ppval (MATLAB Functions)

Evaluate piecewise polynomial.

Syntax

```
v = ppval(pp,xx)
v = ppval(xx,pp)
```

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. If f is [d1,..,dr]-valued and xx has size [n1,...,ns], then v has size [d1,...,dr, n1,...,ns]. v(:,...,:, j1,...,js) is equal to the value of f at xx(j1,...,js), with the following exceptions:

n1 is ignored if it is 1 and s is 2, that is, if xx is a row vector.
ppval ignores any trailing singleton dimensions of xx.

v = ppval(xx,pp) returns the same result but can be used with functions like fminbnd, fzero and quad that take a function as an argument.

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(@ppval,a,b,[],[],pp)

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

power prefdir