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Evaluate piecewise polynomial
v = ppval(pp,xx)
v = ppval(pp,xx) returns the value of the piecewise polynomial f, contained in pp, at the entries of xx. You can construct pp using the functions pchip, spline, or the spline utility mkpp.
v is obtained by replacing each entry of xx by the value of f there. If f is scalar-valued, v is of the same size as xx. xx may be N-dimensional.
If pp was constructed by pchip, spline, or mkpp using the orientation of non-scalar function values specified for those functions, then:
If f is [D1,..,Dr]-valued, and xx is a vector of length N, then V has size [D1,...,Dr, N], with V(:,...,:,J) the value of f at xx(J).
If f is [D1,..,Dr]-valued, and xx has size [N1,...,Ns], then V has size [D1,...,Dr, N1,...,Ns], with V(:,...,:, J1,...,Js) the value of f at xx(J1,...,Js).
Compare the result of integrating cos(x) between 0 and 10 to the result of integrating a piece-wise polynomial approximation of the same function.
a = 0; b = 10; int1 = integral(@cos,a,b) int1 = -0.5440
Create a piece-wise polynomial approximation of cos(x) and integrate over the same interval.
x = a:b; y = cos(x); pp = spline(x,y); int2 = integral(@(x)ppval(pp,x),a,b) int2 = -0.5485