Re: Can I use NonlinearModelFit to model some data with a piece wise linear function??

*To*: mathgroup at smc.vnet.net*Subject*: [mg120013] Re: Can I use NonlinearModelFit to model some data with a piece wise linear function??*From*: Heike Gramberg <heike.gramberg at gmail.com>*Date*: Tue, 5 Jul 2011 05:11:33 -0400 (EDT)*References*: <201107041044.GAA02488@smc.vnet.net>

This seems to work better: m = NonlinearModelFit[curve, f[x], {c1, c2, a1, b1, a2, b2, a3, b3}, {x}, Method -> NMinimize] Heike. On 4 Jul 2011, at 11:44, morris wrote: > I attempt to do this, but it does not seem to work very well. See > example session below. I first create some data out of three linear > functions, plus a little bit of random perturbation. Then I have a > function f[x] which is a piecewise linear function, with three pieces. > > NonlinearModelFit seems however to respond with only two pieces, by > giving the same value to the two parameters which represent the cut > points (c1 and c2 in the below example). > > Thank you for any thoughts. > > Happy Independence Day to Americans. > > -------------------------------------------------------------------------- - > > > In[49]:= > > curve = Join[Table[{i, -2i},{i,-14,6}], Table[{i,5},{i,7,10}], > Table[{i, 3 i}, {i, 11, 20}]] + Table[Random[Real,0.25],{35}] > > Out[49]= {{-13.782,28.218},{-12.8514,26.1486},{-11.9445,24.0555}, > {-10.9566,22.0434},{-9.85094,20.1491},{-8.75561,18.2444}, > {-7.92158,16.0784},{-6.99195,14.008},{-5.79096,12.209}, > {-4.95951,10.0405},{-3.96988,8.03012},{-2.92945,6.07055}, > {-1.98475,4.01525},{-0.877226,2.12277},{0.157389,0.157389}, > {1.10679,-1.89321},{2.17641,-3.82359},{3.22352,-5.77648}, > {4.04408,-7.95592},{5.17738,-9.82262},{6.16403,-11.836}, > = {7.23777,5.23777},{8.03634,5.03634},{9.01375,5.01375},{10.196,5.19598}, > {11.0892,33.0892},{12.2308,36.2308},{13.2204,39.2204}, > {14.0469,42.0469},{15.0948,45.0948},{16.1524,48.1524}, > {17.2123,51.2123},{18.0879,54.0879},{19.0543,57.0543}, > {20.1223,60.1223}} > > In[50]:= f[x_] := Piecewise[{ {a1 + x b1, x < c1}, {a2 + x b2, c1 > <= x <= c2}, {a3 + x b3, x > c2}}] > > > Out[50]= \[Piecewise] a1+b1 x x<c1 > a2+b2 x c1<=x<=c2 > a3+b3 x x>c2 > 0 True > > > In[51]:= m = NonlinearModelFit[curve, f[x], {c1,c2,a1,b1,a2,b2,a3,b3}, > {x}] > > > ] > In[52]:= Normal[m] > > Out[52]= \[Piecewise] 0.227214 -2.0132 x x<1. > 1. +1. x 1.<=x<=1. > -22.4279+4.20451 x x>1. > 0 True > > >

**References**:**Can I use NonlinearModelFit to model some data with a piece wise linear function??***From:*morris <morris.pearl@gmail.com>