Python fitting exponential decay with no initial guessing

Python fitting exponential decay with no initial guessing

Fitting an exponential decay curve without initial guessing can be challenging, but you can use optimization techniques to estimate the parameters of the decay curve from your data. One common approach is to use a nonlinear least squares optimization method like the Levenberg-Marquardt algorithm, which is available in the SciPy library. Here's an example of how to fit an exponential decay curve in Python without initial guessing:

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

# Define the exponential decay function
def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate example data with some noise
x_data = np.linspace(0, 5, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 0.5 * np.random.normal(size=len(x_data))

# Fit the exponential decay curve to the data
params, covariance = curve_fit(exponential_decay, x_data, y_data)

# Extract the fitted parameters
a_fit, b_fit, c_fit = params

# Plot the original data and the fitted curve
plt.scatter(x_data, y_data, label='Data')
plt.plot(x_data, exponential_decay(x_data, a_fit, b_fit, c_fit), 'r', label='Fit')
plt.legend()
plt.xlabel('X')
plt.ylabel('Y')
plt.show()

# Print the fitted parameters
print(f'a: {a_fit}')
print(f'b: {b_fit}')
print(f'c: {c_fit}')

In this example:

  1. We define the exponential decay function exponential_decay(x, a, b, c) where a, b, and c are the parameters to be fitted.

  2. We generate example data with some noise to simulate real-world data.

  3. We use the curve_fit function from SciPy to fit the exponential decay curve to the data. It estimates the parameters a, b, and c that best fit the data.

  4. We extract the fitted parameters and plot the original data along with the fitted curve.

  5. Finally, we print the fitted parameters.

Keep in mind that fitting an exponential decay curve without initial guesses may not always provide accurate results, especially if the data contains noise or if the decay is not well-behaved. In such cases, it may be necessary to provide reasonable initial guesses to improve the fitting process.

Examples

  1. "Python exponential decay curve fitting without initial guess"

    • Description: This query may seek Python code that performs exponential decay curve fitting without requiring an initial guess for the parameters. This approach is useful when the initial parameters are unknown or difficult to estimate.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code demonstrates how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without providing an initial guess for the parameters. The exponential_decay function defines the form of the exponential decay model.

  2. "Python curve fitting exponential decay no initial guess"

    • Description: This query might be interested in Python code that performs curve fitting specifically for exponential decay data without requiring an initial guess for the parameters.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code snippet utilizes SciPy's curve_fit function to fit an exponential decay curve to sample data without requiring an initial guess for the parameters. The exponential_decay function represents the exponential decay model.

  3. "Python fitting exponential decay curve without guessing"

    • Description: This query may aim to find Python code that fits an exponential decay curve to data without the need for manually providing initial parameter guesses.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code demonstrates how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without the need for providing an initial guess for the parameters. The exponential_decay function defines the form of the exponential decay model.

  4. "Python curve fitting exponential decay data without initial guess"

    • Description: This query might seek Python code that performs curve fitting specifically for exponential decay data, allowing the parameters to be estimated without providing an initial guess.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code snippet demonstrates how to fit an exponential decay curve to sample data using SciPy's curve_fit function, which automatically estimates the parameters without requiring an initial guess. The exponential_decay function represents the exponential decay model.

  5. "Python exponential decay fitting no initial guess"

    • Description: This query may be interested in Python code specifically tailored for fitting exponential decay functions to data without providing an initial guess for the parameters.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code illustrates how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without the need for providing an initial guess for the parameters. The exponential_decay function defines the form of the exponential decay model.

  6. "Python fitting exponential decay curve without initial estimate"

    • Description: This query may aim to find Python code for fitting exponential decay curves to data without requiring an initial estimate for the parameters.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code snippet demonstrates how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without requiring an initial estimate for the parameters. The exponential_decay function represents the exponential decay model.

  7. "Python exponential decay fitting without guessing initial values"

    • Description: This query might be interested in Python code specifically designed for fitting exponential decay functions to data without the need for providing initial values as guesses.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code snippet showcases how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without needing to provide initial values as guesses for the parameters. The exponential_decay function represents the exponential decay model.

  8. "Python curve fitting exponential decay model no initial estimate"

    • Description: This query may aim to find Python code for curve fitting specifically tailored to the exponential decay model without requiring an initial estimate for the parameters.
    from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt

def exponential_decay(x, a, b, c):
    return a * np.exp(-b * x) + c

# Generate sample data
x_data = np.linspace(0, 10, 100)
y_data = 3 * np.exp(-0.5 * x_data) + 1 + np.random.normal(0, 0.1, x_data.shape)

# Perform curve fitting
popt, _ = curve_fit(exponential_decay, x_data, y_data)

# Plot original data and fitted curve
plt.scatter(x_data, y_data, label='Original Data')
plt.plot(x_data, exponential_decay(x_data, *popt), color='red', label='Fitted Curve')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Exponential Decay Curve Fitting')
plt.legend()
plt.show()

    This code demonstrates how to fit an exponential decay curve to sample data using the curve_fit function from SciPy without the need for providing an initial estimate for the parameters. The exponential_decay function represents the exponential decay model.

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