 
      SUBROUTINE CPOIR(A,LDA,N,V,ITASK,IND,WORK)
C***BEGIN PROLOGUE  CPOIR
C***DATE WRITTEN   800530   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2D1B
C***KEYWORDS  COMPLEX,HERMITIAN,LINEAR EQUATIONS,POSITIVE DEFINITE
C***AUTHOR  VOORHEES, E., (LANL)
C***PURPOSE  CPOIR solves a POSITIVE DEFINITE HERMITIAN
C            COMPLEX NXN system of linear equations.
C            Iterative refinement is used to obtain an
C            error estimate.
C***DESCRIPTION
C
C    Subroutine CPOIR solves a complex positive definite Hermitian
C    NxN system of single precision linear equations using LINPACK
C    subroutines CPOFA and CPOSL.  One pass of iterative refine-
C    ment is used only to obtain an estimate of the accuracy.  That
C    is, if A is an NxN complex positive definite Hermitian matrix
C    and if X and B are complex N-vectors, then CPOIR solves the
C    equation
C
C                          A*X=B.
C
C    Care should be taken not to use CPOIR with a non-Hermitian
C    matrix.
C
C    The matrix A is first factored into upper and lower
C    triangular matrices R and R-TRANSPOSE.  These
C    factors are used to calculate the solution, X.
C    Then the residual vector is found and used
C    to calculate an estimate of the relative error, IND.
C    IND estimates the accuracy of the solution only when the
C    input matrix and the right hand side are represented
C    exactly in the computer and does not take into account
C    any errors in the input data.
C
C    If the equation A*X=B is to be solved for more than one vector
C    B, the factoring of A does not need to be performed again and
C    the option to only solve (ITASK .GT. 1) will be faster for
C    the succeeding solutions.  In this case, the contents of A,
C    LDA, N, and WORK must not have been altered by the user
C    following factorization (ITASK=1).  IND will not be changed
C    by CPOIR in this case.
C
C  Argument Description ***
C    A       COMPLEX(LDA,N)
C             the doubly subscripted array with dimension (LDA,N)
C             which contains the coefficient matrix.  Only the
C             upper triangle, including the diagonal, of the
C             coefficient matrix need be entered.  A is not
C             altered by the routine.
C    LDA    INTEGER
C             the leading dimension of the array A.  LDA must be great-
C             er than or equal to N.  (terminal error message IND=-1)
C    N      INTEGER
C             the order of the matrix A.  N must be greater than
C             or equal to one.  (terminal error message IND=-2)
C    V      COMPLEX(N)
C             on entry, the singly subscripted array(vector) of di-
C               mension N which contains the right hand side B of a
C               system of simultaneous linear equations A*X=B.
C             on return, V contains the solution vector, X .
C    ITASK  INTEGER
C             if ITASK = 1, the matrix A is factored and then the
C               linear equation is solved.
C             if ITASK .GT. 1, the equation is solved using the existing
C               factored matrix A (stored in WORK).
C             if ITASK .LT. 1, then terminal terminal error IND=-3 is
C               printed.
C    IND    INTEGER
C             GT. 0  IND is a rough estimate of the number of digits
C                     of accuracy in the solution, X.  IND=75 means
C                     that the solution vector X is zero.
C             LT. 0  see error message corresponding to IND below.
C    WORK   COMPLEX(N*(N+1))
C             a singly subscripted array of dimension at least N*(N+1).
C
C  Error Messages Printed ***
C
C    IND=-1  terminal   N is greater than LDA.
C    IND=-2  terminal   N is less than one.
C    IND=-3  terminal   ITASK is less than one.
C    IND=-4  terminal   The matrix A is computationally singular
C                         or is not positive definite.
C                         A solution has not been computed.
C    IND=-10 warning    The solution has no apparent significance.
C                         the solution may be inaccurate or the matrix
C                         a may be poorly scaled.
C
C               NOTE-  the above terminal(*fatal*) error messages are
C                      designed to be handled by XERRWV in which
C                      LEVEL=1 (recoverable) and IFLAG=2 .  LEVEL=0
C                      for warning error messages from XERROR.  Unless
C                      the user provides otherwise, an error message
C                      will be printed followed by an abort.
C***REFERENCES  SUBROUTINE CPOIR WAS DEVELOPED BY GROUP C-3, LOS ALAMOS
C                 SCIENTIFIC LABORATORY, LOS ALAMOS, NM 87545.
C                 THE LINPACK SUBROUTINES USED BY CPOIR ARE DESCRIBED IN
C                 DETAIL IN THE *LINPACK USERS GUIDE* PUBLISHED BY
C                 THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
C                 (SIAM) DATED 1979.
C***ROUTINES CALLED  CCOPY,CPOFA,CPOSL,DCDOT,R1MACH,SCASUM,XERROR,
C                    XERRWV
C***END PROLOGUE  CPOIR
 
 
