SUBROUTINE NL2SN(N, P, X, CALCR, IV, LIV, LV, V,
     1                  UIPARM, URPARM, UFPARM)
C
C  ***  MINIMIZE A NONLINEAR SUM OF SQUARES USING RESIDUAL VALUES ONLY..
C  ***  THIS AMOUNTS TO NL2S1 WITHOUT THE SUBROUTINE PARAMETER CALCJ.
C
C  ***  PARAMETERS  ***
C
      INTEGER N, P, LIV, LV
C
      INTEGER IV(LIV), UIPARM(1)
      REAL X(P), V(LV), URPARM(1)
C
C     INTEGER IV(LIV), UIPARM(*)
C     REAL X(P), V(LV), URPARM(*)
C
      EXTERNAL CALCR, UFPARM
C
C-----------------------------  DISCUSSION  ----------------------------
C
C        THIS AMOUNTS TO SUBROUTINE NL2SNO (REF. 1) MODIFIED TO CALL
C     NL2IT.
C        THE PARAMETERS FOR NL2SN ARE THE SAME AS THOSE FOR NL2S1
C     (WHICH SEE), EXCEPT THAT CALCJ IS OMITTED.  INSTEAD OF CALLING
C     CALCJ TO OBTAIN THE JACOBIAN MATRIX OF R AT X, NL2SN COMPUTES
C     AN APPROXIMATION TO IT BY FINITE (FORWARD) DIFFERENCES -- SEE
C     V(DLTFDJ) BELOW.  NL2SN USES FUNCTION VALUES ONLY WHEN COMPUT-
C     THE COVARIANCE MATRIX (RATHER THAN THE FUNCTIONS AND GRADIENTS
C     THAT NL2S1 MAY USE).  TO DO SO, NL2SN SETS IV(COVREQ) TO -1 IF
C     IV(COVPRT) = 1 WITH IV(COVREQ) = 0 AND TO MINUS ITS ABSOLUTE
C     VALUE OTHERWISE.  THUS V(DELTA0) IS NEVER REFERENCED AND ONLY
C     V(DLTFDC) MATTERS -- SEE NL2SOL FOR A DESCRIPTION OF V(DLTFDC).
C        THE NUMBER OF EXTRA CALLS ON CALCR USED IN COMPUTING THE JACO-
C     BIAN APPROXIMATION ARE NOT INCLUDED IN THE FUNCTION EVALUATION
C     COUNT IV(NFCALL) AND ARE NOT OTHERWISE REPORTED.
C
C V(DLTFDJ)... V(43) HELPS CHOOSE THE STEP SIZE USED WHEN COMPUTING THE
C             FINITE-DIFFERENCE JACOBIAN MATRIX.  FOR DIFFERENCES IN-
C             VOLVING X(I), THE STEP SIZE FIRST TRIED IS
C                       V(DLTFDJ) * MAX(ABS(X(I)), 1/D(I)),
C             WHERE D IS THE CURRENT SCALE VECTOR (SEE REF. 1).  (IF
C             THIS STEP IS TOO BIG, I.E., IF CALCR SETS NF TO 0, THEN
C             SMALLER STEPS ARE TRIED UNTIL THE STEP SIZE IS SHRUNK BE-
C             LOW 1000 * MACHEP, WHERE MACHEP IS THE UNIT ROUNDOFF.
C             DEFAULT = MACHEP**0.5.
C
C  ***  REFERENCES  ***
C
C 1.  DENNIS, J.E., GAY, D.M., AND WELSCH, R.E. (1981), AN ADAPTIVE
C             NONLINEAR LEAST-SQUARES ALGORITHM, ACM TRANS. MATH.
C             SOFTWARE, VOL. 7, NO. 3.
C
C  ***  GENERAL  ***
C
C     CODED BY DAVID M. GAY.