CGTRFS(3)                  MathKeisan LAPACK routine                 CGTRFS(3)



NAME
       CGTRFS - the computed solution to a system of linear equations when the
       coefficient matrix is tridiagonal, and provides error bounds and  back-
       ward error estimates for the solution

SYNOPSIS
       SUBROUTINE CGTRFS( TRANS,  N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
                          B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

           CHARACTER      TRANS

           INTEGER        INFO, LDB, LDX, N, NRHS

           INTEGER        IPIV( * )

           REAL           BERR( * ), FERR( * ), RWORK( * )

           COMPLEX        B( LDB, * ), D( * ), DF( * ), DL( * ), DLF( * ), DU(
                          * ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )

PURPOSE
       CGTRFS  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)

       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) COMPLEX array, dimension (N-1)
               The (n-1) subdiagonal elements of A.

       D       (input) COMPLEX array, dimension (N)
               The diagonal elements of A.

       DU      (input) COMPLEX array, dimension (N-1)
               The (n-1) superdiagonal elements of A.

       DLF     (input) COMPLEX array, dimension (N-1)
               The (n-1) multipliers that define the matrix L from the LU fac-
               torization of A as computed by CGTTRF.

       DF      (input) COMPLEX array, dimension (N)
               The  n  diagonal elements of the upper triangular matrix U from
               the LU factorization of A.

       DUF     (input) COMPLEX array, dimension (N-1)
               The (n-1) elements of the first superdiagonal of U.

       DU2     (input) COMPLEX 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  indicates  a  row  interchange  was  not
               required.

       B       (input) COMPLEX 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 array, dimension (LDX,NRHS)
               On  entry,  the  solution  matrix X, as computed by CGTTRS.  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 solution 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 element 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 vec-
               tor  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 array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.



 LAPACK routine (version 3.1)    November 2006                       CGTRFS(3)