--- rpl/lapack/lapack/dggsvp.f	2010/12/21 13:53:27	1.7
+++ rpl/lapack/lapack/dggsvp.f	2011/07/22 07:38:05	1.8
@@ -2,10 +2,10 @@
      $                   TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
      $                   IWORK, TAU, WORK, INFO )
 *
-*  -- LAPACK routine (version 3.2) --
+*  -- LAPACK routine (version 3.3.1) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
+*  -- April 2011                                                      --
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBQ, JOBU, JOBV
@@ -23,24 +23,23 @@
 *
 *  DGGSVP computes orthogonal matrices U, V and Q such that
 *
-*                   N-K-L  K    L
-*   U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
-*                L ( 0     0   A23 )
-*            M-K-L ( 0     0    0  )
+*                     N-K-L  K    L
+*   U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
+*                  L ( 0     0   A23 )
+*              M-K-L ( 0     0    0  )
 *
 *                   N-K-L  K    L
 *          =     K ( 0    A12  A13 )  if M-K-L < 0;
 *              M-K ( 0     0   A23 )
 *
-*                 N-K-L  K    L
-*   V'*B*Q =   L ( 0     0   B13 )
-*            P-L ( 0     0    0  )
+*                   N-K-L  K    L
+*   V**T*B*Q =   L ( 0     0   B13 )
+*              P-L ( 0     0    0  )
 *
 *  where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 *  upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 *  otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
-*  numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the
-*  transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -99,8 +98,8 @@
 *  K       (output) INTEGER
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
-*          described in Purpose.
-*          K + L = effective numerical rank of (A',B')'.
+*          described in Purpose section.
+*          K + L = effective numerical rank of (A**T,B**T)**T.
 *
 *  U       (output) DOUBLE PRECISION array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the orthogonal matrix U.
@@ -258,14 +257,14 @@
 *
          CALL DGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**T
 *
          CALL DORMR2( 'Right', 'Transpose', M, N, L, B, LDB, TAU, A,
      $                LDA, WORK, INFO )
 *
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**T
 *
             CALL DORMR2( 'Right', 'Transpose', N, N, L, B, LDB, TAU, Q,
      $                   LDQ, WORK, INFO )
@@ -287,7 +286,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**T
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -303,7 +302,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL DORM2R( 'Left', 'Transpose', M, L, MIN( M, N-L ), A, LDA,
      $             TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -345,7 +344,7 @@
 *
          IF( WANTQ ) THEN
 *
-*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1'
+*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T
 *
             CALL DORMR2( 'Right', 'Transpose', N, N-L, K, A, LDA, TAU,
      $                   Q, LDQ, WORK, INFO )