CL_lagrangeFitPoly

Description

• Computes the Lagrange polynomial passing through reference abscissae and ordinates.

  xref and yref describe the reference abscissae and ordinates. Each column in xref and yref define a different set of points. The polynomial p(k) is the polynomial that fits the points P=(x,y) such that x=xref(:,k) and y=y(:,k). The (maximum) degree of the polynomial is equal to the number of rows in x and y minus 1.

  The function also optionally returns the first and second derivative of the polynomial.

  Note:

  If the polynomial cannot be computed (because the abscissae are not all different) a constant polynomial equal to %nan is returned. The derivatives are then set to the same polynomial (%nan), which is not necessarily what the Scilab "derivat" function would do.

Parameters

xref:

Reference abscissae. (PxN)

yref:

Corresponding ordinates. (PxN)

p:

Lagrange polynomials. (1xN)

pdot:

First derivative of the polynomials. (1xN)

p2dot:

Second derivative of the polynomials. (1xN)

Authors

• CNES - DCT/SB

See also

• CL_interpLagrange

Examples

// Generate a degree 2 Lagrange polynomial xref = [-1; 0; 2]; yref = 1 - xref + xref.^2; p = CL_lagrangeFitPoly(xref, yref) // => 1 - x + x^2 // Vectorized form xref = [[-1; 0; 2], [-2; 1; 4]]; yref = 1 - xref + xref.^2; p = CL_lagrangeFitPoly(xref, yref) // => 1 - x + x^2 (2 times)