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Integration (ND)

ND interpolants support exact analytical integration over hyper-rectangular regions using tensor-product decomposition of the 1D cell integrals.

Basic Usage

integrate(itp, lower::NTuple{N}, upper::NTuple{N})  # definite integral over hyper-rectangle
integrate(itp)                                      # full-domain integral
  • itp: Any ND interpolant (e.g., CubicInterpolantND, LinearInterpolantND).
  • lower, upper: Tuples of length N specifying the corners of the integration region. Do not need to be grid points — partial-cell integration is handled automatically.

Example: 2D

using FastInterpolations

x = range(0.0, 1.0, 15)
y = range(0.0, 1.0, 15)
data = [xi * yi for xi in x, yi in y]
itp = cubic_interp((x, y), data)

# ∫∫ xy dx dy over [0,1]×[0,1] = 0.25
integrate(itp, (0.0, 0.0), (1.0, 1.0))

Full-Domain Integration

Omit bounds to integrate over the entire domain:

integrate(itp)
Performance

integrate(itp) uses a specialized summation path that avoids search operations entirely — faster than passing explicit bounds.

See Also

  • 1D Integration — 1D integration reference, Series support, extrapolation behavior
  • Overview — ND API introduction