From 92e796df06808889f622cb84ea94a52ca622a9c8 Mon Sep 17 00:00:00 2001
From: Matthew Ellison <m_ellison@ymail.com>
Date: Wed, 10 Oct 2018 12:27:11 -0400
Subject: [PATCH] From Numerical Analysis 10-10-18

---
 LagrangeInterpolation.m   | 24 ++++++++++++++++++++++++
 LagrangePolynomials.m     | 30 ++++++++++++++++++++++++++++++
 TestLagrangePolynomials.m | 16 ++++++++++++++++
 3 files changed, 70 insertions(+)
 create mode 100644 LagrangeInterpolation.m
 create mode 100644 LagrangePolynomials.m
 create mode 100644 TestLagrangePolynomials.m

diff --git a/LagrangeInterpolation.m b/LagrangeInterpolation.m
new file mode 100644
index 0000000..7e55bbf
--- /dev/null
+++ b/LagrangeInterpolation.m
@@ -0,0 +1,24 @@
+function [value] = LagrangeInterpolation(x_data, y_data, x)
+%LagrangeInterpolation evaluates the lagrange interpolation polynomial for
+%given set of data points
+%
+%   Input
+%       - x_data: One-dimensional list of x-coordinates of point 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
+%       - y_data: One-dimensional list of y-coordinates of point through
+%       which the interpolating polynomial will pass
+%       - x: One-dimensional list of values for which the Lagtrange
+%       polynomial will be evaluated
+%
+%   Output
+%       - value: Value(s) of interpolation polynomial
+
+    %Ensure that the y_data list is a row vector
+    y_data = y_data(:)';
+    
+    %Do the interpolation
+    value = y_data*LagrangePolynomials(x_data, x);
+end
+
diff --git a/LagrangePolynomials.m b/LagrangePolynomials.m
new file mode 100644
index 0000000..07c6e3e
--- /dev/null
+++ b/LagrangePolynomials.m
@@ -0,0 +1,30 @@
+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
+
diff --git a/TestLagrangePolynomials.m b/TestLagrangePolynomials.m
new file mode 100644
index 0000000..07446e8
--- /dev/null
+++ b/TestLagrangePolynomials.m
@@ -0,0 +1,16 @@
+close all
+clear all
+format long
+
+%Set your values
+x_data = [1, 1.3, 1.6, 1.9, 2.2];
+y_data = [0.7651977, 0.6200860, 0.4554022, 0.2818186, 0.1103623];
+x = [1.1, 1.5];
+
+%Get the values for x
+values = LagrangeInterpolation(x_data, y_data, x);
+
+%Display nicely
+for(k = 1:size(x) + 1)
+    disp(['P(' num2str(x(k)) ') = ' num2str(values(k), '%11.7f')])
+end