Integrating Doxygen in comments

1 files changed, 225 insertions, 132 deletions

diff --git a/SRC/cgelsd.f b/SRC/cgelsd.f
index 2b17e7af..d47c9daf 100644
--- a/SRC/cgelsd.f
+++ b/SRC/cgelsd.f
@@ -1,10 +1,233 @@
+*> \brief <b> CGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices</b>
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition
+*  ==========
+*
+*       SUBROUTINE CGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
+*                          WORK, LWORK, RWORK, IWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
+*       REAL               RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IWORK( * )
+*       REAL               RWORK( * ), S( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*  
+*  Purpose
+*  =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> CGELSD computes the minimum-norm solution to a real linear least
+*> squares problem:
+*>     minimize 2-norm(| b - A*x |)
+*> using the singular value decomposition (SVD) of A. A is an M-by-N
+*> matrix which may be rank-deficient.
+*>
+*> Several right hand side vectors b and solution vectors x can be
+*> handled in a single call; they are stored as the columns of the
+*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
+*> matrix X.
+*>
+*> The problem is solved in three steps:
+*> (1) Reduce the coefficient matrix A to bidiagonal form with
+*>     Householder tranformations, reducing the original problem
+*>     into a "bidiagonal least squares problem" (BLS)
+*> (2) Solve the BLS using a divide and conquer approach.
+*> (3) Apply back all the Householder tranformations to solve
+*>     the original least squares problem.
+*>
+*> The effective rank of A is determined by treating as zero those
+*> singular values which are less than RCOND times the largest singular
+*> value.
+*>
+*> The divide and conquer algorithm makes very mild assumptions about
+*> floating point arithmetic. It will work on machines with a guard
+*> digit in add/subtract, or on those binary machines without guard
+*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
+*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
+*> without guard digits, but we know of none.
+*>
+*>\endverbatim
+*
+*  Arguments
+*  =========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrices B and X. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX array, dimension (LDA,N)
+*>          On entry, the M-by-N matrix A.
+*>          On exit, A has been destroyed.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the M-by-NRHS right hand side matrix B.
+*>          On exit, B is overwritten by the N-by-NRHS solution matrix X.
+*>          If m >= n and RANK = n, the residual sum-of-squares for
+*>          the solution in the i-th column is given by the sum of
+*>          squares of the modulus of elements n+1:m in that column.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,M,N).
+*> \endverbatim
+*>
+*> \param[out] S
+*> \verbatim
+*>          S is REAL array, dimension (min(M,N))
+*>          The singular values of A in decreasing order.
+*>          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
+*> \endverbatim
+*>
+*> \param[in] RCOND
+*> \verbatim
+*>          RCOND is REAL
+*>          RCOND is used to determine the effective rank of A.
+*>          Singular values S(i) <= RCOND*S(1) are treated as zero.
+*>          If RCOND < 0, machine precision is used instead.
+*> \endverbatim
+*>
+*> \param[out] RANK
+*> \verbatim
+*>          RANK is INTEGER
+*>          The effective rank of A, i.e., the number of singular values
+*>          which are greater than RCOND*S(1).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX 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 must be at least 1.
+*>          The exact minimum amount of workspace needed depends on M,
+*>          N and NRHS. As long as LWORK is at least
+*>              2 * N + N * NRHS
+*>          if M is greater than or equal to N or
+*>              2 * M + M * NRHS
+*>          if M is less than N, the code will execute correctly.
+*>          For good performance, LWORK should generally be larger.
+*> \endverbatim
+*> \verbatim
+*>          If LWORK = -1, then a workspace query is assumed; the routine
+*>          only calculates the optimal size of the array WORK and the
+*>          minimum sizes of the arrays RWORK and IWORK, and returns
+*>          these values as the first entries of the WORK, RWORK and
+*>          IWORK arrays, and no error message related to LWORK is issued
+*>          by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*>          RWORK is REAL array, dimension (MAX(1,LRWORK))
+*>          LRWORK >=
+*>             10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
+*>             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
+*>          if M is greater than or equal to N or
+*>             10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
+*>             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
+*>          if M is less than N, the code will execute correctly.
+*>          SMLSIZ is returned by ILAENV and is equal to the maximum
+*>          size of the subproblems at the bottom of the computation
+*>          tree (usually about 25), and
+*>             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*>          On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
+*>          LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),
+*>          where MINMN = MIN( M,N ).
+*>          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0: successful exit
+*>          < 0: if INFO = -i, the i-th argument had an illegal value.
+*>          > 0:  the algorithm for computing the SVD failed to converge;
+*>                if INFO = i, i off-diagonal elements of an intermediate
+*>                bidiagonal form did not converge to zero.
+*> \endverbatim
+*>
+*
+*  Authors
+*  =======
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complexGEsolve
+*
+*
+*  Further Details
+*  ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*>  Based on contributions by
+*>     Ming Gu and Ren-Cang Li, Computer Science Division, University of
+*>       California at Berkeley, USA
+*>     Osni Marques, LBNL/NERSC, USA
+*>
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE CGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
      $                   WORK, LWORK, RWORK, IWORK, INFO )
 *
-*  -- LAPACK driver routine (version 3.2) --
+*  -- LAPACK solve routine (version 3.2) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
+*     November 2011
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -16,136 +239,6 @@
       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  CGELSD computes the minimum-norm solution to a real linear least
-*  squares problem:
-*      minimize 2-norm(| b - A*x |)
-*  using the singular value decomposition (SVD) of A. A is an M-by-N
-*  matrix which may be rank-deficient.
-*
-*  Several right hand side vectors b and solution vectors x can be
-*  handled in a single call; they are stored as the columns of the
-*  M-by-NRHS right hand side matrix B and the N-by-NRHS solution
-*  matrix X.
-*
-*  The problem is solved in three steps:
-*  (1) Reduce the coefficient matrix A to bidiagonal form with
-*      Householder tranformations, reducing the original problem
-*      into a "bidiagonal least squares problem" (BLS)
-*  (2) Solve the BLS using a divide and conquer approach.
-*  (3) Apply back all the Householder tranformations to solve
-*      the original least squares problem.
-*
-*  The effective rank of A is determined by treating as zero those
-*  singular values which are less than RCOND times the largest singular
-*  value.
-*
-*  The divide and conquer algorithm makes very mild assumptions about
-*  floating point arithmetic. It will work on machines with a guard
-*  digit in add/subtract, or on those binary machines without guard
-*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-*  Cray-2. It could conceivably fail on hexadecimal or decimal machines
-*  without guard digits, but we know of none.
-*
-*  Arguments
-*  =========
-*
-*  M       (input) INTEGER
-*          The number of rows of the matrix A. M >= 0.
-*
-*  N       (input) INTEGER
-*          The number of columns of the matrix A. N >= 0.
-*
-*  NRHS    (input) INTEGER
-*          The number of right hand sides, i.e., the number of columns
-*          of the matrices B and X. NRHS >= 0.
-*
-*  A       (input/output) COMPLEX array, dimension (LDA,N)
-*          On entry, the M-by-N matrix A.
-*          On exit, A has been destroyed.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A. LDA >= max(1,M).
-*
-*  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
-*          On entry, the M-by-NRHS right hand side matrix B.
-*          On exit, B is overwritten by the N-by-NRHS solution matrix X.
-*          If m >= n and RANK = n, the residual sum-of-squares for
-*          the solution in the i-th column is given by the sum of
-*          squares of the modulus of elements n+1:m in that column.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max(1,M,N).
-*
-*  S       (output) REAL array, dimension (min(M,N))
-*          The singular values of A in decreasing order.
-*          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
-*
-*  RCOND   (input) REAL
-*          RCOND is used to determine the effective rank of A.
-*          Singular values S(i) <= RCOND*S(1) are treated as zero.
-*          If RCOND < 0, machine precision is used instead.
-*
-*  RANK    (output) INTEGER
-*          The effective rank of A, i.e., the number of singular values
-*          which are greater than RCOND*S(1).
-*
-*  WORK    (workspace/output) COMPLEX 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 must be at least 1.
-*          The exact minimum amount of workspace needed depends on M,
-*          N and NRHS. As long as LWORK is at least
-*              2 * N + N * NRHS
-*          if M is greater than or equal to N or
-*              2 * M + M * NRHS
-*          if M is less than N, the code will execute correctly.
-*          For good performance, LWORK should generally be larger.
-*
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the array WORK and the
-*          minimum sizes of the arrays RWORK and IWORK, and returns
-*          these values as the first entries of the WORK, RWORK and
-*          IWORK arrays, and no error message related to LWORK is issued
-*          by XERBLA.
-*
-*  RWORK   (workspace) REAL array, dimension (MAX(1,LRWORK))
-*          LRWORK >=
-*             10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
-*             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
-*          if M is greater than or equal to N or
-*             10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
-*             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
-*          if M is less than N, the code will execute correctly.
-*          SMLSIZ is returned by ILAENV and is equal to the maximum
-*          size of the subproblems at the bottom of the computation
-*          tree (usually about 25), and
-*             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
-*          On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK.
-*
-*  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK))
-*          LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),
-*          where MINMN = MIN( M,N ).
-*          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
-*
-*  INFO    (output) INTEGER
-*          = 0: successful exit
-*          < 0: if INFO = -i, the i-th argument had an illegal value.
-*          > 0:  the algorithm for computing the SVD failed to converge;
-*                if INFO = i, i off-diagonal elements of an intermediate
-*                bidiagonal form did not converge to zero.
-*
-*  Further Details
-*  ===============
-*
-*  Based on contributions by
-*     Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*       California at Berkeley, USA
-*     Osni Marques, LBNL/NERSC, USA
-*
 *  =====================================================================
 *
 *     .. Parameters ..