How does a tensor product spline equation in MatLab code look like?

Hello,

can anyone help me to convert this equation :

into MatLab code, or provide me a comparable equation in MatLab code? I want to use this equation later on as "custom equation" in the "curve fitting tool". Thank you!

Answer 1

[Sachin Meena]

Hi Lukas. If I understand your problem correctly, I believe the documentation link that you have provided contains your answer. In the section "B-form of Tensor Product Splines", the command given

Sp = spmat({s,t},a);

does what you are asking for. Here, the number vectors [m,n] are acquired from the size of "a", the coefficient matrix provided. With size of "s" and "t" known and the number vectors acquired, it also gets the orders vector [h,k].

So the equation is now in variable Sp.

[Lukas Sohlbach]

Hi Sachin,

thanks for your answer. I need an equation for this function of the curve fitting tool. The equation should fit in here:

[Sachin Meena]

So you have "s", "t", "x", "y", and "z", and you need to find the coefficient matrix "a". Is that right?

[Lukas Sohlbach]

I just have data points in three vectors (x,y,z) which i loaded in the curve fitting tool. Now i want to fit a tensor product spline to this data points. The mathematical equation for a tensor product spline is shown in the my question. I need to convert this equation into a form MatLab (the curve fitting tool) can understand and work with.

[Sachin Meena]

And what is the outcome that you are expecting from this? The knots sequence or the coefficient matrix?

[Lukas Sohlbach]

The coefficient matrix.

[Sachin Meena]

Hey Lukas, it turns out that your use case is not yet supported by the cftool. The issue with using

spmat({s,t},a)

is that it does not explicitly uses "x" and "y", while the issue with using

spapi({s,t},[h,k],{x,y},z)

is that the dependent variable "z" cannot occur on both sides of the equation.