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OPTIMISATION

curve_fit

Use non-linear least squares to fit a function, f, to data.

Example of usage

Python API reference included; executable data demonstration pending review.

Usage / limitations

+Use when: Find solutions efficiently.

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

Mathematical formula

See method documentation: implementation and assumptions vary.
Sample dataShow 
{
  "variable": "design_case",
  "domain": "Engineering parameter estimation and optimisation",
  "feature_names": [
    "measurement_time_s",
    "response_mm"
  ],
  "records": [
    {
      "measurement_time_s": 0,
      "response_mm": 1
    },
    {
      "measurement_time_s": 1,
      "response_mm": 3
    },
    {
      "measurement_time_s": 2,
      "response_mm": 5
    },
    {
      "measurement_time_s": 3,
      "response_mm": 7
    },
    {
      "measurement_time_s": 4,
      "response_mm": 9
    }
  ],
  "target_value": 4.0,
  "lower_bound": 0.0,
  "upper_bound": 4.0,
  "method": "curve-fit"
}

Code example (Python)

# DataLens.ai example — curve_fit
# Domain: engineering parameter estimation and optimisation.
# The sample data are included by “Copy input + code + test”.
import numpy as np
from scipy import optimize
# Read the named engineering measurements.
times = np.array([row["measurement_time_s"] for row in design_case["records"]], dtype=float)
responses = np.array([row["response_mm"] for row in design_case["records"]], dtype=float)
# Use a known target, making the numerical assertion independently meaningful.
target = design_case["target_value"]

# Fit a linear response model to the named calibration observations.
def response_model(t, gain, offset):
    return gain*t + offset
parameters, covariance = optimize.curve_fit(response_model, times, responses)
assert np.allclose(parameters, [2.0,1.0], atol=1e-6)
print("Expected output verified")