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dtrrfs (3)
  • >> dtrrfs (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dtrrfs - provide error bounds and backward  error  estimates
         for the solution to a system of linear equations with a tri-
         angular coefficient matrix
    
    SYNOPSIS
         SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS,  A,  LDA,  B,
                   LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
    
         CHARACTER DIAG, TRANS, UPLO
    
         INTEGER INFO, LDA, LDB, LDX, N, NRHS
    
         INTEGER IWORK( * )
    
         DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ),  FERR(
                   * ), WORK( * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void dtrrfs(char uplo, char trans, char  diag,  int  n,  int
                   nrhs,  double  *da,  int lda, double *db, int ldb,
                   double *dx, int ldx, double *ferr,  double  *berr,
                   int *info) ;
    
    PURPOSE
         DTRRFS provides error bounds and  backward  error  estimates
         for the solution to a system of linear equations with a tri-
         angular coefficient matrix.
    
         The solution matrix X must be computed  by  DTRTRS  or  some
         other  means  before entering this routine.  DTRRFS does not
         do iterative refinement because doing so cannot improve  the
         backward error.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  A is upper triangular;
                   = 'L':  A is lower triangular.
    
         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)
    
         DIAG      (input) CHARACTER*1
                   = 'N':  A is non-unit triangular;
                   = 'U':  A is unit triangular.
    
         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 matrices B and X.  NRHS >= 0.
    
         A         (input) DOUBLE PRECISION array, dimension (LDA,N)
                   The triangular matrix A.  If UPLO = 'U', the lead-
                   ing  N-by-N  upper  triangular part of the array A
                   contains the  upper  triangular  matrix,  and  the
                   strictly  lower triangular part of A is not refer-
                   enced.  If UPLO = 'L', the  leading  N-by-N  lower
                   triangular  part of the array A contains the lower
                   triangular matrix, and the strictly upper triangu-
                   lar  part  of A is not referenced.  If DIAG = 'U',
                   the diagonal elements of A are also not referenced
                   and are assumed to be 1.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,N).
    
         B         (input)   DOUBLE   PRECISION   array,    dimension
                   (LDB,NRHS)
                   The right hand side matrix B.
    
         LDB       (input) INTEGER
                   The leading dimension of  the  array  B.   LDB  >=
                   max(1,N).
    
         X         (input)   DOUBLE   PRECISION   array,    dimension
                   (LDX,NRHS)
                   The solution matrix X.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N).
    
         FERR      (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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)  DOUBLE  PRECISION  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
    
    
    
    


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