Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - provides error bounds and backward error estimates for the solution to a system
       of linear equations with a triangular packed coefficient matrix

SYNOPSIS

       SUBROUTINE CTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B,  LDB,  X,  LDX,  FERR,  BERR,  WORK,
                          RWORK, INFO )

           CHARACTER      DIAG, TRANS, UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

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

           COMPLEX        AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       CTPRFS  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 CTPTRS or some other
        means before entering this routine.  CTPRFS 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)

        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) COMPLEX 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)*(2n-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) 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) COMPLEX array, dimension (LDX,NRHS)
                The 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

 LAPACK routine (version 3.2)               April 2011                            CTPRFS(3lapack)