Integrating Doxygen in comments

1 files changed, 177 insertions, 97 deletions

diff --git a/SRC/sggglm.f b/SRC/sggglm.f
index 833dea90..3f483759 100644
--- a/SRC/sggglm.f
+++ b/SRC/sggglm.f
@@ -1,10 +1,185 @@
+*> \brief <b> SGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition
+*  ==========
+*
+*       SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
+*                          INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, LDB, LWORK, M, N, P
+*       ..
+*       .. Array Arguments ..
+*       REAL               A( LDA, * ), B( LDB, * ), D( * ), WORK( * ),
+*      $                   X( * ), Y( * )
+*       ..
+*  
+*  Purpose
+*  =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SGGGLM solves a general Gauss-Markov linear model (GLM) problem:
+*>
+*>         minimize || y ||_2   subject to   d = A*x + B*y
+*>             x
+*>
+*> where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
+*> given N-vector. It is assumed that M <= N <= M+P, and
+*>
+*>            rank(A) = M    and    rank( A B ) = N.
+*>
+*> Under these assumptions, the constrained equation is always
+*> consistent, and there is a unique solution x and a minimal 2-norm
+*> solution y, which is obtained using a generalized QR factorization
+*> of the matrices (A, B) given by
+*>
+*>    A = Q*(R),   B = Q*T*Z.
+*>          (0)
+*>
+*> In particular, if matrix B is square nonsingular, then the problem
+*> GLM is equivalent to the following weighted linear least squares
+*> problem
+*>
+*>              minimize || inv(B)*(d-A*x) ||_2
+*>                  x
+*>
+*> where inv(B) denotes the inverse of B.
+*>
+*>\endverbatim
+*
+*  Arguments
+*  =========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of rows of the matrices A and B.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of columns of the matrix A.  0 <= M <= N.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*>          P is INTEGER
+*>          The number of columns of the matrix B.  P >= N-M.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is REAL array, dimension (LDA,M)
+*>          On entry, the N-by-M matrix A.
+*>          On exit, the upper triangular part of the array A contains
+*>          the M-by-M upper triangular matrix R.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is REAL array, dimension (LDB,P)
+*>          On entry, the N-by-P matrix B.
+*>          On exit, if N <= P, the upper triangle of the subarray
+*>          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
+*>          if N > P, the elements on and above the (N-P)th subdiagonal
+*>          contain the N-by-P upper trapezoidal matrix T.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is REAL array, dimension (N)
+*>          On entry, D is the left hand side of the GLM equation.
+*>          On exit, D is destroyed.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*>          X is REAL array, dimension (M)
+*> \param[out] Y
+*> \verbatim
+*>          Y is REAL array, dimension (P)
+*>          On exit, X and Y are the solutions of the GLM problem.
+*> \endverbatim
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is REAL array, dimension (MAX(1,LWORK))
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          LWORK is INTEGER
+*>          The dimension of the array WORK. LWORK >= max(1,N+M+P).
+*>          For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,
+*>          where NB is an upper bound for the optimal blocksizes for
+*>          SGEQRF, SGERQF, SORMQR and SORMRQ.
+*> \endverbatim
+*> \verbatim
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the WORK array, returns
+*>          this value as the first entry of the WORK array, and no error
+*>          message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>          = 1:  the upper triangular factor R associated with A in the
+*>                generalized QR factorization of the pair (A, B) is
+*>                singular, so that rank(A) < M; the least squares
+*>                solution could not be computed.
+*>          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
+*>                factor T associated with B in the generalized QR
+*>                factorization of the pair (A, B) is singular, so that
+*>                rank( A B ) < N; the least squares solution could not
+*>                be computed.
+*> \endverbatim
+*>
+*
+*  Authors
+*  =======
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup realOTHEReigen
+*
+*  =====================================================================
       SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
      $                   INFO )
 *
-*  -- LAPACK driver routine (version 3.3.1) --
+*  -- LAPACK eigen 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..--
-*  -- April 2011                                                      --
+*     November 2011
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, P
@@ -14,101 +189,6 @@
      $                   X( * ), Y( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  SGGGLM solves a general Gauss-Markov linear model (GLM) problem:
-*
-*          minimize || y ||_2   subject to   d = A*x + B*y
-*              x
-*
-*  where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
-*  given N-vector. It is assumed that M <= N <= M+P, and
-*
-*             rank(A) = M    and    rank( A B ) = N.
-*
-*  Under these assumptions, the constrained equation is always
-*  consistent, and there is a unique solution x and a minimal 2-norm
-*  solution y, which is obtained using a generalized QR factorization
-*  of the matrices (A, B) given by
-*
-*     A = Q*(R),   B = Q*T*Z.
-*           (0)
-*
-*  In particular, if matrix B is square nonsingular, then the problem
-*  GLM is equivalent to the following weighted linear least squares
-*  problem
-*
-*               minimize || inv(B)*(d-A*x) ||_2
-*                   x
-*
-*  where inv(B) denotes the inverse of B.
-*
-*  Arguments
-*  =========
-*
-*  N       (input) INTEGER
-*          The number of rows of the matrices A and B.  N >= 0.
-*
-*  M       (input) INTEGER
-*          The number of columns of the matrix A.  0 <= M <= N.
-*
-*  P       (input) INTEGER
-*          The number of columns of the matrix B.  P >= N-M.
-*
-*  A       (input/output) REAL array, dimension (LDA,M)
-*          On entry, the N-by-M matrix A.
-*          On exit, the upper triangular part of the array A contains
-*          the M-by-M upper triangular matrix R.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A. LDA >= max(1,N).
-*
-*  B       (input/output) REAL array, dimension (LDB,P)
-*          On entry, the N-by-P matrix B.
-*          On exit, if N <= P, the upper triangle of the subarray
-*          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
-*          if N > P, the elements on and above the (N-P)th subdiagonal
-*          contain the N-by-P upper trapezoidal matrix T.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B. LDB >= max(1,N).
-*
-*  D       (input/output) REAL array, dimension (N)
-*          On entry, D is the left hand side of the GLM equation.
-*          On exit, D is destroyed.
-*
-*  X       (output) REAL array, dimension (M)
-*  Y       (output) REAL array, dimension (P)
-*          On exit, X and Y are the solutions of the GLM problem.
-*
-*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
-*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-*  LWORK   (input) INTEGER
-*          The dimension of the array WORK. LWORK >= max(1,N+M+P).
-*          For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,
-*          where NB is an upper bound for the optimal blocksizes for
-*          SGEQRF, SGERQF, SORMQR and SORMRQ.
-*
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit.
-*          < 0:  if INFO = -i, the i-th argument had an illegal value.
-*          = 1:  the upper triangular factor R associated with A in the
-*                generalized QR factorization of the pair (A, B) is
-*                singular, so that rank(A) < M; the least squares
-*                solution could not be computed.
-*          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
-*                factor T associated with B in the generalized QR
-*                factorization of the pair (A, B) is singular, so that
-*                rank( A B ) < N; the least squares solution could not
-*                be computed.
-*
 *  ===================================================================
 *
 *     .. Parameters ..