Evaluate piecewise polynomial
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: [3x5 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 and plot a piecewise polynomial with four intervals that alternate between two quadratic polynomials.
The first two subplots show a quadratic polynomial and its negation shifted to the intervals [-8,-4] and [-4,0]. The polynomial is
The third subplot shows a piecewise polynomial constructed by alternating these two quadratic pieces over four intervals. Vertical lines are added to show the points where the polynomials meet.
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-') hold on line([-4 -4],ylim,'LineStyle','--') line([0 0],ylim,'LineStyle','--') line([4 4],ylim,'LineStyle','--') hold off
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:
xx is a variable-size array that
is not a variable-length vector.
xx becomes a row vector at run time.
In this case, the code generator does not remove the singleton dimensions. However, MATLAB might remove singleton dimensions.
For example, suppose that
xx 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 fixed-size array.
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 is [2,3,5].
backgroundPoolor accelerate code with Parallel Computing Toolbox™
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).