The Origin Forum - Avoiding nonlinear constraints piecewise fit

The Origin Forum

Username:	Password:
Save Password
Forgot your Password? \| Admin Options

All Forums

Origin Forum for Programming

Forum for Origin C

Avoiding nonlinear constraints piecewise fit

New Topic

Reply to Topic

Printer Friendly

Author

Topic

harris.bra2

USA
1 Posts

Posted - 07/29/2018 : 3:39:56 PM

Origin Ver. and Service Release: OriginPro2016 (64-bit) Sr2 b9.3.2.303
Operating System: Windows 7 Enterprise

Hello,

Similar to this forum post, https://my.originlab.com/forum/topic.asp?TOPIC_ID=11148 ,I would like to create various piecewise functions with both fitting and first derivative continuity. However, I am having trouble understanding how the function was re-parameterized to avoid nonlinear constraints. Any help in understanding this derivation is greatly appreciated.

Thanks

yuki_wu

896 Posts

Posted - 07/29/2018 : 10:27:37 PM

Hi,

Actually you could take the issue of re-defining the fitting function as the issue of solving the equations. For example, the post you mentioned:

threshold_1: d0
y value at threshold_1: b0
derivative at threshold_1: k0

So we know that:

b0 = a0+a1*d0+a2*d0^2;
k0 = a1+2*a2*d0;

We define that:

parameter for the first quadratic: a

It means that:

b0 = a0+a1*d0+a*d0^2;
k0 = a1+2*a*d0;

So we can easily get that:

a1 = k0 – 2*a*d0;

and then:

a0 = b0 – k0*d0 + a*d0^2;

Now the function could be rewritten as:

y= b0 – k0*d0 + a*d0^2 + (k0 – 2*a*d0) *x + a*x^2;

and after modified:

y = b0 + k0*(x-d0) + a*(x-d0)^2;

Hope it helps.

Regards,
Yuki

OriginLab

Topic

New Topic

Reply to Topic

Printer Friendly

Jump To:

The Origin Forum

Snitz Forums 2000