--- rpl/lapack/lapack/dorcsd2by1.f	2016/08/27 15:34:33	1.5
+++ rpl/lapack/lapack/dorcsd2by1.f	2017/06/17 10:53:58	1.6
@@ -2,8 +2,8 @@
 *
 *  =========== DOCUMENTATION ===========
 *
-* Online html documentation available at 
-*            http://www.netlib.org/lapack/explore-html/ 
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
 *> Download DORCSD2BY1 + dependencies
@@ -21,7 +21,7 @@
 *       SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
 *                              X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
 *                              LDV1T, WORK, LWORK, IWORK, INFO )
-* 
+*
 *       .. Scalar Arguments ..
 *       CHARACTER          JOBU1, JOBU2, JOBV1T
 *       INTEGER            INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
@@ -33,31 +33,30 @@
 *      $                   X11(LDX11,*), X21(LDX21,*)
 *       INTEGER            IWORK(*)
 *       ..
-*    
-* 
+*
+*
 *> \par Purpose:
 *> =============
 *>
 *>\verbatim
-*> Purpose:
-*> ========
 *>
 *> DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
 *> orthonormal columns that has been partitioned into a 2-by-1 block
 *> structure:
 *>
-*>                                [  I  0  0 ]
+*>                                [  I1 0  0 ]
 *>                                [  0  C  0 ]
 *>          [ X11 ]   [ U1 |    ] [  0  0  0 ]
 *>      X = [-----] = [---------] [----------] V1**T .
 *>          [ X21 ]   [    | U2 ] [  0  0  0 ]
 *>                                [  0  S  0 ]
-*>                                [  0  0  I ]
-*> 
+*>                                [  0  0  I2]
+*>
 *> X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
 *> (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
 *> nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
-*> R = MIN(P,M-P,Q,M-Q).
+*> R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a
+*> K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).
 *> \endverbatim
 *
 *  Arguments:
@@ -220,10 +219,10 @@
 *  Authors:
 *  ========
 *
-*> \author Univ. of Tennessee 
-*> \author Univ. of California Berkeley 
-*> \author Univ. of Colorado Denver 
-*> \author NAG Ltd. 
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
 *
 *> \date July 2012
 *
@@ -250,7 +249,7 @@
      $                   X11(LDX11,*), X21(LDX21,*)
       INTEGER            IWORK(*)
 *     ..
-*  
+*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -526,16 +525,16 @@
             CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
      $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
          END IF
-*   
+*
 *        Simultaneously diagonalize X11 and X21.
-*   
+*
          CALL DBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
      $                WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T,
      $                DUM2, 1, WORK(IB11D), WORK(IB11E),
      $                WORK(IB12D), WORK(IB12E), WORK(IB21D),
      $                WORK(IB21E), WORK(IB22D), WORK(IB22E),
      $                WORK(IBBCSD), LBBCSD, CHILDINFO )
-*   
+*
 *        Permute rows and columns to place zero submatrices in
 *        preferred positions
 *
@@ -580,16 +579,16 @@
             CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
      $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
          END IF
-*   
+*
 *        Simultaneously diagonalize X11 and X21.
-*   
+*
          CALL DBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
      $                WORK(IPHI), V1T, LDV1T, DUM2, 1, U1, LDU1, U2,
      $                LDU2, WORK(IB11D), WORK(IB11E), WORK(IB12D),
      $                WORK(IB12E), WORK(IB21D), WORK(IB21E),
      $                WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD,
      $                CHILDINFO )
-*   
+*
 *        Permute rows and columns to place identity submatrices in
 *        preferred positions
 *
@@ -635,16 +634,16 @@
             CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
      $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
          END IF
-*   
+*
 *        Simultaneously diagonalize X11 and X21.
-*   
+*
          CALL DBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
      $                THETA, WORK(IPHI), DUM2, 1, V1T, LDV1T, U2,
      $                LDU2, U1, LDU1, WORK(IB11D), WORK(IB11E),
      $                WORK(IB12D), WORK(IB12E), WORK(IB21D),
      $                WORK(IB21E), WORK(IB22D), WORK(IB22E),
      $                WORK(IBBCSD), LBBCSD, CHILDINFO )
-*   
+*
 *        Permute rows and columns to place identity submatrices in
 *        preferred positions
 *
@@ -704,16 +703,16 @@
             CALL DORGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
      $                   WORK(IORGLQ), LORGLQ, CHILDINFO )
          END IF
-*   
+*
 *        Simultaneously diagonalize X11 and X21.
-*   
+*
          CALL DBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
      $                THETA, WORK(IPHI), U2, LDU2, U1, LDU1, DUM2,
      $                1, V1T, LDV1T, WORK(IB11D), WORK(IB11E),
      $                WORK(IB12D), WORK(IB12E), WORK(IB21D),
      $                WORK(IB21E), WORK(IB22D), WORK(IB22E),
      $                WORK(IBBCSD), LBBCSD, CHILDINFO )
-*   
+*
 *        Permute rows and columns to place identity submatrices in
 *        preferred positions
 *