SLATEC Routines --- SOSEQS ---

*DECK SOSEQS
      SUBROUTINE SOSEQS (FNC, N, S, RTOLX, ATOLX, TOLF, IFLAG, MXIT,
     +   NCJS, NSRRC, NSRI, IPRINT, FMAX, C, NC, B, P, TEMP, X, Y, FAC,
     +   IS)
C***BEGIN PROLOGUE  SOSEQS
C***SUBSIDIARY
C***PURPOSE  Subsidiary to SOS
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (SOSEQS-S, DSOSEQ-D)
C***AUTHOR  (UNKNOWN)
C***DESCRIPTION
C
C     SOSEQS solves a system of N simultaneous nonlinear equations.
C     See the comments in the interfacing routine SOS for a more
C     detailed description of some of the items in the calling list.
C
C ********************************************************************
C
C   -INPUT-
C     FNC -Function subprogram which evaluates the equations
C     N   -Number of equations
C     S   -Solution vector of initial guesses
C     RTOLX-Relative error tolerance on solution components
C     ATOLX-Absolute error tolerance on solution components
C     TOLF-Residual error tolerance
C     MXIT-Maximum number of allowable iterations.
C     NCJS-Maximum number of consecutive iterative steps to perform
C          using the same triangular Jacobian matrix approximation.
C     NSRRC-Number of consecutive iterative steps for which the
C          limiting precision accuracy test must be satisfied
C          before the routine exits with IFLAG=4.
C     NSRI-Number of consecutive iterative steps for which the
C          diverging condition test must be satisfied before
C          the routine exits with IFLAG=7.
C     IPRINT-Internal printing parameter.  You must set IPRINT=-1 if you
C          want the intermediate solution iterates and a residual norm
C          to be printed.
C     C   -Internal work array, dimensioned at least N*(N+1)/2.
C     NC  -Dimension of C array. NC  .GE.  N*(N+1)/2.
C     B   -Internal work array, dimensioned N.
C     P   -Internal work array, dimensioned N.
C     TEMP-Internal work array, dimensioned N.
C     X   -Internal work array, dimensioned N.
C     Y   -Internal work array, dimensioned N.
C     FAC -Internal work array, dimensioned N.
C     IS  -Internal work array, dimensioned N.
C
C   -OUTPUT-
C     S   -Solution vector
C     IFLAG-Status indicator flag
C     MXIT-The actual number of iterations performed
C     FMAX-Residual norm
C     C   -Upper unit triangular matrix which approximates the
C          forward triangularization of the full Jacobian matrix.
C          stored in a vector with dimension at least N*(N+1)/2.
C     B   -Contains the residuals (function values) divided
C          by the corresponding components of the P vector
C     P   -Array used to store the partial derivatives. After
C          each iteration P(K) contains the maximal derivative
C          occurring in the K-th reduced equation.
C     TEMP-Array used to store the previous solution iterate.
C     X   -Solution vector. Contains the values achieved on the
C          last iteration loop upon exit from SOS.
C     Y   -Array containing the solution increments.
C     FAC -Array containing factors used in computing numerical
C          derivatives.
C     IS  -Records the pivotal information (column interchanges)
C
C **********************************************************************
C *** Three machine dependent parameters appear in this subroutine.
C
C *** The smallest positive magnitude, zero, is defined by the function
C *** routine R1MACH(1).
C
C *** URO, The computer unit roundoff value, is defined by R1MACH(3) for
C *** machines that round or R1MACH(4) for machines that truncate.
C *** URO is the smallest positive number such that 1.+URO  .GT.  1.
C
C *** The output tape unit number, LOUN, is defined by the function
C *** I1MACH(2).
C **********************************************************************
C
C***SEE ALSO  SOS
C***ROUTINES CALLED  I1MACH, R1MACH, SOSSOL
C***REVISION HISTORY  (YYMMDD)
C   801001  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900328  Added TYPE section.  (WRB)
C***END PROLOGUE  SOSEQS