SUBROUTINE SGEFS(A,LDA,N,V,ITASK,IND,WORK,IWORK,RCOND)
C***BEGIN PROLOGUE  SGEFS
C***DATE WRITTEN   800317   (YYMMDD)
C***REVISION DATE  870916   (YYMMDD)
C***CATEGORY NO.  D2A1
C***KEYWORDS  GENERAL SYSTEM OF LINEAR EQUATIONS,LINEAR EQUATIONS
C***AUTHOR  VOORHEES, E., (LOS ALAMOS NATIONAL LABORATORY)
C***PURPOSE  SGEFS solves a GENERAL single precision real
C            NXN system of linear equations.
C***DESCRIPTION
C
C    From the book "Numerical Methods and Software"
C       by  D. Kahaner, C. Moler, S. Nash
C           Prentice Hall 1988
C
C    Subroutine SGEFS solves a general NxN system of single
C    precision linear equations using LINPACK subroutines SGECO
C    and SGESL.  That is, if A is an NxN real matrix and if X
C    and B are real N-vectors, then SGEFS solves the equation
C
C                          A*X=B.
C
C    The matrix A is first factored into upper and lower tri-
C    angular matrices U and L using partial pivoting.  These
C    factors and the pivoting information are used to find the
C    solution vector X.  An approximate condition number is
C    calculated to provide a rough estimate of the number of
C    digits of accuracy in the computed solution.
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 .EQ. 2) will be faster for
C    the succeeding solutions.  In this case, the contents of A,
C    LDA, N and IWORK must not have been altered by the user follow-
C    ing factorization (ITASK=1).  IND will not be changed by SGEFS
C    in this case.  Other settings of ITASK are used to solve linear
C    systems involving the transpose of A.
C
C  Argument Description ***
C
C    A      REAL(LDA,N)
C             on entry, the doubly subscripted array with dimension
C               (LDA,N) which contains the coefficient matrix.
C             on return, an upper triangular matrix U and the
C               multipliers necessary to construct a matrix L
C               so that A=L*U.
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.  The first N elements of
C             the array A are the elements of the first column of
C             the  matrix A.  N must be greater than or equal to 1.
C             (terminal error message IND=-2)
C    V      REAL(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=2, the equation is solved using the existing
C               factored matrix A and IWORK.
C             If ITASK=3, the matrix is factored and A'x=b is solved
C             If ITASK=4, the transposed equation is solved using the
C               existing factored matrix A and IWORK.
C             If ITASK .LT. 1 or ITASK .GT. 4, then the terminal error
C               message IND=-3 is printed.
C    IND    INTEGER
C             GT. 0  IND is a rough estimate of the number of digits
C                     of accuracy in the solution, X.
C             LT. 0  see error message corresponding to IND below.
C    WORK   REAL(N)
C             a singly subscripted array of dimension at least N.
C    IWORK  INTEGER(N)
C             a singly subscripted array of dimension at least N.
C    RCOND  REAL
C             estimate of 1.0/cond(A)
C
C  Error Messages Printed ***
C
C    IND=-1  fatal   N is greater than LDA.
C    IND=-2  fatal   N is less than 1.
C    IND=-3  fatal   ITASK is less than 1 or greater than 4.
C    IND=-4  fatal   The matrix A is computationally singular.
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***REFERENCES  SUBROUTINE SGEFS WAS DEVELOPED BY GROUP C-3, LOS ALAMOS
C                 SCIENTIFIC LABORATORY, LOS ALAMOS, NM 87545.
C                 THE LINPACK SUBROUTINES USED BY SGEFS 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  R1MACH,SGECO,SGESL,XERROR