From 3973eabd9b7d78380cb2ae770a42f2c3444795fb Mon Sep 17 00:00:00 2001
From: Isaac Shoebottom <ir.shoebottom@gmail.com>
Date: Wed, 29 Jan 2025 17:27:17 -0400
Subject: [PATCH] Add Assignment 1 stuff. Formulas from textbook

---
 Assignment/1/HW1.pdf     | Bin 0 -> 136691 bytes
 Assignment/1/eikonal.jl  |  99 +++++++++++++++++++++++++++++++++++++
 Assignment/1/ex1.txt     |   9 ++++
 Assignment/1/test100.txt | 102 +++++++++++++++++++++++++++++++++++++++
 4 files changed, 210 insertions(+)
 create mode 100644 Assignment/1/HW1.pdf
 create mode 100644 Assignment/1/eikonal.jl
 create mode 100644 Assignment/1/ex1.txt
 create mode 100644 Assignment/1/test100.txt

diff --git a/Assignment/1/HW1.pdf b/Assignment/1/HW1.pdf
new file mode 100644
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diff --git a/Assignment/1/eikonal.jl b/Assignment/1/eikonal.jl
new file mode 100644
index 0000000..4ee7854
--- /dev/null
+++ b/Assignment/1/eikonal.jl
@@ -0,0 +1,99 @@
+using DelimitedFiles
+
+# Solves the Eikonal equation using the Fast Sweeping Method
+# Input is in file with name stored in source
+# Input domain has ni x nj values, with a spacing of h
+# Default tolerance is 1E-6
+# Returns ni x nj solution matrix without extra layer of points
+function solveEikonal(ni, nj, h, source, tol = 1E-6)
+	F = zeros(ni+2, nj+2)
+	U = ones(ni+2, nj+2) * Inf
+	initialize!(F, U, ni, nj, source)
+	maxerr = 1
+	while maxerr > tol
+		maxerr = 0
+		maxerr = sweep!(U, ni+1, 2, 2, nj+1, F, h, maxerr) # North-East
+		maxerr = sweep!(U, ni+1, 2, nj+1, 2, F, h, maxerr) # North-West
+		maxerr = sweep!(U, 2, ni+1, nj+1, 2, F, h, maxerr) # South-West
+		maxerr = sweep!(U, 2, ni+1, 2, nj+1, F, h, maxerr) # South-East
+	end
+	U[2:ni+1, 2:nj+1]
+end
+
+# Perform one set of sweeps on matrix U using directions specified in
+# i1,ib,ja,jb, and speed function F, and current value of maximum
+# absolute error (err = (U[i, j]-Unew)/U[i, j]), where Unew
+# is new value of U[i,j] calculated using solveQuadratic()
+# h is the spacing between points
+# Returns updated value of maxerr
+function sweep!(U, ia, ib, ja, jb, F, h, maxerr)
+	#stepi = sign(ib - ia)
+	#stepj = sign(jb - ja)
+	stepi = 0
+	stepj = 0
+	if ib < ia
+		stepi = -1
+	else
+		stepi = 1
+	end
+	if jb < ja
+		stepj = -1
+	else
+		stepj = 1
+	end
+	for i in ia:stepi:ib
+		for j in ja:stepj:jb
+			Unew = solveQuadratic(U, i, j, F, h)
+			if Unew < U[i, j]
+				err = (U[i, j] - Unew) / U[i, j]
+				if err > maxerr
+					maxerr = err
+				end
+			U[i, j] = Unew
+			end
+		end
+	end
+	maxerr
+end
+
+# Solve the discretized Eikonal equation at (i,j), given
+# speed function F, and spacing between points h
+# Returns the new value of U[i,j]
+function solveQuadratic(U, i, j, F, h)
+	if U[i, j] == 0
+		return 0
+	end
+	a = min(U[i-1, j], U[i+1, j])
+	b = min(U[i, j-1], U[i, j+1])
+	if abs(a - b) >= h / F[i, j]
+		return min(a, b) + h / F[i, j]
+	else
+		return (a + b + sqrt(2* h^2 / F[i, j]^2 - (a - b)^2)) / 2
+	end
+end
+
+# Reads from source a speed function F defined a ni x nj grid
+# as well as coordinates of boundary of front
+# (input is terminated with a negative number on last line)
+# Also initializes solution matrix U
+# U and F are (ni+2) x (nj+2) 2D matrices
+# Requires the DelimitedFiles package
+function initialize!(F, U, ni, nj, source)
+    temp = readdlm(source)
+    for j in 1:nj, i in 1:ni
+        F[i+1, j+1] = Float64(temp[i, j])
+    end
+    for i in ni+1:size(temp, 1)-1 # skip last line that has -1 terminator
+        # +2: skip border and convert input from 0-based indexing
+        U[temp[i,1]+2, temp[i,2]+2] = 0
+    end
+	# println(U)
+	# println(F)
+    nothing
+end
+
+# Call on file "ex1.txt" with the following format:
+println(solveEikonal(7, 7, 1, "ex1.txt"))
+
+# Call on file "test100.txt" with the following format:
+# println(solveEikonal(100, 100, 1, "test100.txt"))
\ No newline at end of file
diff --git a/Assignment/1/ex1.txt b/Assignment/1/ex1.txt
new file mode 100644
index 0000000..7fe914a
--- /dev/null
+++ b/Assignment/1/ex1.txt
@@ -0,0 +1,9 @@
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+1 1 1 1 1 1 1
+3 3
+-1
diff --git a/Assignment/1/test100.txt b/Assignment/1/test100.txt
new file mode 100644
index 0000000..8684f09
--- /dev/null
+++ b/Assignment/1/test100.txt
@@ -0,0 +1,102 @@
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+1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
+1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
+50 50
+-1