From Numerical Analysis 10-10-18

LagrangePolynomials.m

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+function [Ln] = LagrangePolynomials(x_data, x)
+%LagrangePolynomials evaluates the entire collection of Lagrange
+%polynomials
+%
+%   Input:
+%       - x_data: One-dimensional list of x-coordinates of points through
+%       which the interpolating polynomial will pass. The degree of the
+%       interpolating polynomial, n, will be inferred from the number of
+%       entries in x_data
+%       - x: One-dimensional list of values for which the Lagrange
+%       polynomial will be evaluated
+%
+%   Output:
+%       -Ln: Matrix of values of Lagrange polynomials of degree n. The
+%       matrix has a row for each polynomial and a column for each value of
+%       x
+
+    %Allocate space for the output matrix by initializing it to zero
+
+    value_count = length(x);
+    n = length(x_data) - 1;
+    Ln = zeros(n + 1, value_count);
+
+    %Build each row of the output matrix by evaluating the corresponding
+    %polynomial at the x value(s)
+    for(k = 0:n)
+        Ln(k + 1, :) = LagrangePolynomial(x_data, k, x);
+    end
+end
+