cptrfs(l) [redhat man page]

CPTRFS(l)								 )								 CPTRFS(l)

NAME

       CPTRFS  -  improve  the	computed  solution  to a system of linear equations when the coefficient matrix is Hermitian positive definite and
       tridiagonal, and provides error bounds and backward error estimates for the solution

SYNOPSIS

       SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

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

	   COMPLEX	  B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE

       CPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridi-
       agonal, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:
	       = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
	       = 'L':  E is the subdiagonal of A, and A = L*D*L**H.  (The two forms are equivalent if A is real.)

       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.

       D       (input) REAL array, dimension (N)
	       The n real diagonal elements of the tridiagonal matrix A.

       E       (input) COMPLEX array, dimension (N-1)
	       The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

       DF      (input) REAL array, dimension (N)
	       The n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.

       EF      (input) COMPLEX array, dimension (N-1)
	       The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).

       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 CPTTRS.	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  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).

       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 (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 version 3.0						   15 June 2000 							 CPTRFS(l)

CGTRFS(l)								 )								 CGTRFS(l)

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.

       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

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 CGTRFS(l)