Sampled-curve integration
Estimate the area under experimentally or computationally sampled curves.
SciPy · Function
integrate.trapezoid
Numerically integrates sampled values with the composite trapezoidal rule. It can use explicit sample points or uniform spacing and integrates along a selected axis.
How it works
The function applies the composite trapezoidal rule to each one-dimensional slice of y along the selected axis. With x supplied, it uses the sample points in their given order; otherwise, it assumes uniform spacing specified by dx.
Syntax
scipy.integrate.trapezoid(y, x=None, dx=1.0, axis=-1)Parameters
| Name | Type | Description |
|---|---|---|
y | array_like | Input samples to integrate. |
x | array_like, optional | Sample points corresponding to y; defaults to uniform spacing when omitted. |
dx | scalar, optional | Spacing between sample points when x is None; default 1. |
axis | int, optional | Axis along which to integrate; default is the last axis. |
Returns
float for one-dimensional y; an n-1 dimensional array for higher-dimensional y.
Key points
- Uses the composite trapezoidal rule along a chosen array axis.
- The optional x argument supplies sample points aligned with y.
- Without x, points are assumed to have uniform spacing given by dx.
- axis chooses the dimension reduced by the integration.
- One-dimensional input returns a scalar float.
- For multidimensional input, the result has one fewer dimension.
Common mistakes
- Sample points are consumed in their supplied order, so unsorted x values change the signed integral rather than being reordered.
- Providing x also supports integration along a parametric curve, not only ordinary uniformly sampled functions.
Example: Integrate sampled values
import numpy as np
from scipy.integrate import trapezoid
x = np.linspace(0.0, np.pi, 1001)
area = trapezoid(np.sin(x), x=x)
print(area) # approximately 2.0Computes the area under sampled sine values over the interval from 0 to π.
When to use it
Array-wise reduction
Integrate arrays of signals or measurements along rows, columns, or another dimension.
Nonuniform-grid integration
Compute signed integrals for data whose sample coordinates are explicitly known.
Parametric-curve integration
Evaluate integrals represented by coordinates along a parametric path.
Interview questions
QWhat does scipy.integrate.trapezoid compute?
It computes a numerical integral with the composite trapezoidal rule along the requested axis. For one-dimensional y, the result is a float; higher-dimensional input produces one fewer dimension along that axis.
Follow-up: What happens when x is omitted? The samples are treated as evenly spaced, using dx as the spacing.
QHow do x and dx affect the calculation?
x contains sample points corresponding to y and determines the interval widths. If x is None, the function instead uses a constant spacing of dx, whose default is 1.
Follow-up: Does the function sort x first? No; it integrates in the sequence supplied by the caller.
QHow is multidimensional input handled?
axis selects the dimension over which integration occurs, and its default is the last axis, represented by -1. This lets the same function reduce rows, columns, or another dimension of an array.
Follow-up: What shape results from integrating an n-dimensional array? The selected axis is removed, so the result has one fewer dimension.
Related
scipy.integrate.simpsonscipy.integrate.cumulative_trapezoid