SciPy in Python

SciPy in Python

Here are a few useful SciPy sample codes showcasing different aspects of the library, including optimization, integration, interpolation, and signal processing.

1. Optimization: Minimizing a Function

This example demonstrates how to minimize a mathematical function using scipy.optimize.

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import numpy as np
from scipy.optimize import minimize

# Define a function to minimize
def objective_function(x):
    return x**2 + 10*np.sin(x)

# Initial guess
x0 = 2.0

# Perform the minimization
result = minimize(objective_function, x0, method='BFGS')

print("Minimum value of the function:", result.fun)
print("Value of x that minimizes the function:", result.x)

[Output]

Minimum value of the function: 8.31558557947746
Value of x that minimizes the function: [3.83746713]

2. Integration: Calculating the Area Under a Curve

This example shows how to calculate the definite integral of a function using scipy.integrate.quad.

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from scipy.integrate import quad

# Define a function to integrate
def integrand(x):
    return np.exp(-x**2)

# Compute the integral from 0 to infinity
result, error = quad(integrand, 0, np.inf)

print("Integral result:", result)

[Output]

Integral result: 0.8862269254527579

3. Interpolation: Interpolating Data Points

This example demonstrates how to interpolate data points using scipy.interpolate.interp1d.

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import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

# Sample data points
x = np.linspace(0, 10, 10)
y = np.sin(x)

# Create an interpolation function
f = interp1d(x, y, kind='cubic')

# Generate new x values and interpolate
x_new = np.linspace(0, 10, 100)
y_new = f(x_new)

# Plot the results
plt.plot(x, y, 'o', label='Data points')
plt.plot(x_new, y_new, '-', label='Cubic interpolation')
plt.legend()
plt.show()

[Output]

4. Signal Processing: Filtering a Signal

This example shows how to apply a low-pass filter to a noisy signal using scipy.signal.

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import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import butter, lfilter

# Generate a noisy signal
np.random.seed(0)
t = np.linspace(0, 1, 500, endpoint=False)
signal = np.sin(2 * np.pi * 7 * t) + 0.5 * np.random.randn(500)

# Design a low-pass filter
def butter_lowpass(cutoff, fs, order=5):
    nyquist = 0.5 * fs
    normal_cutoff = cutoff / nyquist
    b, a = butter(order, normal_cutoff, btype='low', analog=False)
    return b, a

# Apply the filter to the signal
def lowpass_filter(data, cutoff, fs, order=5):
    b, a = butter_lowpass(cutoff, fs, order=order)
    y = lfilter(b, a, data)
    return y

# Parameters
cutoff = 3.5  # Desired cutoff frequency of the filter, Hz
fs = 50.0     # Sample rate, Hz

# Filter the signal
filtered_signal = lowpass_filter(signal, cutoff, fs)

# Plot the results
plt.plot(t, signal, label='Noisy signal')
plt.plot(t, filtered_signal, label='Filtered signal', linewidth=2)
plt.legend()
plt.show()

[Output]

These examples provide a glimpse of the powerful tools available in SciPy for scientific computing, including optimization, integration, interpolation, and signal processing.