This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.


Evaluate piecewise polynomial


v = ppval(pp,xq)



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


collapse all

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;
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.

cc = [-1/4 1 0]; 
pp1 = mkpp([-8 -4],cc);
xx1 = -8:0.1:-4; 

pp2 = mkpp([-4 0],-cc);
xx2 = -4:0.1:0; 

pp = mkpp([-8 -4 0 4 8],[cc;-cc;cc;-cc]);
xx = -8:0.1:8;
hold on
line([-4 -4],ylim,'LineStyle','--')
line([0 0],ylim,'LineStyle','--')
line([4 4],ylim,'LineStyle','--')
hold off

Input Arguments

collapse all

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

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

Data Types: single | double

Output Arguments

collapse all

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

See Also

| | |

Introduced before R2006a