POLYEVAL Function

Evaluates a polynomial in n variables.

Usage

y = POLYEVAL ( p, x)

Input Parameters

p—n-dimensional array of polynomial coefficients: p(j₁, ..., j_n) is the coefficient for:

 

where the x_i are the indeterminants of the polynomial.

x—(m,n) array of m points at which to evaluate the polynomial.

Returned Value

y—m-element vector containing the value of the polynomial at each of the m input points.

Keywords

Form—If set and n=1 then x need not be 1-dimensional but instead can have any desired dimensionality, and output y has the same dimensions as x. Also, setting Form invokes a faster algorithm specific to the case n=1.

Discussion

POLYEVAL evaluates a n-variate polynomial which is defined by an n-dimensional array of coefficients. The coefficients usually represent a regression model obtained by POLYFITN.

Example 1

; make 10 points in 3-space and store the range of the data

seed = 0

data = [ [RANDOMU(seed,10,2)], [RANDOMU(seed,10)/10] ]

drng = [ MIN(data,Dimension=0,Max=dmax), dmax ]

; coefficients of an exact bivariate 3rd order polynomial fit

MATH_INIT

coef = POLYFITN(data, [[1,1,1,1],[1,1,1,0],[1,1,0,0],[1,0,0,0]])

; grid of points that spans the range of the 2 independent

; variables

axes = LIST( INTERPOL(drng(*,0),101), INTERPOL(drng(*,1),101) )

grid = CPROD(axes)

; evaluate the polynomial on the grid;  display the surface and 

; data

surf = POLYEVAL( coef, grid )

vtkWINDOW, /Norender

vtkSURFACE, REFORM(surf,101,101), axes(0), axes(1)

vtkSCATTER, TRANSPOSE(data), Color=255L, Scale=0.2, /Noerase, $

   / Noaxes

vtkRENDERWINDOW

Example 2

See wave/lib/user/examples/polyexam.

This routine displays a univariate polynomial fit to random data, a bivariate polynomial fit to random data, and an image warping accomplished with a bivariate polynomial fit to each of two image coordinate mappings.