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
>
>
>

```

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