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sgtrfs (3)
  • >> sgtrfs (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgtrfs - improve the computed solution to a system of linear
         equations  when  the  coefficient matrix is tridiagonal, and
         provides error bounds and backward error estimates  for  the
         solution
    
    SYNOPSIS
         SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF,  DUF,
                   DU2,  IPIV,  B,  LDB,  X,  LDX,  FERR, BERR, WORK,
                   IWORK, INFO )
    
         CHARACTER TRANS
    
         INTEGER INFO, LDB, LDX, N, NRHS
    
         INTEGER IPIV( * ), IWORK( * )
    
         REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ),  DLF(
                   * ), DU( * ), DU2( * ), DUF( * ), FERR( * ), WORK(
                   * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void sgtrfs(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 *ferr, float *berr, int *info)
                   ;
    
    PURPOSE
         SGTRFS improves the computed solution to a system of  linear
         equations  when  the  coefficient matrix is tridiagonal, and
         provides error bounds and backward error estimates  for  the
         solution.
    
    
    ARGUMENTS
         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 diagonal elements of A.
    
         DU        (input) REAL array, dimension (N-1)
                   The (n-1) superdiagonal elements of A.
    
         DLF       (input) REAL array, dimension (N-1)
                   The (n-1) multipliers that  define  the  matrix  L
                   from  the  LU  factorization  of  A as computed by
                   SGTTRF.
    
         DF        (input) REAL array, dimension (N)
                   The n diagonal elements of  the  upper  triangular
                   matrix U from the LU factorization of A.
    
         DUF       (input) REAL array, dimension (N-1)
                   The (n-1) elements of the first  superdiagonal  of
                   U.
    
         DU2       (input) REAL array, dimension (N-2)
                   The (n-2) elements of the second superdiagonal  of
                   U.
    
         IPIV      (input) INTEGER array, dimension (N)
                   The pivot indices; for 1 <= i <= n, row i  of  the
                   matrix was interchanged with row IPIV(i).  IPIV(i)
                   will always be either i or i+1; IPIV(i) = i  indi-
                   cates a row interchange was not required.
    
         B         (input) REAL 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/output) REAL array, dimension (LDX,NRHS)
                   On entry, the solution matrix X,  as  computed  by
                   SGTTRS.  On exit, the improved solution matrix X.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N).
    
         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
    
    
    
    


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