* =================== -* -* MAXITS INTEGER, default = 5 -* The maximum number of iterations performed. -* -* EXTRA INTEGER, default = 2 -* The number of iterations performed after norm growth -* criterion is satisfied, should be at least 1. -* * ===================================================================== * * .. Parameters ..