Simulated experimential data : 60.6476258 72.6240332 83.5171408 92.3190858 98.0172436 99.9969519 98.0276062 92.3016958 83.5359611 72.6098401 60.6526235 N L S C O N ***** V e r s i o n 2 . 3 . 2 *** Gauss-Newton-Method for the solution of nonlinear least squares problems Number of parameters to be estimated (N) : 3 Number of data to fitted, e.g. observations (MFIT) : 11 Number of equality constraints (MCON) : : 1 Prescribed relative precision (RTOL) : : 1.00e-04 The Jacobian is supplied by a user function Automatic row scaling of the jacobian is allowed Rank-1 updates are inhibited Problem is specified as being highly nonlinear Bounded damping strategy is off Maximum permitted number of iteration steps : 50 Internal parameters: Starting value for damping factor FCSTART = 1.00e-02 Minimum allowed damping factor FCMIN = 1.00e-02 Rank-1 updates decision parameter SIGMA = 1.00e+03 Initial Jacobian pseudo-rank IRANK = 3 Maximum permitted subcondition COND = 4.50e+15 ************************************************************************** It Normf Normx Damp.Fct. New Rank 0 8.3099014e+01 6.988e+01 0 3 1 8.2334158e+01 * 6.910e+01 0.010 Returned from call 1 of NLSCON 1 8.2334158e+01 4.391e+01 0 3 2 8.1472579e+01 * 4.326e+01 0.014 Returned from call 2 of NLSCON 2 8.1472579e+01 2.439e+01 0 3 3 7.8479019e+01 * 2.306e+01 0.052 Returned from call 3 of NLSCON 3 7.8479019e+01 9.814e+00 0 3 4 4.6199151e+01 * 5.612e+00 0.392 Returned from call 4 of NLSCON 4 4.6199151e+01 1.195e+00 0 3 5 5.5950642e+00 * 1.699e-01 1.000 Returned from call 5 of NLSCON 5 5.5950642e+00 6.203e-02 0 3 6 4.3348625e-01 * 3.558e-03 1.000 Returned from call 6 of NLSCON 6 4.3348625e-01 3.144e-03 0 3 7 6.8151570e-03 * 8.892e-06 1.000 Returned from call 7 of NLSCON 7 6.8151570e-03 8.955e-06 0 3 8 6.7420296e-03 * 1.144e-10 1.000 Solution of nonlinear least squares problem obtained within 8 iteration steps Incompatibility factor kappa 2.762e-03 Achieved relative accuracy 2.480e-08 Subcondition ( 1, 1) of constrained part 1.000e+00 Subcondition ( 2, 3) of least squares part 1.545e+00 Sensitivity ( lsq ) 2.890e+02 Under the assumptions of the classical linear model: Best unbiased estimate of variance and standard deviation of residuals: ----------------------------------------------------------------------- sigma2 = 6.061e-05 sigma = 7.785e-03 Covariance matrix of parameters ----------------- 1 2 3 1 7.55e-06 2 -2.34e-07 1.73e-07 3 6.11e-07 -1.85e-07 2.15e-07 Correlation coefficients ------------------------ 1 2 3 1 1.00 2 -0.20 1.00 3 0.48 -0.96 1.00 Standard deviation of parameters -------------------------------- No. Estimate sigma(X) 1 1.000e+02 +/- 2.748e-03 = 0.00 % 2 1.000e+01 +/- 4.158e-04 = 0.00 % 3 1.000e+01 +/- 4.638e-04 = 0.00 % independent confidence intervals -------------------------------- (on 95%-probability level using F-distribution F(alfa,1,m-n)= 5.12) 1 ( 9.999e+01 , 1.000e+02 ) 2 ( 9.999e+00 , 1.000e+01 ) 3 ( 9.999e+00 , 1.000e+01 ) ########################################################################### # # # # # Results from time monitor program for: NLSCON # # # # Total time: 0.710 Sum of parts: 0.190 # # # # name calls time av-time % total % sum # # NLSCON 1 0.520 0.5200 73.24 273.68 # # FCN 10 0.010 0.0010 1.41 5.26 # # Jacobi 9 0.000 0.0000 0.00 0.00 # # Lin-Fact 9 0.050 0.0056 7.04 26.32 # # Lin-Sol 23 0.030 0.0013 4.23 15.79 # # Output 25 0.100 0.0040 14.08 52.63 # # # ########################################################################### ****** Statistics * NLSCON ******* *** Gauss-Newton iter.: 8 *** *** Corrector steps : 0 *** *** Rejected rk-1 st. : 0 *** *** Jacobian eval. : 9 *** *** Function eval. : 10 *** *** ... for Jacobian : 0 *** ************************************* Returned from call 8 of NLSCON Time used = 0.840 Sec