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dpbrfs (3)
  • >> dpbrfs (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dpbrfs - improve the computed solution to a system of linear
         equations  when the coefficient matrix is symmetric positive
         definite and banded, and provides error bounds and  backward
         error estimates for the solution
    
    SYNOPSIS
         SUBROUTINE DPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB,  LDAFB,
                   B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS
    
         INTEGER IWORK( * )
    
         DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B(  LDB,  *
                   ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void dpbrfs(char uplo, int n, int kd, int nrhs, double *dab,
                   int  ldab, double *afb, int ldafb, double *db, int
                   ldb, double *dx, int  ldx,  double  *ferr,  double
                   *berr, int *info) ;
    
    PURPOSE
         DPBRFS improves the computed solution to a system of  linear
         equations  when the coefficient matrix is symmetric positive
         definite and banded, and provides error bounds and  backward
         error estimates for the solution.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KD        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KD >= 0.
    
         NRHS      (input) INTEGER
                   The number of right hand sides, i.e.,  the  number
                   of columns of the matrices B and X.  NRHS >= 0.
    
         AB        (input) DOUBLE PRECISION array, dimension (LDAB,N)
                   The upper or lower triangle of the symmetric  band
                   matrix  A,  stored  in  the first KD+1 rows of the
                   array.  The j-th column of A is stored in the j-th
                   column of the array AB as follows:  if UPLO = 'U',
                   AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;  if
                   UPLO   =   'L',   AB(1+i-j,j)      =   A(i,j)  for
                   j<=i<=min(n,j+kd).
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KD+1.
    
         AFB       (input)   DOUBLE   PRECISION   array,    dimension
                   (LDAFB,N)
                   The triangular factor U or  L  from  the  Cholesky
                   factorization A = U**T*U or A = L*L**T of the band
                   matrix A  as  computed  by  DPBTRF,  in  the  same
                   storage format as A (see AB).
    
         LDAFB     (input) INTEGER
                   The leading dimension of the array AFB.  LDAFB  >=
                   KD+1.
    
         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/output) DOUBLE PRECISION  array,  dimension
                   (LDX,NRHS)
                   On entry, the solution matrix X,  as  computed  by
                   DPBTRS.  On exit, the improved 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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