ppval - Evaluate piecewise polynomial

Syntax

Description

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).

Examples

Compare the results of integrating the function cos

a = 0; b = 10;
int1 = quad(@cos,a,b)

int1 =
   -0.5440

with the results of integrating the piecewise polynomial pp that approximates the cosine function by interpolating the computed values x and y.

x = a:b; 
y = cos(x);
pp = spline(x,y);
int2 = quad(@(x)ppval(pp,x),a,b)

int2 =
   -0.5485

int1 provides the integral of the cosine function over the interval [a,b], while int2 provides the integral over the same interval of the piecewise polynomial pp.

See Also

mkpp | spline | unmkpp

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