computeHermiteDerivativeInterpolation.m
041b8992f8b7master

computeHermiteDerivativeInterpolation.m
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			function [ output ] = computeHermiteDerivativeInterpolation(herm_c, herm_d, X, H, Npts)
			% computeHermiteDerivativeInterpolation(herm_c, herm_d, X, H, Npts)
			% evaluates derivative of Hermite cubic interpolation at points X.
			% Interpolation coefficients are given by herm_c and herm_d.

			output = zeros(size(X));
			precision = 12;

			leftIndices = floor(round(X * (Npts - 1), precision)) + 1;
			leftShifts = H * (leftIndices - 1);
			[~, upperBoundary] = find(leftIndices == Npts);

			output = output + herm_c(leftIndices) .* round(cubicHermite1Prime(X, leftShifts, H), precision);
			output = output + herm_d(leftIndices) .* round(cubicHermite2Prime(X, leftShifts, H), precision);

			% rightIndices = ceil(round(X *(Npts - 1), precision)) + 1;
			rightIndices = leftIndices + 1;
			rightShifts = H * (rightIndices -1);

			% Trick for x-values corresponding to upper boundary b. Has to be done
			% after defining rightShifts in order to get the correct solution.
			rightIndices(upperBoundary) = Npts;

			output = output + herm_c(rightIndices) .* round(cubicHermite1Prime(X, rightShifts, H), precision);
			output = output + herm_d(rightIndices) .* round(cubicHermite2Prime(X, rightShifts, H), precision);

			end