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NUMERICAL

cumulative_trapezoid

Cumulatively integrate y(x) using the composite trapezoidal rule.

Example of usage

Cumulative trapezoidal area under an assay trace.

Usage / limitations

+Use when: Compute approximations and solve equations.

−Limitations: Check input requirements, mathematical assumptions and version-specific behaviour before using.

Mathematical formula

See method documentation: implementation and assumptions vary.
Sample dataShow 
{
  "variable": "observations",
  "domain": "Laboratory sensor signal integration",
  "feature_names": [
    "minute",
    "fluorescence_au"
  ],
  "records": [
    {
      "minute": 0,
      "fluorescence_au": 1.0
    },
    {
      "minute": 1,
      "fluorescence_au": 2.0
    },
    {
      "minute": 2,
      "fluorescence_au": 5.0
    },
    {
      "minute": 3,
      "fluorescence_au": 10.0
    },
    {
      "minute": 4,
      "fluorescence_au": 17.0
    },
    {
      "minute": 5,
      "fluorescence_au": 26.0
    },
    {
      "minute": 6,
      "fluorescence_au": 37.0
    },
    {
      "minute": 7,
      "fluorescence_au": 50.0
    },
    {
      "minute": 8,
      "fluorescence_au": 65.0
    }
  ]
}

Code example (Python)

# DataLens.ai example — cumulative_trapezoid
# Domain: laboratory sensor measurements and numerical analysis.
# Sample input is supplied by the Copy input + code + test action.
import numpy as np
from scipy import integrate, special
# Read a labelled time-series from the sample input.
t = np.array([row["minute"] for row in observations["records"]], dtype=float)
y = np.array([row["fluorescence_au"] for row in observations["records"]], dtype=float)

# Compute the method-specific result and check a numerical property.
result = integrate.cumulative_trapezoid(y, x=t, initial=0)
assert result.shape == t.shape and np.isclose(result[0],0) and np.all(np.diff(result)>0)
print("Expected output verified")