xORCSD2BY1, xUNCSD2BY1: fix U2 orthogonality

The xORCSD2BY1/xUNCSD2BY1 output matrix U2 was clearly not
orthogonal/unitary for certain input matrix dimensions m, p, and q
(e.g., m = 260, p=130, q=131). The reason was an accidental overwrite of
data by xORGQR()/xUNGQR() when the WORK array was apparently large
enough to use blocking.

Author: christoph-conrads

SRC/cuncsd2by1.f

@@ -711,6 +711,10 @@ SUBROUTINE CUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
 *
 *        Accumulate Householder reflectors
 *
+
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL CCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+         END IF
          IF( WANTU1 .AND. P .GT. 0 ) THEN
             CALL CCOPY( P, WORK(IORBDB), 1, U1, 1 )
             DO J = 2, P
@@ -722,7 +726,6 @@ SUBROUTINE CUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
      $                   WORK(IORGQR), LORGQR, CHILDINFO )
          END IF
          IF( WANTU2 .AND. M-P .GT. 0 ) THEN
-            CALL CCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
             DO J = 2, M-P
                U2(1,J) = ZERO
             END DO

SRC/dorcsd2by1.f

@@ -674,6 +674,9 @@ SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
 *
 *        Accumulate Householder reflectors
 *
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL DCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+         END IF
          IF( WANTU1 .AND. P .GT. 0 ) THEN
             CALL DCOPY( P, WORK(IORBDB), 1, U1, 1 )
             DO J = 2, P
@@ -685,7 +688,6 @@ SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
      $                   WORK(IORGQR), LORGQR, CHILDINFO )
          END IF
          IF( WANTU2 .AND. M-P .GT. 0 ) THEN
-            CALL DCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
             DO J = 2, M-P
                U2(1,J) = ZERO
             END DO

SRC/sorcsd2by1.f

@@ -674,6 +674,9 @@ SUBROUTINE SORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
 *
 *        Accumulate Householder reflectors
 *
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL SCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+         END IF
          IF( WANTU1 .AND. P .GT. 0 ) THEN
             CALL SCOPY( P, WORK(IORBDB), 1, U1, 1 )
             DO J = 2, P
@@ -685,7 +688,6 @@ SUBROUTINE SORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
      $                   WORK(IORGQR), LORGQR, CHILDINFO )
          END IF
          IF( WANTU2 .AND. M-P .GT. 0 ) THEN
-            CALL SCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
             DO J = 2, M-P
                U2(1,J) = ZERO
             END DO

SRC/zuncsd2by1.f

@@ -709,6 +709,9 @@ SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
 *
 *        Accumulate Householder reflectors
 *
+         IF( WANTU2 .AND. M-P .GT. 0 ) THEN
+            CALL ZCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
+         END IF
          IF( WANTU1 .AND. P .GT. 0 ) THEN
             CALL ZCOPY( P, WORK(IORBDB), 1, U1, 1 )
             DO J = 2, P
@@ -720,7 +723,6 @@ SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
      $                   WORK(IORGQR), LORGQR, CHILDINFO )
          END IF
          IF( WANTU2 .AND. M-P .GT. 0 ) THEN
-            CALL ZCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
             DO J = 2, M-P
                U2(1,J) = ZERO
             END DO