ppval

Evaluate piecewise polynomial

Syntax

v = ppval(pp,xq)

Description

v = ppval(pp,xq) evaluates the piecewise polynomial pp at the query points xq.

Examples

Create Piecewise Polynomial with Polynomials of Several Degrees

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 Piecewise Polynomial with Repeated Pieces

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

$$1-{(\frac{x}{2}-1)}^2=\frac{-x^2}{4}+x.$$

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

Input Arguments

pp — Piecewise polynomial

structure

Piecewise polynomial, specified as a structure. You can create pp using spline, pchip, makima, interp1, or the spline utility function mkpp.

xq — Query points

vector | array

Query points, specified as a vector or array. xq specifies the points where ppval evaluates the piecewise polynomial.

Data Types: single | double

Output Arguments

v — Piecewise polynomial values at query points

vector | matrix | array

Piecewise polynomial values at query points, returned as a vector, matrix, or array.

If pp has [d1,..,dr]-valued coefficients (nonscalar coefficient values), then:

• When xq is a vector of length N, v has size [d1,...,dr,N], and v(:,...,:,j) is the value at xq(j).

• When xq has size [N1,...,Ns], v has size [d1,...,dr,N1,...,Ns], and v(:,...,:, j1,...,js) is the value at xq(j1,...,js).

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The size of output v does not match MATLAB^® when both of the following statements are true:

  • The input 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].