dtprfs(3F)

NAME
     DTPRFS - provide error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular packed
     coefficient matrix

SYNOPSIS
     SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR,
                        BERR, WORK, IWORK, INFO )

         CHARACTER      DIAG, TRANS, UPLO

         INTEGER        INFO, LDB, LDX, N, NRHS

         INTEGER        IWORK( * )

         DOUBLE         PRECISION AP( * ), B( LDB, * ), BERR( * ), FERR( * ),
                        WORK( * ), X( LDX, * )

PURPOSE
     DTPRFS provides error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular packed
     coefficient matrix.

     The solution matrix X must be computed by DTPTRS or some other means
     before entering this routine.  DTPRFS does not do iterative refinement
     because doing so cannot improve the backward error.


ARGUMENTS
     UPLO    (input) CHARACTER*1
             = 'U':  A is upper triangular;
             = 'L':  A is lower triangular.

     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 = Transpose)

     DIAG    (input) CHARACTER*1
             = 'N':  A is non-unit triangular;
             = 'U':  A is unit triangular.

     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 matrices B and X.  NRHS >= 0.
     AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
             The upper or lower triangular matrix A, packed columnwise in a
             linear array.  The j-th column of A is stored in the array AP as
             follows:  if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
             if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.  If
             DIAG = 'U', the diagonal elements of A are not referenced and are
             assumed to be 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
             The 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 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) 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 illegal value