CGTRFS man page on IRIX

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CGTRFS(3F)							    CGTRFS(3F)

NAME
     CGTRFS - 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 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
	     factorization of A as computed by CGTTRF.

									Page 1

CGTRFS(3F)							    CGTRFS(3F)

     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 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 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

									Page 2

CGTRFS(3F)							    CGTRFS(3F)

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

									Page 3

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