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Diff for /rpl/lapack/lapack/dorcsd2by1.f between versions 1.2 and 1.3

version 1.2, 2014/01/27 09:28:24 version 1.3, 2015/11/26 11:44:19
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 *>                                [  0  S  0 ]  *>                                [  0  S  0 ]
 *>                                [  0  0  I ]  *>                                [  0  0  I ]
 *>   *> 
 *> X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,  *> X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
 *> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are  *> (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
 *> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in  *> nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
 *> which R = MIN(P,M-P,Q,M-Q).  *> R = MIN(P,M-P,Q,M-Q).
 *>  *> \endverbatim
 *>\endverbatim  
 *  *
 *  Arguments:  *  Arguments:
 *  ==========  *  ==========
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 *> \param[in] JOBU1  *> \param[in] JOBU1
 *> \verbatim  *> \verbatim
 *>          JOBU1 is CHARACTER  *>          JOBU1 is CHARACTER
 *>           = 'Y':      U1 is computed;  *>          = 'Y':      U1 is computed;
 *>           otherwise:  U1 is not computed.  *>          otherwise:  U1 is not computed.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] JOBU2  *> \param[in] JOBU2
 *> \verbatim  *> \verbatim
 *>          JOBU2 is CHARACTER  *>          JOBU2 is CHARACTER
 *>           = 'Y':      U2 is computed;  *>          = 'Y':      U2 is computed;
 *>           otherwise:  U2 is not computed.  *>          otherwise:  U2 is not computed.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] JOBV1T  *> \param[in] JOBV1T
 *> \verbatim  *> \verbatim
 *>          JOBV1T is CHARACTER  *>          JOBV1T is CHARACTER
 *>           = 'Y':      V1T is computed;  *>          = 'Y':      V1T is computed;
 *>           otherwise:  V1T is not computed.  *>          otherwise:  V1T is not computed.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] M  *> \param[in] M
 *> \verbatim  *> \verbatim
 *>          M is INTEGER  *>          M is INTEGER
 *>           The number of rows and columns in X.  *>          The number of rows in X.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] P  *> \param[in] P
 *> \verbatim  *> \verbatim
 *>          P is INTEGER  *>          P is INTEGER
 *>           The number of rows in X11 and X12. 0 <= P <= M.  *>          The number of rows in X11. 0 <= P <= M.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] Q  *> \param[in] Q
 *> \verbatim  *> \verbatim
 *>          Q is INTEGER  *>          Q is INTEGER
 *>           The number of columns in X11 and X21. 0 <= Q <= M.  *>          The number of columns in X11 and X21. 0 <= Q <= M.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] X11  *> \param[in,out] X11
 *> \verbatim  *> \verbatim
 *>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)  *>          X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
 *>           On entry, part of the orthogonal matrix whose CSD is  *>          On entry, part of the orthogonal matrix whose CSD is desired.
 *>           desired.  
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDX11  *> \param[in] LDX11
 *> \verbatim  *> \verbatim
 *>          LDX11 is INTEGER  *>          LDX11 is INTEGER
 *>           The leading dimension of X11. LDX11 >= MAX(1,P).  *>          The leading dimension of X11. LDX11 >= MAX(1,P).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] X21  *> \param[in,out] X21
 *> \verbatim  *> \verbatim
 *>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)  *>          X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
 *>           On entry, part of the orthogonal matrix whose CSD is  *>          On entry, part of the orthogonal matrix whose CSD is desired.
 *>           desired.  
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDX21  *> \param[in] LDX21
 *> \verbatim  *> \verbatim
 *>          LDX21 is INTEGER  *>          LDX21 is INTEGER
 *>           The leading dimension of X21. LDX21 >= MAX(1,M-P).  *>          The leading dimension of X21. LDX21 >= MAX(1,M-P).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] THETA  *> \param[out] THETA
 *> \verbatim  *> \verbatim
 *>          THETA is DOUBLE PRECISION array, dimension (R), in which R =  *>          THETA is DOUBLE PRECISION array, dimension (R), in which R =
 *>           MIN(P,M-P,Q,M-Q).  *>          MIN(P,M-P,Q,M-Q).
 *>           C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and  *>          C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
 *>           S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).  *>          S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] U1  *> \param[out] U1
 *> \verbatim  *> \verbatim
 *>          U1 is DOUBLE PRECISION array, dimension (P)  *>          U1 is DOUBLE PRECISION array, dimension (P)
 *>           If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.  *>          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDU1  *> \param[in] LDU1
 *> \verbatim  *> \verbatim
 *>          LDU1 is INTEGER  *>          LDU1 is INTEGER
 *>           The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=  *>          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
 *>           MAX(1,P).  *>          MAX(1,P).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] U2  *> \param[out] U2
 *> \verbatim  *> \verbatim
 *>          U2 is DOUBLE PRECISION array, dimension (M-P)  *>          U2 is DOUBLE PRECISION array, dimension (M-P)
 *>           If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal  *>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
 *>           matrix U2.  *>          matrix U2.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDU2  *> \param[in] LDU2
 *> \verbatim  *> \verbatim
 *>          LDU2 is INTEGER  *>          LDU2 is INTEGER
 *>           The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=  *>          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
 *>           MAX(1,M-P).  *>          MAX(1,M-P).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] V1T  *> \param[out] V1T
 *> \verbatim  *> \verbatim
 *>          V1T is DOUBLE PRECISION array, dimension (Q)  *>          V1T is DOUBLE PRECISION array, dimension (Q)
 *>           If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal  *>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
 *>           matrix V1**T.  *>          matrix V1**T.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDV1T  *> \param[in] LDV1T
 *> \verbatim  *> \verbatim
 *>          LDV1T is INTEGER  *>          LDV1T is INTEGER
 *>           The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=  *>          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
 *>           MAX(1,Q).  *>          MAX(1,Q).
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] WORK  *> \param[out] WORK
 *> \verbatim  *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))  *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 *>           On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *>           If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),  *>          If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
 *>           ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),  *>          ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
 *>           define the matrix in intermediate bidiagonal-block form  *>          define the matrix in intermediate bidiagonal-block form
 *>           remaining after nonconvergence. INFO specifies the number  *>          remaining after nonconvergence. INFO specifies the number
 *>           of nonzero PHI's.  *>          of nonzero PHI's.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LWORK  *> \param[in] LWORK
 *> \verbatim  *> \verbatim
 *>          LWORK is INTEGER  *>          LWORK is INTEGER
 *>           The dimension of the array WORK.  *>          The dimension of the array WORK.
   *>
   *>          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  *> \endverbatim
 *>  *>
 *>           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.  
 *> \param[out] IWORK  *> \param[out] IWORK
 *> \verbatim  *> \verbatim
 *>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))  *>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
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 *> \param[out] INFO  *> \param[out] INFO
 *> \verbatim  *> \verbatim
 *>          INFO is INTEGER  *>          INFO is INTEGER
 *>           = 0:  successful exit.  *>          = 0:  successful exit.
 *>           < 0:  if INFO = -i, the i-th argument had an illegal value.  *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>           > 0:  DBBCSD did not converge. See the description of WORK  *>          > 0:  DBBCSD did not converge. See the description of WORK
 *>                above for details.  *>                above for details.
 *> \endverbatim  *> \endverbatim
 *  *
   *> \par References:
   *  ================
   *>
   *>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
   *>      Algorithms, 50(1):33-65, 2009.
   *
 *  Authors:  *  Authors:
 *  ========  *  ========
 *  *
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 *  *
 *> \ingroup doubleOTHERcomputational  *> \ingroup doubleOTHERcomputational
 *  *
 *> \par References:  
 *  ================  
 *>  
 *>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.  
 *>      Algorithms, 50(1):33-65, 2009.  
 *> \endverbatim  
 *>  
 *  =====================================================================  *  =====================================================================
       SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,        SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
      $                       X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,       $                       X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
Removed from v.1.2  
changed lines
  Added in v.1.3

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