NumPy trapezoid()
The numpy.trapezoid() function computes the definite integral of an array using the composite trapezoidal rule. It integrates along a specified axis and can work with evenly or unevenly spaced sample points.
Syntax
numpy.trapezoid(y, x=None, dx=1.0, axis=-1)Parameters
| Parameter | Type | Description |
|---|---|---|
y | array_like | Input array to integrate. |
x | array_like, optional | Sample points corresponding to y values. If not provided, the spacing is assumed to be uniform. |
dx | scalar, optional | The spacing between sample points when x is not provided. Default is 1.0. |
axis | int, optional | Axis along which to integrate. Default is -1 (last axis). |
Return Value
Returns a float if the input y is 1D, otherwise returns an array with one dimension reduced by integration.
Examples
1. Integrating a 1D Function with Evenly Spaced Points
Here, we compute the integral of a function using evenly spaced sample points.
import numpy as np
# Define the y values (function values)
y = np.array([1, 2, 3, 4, 5])
# Compute the integral using the trapezoidal rule with default dx=1
result = np.trapezoid(y)
# Print the result
print("Integral of y using the trapezoidal rule:", result)Output:
Integral of y using the trapezoidal rule: 10.0
2. Integrating with Unevenly Spaced Sample Points
We specify the x values explicitly to integrate along unevenly spaced points.
import numpy as np
# Define y values
y = np.array([1, 2, 3, 4, 5])
# Define corresponding x values (unevenly spaced)
x = np.array([0, 1, 1.5, 3, 4])
# Compute the integral
result = np.trapezoid(y, x=x)
# Print the result
print("Integral with unevenly spaced x values:", result)Output:
Integral with unevenly spaced x values: 10.75
3. Using a Custom dx Value
Setting a custom spacing between points instead of using the default dx=1.
import numpy as np
# Define y values
y = np.array([1, 3, 7, 9])
# Compute the integral using a dx of 2
result = np.trapezoid(y, dx=2)
# Print the result
print("Integral with dx=2:", result)Output:
Integral with dx=2: 30.0
4. Integrating Along a Specific Axis
Computing the integral along a specified axis in a multidimensional array.
import numpy as np
# Define a 2D array
y = np.array([[1, 2, 3], [4, 5, 6]])
# Integrate along axis 0 (columns)
result_axis0 = np.trapezoid(y, axis=0)
# Integrate along axis 1 (rows)
result_axis1 = np.trapezoid(y, axis=1)
# Print the results
print("Integral along axis 0:", result_axis0)
print("Integral along axis 1:", result_axis1)Output:
Integral along axis 0: [2.5 3.5 4.5]
Integral along axis 1: [4. 10.]
When integrating along axis=0, each column is integrated separately, reducing the number of rows. When integrating along axis=1, each row is integrated, reducing the number of columns.