wrapnls: Nash variant of Marquardt nonlinear least squares solution... In nlmrt: Functions for Nonlinear Least Squares Solutions

Description

Given a nonlinear model expressed as an expression of the form lhs ~ formula_for_rhs and a start vector where parameters used in the model formula are named, attempts to find the minimum of the residual sum of squares using the Nash variant (Nash, 1979) of the Marquardt algorithm, where the linear sub-problem is solved by a qr method.

Usage

 ```1 2``` ``` wrapnls(formula, start, trace=FALSE, data, lower=-Inf, upper=Inf, control=list(), ...) ```

Arguments

 `formula` This is a modeling formula of the form (as in `nls`) lhsvar ~ rhsexpression for example, y ~ b1/(1+b2*exp(-b3*tt)) You may also give this as a string. `start` A named parameter vector. For our example, we could use start=c(b1=1, b2=2.345, b3=0.123) `trace` Logical TRUE if we want intermediate progress to be reported. Default is FALSE. `data` A data frame containing the data of the variables in the formula. This data may, however, be supplied directly in the parent frame. `lower` Lower bounds on the parameters. If a single number, this will be applied to all parameters. Default -Inf. `upper` Upper bounds on the parameters. If a single number, this will be applied to all parameters. Default Inf. `control` A list of controls for the algorithm. These are as for `nlxb()`. `...` Any data needed for computation of the residual vector from the expression rhsexpression - lhsvar. Note that this is the negative of the usual residual, but the sum of squares is the same.

Details

`wrapnls` first attempts to solve the nonlinear sum of squares problem by using `nlsmnq`, then takes the parameters from that method to call `nls`.

Value

An object of type nls.

Note

Special notes, if any, will appear here.

Author(s)

John C Nash <nashjc@uottawa.ca>

Function `nls()`, packages `optim` and `optimx`.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```cat("See examples in nlmrt-package.Rd\n") ## Not run: cat("kvanderpoel.R test\n") # require(nlmrt) x<-c(1,3,5,7) y<-c(37.98,11.68,3.65,3.93) pks28<-data.frame(x=x,y=y) fit0<-try(nls(y~(a+b*exp(1)^(-c*x)), data=pks28, start=c(a=0,b=1,c=1), trace=TRUE)) print(fit0) cat("\n\n") fit1<-nlxb(y~(a+b*exp(-c*x)), data=pks28, start=c(a=0,b=1,c=1), trace = TRUE) print(fit1) cat("\n\nor better\n") fit2<-wrapnls(y~(a+b*exp(-c*x)), data=pks28, start=c(a=0,b=1,c=1), lower=-Inf, upper=Inf, trace = TRUE) ## End(Not run) ```

Example output

```See examples in nlmrt-package.Rd
kvanderpoel.R test
1578.645 :  0 1 1
Error in nls(y ~ (a + b * exp(1)^(-c * x)), data = pks28, start = c(a = 0,  :
[1] "Error in nls(y ~ (a + b * exp(1)^(-c * x)), data = pks28, start = c(a = 0,  : \n  singular gradient\n"
attr(,"class")
[1] "try-error"
attr(,"condition")
<simpleError in nls(y ~ (a + b * exp(1)^(-c * x)), data = pks28, start = c(a = 0,     b = 1, c = 1), trace = TRUE): singular gradient>

formula: y ~ (a + b * exp(-c * x))
lower:[1] -Inf -Inf -Inf
upper:[1] Inf Inf Inf
\$watch
[1] FALSE

\$phi
[1] 1

\$lamda
[1] 1e-04

\$offset
[1] 100

\$laminc
[1] 10

\$lamdec
[1] 4

\$femax
[1] 10000

\$jemax
[1] 5000

\$rofftest
[1] TRUE

\$smallsstest
[1] TRUE

Data variable  y :[1] 37.98 11.68  3.65  3.93
Data variable  x :[1] 1 3 5 7
ssminval = 3.837472e-52
Start:lamda: 1e-04  SS= 1578.645  at  a = 0  b = 1  c = 1  1 / 0
roff = 0.01798225   converged =  FALSE
delta:         a          b          c
2.898802  55.764363 -38.578881
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -1576.673  g-delta-angle= 112.5043
Stepsize= 1
lamda: 0.001  SS= 9.825646e+231  at  a = 2.898802  b = 56.76436  c = -37.57888  2 / 1
roff = 0.01797215   converged =  FALSE
delta:         a          b          c
2.891989  53.826779 -40.083111
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -1571.948  g-delta-angle= 112.6787
Stepsize= 1
lamda: 0.01  SS= 1.28262e+241  at  a = 2.891989  b = 54.82678  c = -39.08311  3 / 1
roff = 0.01787202   converged =  FALSE
delta:         a          b          c
3.329004  47.604273 -41.422536
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -1527.958  g-delta-angle= 113.478
Stepsize= 1
lamda: 0.1  SS= 1.403869e+249  at  a = 3.329004  b = 48.60427  c = -40.42254  4 / 1
roff = 0.01695489   converged =  FALSE
delta:        a         b         c
6.16719  30.61928 -28.77994
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -1245.117  g-delta-angle= 118.8829
Stepsize= 1
lamda: 1  SS= 8.041638e+171  at  a = 6.16719  b = 31.61928  c = -27.77994  5 / 1
roff = 0.01198892   converged =  FALSE
delta:        a         b         c
5.367741  8.553635 -8.732985
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -565.8112  g-delta-angle= 134.2884
Stepsize= 1
lamda: 10  SS= 9.502462e+48  at  a = 5.367741  b = 9.553635  c = -7.732985  6 / 1
roff = 0.004894455   converged =  FALSE
delta:        a         b         c
1.029512  1.200343 -1.274897
gjty:       [,1]
a -56.81468
b -14.44389
c  15.72165
gradient projection =  -95.87249  g-delta-angle= 141.0457
Stepsize= 1
<<lamda: 4  SS= 1376.483  at  a = 1.029512  b = 2.200343  c = -0.2748967  7 / 1
roff = 0.003432671   converged =  FALSE
delta:          a           b           c
1.12138993 -0.13017194  0.02158386
gjty:         [,1]
a   -21.43526
b    49.73320
c -1365.17201
gradient projection =  -59.97684  g-delta-angle= 92.22815
Stepsize= 1
<<lamda: 1.6  SS= 1268.393  at  a = 2.150902  b = 2.070171  c = -0.2533128  8 / 2
roff = 0.004512416   converged =  FALSE
delta:          a           b           c
2.63999160 -0.20066214  0.05139754
gjty:        [,1]
a  -22.00430
b   28.44767
c -947.33154
gradient projection =  -112.4901  g-delta-angle= 92.56822
Stepsize= 1
<<lamda: 0.64  SS= 1079.224  at  a = 4.790893  b = 1.869509  c = -0.2019153  9 / 3
roff = 0.005898425   converged =  FALSE
delta:         a          b          c
4.9134326 -0.2008255  0.1504071
gjty:         [,1]
a  -19.548218
b    8.167601
c -514.163985
gradient projection =  -175.023  g-delta-angle= 93.96409
Stepsize= 1
<<lamda: 0.256  SS= 837.4101  at  a = 9.704326  b = 1.668684  c = -0.05150818  10 / 4
roff = 0.009114429   converged =  FALSE
delta:        a         b         c
5.5922846 2.4711714 0.8987755
gjty:         [,1]
a  -10.166327
b   -5.614464
c -178.718897
gradient projection =  -231.3555  g-delta-angle= 102.0661
Stepsize= 1
<<lamda: 0.1024  SS= 719.2259  at  a = 15.29661  b = 4.139855  c = 0.8472674  11 / 5
roff = 0.0115773   converged =  FALSE
delta:         a          b          c
-10.068376  18.449543  -9.473408
gjty:       [,1]
a  6.117488
b -8.451447
c 28.864116
gradient projection =  -490.96  g-delta-angle= 133.9363
Stepsize= 1
lamda: 1.024  SS= 1.431537e+55  at  a = 5.228235  b = 22.5894  c = -8.626141  12 / 6
roff = 0.005934697   converged =  FALSE
delta:        a         b         c
-2.074776  4.806960 -3.287280
gjty:       [,1]
a  6.117488
b -8.451447
c 28.864116
gradient projection =  -148.2026  g-delta-angle= 141.3604
Stepsize= 1
lamda: 10.24  SS= 5.481975e+16  at  a = 13.22183  b = 8.946815  c = -2.440012  13 / 6
roff = 0.002398028   converged =  FALSE
delta:         a          b          c
-0.1454281  0.6549456 -0.5008065
gjty:       [,1]
a  6.117488
b -8.451447
c 28.864116
gradient projection =  -20.88023  g-delta-angle= 144.3516
Stepsize= 1
<<lamda: 4.096  SS= 692.6514  at  a = 15.15118  b = 4.7948  c = 0.3464608  14 / 6
roff = 0.002146874   converged =  FALSE
delta:         a          b          c
-0.3757641  1.3318075  0.1460450
gjty:        [,1]
a   9.723566
b  -8.704454
c -47.316542
gradient projection =  -22.15677  g-delta-angle= 108.9298
Stepsize= 1
<<lamda: 1.6384  SS= 656.4639  at  a = 14.77542  b = 6.126608  c = 0.4925059  15 / 7
roff = 0.003896466   converged =  FALSE
delta:          a           b           c
-0.98865317  3.67502143 -0.06868624
gjty:       [,1]
a  7.720791
b -9.522894
c  8.537827
gradient projection =  -43.21645  g-delta-angle= 139.4633
Stepsize= 1
<<lamda: 0.65536  SS= 574.9895  at  a = 13.78677  b = 9.801629  c = 0.4238196  16 / 8
roff = 0.005282929   converged =  FALSE
delta:         a          b          c
-1.8320566  7.6102480  0.1595926
gjty:        [,1]
a   8.753300
b  -8.382064
c -29.189998
gradient projection =  -84.48463  g-delta-angle= 109.9633
Stepsize= 1
<<lamda: 0.262144  SS= 431.5791  at  a = 11.95471  b = 17.41188  c = 0.5834122  17 / 9
roff = 0.007153294   converged =  FALSE
delta:         a          b          c
-4.4478256 12.8527844 -0.3424349
gjty:       [,1]
a  4.554621
b -7.887093
c 67.894773
gradient projection =  -144.8788  g-delta-angle= 98.94307
Stepsize= 1
<<lamda: 0.1048576  SS= 406.7021  at  a = 7.506883  b = 30.26466  c = 0.2409773  18 / 10
roff = 0.00771817   converged =  FALSE
delta:         a          b          c
-1.3777045 10.0998150  0.2456068
gjty:          [,1]
a    25.932764
b     5.420315
c -1250.555827
gradient projection =  -288.1285  g-delta-angle= 91.2945
Stepsize= 1
<<lamda: 0.04194304  SS= 112.9539  at  a = 6.129179  b = 40.36448  c = 0.4865841  19 / 11
roff = 0.005099782   converged =  FALSE
delta:         a          b          c
-3.2222965 17.5720980  0.1223591
gjty:        [,1]
a   6.348208
b  -2.791665
c -72.833953
gradient projection =  -78.42311  g-delta-angle= 93.43968
Stepsize= 1
<<lamda: 0.01677722  SS= 17.07995  at  a = 2.906882  b = 57.93657  c = 0.6089431  20 / 12
roff = 0.002151038   converged =  FALSE
delta:          a           b           c
-0.56364638  9.23948056  0.04531169
gjty:       [,1]
a -1.201547
b -1.754773
c 70.184908
gradient projection =  -12.35575  g-delta-angle= 91.08922
Stepsize= 1
<<lamda: 0.006710886  SS= 2.874758  at  a = 2.343236  b = 67.17606  c = 0.6542548  21 / 13
roff = 0.000412064   converged =  FALSE
delta:         a          b          c
0.26451237 3.51094254 0.04062555
gjty:        [,1]
a -0.2718822
b -0.3206090
c 10.6931805
gradient projection =  -0.7631395  g-delta-angle= 91.16047
Stepsize= 1
<<lamda: 0.002684355  SS= 2.00806  at  a = 2.607748  b = 70.687  c = 0.6948804  22 / 14
roff = 8.729957e-05   converged =  FALSE
delta:         a          b          c
0.05972416 0.91068705 0.01101228
gjty:          [,1]
a -0.001170592
b -0.050432556
c  1.015417300
gradient projection =  -0.03481612  g-delta-angle= 92.15027
Stepsize= 1
<<lamda: 0.001073742  SS= 1.970968  at  a = 2.667472  b = 71.59769  c = 0.7058927  23 / 15
roff = 7.24721e-06   converged =  FALSE
delta:           a            b            c
0.0046798671 0.0817740881 0.0009587026
gjty:           [,1]
a  0.0002227431
b -0.0043130928
c  0.1026428862
gradient projection =  -0.0002532528  g-delta-angle= 91.72454
Stepsize= 1
<<lamda: 0.0004294967  SS= 1.970713  at  a = 2.672152  b = 71.67946  c = 0.7068514  24 / 16
roff = 1.889931e-07   converged =  FALSE
delta:            a             b             c
-1.530179e-04  5.600060e-04 -3.575195e-06
gjty:           [,1]
a -2.003162e-05
b -1.202886e-04
c  7.466808e-03
gradient projection =  -9.099242e-08  g-delta-angle= 91.20262
Stepsize= 1
<<lamda: 0.0001717987  SS= 1.970712  at  a = 2.671999  b = 71.68002  c = 0.7068478  25 / 17
roff = 2.424471e-09   converged =  TRUE
delta:           a            b            c
2.695436e-06 2.083874e-05 3.279176e-07
gjty:           [,1]
a  3.319170e-07
b -3.019386e-07
c -3.087135e-05
gradient projection =  -1.552062e-11  g-delta-angle= 91.37071
Stepsize= 1
<<lamda: 6.871948e-05  SS= 1.970712  at  a = 2.672002  b = 71.68004  c = 0.7068481  26 / 18
nlmrt class object: x
residual sumsquares =  1.9707  on  4 observations
after  18    Jacobian and  26 function evaluations
name            coeff          SE       tstat      pval      gradient    JSingval
a                  2.672         1.476      1.811     0.3212  -2.312e-09       45.17
b                  71.68          7.71      9.297    0.06821  -4.506e-09       1.112
c               0.706848        0.1207      5.856     0.1077  -1.148e-07      0.1812

or better
wrapnls call with lower=[1] -Inf -Inf -Inf
and upper=[1] Inf Inf Inf
formula: y ~ (a + b * exp(-c * x))
lower:[1] -Inf -Inf -Inf
upper:[1] Inf Inf Inf
\$watch
[1] FALSE

\$phi
[1] 1

\$lamda
[1] 1e-04

\$offset
[1] 100

\$laminc
[1] 10

\$lamdec
[1] 4

\$femax
[1] 10000

\$jemax
[1] 5000

\$rofftest
[1] TRUE

\$smallsstest
[1] TRUE

Data variable  y :[1] 37.98 11.68  3.65  3.93
Data variable  x :[1] 1 3 5 7
ssminval = 3.8375e-52
Start:lamda: 1e-04  SS= 1578.6  at  a = 0  b = 1  c = 1  1 / 0
roff = 0.017982   converged =  FALSE
delta:       a        b        c
2.8988  55.7644 -38.5789
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -1576.7  g-delta-angle= 112.5
Stepsize= 1
lamda: 0.001  SS= 9.8256e+231  at  a = 2.8988  b = 56.764  c = -37.579  2 / 1
roff = 0.017972   converged =  FALSE
delta:      a       b       c
2.892  53.827 -40.083
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -1571.9  g-delta-angle= 112.68
Stepsize= 1
lamda: 0.01  SS= 1.2826e+241  at  a = 2.892  b = 54.827  c = -39.083  3 / 1
roff = 0.017872   converged =  FALSE
delta:      a       b       c
3.329  47.604 -41.423
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -1528  g-delta-angle= 113.48
Stepsize= 1
lamda: 0.1  SS= 1.4039e+249  at  a = 3.329  b = 48.604  c = -40.423  4 / 1
roff = 0.016955   converged =  FALSE
delta:       a        b        c
6.1672  30.6193 -28.7799
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -1245.1  g-delta-angle= 118.88
Stepsize= 1
lamda: 1  SS= 8.0416e+171  at  a = 6.1672  b = 31.619  c = -27.78  5 / 1
roff = 0.011989   converged =  FALSE
delta:      a       b       c
5.3677  8.5536 -8.7330
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -565.81  g-delta-angle= 134.29
Stepsize= 1
lamda: 10  SS= 9.5025e+48  at  a = 5.3677  b = 9.5536  c = -7.733  6 / 1
roff = 0.0048945   converged =  FALSE
delta:      a       b       c
1.0295  1.2003 -1.2749
gjty:     [,1]
a -56.815
b -14.444
c  15.722
gradient projection =  -95.872  g-delta-angle= 141.05
Stepsize= 1
<<lamda: 4  SS= 1376.5  at  a = 1.0295  b = 2.2003  c = -0.2749  7 / 1
roff = 0.0034327   converged =  FALSE
delta:        a         b         c
1.121390 -0.130172  0.021584
gjty:       [,1]
a   -21.435
b    49.733
c -1365.172
gradient projection =  -59.977  g-delta-angle= 92.228
Stepsize= 1
<<lamda: 1.6  SS= 1268.4  at  a = 2.1509  b = 2.0702  c = -0.25331  8 / 2
roff = 0.0045124   converged =  FALSE
delta:        a         b         c
2.639992 -0.200662  0.051398
gjty:      [,1]
a  -22.004
b   28.448
c -947.332
gradient projection =  -112.49  g-delta-angle= 92.568
Stepsize= 1
<<lamda: 0.64  SS= 1079.2  at  a = 4.7909  b = 1.8695  c = -0.20192  9 / 3
roff = 0.0058984   converged =  FALSE
delta:       a        b        c
4.91343 -0.20083  0.15041
gjty:       [,1]
a  -19.5482
b    8.1676
c -514.1640
gradient projection =  -175.02  g-delta-angle= 93.964
Stepsize= 1
<<lamda: 0.256  SS= 837.41  at  a = 9.7043  b = 1.6687  c = -0.051508  10 / 4
roff = 0.0091144   converged =  FALSE
delta:      a       b       c
5.59228 2.47117 0.89878
gjty:       [,1]
a  -10.1663
b   -5.6145
c -178.7189
gradient projection =  -231.36  g-delta-angle= 102.07
Stepsize= 1
<<lamda: 0.1024  SS= 719.23  at  a = 15.297  b = 4.1399  c = 0.84727  11 / 5
roff = 0.011577   converged =  FALSE
delta:       a        b        c
-10.0684  18.4495  -9.4734
gjty:     [,1]
a  6.1175
b -8.4514
c 28.8641
gradient projection =  -490.96  g-delta-angle= 133.94
Stepsize= 1
lamda: 1.024  SS= 1.4315e+55  at  a = 5.2282  b = 22.589  c = -8.6261  12 / 6
roff = 0.0059347   converged =  FALSE
delta:      a       b       c
-2.0748  4.8070 -3.2873
gjty:     [,1]
a  6.1175
b -8.4514
c 28.8641
gradient projection =  -148.2  g-delta-angle= 141.36
Stepsize= 1
lamda: 10.24  SS= 5.482e+16  at  a = 13.222  b = 8.9468  c = -2.44  13 / 6
roff = 0.002398   converged =  FALSE
delta:       a        b        c
-0.14543  0.65495 -0.50081
gjty:     [,1]
a  6.1175
b -8.4514
c 28.8641
gradient projection =  -20.88  g-delta-angle= 144.35
Stepsize= 1
<<lamda: 4.096  SS= 692.65  at  a = 15.151  b = 4.7948  c = 0.34646  14 / 6
roff = 0.0021469   converged =  FALSE
delta:       a        b        c
-0.37576  1.33181  0.14605
gjty:      [,1]
a   9.7236
b  -8.7045
c -47.3165
gradient projection =  -22.157  g-delta-angle= 108.93
Stepsize= 1
<<lamda: 1.6384  SS= 656.46  at  a = 14.775  b = 6.1266  c = 0.49251  15 / 7
roff = 0.0038965   converged =  FALSE
delta:        a         b         c
-0.988653  3.675021 -0.068686
gjty:     [,1]
a  7.7208
b -9.5229
c  8.5378
gradient projection =  -43.216  g-delta-angle= 139.46
Stepsize= 1
<<lamda: 0.65536  SS= 574.99  at  a = 13.787  b = 9.8016  c = 0.42382  16 / 8
roff = 0.0052829   converged =  FALSE
delta:       a        b        c
-1.83206  7.61025  0.15959
gjty:      [,1]
a   8.7533
b  -8.3821
c -29.1900
gradient projection =  -84.485  g-delta-angle= 109.96
Stepsize= 1
<<lamda: 0.26214  SS= 431.58  at  a = 11.955  b = 17.412  c = 0.58341  17 / 9
roff = 0.0071533   converged =  FALSE
delta:       a        b        c
-4.44783 12.85278 -0.34243
gjty:     [,1]
a  4.5546
b -7.8871
c 67.8948
gradient projection =  -144.88  g-delta-angle= 98.943
Stepsize= 1
<<lamda: 0.10486  SS= 406.7  at  a = 7.5069  b = 30.265  c = 0.24098  18 / 10
roff = 0.0077182   converged =  FALSE
delta:       a        b        c
-1.37770 10.09982  0.24561
gjty:        [,1]
a    25.9328
b     5.4203
c -1250.5558
gradient projection =  -288.13  g-delta-angle= 91.295
Stepsize= 1
<<lamda: 0.041943  SS= 112.95  at  a = 6.1292  b = 40.364  c = 0.48658  19 / 11
roff = 0.0050998   converged =  FALSE
delta:       a        b        c
-3.22230 17.57210  0.12236
gjty:      [,1]
a   6.3482
b  -2.7917
c -72.8340
gradient projection =  -78.423  g-delta-angle= 93.44
Stepsize= 1
<<lamda: 0.016777  SS= 17.08  at  a = 2.9069  b = 57.937  c = 0.60894  20 / 12
roff = 0.002151   converged =  FALSE
delta:        a         b         c
-0.563646  9.239481  0.045312
gjty:     [,1]
a -1.2015
b -1.7548
c 70.1849
gradient projection =  -12.356  g-delta-angle= 91.089
Stepsize= 1
<<lamda: 0.0067109  SS= 2.8748  at  a = 2.3432  b = 67.176  c = 0.65425  21 / 13
roff = 0.00041206   converged =  FALSE
delta:       a        b        c
0.264512 3.510943 0.040626
gjty:      [,1]
a -0.27188
b -0.32061
c 10.69318
gradient projection =  -0.76314  g-delta-angle= 91.16
Stepsize= 1
<<lamda: 0.0026844  SS= 2.0081  at  a = 2.6077  b = 70.687  c = 0.69488  22 / 14
roff = 8.73e-05   converged =  FALSE
delta:       a        b        c
0.059724 0.910687 0.011012
gjty:        [,1]
a -0.0011706
b -0.0504326
c  1.0154173
gradient projection =  -0.034816  g-delta-angle= 92.15
Stepsize= 1
<<lamda: 0.0010737  SS= 1.971  at  a = 2.6675  b = 71.598  c = 0.70589  23 / 15
roff = 7.2472e-06   converged =  FALSE
delta:        a         b         c
0.0046799 0.0817741 0.0009587
gjty:         [,1]
a  0.00022274
b -0.00431309
c  0.10264289
gradient projection =  -0.00025325  g-delta-angle= 91.725
Stepsize= 1
<<lamda: 0.0004295  SS= 1.9707  at  a = 2.6722  b = 71.679  c = 0.70685  24 / 16
roff = 1.8899e-07   converged =  FALSE
delta:          a           b           c
-1.5302e-04  5.6001e-04 -3.5752e-06
gjty:         [,1]
a -2.0032e-05
b -1.2029e-04
c  7.4668e-03
gradient projection =  -9.0992e-08  g-delta-angle= 91.203
Stepsize= 1
<<lamda: 0.0001718  SS= 1.9707  at  a = 2.672  b = 71.68  c = 0.70685  25 / 17
roff = 2.4245e-09   converged =  TRUE
delta:         a          b          c
2.6954e-06 2.0839e-05 3.2792e-07
gjty:         [,1]
a  3.3192e-07
b -3.0194e-07
c -3.0871e-05
gradient projection =  -1.5521e-11  g-delta-angle= 91.371
Stepsize= 1
<<lamda: 6.8719e-05  SS= 1.9707  at  a = 2.672  b = 71.68  c = 0.70685  26 / 18
nlmrt class object: x
residual sumsquares =  1.9707  on  4 observations
after  18    Jacobian and  26 function evaluations
name            coeff          SE       tstat      pval      gradient    JSingval
a                  2.672         1.476      1.811     0.3212  -2.312e-09       45.17
b                  71.68          7.71      9.297    0.06821  -4.506e-09       1.112
c               0.706848        0.1207      5.856     0.1077  -1.148e-07      0.1812
newstart:       a        b        c
2.67200 71.68004  0.70685
nls call with no bounds
1.9707 :   2.67200 71.68004  0.70685
```

nlmrt documentation built on May 1, 2019, 11:31 p.m.