--- rpl/lapack/lapack/zggsvp.f	2010/12/21 13:53:45	1.7
+++ rpl/lapack/lapack/zggsvp.f	2011/07/22 07:38:14	1.8
@@ -2,10 +2,10 @@
      $                   TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
      $                   IWORK, RWORK, 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
@@ -24,24 +24,23 @@
 *
 *  ZGGSVP computes unitary 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**H*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**H*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
-*  conjugate transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -101,7 +100,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**H,B**H)**H.
 *
 *  U       (output) COMPLEX*16 array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the unitary matrix U.
@@ -268,13 +267,13 @@
 *
          CALL ZGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**H
 *
          CALL ZUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB,
      $                TAU, A, LDA, WORK, INFO )
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**H
 *
             CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N, L, B,
      $                   LDB, TAU, Q, LDQ, WORK, INFO )
@@ -296,7 +295,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**H
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -312,7 +311,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL ZUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ),
      $             A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -354,7 +353,7 @@
 *
          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**H
 *
             CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A,
      $                   LDA, TAU, Q, LDQ, WORK, INFO )