integralMatrixForDataPoints

Return the exact interpolation-to-antiderivative linear map.

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Declaration

 W = integralMatrixForDataPoints(dataPoints, queryPoints, options)

Parameters

• dataPoints interpolation sample locations
• queryPoints points at which to evaluate the antiderivative
• options.knotPoints terminated knot sequence for the interpolation basis
• options.S spline degree of the interpolation basis

Returns

• W linear map from interpolation values on dataPoints to antiderivative values on queryPoints

Discussion

Use this expert utility when one-dimensional interpolation values are sampled on dataPoints and the zero-anchored antiderivative should be evaluated at queryPoints without constructing an intermediate spline object.

If y is the column vector of interpolation values and f is the corresponding exact interpolating spline on the supplied terminated knot sequence, then the returned matrix satisfies

\[W y = F(t_q), \qquad F(t) = \int_{t_1}^{t} f(s)\,ds.\]

  W = BSpline.integralMatrixForDataPoints(t, tq, knotPoints=knotPoints, S=3);
  valuesInt = W * values;