Create Gaussian Function from Coords: Learn Integration & Matrix

In summary, The user is new and wants to create a Gaussian function using coordinates. They already have the function and need to find the values of a, b, and c. They ask for help with using integration and if it's possible to solve with a matrix. They mention that a power function or any function with the closest curve fit will also work. They are suggested to try a least squares fit using a second degree polynomial on the logarithm of the data.
  • #1
SHRock
8
0
I am completely new to this so bare with me.

I have co-ordinates and I want to create a Gaussian function. I already know the function which is

y=0.01235140544*e^(-(x-36.28663863)^2/(-135.1643617))

But I need to know how to get a,b,c

The Coordinates are

{35,.01}
{28,0.03}
{20,.1}
{15,.3}
{11,1}
{9,3}
{6,10}
{4.5,30}

Thanks

Edit: If your going to use integration then please give a basis or send a link to website where I can learn integration. Also is it possible to solve with a matrix. Well I don't really need a gaussian function, a power function will also work or any function with the closest curve fit
 
Last edited:
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  • #2
SHRock said:
I am completely new to this so bare with me.

Well, I'm certainly not going to take off my clothes with you. :blushing:

I have co-ordinates and I want to create a Gaussian function. I already know the function which is

y=0.01235140544*e^(-(x-36.28663863)^2/(-135.1643617))

But I need to know how to get a,b,c

The Coordinates are

{35,.01}
{28,0.03}
{20,.1}
{15,.3}
{11,1}
{9,3}
{6,10}
{4.5,30}

Thanks

Edit: If your going to use integration then please give a basis or send a link to website where I can learn integration. Also is it possible to solve with a matrix. Well I don't really need a gaussian function, a power function will also work or any function with the closest curve fit

Hard to say. I suppose you want to do a least squares regression. Since the logarithm of a Gaussian is a second degree polynomial you might take the log of the data and try a least squares fit by a second degree polynomial.
 

1. What is a Gaussian function?

A Gaussian function is a mathematical function that is commonly used to represent a normal distribution of data. It is also known as a bell curve due to its characteristic shape. It can be expressed as a function of the form f(x) = ae^(-b(x-c)^2), where a, b, and c are constants.

2. How do you create a Gaussian function from coordinates?

To create a Gaussian function from coordinates, you first need to have a set of data points that represent the curve of the function. Then, you can use a mathematical method called curve fitting to find the best-fitting Gaussian function that passes through these points. This can be done using techniques such as least squares regression or matrix operations.

3. Why is integration important in creating a Gaussian function?

Integration is important in creating a Gaussian function because it allows us to find the area under the curve, which is a crucial component of the function. The integral of a Gaussian function is equal to the standard deviation, which is a measure of the spread of the data. Without integration, we cannot accurately represent the shape and characteristics of the Gaussian function.

4. Can a Gaussian function be represented using a matrix?

Yes, a Gaussian function can be represented using a matrix. In fact, matrix operations are often used to create a Gaussian function from coordinates. This is because matrices allow us to perform mathematical operations on a set of data points, making it easier to find the best-fitting function that represents the data.

5. How is a Gaussian function used in science?

A Gaussian function has many applications in science, particularly in statistics, physics, and engineering. It is commonly used to model natural phenomena such as the distribution of particles in a gas, the distribution of errors in measurement data, and the intensity of light in an optical beam. It is also used in various computational methods and algorithms to solve complex problems in these fields.

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