The OpenNET Project / Index page

[ новости /+++ | форум | теги | ]

Интерактивная система просмотра системных руководств (man-ов)

 ТемаНаборКатегория 
 
 [Cписок руководств | Печать]

sgtsvx (3)
  • >> sgtsvx (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgtsvx - use the LU factorization to compute the solution to
         a real system of linear equations A * X = B or A**T * X = B,
    
    SYNOPSIS
         SUBROUTINE SGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF,
                   DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
                   WORK, IWORK, INFO )
    
         CHARACTER FACT, TRANS
    
         INTEGER INFO, LDB, LDX, N, NRHS
    
         REAL RCOND
    
         INTEGER IPIV( * ), IWORK( * )
    
         REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ),  DLF(
                   * ), DU( * ), DU2( * ), DUF( * ), FERR( * ), WORK(
                   * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void sgtsvx(char fact, char trans, int n,  int  nrhs,  float
                   *dl,  float  *d, float *du, float *dlf, float *df,
                   float *duf, float *du2, int  *ipivot,  float  *sb,
                   int  ldb, float *sx, int ldx, float *srcond, float
                   *ferr, float *berr, int *info);
    
    PURPOSE
         SGTSVX uses the LU factorization to compute the solution  to
         a real system of linear equations A * X = B or A**T * X = B,
         where A is a tridiagonal matrix of order N and X and  B  are
         N-by-NRHS matrices.
    
         Error bounds on the solution and a  condition  estimate  are
         also provided.
    
    
    DESCRIPTION
         The following steps are performed:
    
         1. If FACT = 'N', the LU decomposition is used to factor the
         matrix  A  as A = L * U, where L is a product of permutation
         and unit lower bidiagonal matrices and U is upper triangular
         with nonzeros in only the main diagonal and first two super-
         diagonals.
    
         2. The factored form of A is used to estimate the  condition
         number  of the matrix A.  If the reciprocal of the condition
         number is less than machine precision, steps  3  and  4  are
         skipped.
    
         3. The system of equations is solved for X  using  the  fac-
         tored form of A.
    
         4. Iterative refinement is applied to improve  the  computed
         solution  matrix  and  calculate  error  bounds and backward
         error estimates for it.
    
    
    ARGUMENTS
         FACT      (input) CHARACTER*1
                   Specifies whether or not the factored  form  of  A
                   has been supplied on entry.  = 'F':  DLF, DF, DUF,
                   DU2, and IPIV contain the factored form of A;  DL,
                   D,  DU,  DLF,  DF,  DUF,  DU2 and IPIV will not be
                   modified.  = 'N':  The matrix will  be  copied  to
                   DLF, DF, and DUF and factored.
    
         TRANS     (input) CHARACTER*1
                   Specifies the form of the system of equations:
                   = 'N':  A * X = B     (No transpose)
                   = 'T':  A**T * X = B  (Transpose)
                   = 'C':  A**H * X = B  (Conjugate transpose = Tran-
                   spose)
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         NRHS      (input) INTEGER
                   The number of right hand sides, i.e.,  the  number
                   of columns of the matrix B.  NRHS >= 0.
    
         DL        (input) REAL array, dimension (N-1)
                   The (n-1) subdiagonal elements of A.
    
         D         (input) REAL array, dimension (N)
                   The n diagonal elements of A.
    
         DU        (input) REAL array, dimension (N-1)
                   The (n-1) superdiagonal elements of A.
    
         DLF       (input or output) REAL array, dimension (N-1)
                   If FACT = 'F', then DLF is an input  argument  and
                   on  entry  contains  the  (n-1)  multipliers  that
                   define the matrix L from the LU factorization of A
                   as computed by SGTTRF.
    
                   If FACT = 'N', then DLF is an output argument  and
                   on exit contains the (n-1) multipliers that define
                   the matrix L from the LU factorization of A.
    
         DF        (input or output) REAL array, dimension (N)
                   If FACT = 'F', then DF is an input argument and on
                   entry  contains  the  n  diagonal  elements of the
                   upper triangular matrix U from the  LU  factoriza-
                   tion of A.
    
                   If FACT = 'N', then DF is an output  argument  and
                   on  exit  contains  the n diagonal elements of the
                   upper triangular matrix U from the  LU  factoriza-
                   tion of A.
    
         DUF       (input or output) REAL array, dimension (N-1)
                   If FACT = 'F', then DUF is an input  argument  and
                   on  entry contains the (n-1) elements of the first
                   superdiagonal of U.
    
                   If FACT = 'N', then DUF is an output argument  and
                   on  exit  contains the (n-1) elements of the first
                   superdiagonal of U.
    
         DU2       (input or output) REAL array, dimension (N-2)
                   If FACT = 'F', then DU2 is an input  argument  and
                   on entry contains the (n-2) elements of the second
                   superdiagonal of U.
    
                   If FACT = 'N', then DU2 is an output argument  and
                   on  exit contains the (n-2) elements of the second
                   superdiagonal of U.
    
         IPIV      (input or output) INTEGER array, dimension (N)
                   If FACT = 'F', then IPIV is an input argument  and
                   on  entry  contains  the pivot indices from the LU
                   factorization of A as computed by SGTTRF.
    
                   If FACT = 'N', then IPIV is an output argument and
                   on  exit  contains  the  pivot indices from the LU
                   factorization of A; row i of the matrix was inter-
                   changed  with row IPIV(i).  IPIV(i) will always be
                   either i or i+1;  IPIV(i)  =  i  indicates  a  row
                   interchange was not required.
    
         B         (input) REAL array, dimension (LDB,NRHS)
                   The N-by-NRHS right hand side matrix B.
    
         LDB       (input) INTEGER
                   The leading dimension of  the  array  B.   LDB  >=
                   max(1,N).
    
         X         (output) REAL array, dimension (LDX,NRHS)
                   If INFO = 0, the N-by-NRHS solution matrix X.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N).
    
         RCOND     (output) REAL
                   The estimate of the reciprocal condition number of
                   the  matrix  A.  If RCOND is less than the machine
                   precision (in  particular,  if  RCOND  =  0),  the
                   matrix  is  singular  to  working precision.  This
                   condition is indicated by a return code of INFO  >
                   0,  and the solution and error bounds are not com-
                   puted.
    
         FERR      (output) REAL array, dimension (NRHS)
                   The estimated forward error bound for  each  solu-
                   tion  vector X(j) (the j-th column of the solution
                   matrix  X).   If  XTRUE  is  the   true   solution
                   corresponding  to  X(j),  FERR(j)  is an estimated
                   upper bound for the magnitude of the largest  ele-
                   ment in (X(j) - XTRUE) divided by the magnitude of
                   the largest element in X(j).  The estimate  is  as
                   reliable  as the estimate for RCOND, and is almost
                   always a slight overestimate of the true error.
    
         BERR      (output) REAL array, dimension (NRHS)
                   The componentwise relative backward error of  each
                   solution  vector X(j) (i.e., the smallest relative
                   change in any element of A or B that makes X(j) an
                   exact solution).
    
         WORK      (workspace) REAL array, dimension (3*N)
    
         IWORK     (workspace) INTEGER array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  if INFO = i, and i is
                   <= N:  U(i,i) is exactly zero.  The  factorization
                   has  not been completed unless i = N, but the fac-
                   tor U is exactly singular,  so  the  solution  and
                   error bounds could not be computed.  = N+1:  RCOND
                   is less than machine precision.  The factorization
                   has  been completed, but the matrix is singular to
                   working precision,  and  the  solution  and  error
                   bounds have not been computed.
    
    
    
    


    Поиск по тексту MAN-ов: 




    Партнёры:
    PostgresPro
    Inferno Solutions
    Hosting by Hoster.ru
    Хостинг:

    Закладки на сайте
    Проследить за страницей
    Created 1996-2024 by Maxim Chirkov
    Добавить, Поддержать, Вебмастеру