Fitting Hamilton Peak Equations Using SciDavis

When working with complex datasets, scientists often need to find the best fit for their data. In this case, we'll explore how to fit a Hamilton peak equation using SciDavis and the genetic algorithm from scipy.optimize.

The Hamilton peak equation is a mathematical representation of the relationship between variables in a specific context. In our example, we're trying to model the behavior of angles and corresponding measured values. The equation takes the form of y = Gb * pow(x / mu, log(mu/x)/(B*B)) + (Vbmax * x) / (x + sigma_b).

To fit this equation to our data, we'll use SciDavis's genetic algorithm capabilities. We first generate initial parameters using the `generate_Initial_Parameters()` function and then call the `differential_evolution` function from scipy.optimize. This function minimizes the sum of squared errors between the predicted values and actual measured values.

After running the genetic algorithm, we can visualize our results using Matplotlib's plotting capabilities. We'll plot both the fitted data and the original measured data for comparison.

In this example, we were unable to fit the data to a Gaussian peak equation, likely due to the non-Gaussian shape of the data. The code provided below demonstrates how to fit a Gaussian distribution to some data points using SciDavis.

Here is the Python code used in this example:

```

import matplotlib.pyplot as plt

from scipy.optimize import differential_evolution

# Define the Hamilton peak equation

def func(x, Gb, mu, B, Vbmax, sigma_b):

return Gb * numpy.power(x / mu, numpy.log(mu/x)/(B*B)) + (Vbmax * x) / (x + sigma_b)

# Generate initial parameters using SciDavis's genetic algorithm

parameterBounds = ''

# Add search bounds for each parameter

Result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)

ParameterBounds.append()

# Visualize the results

plt.plot(angles, func(angles, *Result.x), 'r', label='Fit')

plt.plot(angles, data, 'ob', label = 'Measured')

# Calculate the sum of squared errors for each parameter

Sigma = sqrt(sum(data*(angles-mean)2)/sum(data))

```

By using SciDavis's genetic algorithm capabilities and plotting our results, we can effectively fit a Hamilton peak equation to our data. This is particularly useful when dealing with non-linear relationships between variables.

Scidavis line of best fit