Function derivative problem: 500 pts, fcn is in form of Gauss bell; can deriv. be...?

[staler]

Hello good ones!

I have to solve the next problem:

I have a graph (taken from a program) with more than 500 points among which there is very little variation.
This function is in the form of a Gauss bell, and I would like to calculate the derivative at one point precisely.

Is there any way I can use the points I have to calculate the derivative?

IMPORTANT: the point is at the right end of the function, the derivative can be said to be between 0 and 1.

Would something like this work? :

. . .\(\displaystyle \mbox{derived on }x(0)\, =\, \dfrac{\sum_{i=1}^{100?}\, \frac{x(-i)\, -\, x(i)}{2\times i}}{100}\)

Basically, it calculates the derivative of an interval centered on x₀ that grows and makes the mean.

The ideal answer would be for someone to tell me a program to create a function (like linear regression but with a curve) and be able to calculate the tangent slope of this curve in x0. (or maybe it's a lot easier jejeje):smile:

 

[tkhunny]

Hello good ones!

I have to solve the next problem:

I have a graph (taken from a program) with more than 500 points among which there is very little variation.
This function is in the form of a Gauss bell, and I would like to calculate the derivative at one point precisely.

Is there any way I can use the points I have to calculate the derivative?

IMPORTANT: the point is at the right end of the function, the derivative can be said to be between 0 and 1.

Would something like this work? :

. . .\(\displaystyle \mbox{derived on }x(0)\, =\, \dfrac{\sum_{i=1}^{100?}\, \frac{x(-i)\, -\, x(i)}{2\times i}}{100}\)

Basically, it calculates the derivative of an interval centered on x₀ that grows and makes the mean.

The ideal answer would be for someone to tell me a program to create a function (like linear regression but with a curve) and be able to calculate the tangent slope of this curve in x0. (or maybe it's a lot easier jejeje):smile:

There are various ways to go abut it. You have suggested one way.

1) Forward difference, \(\displaystyle x_{i+1}-x_{i}\)
2) Backward difference, \(\displaystyle x_{i}-x_{i-1}\)
3) Central difference, \(\displaystyle \dfrac{x_{i+1}-x_{i-1}}{2}\) <== This seems to be what you are contemplating.

These are just linear functions, but they may be sufficient for your needs - particularly far out in the tails where all the slopes are very close to zero (0), anyway.

There certainly are quadratic methods. Essentially, fit a quadratic polynomial (parabola?) to the three points \(\displaystyle x_{i-1},\;x_{i},\;x_{i+1}\), and find the derivative of that.

Cubic Spline methods are also very popular and you shouldn't have much trouble finding fully programmed solutions of this sort.

 

[staler]

There are various ways to go abut it. You have suggested one way.

1) Forward difference, \(\displaystyle x_{i+1}-x_{i}\)
2) Backward difference, \(\displaystyle x_{i}-x_{i-1}\)
3) Central difference, \(\displaystyle \dfrac{x_{i+1}-x_{i-1}}{2}\) <== This seems to be what you are contemplating.

These are just linear functions, but they may be sufficient for your needs - particularly far out in the tails where all the slopes are very close to zero (0), anyway.

There certainly are quadratic methods. Essentially, fit a quadratic polynomial (parabola?) to the three points \(\displaystyle x_{i-1},\;x_{i},\;x_{i+1}\), and find the derivative of that.

Cubic Spline methods are also very popular and you shouldn't have much trouble finding fully programmed solutions of this sort.

Fantastic, I think Spline's methods will help me, besides what I've seen programming requires using a simple and sad function.

Thanks!!!

 

[staler]

Fantastic, I think Spline's methods will help me, besides what I've seen programming requires using a simple and sad function.