plq_function - Piecewise linear quadratic (plq) function description
A plq function is a piecewise function, where each piece is either a linear or a quadratic polynomial. It is stored as a matrix, where each row represents one piece of the function.
Typical plq matrix
[x(1) a(1) b(1) c(1) ] f(x) = a(1)*x^2 + b(1)*x + c(1), if -%inf < x <= x(1)
[x(2) a(2) b(2) c(2) ] f(x) = a(2)*x^2 + b(2)*x + c(2), if x(1) < x <= x(2)
[ ' ' ' ' ] ' ' ' ' '
[ ' ' ' ' ] ' ' ' ' '
[x(n-1) a(n-1) b(n-1) c(n-1)] f(x) = a(n-1)*x^2 + b(n-1)*x + c(n-1), if x(n-2) < x <= x(n-1)
[%inf a(n) b(n) c(n) ] f(x) = a(n)*x^2 + b(n)*x + c(n), if x(n-1) < x <= %inf
Where
'x' is where the domain is defined
'a' is the quadratic term
'b' is the linear term
'c' is the constant term
And a typical row is a(i)*x^2 + b(i)*x + c(i) if x(i-1) < x <= x(i).
Note that singleton indicator functions are given in a special form such that [x(1),0,0,c(1)] = I[x=x(1)] + c(1).
plqAbs = [0,0,-1,0;%inf,0,1,0]; // The function y = |x| plqQuad = [%inf,1/5,-4/5,4/5]; // The function y = (x-2)^2 / 5 = (x^2 - 4*x + 4) / 5 plq_plot(plqAbs, plqQuad); // Plot the functions together
plq_add, plq_build, plq_clean, plq_co, plq_eval, plq_lft, plq_me, plq_me_max_scale, plq_pa, plq_pa_mu, plq_plot, plq_plot2, plq_plotpa, plq_plotpa_lambdaSet, plq_plotpa_muSet, plq_proj, plq_scalar,
Bryan Gardiner, University of British Columbia, BC, Canada