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 ZPBRFS( 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

           DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )

           COMPLEX*16     AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       ZPBRFS 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) DOUBLE PRECISION 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*16 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
                ZPBTRF, 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*16 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*16 array, dimension (LDX,NRHS)
                On entry, the solution matrix X, as computed by ZPBTRS.
                On exit, the improved 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) COMPLEX*16 array, dimension (2*N)

        RWORK   (workspace) DOUBLE PRECISION 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                            ZPBRFS(3lapack)