| T O P I C R E V I E W |
| harris.bra2 |
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 |
| 1 L A T E S T R E P L I E S (Newest First) |
| yuki_wu |
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
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