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dgels (3)
  • >> dgels (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dgels - solve overdetermined or underdetermined real  linear
         systems  involving  an  M-by-N  matrix  A, or its transpose,
         using a QR or LQ factorization of A
    
    SYNOPSIS
         SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B,  LDB,  WORK,
                   LWORK, INFO )
    
         CHARACTER TRANS
    
         INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
    
         DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( LWORK )
    
    
    
         #include <sunperf.h>
    
         void dgels(char trans, int m, int n, int nrhs,  double  *da,
                   int lda, double *db, int ldb, int *info) ;
    
    PURPOSE
         DGELS solves overdetermined or underdetermined  real  linear
         systems  involving  an  M-by-N  matrix  A, or its transpose,
         using a QR or LQ factorization of A.  It is assumed  that  A
         has full rank.
    
         The following options are provided:
    
         1. If TRANS = 'N' and m >= n:  find the least squares  solu-
         tion  of  an  overdetermined  system,  i.e., solve the least
         squares problem
                         minimize || B - A*X ||.
    
         2. If TRANS = 'N' and m < n:  find the minimum norm solution
         of an underdetermined system A * X = B.
    
         3. If TRANS = 'T' and m >= n:  find the minimum  norm  solu-
         tion of an undetermined system A**T * X = B.
    
         4. If TRANS = 'T' and m < n:  find the least  squares  solu-
         tion  of  an  overdetermined  system,  i.e., solve the least
         squares problem
                         minimize || B - A**T * X ||.
    
         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.
    
    
    ARGUMENTS
         TRANS     (input) CHARACTER
                   = 'N': the linear system involves A;
                   = 'T': the linear system involves A**T.
    
         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) DOUBLE PRECISION  array,  dimension
                   (LDA,N)
                   On entry, the M-by-N matrix A.  On exit, if  M  >=
                   N,  A is overwritten by details of its QR factori-
                   zation as returned by DGEQRF; if  M  <   N,  A  is
                   overwritten  by details of its LQ factorization as
                   returned by DGELQF.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,M).
    
         B         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDB,NRHS)
                   On entry, the matrix B of right hand side vectors,
                   stored  columnwise; B is M-by-NRHS if TRANS = 'N',
                   or N-by-NRHS if  TRANS  =  'T'.   On  exit,  B  is
                   overwritten   by   the  solution  vectors,  stored
                   columnwise:  if TRANS = 'N' and m >= n, rows 1  to
                   n of B contain the least squares solution vectors;
                   the residual sum of squares for  the  solution  in
                   each column is given by the sum of squares of ele-
                   ments N+1 to M in that column; if TRANS = 'N'  and
                   m  <  n, rows 1 to N of B contain the minimum norm
                   solution vectors; if TRANS = 'T' and m >= n,  rows
                   1 to M of B contain the minimum norm solution vec-
                   tors; if TRANS = 'T' and m < n, rows 1 to M  of  B
                   contain  the  least  squares solution vectors; the
                   residual sum of squares for the solution  in  each
                   column  is given by the sum of squares of elements
                   M+1 to N in that column.
    
         LDB       (input) INTEGER
                   The leading dimension  of  the  array  B.  LDB  >=
                   MAX(1,M,N).
    
         WORK      (workspace/output)   DOUBLE    PRECISION    array,
                   dimension (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The  dimension  of  the  array  WORK.   LWORK   >=
                   min(M,N)  +  MAX(1,M,N,NRHS).  For optimal perfor-
                   mance, LWORK >= min(M,N) +  MAX(1,M,N,NRHS)  *  NB
                   where NB is the optimum block size.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    
    
    


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