[BACK]Return to zgelss.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/zgelss.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:43 version 1.8, 2011/11/21 20:43:09
Line 1 Line 1
   *> \brief <b> ZGELSS solves overdetermined or underdetermined systems for GE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZGELSS + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelss.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelss.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelss.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
   *                          WORK, LWORK, RWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
   *       DOUBLE PRECISION   RCOND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * ), S( * )
   *       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGELSS computes the minimum norm solution to a complex linear
   *> least squares problem:
   *>
   *> Minimize 2-norm(| b - A*x |).
   *>
   *> using the singular value decomposition (SVD) of A. A is an M-by-N
   *> matrix which may be rank-deficient.
   *>
   *> Several right hand side vectors b and solution vectors x can be
   *> handled in a single call; they are stored as the columns of the
   *> M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
   *> X.
   *>
   *> The effective rank of A is determined by treating as zero those
   *> singular values which are less than RCOND times the largest singular
   *> value.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A. M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix A. N >= 0.
   *> \endverbatim
   *>
   *> \param[in] NRHS
   *> \verbatim
   *>          NRHS is INTEGER
   *>          The number of right hand sides, i.e., the number of columns
   *>          of the matrices B and X. NRHS >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA,N)
   *>          On entry, the M-by-N matrix A.
   *>          On exit, the first min(m,n) rows of A are overwritten with
   *>          its right singular vectors, stored rowwise.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A. LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
   *>          On entry, the M-by-NRHS right hand side matrix B.
   *>          On exit, B is overwritten by the N-by-NRHS solution matrix X.
   *>          If m >= n and RANK = n, the residual sum-of-squares for
   *>          the solution in the i-th column is given by the sum of
   *>          squares of the modulus of elements n+1:m in that column.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B.  LDB >= max(1,M,N).
   *> \endverbatim
   *>
   *> \param[out] S
   *> \verbatim
   *>          S is DOUBLE PRECISION array, dimension (min(M,N))
   *>          The singular values of A in decreasing order.
   *>          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
   *> \endverbatim
   *>
   *> \param[in] RCOND
   *> \verbatim
   *>          RCOND is DOUBLE PRECISION
   *>          RCOND is used to determine the effective rank of A.
   *>          Singular values S(i) <= RCOND*S(1) are treated as zero.
   *>          If RCOND < 0, machine precision is used instead.
   *> \endverbatim
   *>
   *> \param[out] RANK
   *> \verbatim
   *>          RANK is INTEGER
   *>          The effective rank of A, i.e., the number of singular values
   *>          which are greater than RCOND*S(1).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK. LWORK >= 1, and also:
   *>          LWORK >=  2*min(M,N) + max(M,N,NRHS)
   *>          For good performance, LWORK should generally be larger.
   *>
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (5*min(M,N))
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
   *>          > 0:  the algorithm for computing the SVD failed to converge;
   *>                if INFO = i, i off-diagonal elements of an intermediate
   *>                bidiagonal form did not converge to zero.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GEsolve
   *
   *  =====================================================================
       SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,        SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
      $                   WORK, LWORK, RWORK, INFO )       $                   WORK, LWORK, RWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK        INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
Line 15 Line 192
       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )        COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGELSS computes the minimum norm solution to a complex linear  
 *  least squares problem:  
 *  
 *  Minimize 2-norm(| b - A*x |).  
 *  
 *  using the singular value decomposition (SVD) of A. A is an M-by-N  
 *  matrix which may be rank-deficient.  
 *  
 *  Several right hand side vectors b and solution vectors x can be  
 *  handled in a single call; they are stored as the columns of the  
 *  M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix  
 *  X.  
 *  
 *  The effective rank of A is determined by treating as zero those  
 *  singular values which are less than RCOND times the largest singular  
 *  value.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix A. M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix A. N >= 0.  
 *  
 *  NRHS    (input) INTEGER  
 *          The number of right hand sides, i.e., the number of columns  
 *          of the matrices B and X. NRHS >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the M-by-N matrix A.  
 *          On exit, the first min(m,n) rows of A are overwritten with  
 *          its right singular vectors, stored rowwise.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,M).  
 *  
 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)  
 *          On entry, the M-by-NRHS right hand side matrix B.  
 *          On exit, B is overwritten by the N-by-NRHS solution matrix X.  
 *          If m >= n and RANK = n, the residual sum-of-squares for  
 *          the solution in the i-th column is given by the sum of  
 *          squares of the modulus of elements n+1:m in that column.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,M,N).  
 *  
 *  S       (output) DOUBLE PRECISION array, dimension (min(M,N))  
 *          The singular values of A in decreasing order.  
 *          The condition number of A in the 2-norm = S(1)/S(min(m,n)).  
 *  
 *  RCOND   (input) DOUBLE PRECISION  
 *          RCOND is used to determine the effective rank of A.  
 *          Singular values S(i) <= RCOND*S(1) are treated as zero.  
 *          If RCOND < 0, machine precision is used instead.  
 *  
 *  RANK    (output) INTEGER  
 *          The effective rank of A, i.e., the number of singular values  
 *          which are greater than RCOND*S(1).  
 *  
 *  WORK    (workspace/output) COMPLEX*16 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 >= 1, and also:  
 *          LWORK >=  2*min(M,N) + max(M,N,NRHS)  
 *          For good performance, LWORK should generally be larger.  
 *  
 *          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.  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (5*min(M,N))  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *          > 0:  the algorithm for computing the SVD failed to converge;  
 *                if INFO = i, i off-diagonal elements of an intermediate  
 *                bidiagonal form did not converge to zero.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 115 Line 206
       INTEGER            BL, CHUNK, I, IASCL, IBSCL, IE, IL, IRWORK,        INTEGER            BL, CHUNK, I, IASCL, IBSCL, IE, IL, IRWORK,
      $                   ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN,       $                   ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN,
      $                   MAXWRK, MINMN, MINWRK, MM, MNTHR       $                   MAXWRK, MINMN, MINWRK, MM, MNTHR
         INTEGER            LWORK_ZGEQRF, LWORK_ZUNMQR, LWORK_ZGEBRD,
        $                   LWORK_ZUNMBR, LWORK_ZUNGBR, LWORK_ZUNMLQ,
        $                   LWORK_ZGELQF
       DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR        DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR
 *     ..  *     ..
 *     .. Local Arrays ..  *     .. Local Arrays ..
       COMPLEX*16         VDUM( 1 )        COMPLEX*16         DUM( 1 )
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           DLABAD, DLASCL, DLASET, XERBLA, ZBDSQR, ZCOPY,        EXTERNAL           DLABAD, DLASCL, DLASET, XERBLA, ZBDSQR, ZCOPY,
Line 173 Line 267
 *              Path 1a - overdetermined, with many more rows than  *              Path 1a - overdetermined, with many more rows than
 *                        columns  *                        columns
 *  *
   *              Compute space needed for ZGEQRF
                  CALL ZGEQRF( M, N, A, LDA, DUM(1), DUM(1), -1, INFO )
                  LWORK_ZGEQRF=DUM(1)
   *              Compute space needed for ZUNMQR
                  CALL ZUNMQR( 'L', 'C', M, NRHS, N, A, LDA, DUM(1), B,
        $                   LDB, DUM(1), -1, INFO )
                  LWORK_ZUNMQR=DUM(1)
                MM = N                 MM = N
                MAXWRK = MAX( MAXWRK, N + N*ILAENV( 1, 'ZGEQRF', ' ', M,                 MAXWRK = MAX( MAXWRK, N + N*ILAENV( 1, 'ZGEQRF', ' ', M,
      $                       N, -1, -1 ) )       $                       N, -1, -1 ) )
Line 183 Line 284
 *  *
 *              Path 1 - overdetermined or exactly determined  *              Path 1 - overdetermined or exactly determined
 *  *
                MAXWRK = MAX( MAXWRK, 2*N + ( MM + N )*ILAENV( 1,  *              Compute space needed for ZGEBRD
      $                       'ZGEBRD', ' ', MM, N, -1, -1 ) )                 CALL ZGEBRD( MM, N, A, LDA, S, DUM(1), DUM(1),
                MAXWRK = MAX( MAXWRK, 2*N + NRHS*ILAENV( 1, 'ZUNMBR',       $                      DUM(1), DUM(1), -1, INFO )
      $                       'QLC', MM, NRHS, N, -1 ) )                 LWORK_ZGEBRD=DUM(1)
                MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1,  *              Compute space needed for ZUNMBR
      $                       'ZUNGBR', 'P', N, N, N, -1 ) )                 CALL ZUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, DUM(1),
        $                B, LDB, DUM(1), -1, INFO )
                  LWORK_ZUNMBR=DUM(1)
   *              Compute space needed for ZUNGBR
                  CALL ZUNGBR( 'P', N, N, N, A, LDA, DUM(1),
        $                   DUM(1), -1, INFO )
                  LWORK_ZUNGBR=DUM(1)
   *              Compute total workspace needed 
                  MAXWRK = MAX( MAXWRK, 2*N + LWORK_ZGEBRD )
                  MAXWRK = MAX( MAXWRK, 2*N + LWORK_ZUNMBR )
                  MAXWRK = MAX( MAXWRK, 2*N + LWORK_ZUNGBR )
                MAXWRK = MAX( MAXWRK, N*NRHS )                 MAXWRK = MAX( MAXWRK, N*NRHS )
                MINWRK = 2*N + MAX( NRHS, M )                 MINWRK = 2*N + MAX( NRHS, M )
             END IF              END IF
Line 199 Line 310
 *                 Path 2a - underdetermined, with many more columns  *                 Path 2a - underdetermined, with many more columns
 *                 than rows  *                 than rows
 *  *
                   MAXWRK = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1,  *                 Compute space needed for ZGELQF
      $                     -1 )                    CALL ZGELQF( M, N, A, LDA, DUM(1), DUM(1),
                   MAXWRK = MAX( MAXWRK, 3*M + M*M + 2*M*ILAENV( 1,       $                -1, INFO )
      $                          'ZGEBRD', ' ', M, M, -1, -1 ) )                    LWORK_ZGELQF=DUM(1)
                   MAXWRK = MAX( MAXWRK, 3*M + M*M + NRHS*ILAENV( 1,  *                 Compute space needed for ZGEBRD
      $                          'ZUNMBR', 'QLC', M, NRHS, M, -1 ) )                    CALL ZGEBRD( M, M, A, LDA, S, DUM(1), DUM(1),
                   MAXWRK = MAX( MAXWRK, 3*M + M*M + ( M - 1 )*ILAENV( 1,       $                      DUM(1), DUM(1), -1, INFO )
      $                          'ZUNGBR', 'P', M, M, M, -1 ) )                    LWORK_ZGEBRD=DUM(1)
   *                 Compute space needed for ZUNMBR
                     CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, 
        $                DUM(1), B, LDB, DUM(1), -1, INFO )
                     LWORK_ZUNMBR=DUM(1)
   *                 Compute space needed for ZUNGBR
                     CALL ZUNGBR( 'P', M, M, M, A, LDA, DUM(1),
        $                   DUM(1), -1, INFO )
                     LWORK_ZUNGBR=DUM(1)
   *                 Compute space needed for ZUNMLQ
                     CALL ZUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, DUM(1),
        $                 B, LDB, DUM(1), -1, INFO )
                     LWORK_ZUNMLQ=DUM(1)
   *                 Compute total workspace needed 
                     MAXWRK = M + LWORK_ZGELQF
                     MAXWRK = MAX( MAXWRK, 3*M + M*M + LWORK_ZGEBRD )
                     MAXWRK = MAX( MAXWRK, 3*M + M*M + LWORK_ZUNMBR )
                     MAXWRK = MAX( MAXWRK, 3*M + M*M + LWORK_ZUNGBR )
                   IF( NRHS.GT.1 ) THEN                    IF( NRHS.GT.1 ) THEN
                      MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS )                       MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS )
                   ELSE                    ELSE
                      MAXWRK = MAX( MAXWRK, M*M + 2*M )                       MAXWRK = MAX( MAXWRK, M*M + 2*M )
                   END IF                    END IF
                   MAXWRK = MAX( MAXWRK, M + NRHS*ILAENV( 1, 'ZUNMLQ',                    MAXWRK = MAX( MAXWRK, M + LWORK_ZUNMLQ )
      $                          'LC', N, NRHS, M, -1 ) )  
                ELSE                 ELSE
 *  *
 *                 Path 2 - underdetermined  *                 Path 2 - underdetermined
 *  *
                   MAXWRK = 2*M + ( N + M )*ILAENV( 1, 'ZGEBRD', ' ', M,  *                 Compute space needed for ZGEBRD
      $                     N, -1, -1 )                    CALL ZGEBRD( M, N, A, LDA, S, DUM(1), DUM(1),
                   MAXWRK = MAX( MAXWRK, 2*M + NRHS*ILAENV( 1, 'ZUNMBR',       $                      DUM(1), DUM(1), -1, INFO )
      $                          'QLC', M, NRHS, M, -1 ) )                    LWORK_ZGEBRD=DUM(1)
                   MAXWRK = MAX( MAXWRK, 2*M + M*ILAENV( 1, 'ZUNGBR',  *                 Compute space needed for ZUNMBR
      $                          'P', M, N, M, -1 ) )                    CALL ZUNMBR( 'Q', 'L', 'C', M, NRHS, M, A, LDA, 
        $                DUM(1), B, LDB, DUM(1), -1, INFO )
                     LWORK_ZUNMBR=DUM(1)
   *                 Compute space needed for ZUNGBR
                     CALL ZUNGBR( 'P', M, N, M, A, LDA, DUM(1),
        $                   DUM(1), -1, INFO )
                     LWORK_ZUNGBR=DUM(1)
                     MAXWRK = 2*M + LWORK_ZGEBRD
                     MAXWRK = MAX( MAXWRK, 2*M + LWORK_ZUNMBR )
                     MAXWRK = MAX( MAXWRK, 2*M + LWORK_ZUNGBR )
                   MAXWRK = MAX( MAXWRK, N*NRHS )                    MAXWRK = MAX( MAXWRK, N*NRHS )
                END IF                 END IF
             END IF              END IF
Line 371 Line 507
 *        (CWorkspace: none)  *        (CWorkspace: none)
 *        (RWorkspace: need BDSPAC)  *        (RWorkspace: need BDSPAC)
 *  *
          CALL ZBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,           CALL ZBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, DUM,
      $                1, B, LDB, RWORK( IRWORK ), INFO )       $                1, B, LDB, RWORK( IRWORK ), INFO )
          IF( INFO.NE.0 )           IF( INFO.NE.0 )
      $      GO TO 70       $      GO TO 70
Line 568 Line 704
 *        (CWorkspace: none)  *        (CWorkspace: none)
 *        (RWorkspace: need BDSPAC)  *        (RWorkspace: need BDSPAC)
 *  *
          CALL ZBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,           CALL ZBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, DUM,
      $                1, B, LDB, RWORK( IRWORK ), INFO )       $                1, B, LDB, RWORK( IRWORK ), INFO )
          IF( INFO.NE.0 )           IF( INFO.NE.0 )
      $      GO TO 70       $      GO TO 70
Removed from v.1.7  
changed lines
  Added in v.1.8

CVSweb interface <joel.bertrand@systella.fr>