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

NAME

       LAPACK-3  -  improves  the  computed  solution  to  a  system of linear equations when the
       coefficient matrix is Hermitian positive definite and banded, and  provides  error  bounds
       and backward error estimates for the solution

SYNOPSIS

       SUBROUTINE CPBRFS( UPLO,  N,  KD,  NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR,
                          WORK, RWORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS

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

           COMPLEX        AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

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

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        KD      (input) INTEGER
                The number of superdiagonals of the matrix A if UPLO = 'U',
                or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

        NRHS    (input) INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrices B and X.  NRHS >= 0.

        AB      (input) COMPLEX array, dimension (LDAB,N)
                The upper or lower triangle of the Hermitian band matrix A,
                stored in the first KD+1 rows of the array.  The j-th column
                of A is stored in the j-th column of the array AB as follows:
                if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

        LDAB    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= KD+1.

        AFB     (input) COMPLEX array, dimension (LDAFB,N)
                The triangular factor U or L from the Cholesky factorization
                A = U**H*U or A = L*L**H of the band matrix A as computed by
                CPBTRF, in the same storage format as A (see AB).

        LDAFB   (input) INTEGER
                The leading dimension of the array AFB.  LDAFB >= KD+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/output) COMPLEX array, dimension (LDX,NRHS)
                On entry, the solution matrix X, as computed by CPBTRS.
                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 routine (version 3.2)               April 2011                            CPBRFS(3lapack)