From fc8c9456d131643fb9d0c6006d0680b37dab03f6 Mon Sep 17 00:00:00 2001
From: =?utf8?q?Nils=20Forss=C3=A9n?= <forssennils@gmail.com>
Date: Mon, 26 Sep 2022 15:20:26 +0200
Subject: [PATCH] pushing

---
 builder.m       |  9 +++++++++
 lufact.asv      | 48 ------------------------------------------------
 newtonRaphson.m | 37 +++++++++++++++++++++++++++++++++++++
 3 files changed, 46 insertions(+), 48 deletions(-)
 create mode 100644 builder.m
 delete mode 100644 lufact.asv
 create mode 100644 newtonRaphson.m

diff --git a/builder.m b/builder.m
new file mode 100644
index 0000000..e8dc626
--- /dev/null
+++ b/builder.m
@@ -0,0 +1,9 @@
+
+A = zeros(length(t), 5);
+
+for i=1:length(t)
+    A(i, :) = [1 cos(2*pi*t(i,1)/0.3840) sin(2*pi*t(i,1)/0.3840) cos(4*pi*t(i,1)/0.3840) sin(2*pi*t(i,1)/0.3840)];
+
+
+    
+end
\ No newline at end of file
diff --git a/lufact.asv b/lufact.asv
deleted file mode 100644
index 17f9c12..0000000
--- a/lufact.asv
+++ /dev/null
@@ -1,48 +0,0 @@
-function [L,U,P] = lufact(A)
-%%
-%  Computes the LU factorization of the matrix A. The factorization is done
-%  in-place and then the L and U matrices are extracted at the end for
-%  output. The factorization is PA = LU
-%
-%  INPUT: 
-%    A - n by n square, non-singular matrix
-%
-%  OUTPUT:
-%    L - lower triangular matrix with ones along the main diagonal
-%    U - upper triangular matrix
-%    P - permutation matrix for pivoting
-%%
-%  get the size of the system
-   n  = length(A);
-%%
-%  initialize the pivoting matrix
-   P = eye(n);
-%%
-%  Vectorized in-place LU factorization (with row pivoting) that keeps
-%  track of the total permutations by scrambleing the matrix P
-   for j = 1:n-1
-
-        [v i] = max(abs(A(:, j)));
-        A([k i],:) = A([i k],:);
-        P([k i],:) = P([i k],:);
-%%
-% Find the index of the largest pivot element in the current column
-
-
-%%
-% Swap the rows within the in-place array as well as the permutation matrix P
-    
-
-
-%%
-% Perform the in-place elimination and save the new column of L
-      i = j+1:n; % indices for the "active" matrix portion
-      A(i,j) = A(i,j)/A(j,j);
-      A(i,i) = A(i,i) - A(i,j)*A(j,i);
-      %A, return
-   end
-%%
-% Extract L and U from the in-place form
-   U = triu(A);
-   L = eye(n) + tril(A,-1);
-end
diff --git a/newtonRaphson.m b/newtonRaphson.m
new file mode 100644
index 0000000..fd5da88
--- /dev/null
+++ b/newtonRaphson.m
@@ -0,0 +1,37 @@
+function [xVals,iter] = newtonRaphson(f,x0,tol)
+%%
+%  Implementation of the Newton-Raphson method to approximate 
+%  the root of a nonlinear function f(x)
+%
+%  INPUT: 
+%    f      - function f(x)                         OBS! passed as an anonyomous function
+%    fprime - first derivative of the function f(x) OBS! passed as an anonyomous function
+%    x0     - initial guess of the root location
+%    tol    - error tolerance to stop the iteration
+%
+%  OUTPUT:
+%    xVals  - sequence of approximate values for the root of the function f(x)
+%    iter   - number of iterations it took to achieve user set tolerance
+%%
+%  initialize a vector to store the sequence of guesses
+   xVals = zeros(16,1);
+%%
+%  save the initial guess
+   xVals(1) = x0;
+%%
+%  perform Newton-Raphson for a fixed number of iterations
+   for k = 1:15
+%%
+%  update to the next value
+      fk  = f(xVals(k));
+      xVals(k+1) = xVals(k) - ((fk)^2) / (f(xVals(k) + fk) - fk);
+%%
+% check the stopping condition
+      stopCond = abs(f(xVals(k+1)));
+      if stopCond < tol
+         xVals = xVals(1:k+1);
+         iter  = k+1;
+         break;
+      end
+   end
+end
\ No newline at end of file
-- 
2.30.2