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sggglm (3)
  • >> sggglm (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sggglm - solve a general  Gauss-Markov  linear  model  (GLM)
         problem
    
    SYNOPSIS
         SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X,  Y,  WORK,
                   LWORK, INFO )
    
         INTEGER INFO, LDA, LDB, LWORK, M, N, P
    
         REAL A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ), Y(
                   * )
    
    
    
         #include <sunperf.h>
    
         void sggglm(int n, int m, int p, float *sa, int  lda,  float
                   *sb,  int ldb, float *d, float *sx, float *sy, int
                   *info) ;
    
    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 A and B.
    
         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, A is des-
                   troyed.
    
         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, B is des-
                   troyed.
    
         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 equa-
                   tion.  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 prob-
                   lem.
    
         WORK      (workspace/output) REAL array, dimension (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.
    
         INFO      (output) INTEGER
                   = 0:  successful exit.
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    
    
    


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