dlib C++ Library - syevr.h

    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_LAPACk_EVR_Hh_
    #define DLIB_LAPACk_EVR_Hh_

    #include "fortran_id.h"
    #include "../matrix.h"

    namespace dlib
    {
        namespace lapack
        {
            namespace binding
            {
                extern "C"
                {
                    void DLIB_FORTRAN_ID(dsyevr) (const char *jobz, const char *range, const char *uplo, const integer *n,
                                                  double *a, const integer *lda, const double *vl, const double *vu, const integer *il,
                                                  const integer *iu, const double *abstol, integer *m, double *w,
                                                  double *z_, const integer *ldz, integer *isuppz, double *work,
                                                  const integer *lwork, integer *iwork, const integer *liwork, integer *info);

                    void DLIB_FORTRAN_ID(ssyevr) (const char *jobz, const char *range, const char *uplo, const integer *n,
                                                  float *a, const integer *lda, const float *vl, const float *vu, const integer *il,
                                                  const integer *iu, const float *abstol, integer *m, float *w,
                                                  float *z_, const integer *ldz, integer *isuppz, float *work,
                                                  const integer *lwork, integer *iwork, const integer *liwork, integer *info);
                }

                inline int syevr (char jobz, char range, char uplo, integer n,
                                  double* a, integer lda, double vl, double vu, integer il,
                                  integer iu, double abstol, integer *m, double *w,
                                  double *z, integer ldz, integer *isuppz, double *work,
                                  integer lwork, integer *iwork, integer liwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(dsyevr)(&jobz, &range, &uplo, &n,
                                            a, &lda, &vl, &vu, &il,
                                            &iu, &abstol, m, w,
                                            z, &ldz, isuppz, work,
                                            &lwork, iwork, &liwork, &info);
                    return info;
                }

                inline int syevr (char jobz, char range, char uplo, integer n,
                                  float* a, integer lda, float vl, float vu, integer il,
                                  integer iu, float abstol, integer *m, float *w,
                                  float *z, integer ldz, integer *isuppz, float *work,
                                  integer lwork, integer *iwork, integer liwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(ssyevr)(&jobz, &range, &uplo, &n,
                                            a, &lda, &vl, &vu, &il,
                                            &iu, &abstol, m, w,
                                            z, &ldz, isuppz, work,
                                            &lwork, iwork, &liwork, &info);
                    return info;
                }

            }

        // ------------------------------------------------------------------------------------

            /*

    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, RANGE, UPLO
          INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N
          DOUBLE PRECISION   ABSTOL, VL, VU
    *     ..
    *     .. Array Arguments ..
          INTEGER            ISUPPZ( * ), IWORK( * )
          DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DSYEVR computes selected eigenvalues and, optionally, eigenvectors
    *  of a real symmetric matrix A.  Eigenvalues and eigenvectors can be
    *  selected by specifying either a range of values or a range of
    *  indices for the desired eigenvalues.
    *
    *  DSYEVR first reduces the matrix A to tridiagonal form T with a call
    *  to DSYTRD.  Then, whenever possible, DSYEVR calls DSTEMR to compute
    *  the eigenspectrum using Relatively Robust Representations.  DSTEMR
    *  computes eigenvalues by the dqds algorithm, while orthogonal
    *  eigenvectors are computed from various "good" L D L^T representations
    *  (also known as Relatively Robust Representations). Gram-Schmidt
    *  orthogonalization is avoided as far as possible. More specifically,
    *  the various steps of the algorithm are as follows.
    *
    *  For each unreduced block (submatrix) of T,
    *     (a) Compute T - sigma I  = L D L^T, so that L and D
    *         define all the wanted eigenvalues to high relative accuracy.
    *         This means that small relative changes in the entries of D and L
    *         cause only small relative changes in the eigenvalues and
    *         eigenvectors. The standard (unfactored) representation of the
    *         tridiagonal matrix T does not have this property in general.
    *     (b) Compute the eigenvalues to suitable accuracy.
    *         If the eigenvectors are desired, the algorithm attains full
    *         accuracy of the computed eigenvalues only right before
    *         the corresponding vectors have to be computed, see steps c) and d).
    *     (c) For each cluster of close eigenvalues, select a new
    *         shift close to the cluster, find a new factorization, and refine
    *         the shifted eigenvalues to suitable accuracy.
    *     (d) For each eigenvalue with a large enough relative separation compute
    *         the corresponding eigenvector by forming a rank revealing twisted
    *         factorization. Go back to (c) for any clusters that remain.
    *
    *  The desired accuracy of the output can be specified by the input
    *  parameter ABSTOL.
    *
    *  For more details, see DSTEMR's documentation and:
    *  - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
    *    to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
    *    Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
    *  - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
    *    Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
    *    2004.  Also LAPACK Working Note 154.
    *  - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
    *    tridiagonal eigenvalue/eigenvector problem",
    *    Computer Science Division Technical Report No. UCB/CSD-97-971,
    *    UC Berkeley, May 1997.
    *
    *
    *  Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested
    *  on machines which conform to the ieee-754 floating point standard.
    *  DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and
    *  when partial spectrum requests are made.
    *
    *  Normal execution of DSTEMR may create NaNs and infinities and
    *  hence may abort due to a floating point exception in environments
    *  which do not handle NaNs and infinities in the ieee standard default
    *  manner.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  RANGE   (input) CHARACTER*1
    *          = 'A': all eigenvalues will be found.
    *          = 'V': all eigenvalues in the half-open interval (VL,VU]
    *                 will be found.
    *          = 'I': the IL-th through IU-th eigenvalues will be found.
    ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
    ********** DSTEIN are called
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
    *          On entry, the symmetric matrix A.  If UPLO = 'U', the
    *          leading N-by-N upper triangular part of A contains the
    *          upper triangular part of the matrix A.  If UPLO = 'L',
    *          the leading N-by-N lower triangular part of A contains
    *          the lower triangular part of the matrix A.
    *          On exit, the lower triangle (if UPLO='L') or the upper
    *          triangle (if UPLO='U') of A, including the diagonal, is
    *          destroyed.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  VL      (input) DOUBLE PRECISION
    *  VU      (input) DOUBLE PRECISION
    *          If RANGE='V', the lower and upper bounds of the interval to
    *          be searched for eigenvalues. VL < VU.
    *          Not referenced if RANGE = 'A' or 'I'.
    *
    *  IL      (input) INTEGER
    *  IU      (input) INTEGER
    *          If RANGE='I', the indices (in ascending order) of the
    *          smallest and largest eigenvalues to be returned.
    *          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
    *          Not referenced if RANGE = 'A' or 'V'.
    *
    *  ABSTOL  (input) DOUBLE PRECISION
    *          The absolute error tolerance for the eigenvalues.
    *          An approximate eigenvalue is accepted as converged
    *          when it is determined to lie in an interval [a,b]
    *          of width less than or equal to
    *
    *                  ABSTOL + EPS *   max( |a|,|b| ) ,
    *
    *          where EPS is the machine precision.  If ABSTOL is less than
    *          or equal to zero, then  EPS*|T|  will be used in its place,
    *          where |T| is the 1-norm of the tridiagonal matrix obtained
    *          by reducing A to tridiagonal form.
    *
    *          See "Computing Small Singular Values of Bidiagonal Matrices
    *          with Guaranteed High Relative Accuracy," by Demmel and
    *          Kahan, LAPACK Working Note #3.
    *
    *          If high relative accuracy is important, set ABSTOL to
    *          DLAMCH( 'Safe minimum' ).  Doing so will guarantee that
    *          eigenvalues are computed to high relative accuracy when
    *          possible in future releases.  The current code does not
    *          make any guarantees about high relative accuracy, but
    *          future releases will. See J. Barlow and J. Demmel,
    *          "Computing Accurate Eigensystems of Scaled Diagonally
    *          Dominant Matrices", LAPACK Working Note #7, for a discussion
    *          of which matrices define their eigenvalues to high relative
    *          accuracy.
    *
    *  M       (output) INTEGER
    *          The total number of eigenvalues found.  0 <= M <= N.
    *          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
    *
    *  W       (output) DOUBLE PRECISION array, dimension (N)
    *          The first M elements contain the selected eigenvalues in
    *          ascending order.
    *
    *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
    *          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
    *          contain the orthonormal eigenvectors of the matrix A
    *          corresponding to the selected eigenvalues, with the i-th
    *          column of Z holding the eigenvector associated with W(i).
    *          If JOBZ = 'N', then Z is not referenced.
    *          Note: the user must ensure that at least max(1,M) columns are
    *          supplied in the array Z; if RANGE = 'V', the exact value of M
    *          is not known in advance and an upper bound must be used.
    *          Supplying N columns is always safe.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', LDZ >= max(1,N).
    *
    *  ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )
    *          The support of the eigenvectors in Z, i.e., the indices
    *          indicating the nonzero elements in Z. The i-th eigenvector
    *          is nonzero only in elements ISUPPZ( 2*i-1 ) through
    *          ISUPPZ( 2*i ).
    ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.  LWORK >= max(1,26*N).
    *          For optimal efficiency, LWORK >= (NB+6)*N,
    *          where NB is the max of the blocksize for DSYTRD and DORMTR
    *          returned by ILAENV.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
    *          On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.
    *
    *  LIWORK  (input) INTEGER
    *          The dimension of the array IWORK.  LIWORK >= max(1,10*N).
    *
    *          If LIWORK = -1, then a workspace query is assumed; the
    *          routine only calculates the optimal size of the IWORK array,
    *          returns this value as the first entry of the IWORK array, and
    *          no error message related to LIWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  Internal error
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Inderjit Dhillon, IBM Almaden, USA
    *     Osni Marques, LBNL/NERSC, USA
    *     Ken Stanley, Computer Science Division, University of
    *       California at Berkeley, USA
    *     Jason Riedy, Computer Science Division, University of
    *       California at Berkeley, USA
    *
    * =====================================================================

            */

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2, long NR3, long NR4,
                long NC1, long NC2, long NC3, long NC4,
                typename MM
                >
            int syevr (
                const char jobz,
                const char range,
                const char uplo,
                matrix<T,NR1,NC1,MM,column_major_layout>& a,
                const double vl,
                const double vu,
                const integer il,
                const integer iu,
                const double abstol,
                integer& num_eigenvalues_found,
                matrix<T,NR2,NC2,MM,column_major_layout>& w,
                matrix<T,NR3,NC3,MM,column_major_layout>& z,
                matrix<integer,NR4,NC4,MM,column_major_layout>& isuppz
            )
            {
                matrix<T,0,1,MM,column_major_layout> work;
                matrix<integer,0,1,MM,column_major_layout> iwork;

                const long n = a.nr();

                w.set_size(n,1);

                isuppz.set_size(2*n, 1);

                if (jobz == 'V')
                {
                    z.set_size(n,n);
                }
                else
                {
                    z.set_size(NR3?NR3:1, NC3?NC3:1);
                }

                // figure out how big the workspace needs to be.
                T work_size = 1;
                integer iwork_size = 1;
                int info = binding::syevr(jobz, range, uplo, n, &a(0,0),
                                          a.nr(), vl, vu, il, iu, abstol, &num_eigenvalues_found,
                                          &w(0,0), &z(0,0), z.nr(), &isuppz(0,0), &work_size, -1,
                                          &iwork_size, -1);

                if (info != 0)
                    return info;

                if (work.size() < work_size)
                    work.set_size(static_cast<long>(work_size), 1);
                if (iwork.size() < iwork_size)
                    iwork.set_size(iwork_size, 1);

                // compute the actual decomposition
                info = binding::syevr(jobz, range, uplo, n, &a(0,0),
                                      a.nr(), vl, vu, il, iu, abstol, &num_eigenvalues_found,
                                      &w(0,0), &z(0,0), z.nr(), &isuppz(0,0), &work(0,0), work.size(),
                                      &iwork(0,0), iwork.size());

                return info;
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2, long NR3, long NR4,
                long NC1, long NC2, long NC3, long NC4,
                typename MM
                >
            int syevr (
                const char jobz,
                const char range,
                char uplo,
                matrix<T,NR1,NC1,MM,row_major_layout>& a,
                const double vl,
                const double vu,
                const integer il,
                const integer iu,
                const double abstol,
                integer& num_eigenvalues_found,
                matrix<T,NR2,NC2,MM,row_major_layout>& w,
                matrix<T,NR3,NC3,MM,row_major_layout>& z,
                matrix<integer,NR4,NC4,MM,row_major_layout>& isuppz
            )
            {
                matrix<T,0,1,MM,row_major_layout> work;
                matrix<integer,0,1,MM,row_major_layout> iwork;

                if (uplo == 'L')
                    uplo = 'U';
                else
                    uplo = 'L';

                const long n = a.nr();

                w.set_size(n,1);

                isuppz.set_size(2*n, 1);

                if (jobz == 'V')
                {
                    z.set_size(n,n);
                }
                else
                {
                    z.set_size(NR3?NR3:1, NC3?NC3:1);
                }

                // figure out how big the workspace needs to be.
                T work_size = 1;
                integer iwork_size = 1;
                int info = binding::syevr(jobz, range, uplo, n, &a(0,0),
                                          a.nc(), vl, vu, il, iu, abstol, &num_eigenvalues_found,
                                          &w(0,0), &z(0,0), z.nc(), &isuppz(0,0), &work_size, -1,
                                          &iwork_size, -1);

                if (info != 0)
                    return info;

                if (work.size() < work_size)
                    work.set_size(static_cast<long>(work_size), 1);
                if (iwork.size() < iwork_size)
                    iwork.set_size(iwork_size, 1);

                // compute the actual decomposition
                info = binding::syevr(jobz, range, uplo, n, &a(0,0),
                                      a.nc(), vl, vu, il, iu, abstol, &num_eigenvalues_found,
                                      &w(0,0), &z(0,0), z.nc(), &isuppz(0,0), &work(0,0), work.size(),
                                      &iwork(0,0), iwork.size());

                z = trans(z);

                return info;
            }

        // ------------------------------------------------------------------------------------

        }

    }

    // ----------------------------------------------------------------------------------------

    #endif // DLIB_LAPACk_EVR_Hh_