--- rpl/lapack/lapack/dggsvd.f	2010/12/21 13:53:27	1.7
+++ rpl/lapack/lapack/dggsvd.f	2011/07/22 07:38:05	1.8
@@ -2,10 +2,10 @@
      $                   LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
      $                   IWORK, INFO )
 *
-*  -- LAPACK driver routine (version 3.2) --
+*  -- LAPACK driver 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
@@ -24,10 +24,10 @@
 *  DGGSVD computes the generalized singular value decomposition (GSVD)
 *  of an M-by-N real matrix A and P-by-N real matrix B:
 *
-*      U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R )
+*        U**T*A*Q = D1*( 0 R ),    V**T*B*Q = D2*( 0 R )
 *
-*  where U, V and Q are orthogonal matrices, and Z' is the transpose
-*  of Z.  Let K+L = the effective numerical rank of the matrix (A',B')',
+*  where U, V and Q are orthogonal matrices.
+*  Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T,
 *  then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
 *  D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
 *  following structures, respectively:
@@ -86,13 +86,13 @@
 *
 *  In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
 *  A and B implicitly gives the SVD of A*inv(B):
-*                       A*inv(B) = U*(D1*inv(D2))*V'.
-*  If ( A',B')' has orthonormal columns, then the GSVD of A and B is
+*                       A*inv(B) = U*(D1*inv(D2))*V**T.
+*  If ( A**T,B**T)**T  has orthonormal columns, then the GSVD of A and B is
 *  also equal to the CS decomposition of A and B. Furthermore, the GSVD
 *  can be used to derive the solution of the eigenvalue problem:
-*                       A'*A x = lambda* B'*B x.
+*                       A**T*A x = lambda* B**T*B x.
 *  In some literature, the GSVD of A and B is presented in the form
-*                   U'*A*X = ( 0 D1 ),   V'*B*X = ( 0 D2 )
+*                   U**T*A*X = ( 0 D1 ),   V**T*B*X = ( 0 D2 )
 *  where U and V are orthogonal and X is nonsingular, D1 and D2 are
 *  ``diagonal''.  The former GSVD form can be converted to the latter
 *  form by taking the nonsingular matrix X as
@@ -128,7 +128,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in the Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**T,B**T)**T.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
@@ -209,7 +209,7 @@
 *  TOLA    DOUBLE PRECISION
 *  TOLB    DOUBLE PRECISION
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')'. Generally, they are set to
+*          rank of (A',B')**T. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MAZHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MAZHEPS.
 *          The size of TOLA and TOLB may affect the size of backward