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SSM (version 1.0.1)

construct.P.1d: Construct the change of basis matrix from univariate monomials to Legendre polynomials.

Description

Let \(f(x)\) be the vector of monomials implied by the matrix basis. Let \(P\) be the matrix generated by Legendre_P_1d. Then \(g(x)=P^Tf(x)\) is the vector of Legendre polynomials with leading terms corresponding to basis. e.g. the matrix \((0 1 2)^T\) implies \(f(x)^T = (1 x x^2)\). Then \(g(x)^T = (L_0, L_1, L_2)\).

Usage

construct.P.1d(basis)

Arguments

basis

A matrix. Rows are taken as the degree of the associated monomial.

Value

A matrix which functions as a change of basis from monomials to Legendre.