SciPy with Matplotlib for visualization

Introduction

SciPy helps us do math and science calculations easily. Matplotlib lets us draw pictures of data so we can understand it better.

You want to find the best curve that fits your data points.

You need to solve math problems like integration or optimization and show the results.

You want to compare two sets of data visually after doing calculations.

You have scientific data and want to plot graphs to explain it clearly.

Syntax

SciPy

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

# Define a function to fit
def f(x, a, b):
    return a * x + b

# Sample data
xdata = np.array([1, 2, 3, 4, 5])
ydata = np.array([2, 4, 6, 8, 10])

# Use optimize.curve_fit to find best a, b
params, covariance = optimize.curve_fit(f, xdata, ydata)

# Plot original data and fitted curve
plt.scatter(xdata, ydata)
plt.plot(xdata, f(xdata, *params))
plt.show()

Use optimize.curve_fit to fit a function to data points.

Matplotlib's plt.scatter shows data points, plt.plot draws lines.

Examples

This example fits a straight line to points and shows both on a graph.

SciPy

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

# Sample data
xdata = np.array([1, 2, 3, 4, 5])
ydata = np.array([2.1, 4.1, 6.0, 8.1, 10.2])

# Define linear function
def linear(x, a, b):
    return a * x + b

# Fit data
params, _ = optimize.curve_fit(linear, xdata, ydata)

# Plot
plt.scatter(xdata, ydata, label='Data')
plt.plot(xdata, linear(xdata, *params), label='Fit', color='red')
plt.legend()
plt.show()

This example calculates the area under sin(x) from 0 to π and shows it shaded on the plot.

SciPy

import numpy as np
from scipy import integrate
import matplotlib.pyplot as plt

# Define function to integrate
def f(x):
    return np.sin(x)

# Calculate integral from 0 to pi
result, error = integrate.quad(f, 0, np.pi)

# Plot function
x = np.linspace(0, np.pi, 100)
y = f(x)
plt.plot(x, y, label='sin(x)')
plt.fill_between(x, 0, y, alpha=0.3)
plt.title(f'Integral from 0 to pi = {result:.2f}')
plt.legend()
plt.show()

Sample Program

This program creates noisy data points that roughly follow a line. It uses SciPy to find the best line that fits the points. Then it draws the points and the fitted line on a graph.

SciPy

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

# Data points with some noise
xdata = np.linspace(0, 10, 20)
ydata = 3.5 * xdata + 2 + np.random.normal(0, 2, size=xdata.size)

# Define linear function to fit
def linear_func(x, a, b):
    return a * x + b

# Fit the data
params, covariance = optimize.curve_fit(linear_func, xdata, ydata)

# Print fitted parameters
a_fit, b_fit = params
print(f'Fitted line: y = {a_fit:.2f} * x + {b_fit:.2f}')

# Plot data and fitted line
plt.scatter(xdata, ydata, label='Data points')
plt.plot(xdata, linear_func(xdata, *params), color='red', label='Fitted line')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Linear Fit using SciPy and Matplotlib')
plt.legend()
plt.show()

Important Notes

Always check your data before fitting to avoid errors.

Matplotlib plots appear in a window or inline if using notebooks.

Fitting results depend on data quality and initial guesses.

Summary

SciPy helps with math tasks like fitting and integration.

Matplotlib shows data and results visually with plots.

Combining both makes data science easier and clearer.