Evaluate piecewise polynomial
v = ppval(pp,xq)
Create a piecewise polynomial that has a cubic polynomial in the interval [0,4], a quadratic polynomial in the interval [4,10], and a quartic polynomial in the interval [10,15].
breaks = [0 4 10 15]; coefs = [0 1 -1 1 1; 0 0 1 -2 53; -1 6 1 4 77]; pp = mkpp(breaks,coefs)
pp = struct with fields: form: 'pp' breaks: [0 4 10 15] coefs: [3×5 double] pieces: 3 order: 5 dim: 1
Evaluate the piecewise polynomial at many points in the interval [0,15] and plot the results. Plot vertical dashed lines at the break points where the polynomials meet.
xq = 0:0.01:15; plot(xq,ppval(pp,xq)) line([4 4],ylim,'LineStyle','--','Color','k') line([10 10],ylim,'LineStyle','--','Color','k')
Create two quadratic polynomials, evaluate them at several query points, and plot the results. Then create a single piecewise polynomial with four intervals that alternate between the two quadratic polynomials.
The first two plots show a quadratic polynomial and its negation shifted to the intervals [-8,-4] and [-4,0]. The polynomial is
The last plot shows a piecewise polynomial constructed by alternating these two quadratic pieces over four intervals. It also shows its first derivative, which was constructed after breaking the piecewise polynomial apart using
subplot(2,2,1) cc = [-1/4 1 0]; pp1 = mkpp([-8 -4],cc); xx1 = -8:0.1:-4; plot(xx1,ppval(pp1,xx1),'k-') subplot(2,2,2) pp2 = mkpp([-4 0],-cc); xx2 = -4:0.1:0; plot(xx2,ppval(pp2,xx2),'k-') subplot(2,1,2) pp = mkpp([-8 -4 0 4 8],[cc;-cc;cc;-cc]); xx = -8:0.1:8; plot(xx,ppval(pp,xx),'k-') [breaks,coefs,l,k,d] = unmkpp(pp); dpp = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d); hold on plot(xx,ppval(dpp,xx),'r-') hold off
pp— Piecewise polynomial
xq— Query points
Query points, specified as a vector or array.
the points where
ppval evaluates the piecewise
v— Piecewise polynomial values at query points
Piecewise polynomial values at query points, returned as a vector, matrix, or array.
coefficients (nonscalar coefficient values), then:
xq is a vector of length
the value at
xq has size
j1,...,js) is the value at
Usage notes and limitations:
The size of output
v does not match MATLAB® when
both of the following statements are true:
x is a variable-size
array that is not a variable-length vector.
x becomes a row vector at run time.
The code generator does not remove the singleton dimensions. However, MATLAB might remove singleton dimensions.
For example, suppose that
x is a :4-by-:5
array (the first dimension is variable size with an upper bound of
4 and the second dimension is variable size with an upper bound of
5). Suppose that
ppval(pp,0) returns a 2-by-3
v has size 2-by-3-by-:4-by-:5.
At run time, suppose that, size(x,1) =1 and size (x,2) = 5. In the
generated code, the size(v) is [2,3,1,5]. In MATLAB, the size