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zgbrfs (3)
  • >> zgbrfs (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zgbrfs - improve the computed solution to a system of linear
         equations  when  the  coefficient matrix is banded, and pro-
         vides error bounds and  backward  error  estimates  for  the
         solution
    
    SYNOPSIS
         SUBROUTINE ZGBRFS( TRANS, N, KL, KU, NRHS,  AB,  LDAB,  AFB,
                   LDAFB,  IPIV,  B,  LDB,  X, LDX, FERR, BERR, WORK,
                   RWORK, INFO )
    
         CHARACTER TRANS
    
         INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
    
         INTEGER IPIV( * )
    
         DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
    
         COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, *  ),  B(  LDB,  *  ),
                   WORK( * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void zgbrfs(char trans, int n, int kl,  int  ku,  int  nrhs,
                   doublecomplex  *zab, int ldab, doublecomplex *afb,
                   int ldafb, int  *ipivot,  doublecomplex  *zb,  int
                   ldb,  doublecomplex  *zx,  int  ldx, double *ferr,
                   double *berr, int *info);
    
    PURPOSE
         ZGBRFS improves the computed solution to a system of  linear
         equations  when  the  coefficient matrix is banded, and pro-
         vides 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)
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KL        (input) INTEGER
                   The number of subdiagonals within the band  of  A.
                   KL >= 0.
    
         KU        (input) INTEGER
                   The number of superdiagonals within the band of A.
                   KU >= 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) COMPLEX*16 array, dimension (LDAB,N)
                   The original band matrix A, stored in  rows  1  to
                   KL+KU+1.   The  j-th  column of A is stored in the
                   j-th  column  of  the   array   AB   as   follows:
                   AB(ku+1+i-j,j)     =     A(i,j)    for    max(1,j-
                   ku)<=i<=min(n,j+kl).
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KL+KU+1.
    
         AFB       (input) COMPLEX*16 array, dimension (LDAFB,N)
                   Details of the LU factorization of the band matrix
                   A, as computed by ZGBTRF.  U is stored as an upper
                   triangular band matrix with  KL+KU  superdiagonals
                   in  rows  1  to  KL+KU+1, and the multipliers used
                   during  the  factorization  are  stored  in   rows
                   KL+KU+2 to 2*KL+KU+1.
    
         LDAFB     (input) INTEGER
                   The leading dimension of the array AFB.  LDAFB  >=
                   2*KL*KU+1.
    
         IPIV      (input) INTEGER array, dimension (N)
                   The pivot indices from ZGBTRF; for 1<=i<=N, row  i
                   of the matrix was interchanged with row IPIV(i).
    
         B         (input) COMPLEX*16 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)   COMPLEX*16    array,    dimension
                   (LDX,NRHS)
                   On entry, the solution matrix X,  as  computed  by
                   ZGBTRS.  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) COMPLEX*16 array, dimension (2*N)
    
         RWORK     (workspace) DOUBLE PRECISION 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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