Update lab01

lab01/inlab/1/readme.txt

+Group 33 : Lab01_inlab
+
+Group Members:
+(Vinayak K, 150050098), (Shriram S B, 150050099), (Anubhaw Kuntal Xess, 150050100)
+Vinayak K - 100%
+Shriram S B - 100%
+Anubhaw Kuntal Xess - 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Reflection essay:
+	- octave function declaration, global variables
+	- tried fsolve()
+	- found that fzero() better for single variable
+	- File I/O in octave
+
+Citations: Gnu octave Documentation
\ No newline at end of file

lab01/inlab/1/refraction.m

+% nx, ny global variable to hold tensor values 
+global nx;
+global ny;
+
+% reading nx, ny from input file 
+input_ptr = fopen("input_inlab_task_A1.txt", "r");
+[nx, ny, count, errmsg] = fscanf(input_ptr, "%lf %lf", "C");
+fclose(input_ptr);
+
+% function which returns value of the expression for some incident angle x(rad)
+function ret_val = f (x)
+	global nx;
+	global ny;
+  	ret_val = ( sin(x) / sin(x/3) - nx * cos(x) - ny * sin(x) );
+endfunction
+
+% finding interval in which function changes sign
+a = 1e-10;
+dx = 0.1 + 1e-10;
+b = dx;
+while (f(a)*f(b) >= 0)
+	a += dx;
+	b += dx;
+endwhile
+
+% the interval in which expression has a root
+
+bracket = [a; b];
+
+% fzero to find value at which expression is zero
+[x, fval, info, output] = fzero("f", bracket);
+
+output_ptr = fopen("output_inlab_task_01.txt", "w");
+fprintf(output_ptr, "%f", x);
+fclose(output_ptr);
+

lab01/inlab/2/final_state_3.m

+
+% 'final' stores final state of the board
+function final = final_state_3(b,x)
+	% numbering the buttons
+	a = [1, 2, 3; 4, 5, 6; 7, 8, 9];
+
+	% A(i, j) = 1 if button i is toggled on pressing button j
+	A = zeros(9,9);
+
+	% initializing A 
+	for i = 1 : 3
+		for j = 1 : 3
+			A(a(i,j), a(i,j)) = 1;
+			if (i + 1 <= 3)
+				A(a(i,j), a(i + 1, j)) = 1;
+			end
+			if (i - 1 >= 1)
+				A(a(i,j), a(i - 1, j)) = 1;
+			end
+			if (j + 1 <= 3)
+				A(a(i,j), a(i, j + 1)) = 1;
+			end
+			if (j - 1 >= 1)
+				A(a(i,j), a(i, j - 1)) = 1;
+			end
+		endfor
+	endfor
+
+	% b - initial state of board
+	% x - action vector
+	% reshaping x and b from 3x3 to 9x1
+	x = reshape(x, 9, 1);
+	b = reshape(b, 9, 1);
+
+	final = reshape(mod((A*x + b), 2), 3, 3);
+endfunction
+

lab01/inlab/2/lookup_solve_3.m

+% output stores final result
+% input - matrix given by user
+function output = lookup_solve_3(input)
+	output = [0, 0, 0; 0, 0, 0; 0, 0, 0];
+	% input used to store state of game after every press of button
+	% presses (r,c) button and toggles the neighbouring buttons too
+	function toggle(r, c)			
+		input(r, c) = ~input(r, c);
+		if r - 1 >= 1
+			input(r - 1, c) = ~input(r - 1, c);
+		end
+		if r + 1 <= 3
+			input(r + 1, c) = ~input(r + 1, c);
+		end
+		if c - 1 >= 1
+			input(r, c - 1) = ~input(r, c - 1);
+		end
+		if c + 1 <= 3
+			input(r, c + 1) = ~input(r, c + 1);
+		end
+	endfunction
+
+	% takes a row and the button to press in it as input and presses corresponding buttons
+	function toggle_row(row, but_press)
+		for k = 1 : 3
+			if (but_press(1, k) == 1)
+				toggle(row, k);
+				output(row, k) = ~output(row, k);	
+			end
+		endfor	
+	endfunction
+	
+	% the table given in problem statement
+	bot_top_toggle = [0, 1, 1;
+					  1, 1, 1;
+					  1, 0, 0;
+					  1, 1, 0;
+					  1, 0, 1;
+					  0, 0, 1;
+					  0, 1, 0];
+	
+	while (true)
+		% 1st and 2nd row made zero
+		for i = 1 : 2
+			toggle_row(i + 1, input(i, :) );
+		endfor
+
+		% binary_equivalent of last row for easy access
+		bottom_binary = 4 * input(3, 1) + 2 * input(3, 2) + input(3, 3);
+		
+		if (bottom_binary ~= 0)
+			% toggling top row according to state of bottom row
+			toggle_row(1, bot_top_toggle(bottom_binary, :));
+		else 
+			break;
+		end
+	endwhile
+endfunction
+
+
+	

lab01/inlab/2/readme.txt

+Group 33 : Lab01_inlab
+
+Tasks : B1, B2
+
+Group Members:
+(Vinayak K, 150050098), (Shriram S B, 150050099), (Anubhaw Kuntal Xess, 150050100)
+Vinayak K - 100%
+Shriram S B - 100%
+Anubhaw Kuntal Xess - 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Reflection essay:
+	- matrix multiplication
+	- reshaping of matrices
+	- nested functions
+
+Citations: Gnu octave Documentation
\ No newline at end of file

lab01/outlab/backward_solve.m

+function solution = backward_solve(input)
+	
+	% number of rows, columns in input
+	[rows, cols] = size(input);
+	% no_buttons = number of buttons
+	no_buttons = rows*cols;
+	A = zeros(no_buttons, no_buttons);
+
+
+	% numbering the buttons
+	a = zeros(rows, cols);	
+	for i = 1 : rows
+		for j = 1 : cols
+			a(i, j) = cols * (i - 1) + j;
+		endfor
+	endfor
+
+
+	% A(i,j) = 1 if ith bulb is toggled with jth switch is pressed
+	
+
+	% initializing A
+
+	for i = 1 : rows
+		for j = 1 : cols
+			A(a(i,j), a(i,j)) = 1;
+			if (i + 1 <= rows)
+				A(a(i,j), a(i + 1, j)) = 1;
+			end
+			if (i - 1 >= 1)
+				A(a(i,j), a(i - 1, j)) = 1;
+			end
+			if (j + 1 <= cols)
+				A(a(i,j), a(i, j + 1)) = 1;
+			end
+			if (j - 1 >= 1)
+				A(a(i,j), a(i, j - 1)) = 1;
+			end
+		endfor
+	endfor
+
+	% vectorization of input as a column vector
+	input_col_vec = reshape(input', no_buttons, 1);
+	
+	% ith index of row_of_x contains row_number of A which has (i - 1) zeros before the first one
+	row_for_x = zeros(1,no_buttons);
+
+	% Gaussian elimination of A
+	for i = 1 : no_buttons
+		target_rows = find_rows(A, i - 1);
+		no_of_rows_to_be_added = size(target_rows)(2);
+		if (no_of_rows_to_be_added >= 2)
+			for j = 2 : no_of_rows_to_be_added
+				A(target_rows(j), :) = mod((A(target_rows(j), :) + A(target_rows(1), :)), 2);
+				input_col_vec(target_rows(j)) = input_col_vec(target_rows(j)) + input_col_vec(target_rows(1));
+			endfor
+		end
+		if (no_of_rows_to_be_added >= 1)
+			row_for_x(i) = target_rows(1);
+		end
+	endfor
+
+	
+	% x - vector form of solution
+	x = zeros(no_buttons, 1);
+	input_col_vec = mod(input_col_vec, 2);
+	for i = no_buttons : -1 : 1
+		if (row_for_x(i) != 0)
+			x(i) = mod((input_col_vec(row_for_x(i)) + A(row_for_x(i),:)*x), 2);
+		end
+	endfor
+	
+	% solution	
+	x = reshape(x, cols, rows)';
+	solution = x;
+endfunction

lab01/outlab/backward_solve_3.m

+function solution = backward_solve_3(input)
+	
+	% number of rows, columns in input
+	[rows, cols] = size(input);
+	% no_buttons = number of buttons
+	no_buttons = rows*cols;
+	A = zeros(no_buttons, no_buttons);
+
+
+	% numbering the buttons
+	a = zeros(rows, cols);	
+	for i = 1 : rows
+		for j = 1 : cols
+			a(i, j) = cols * (i - 1) + j;
+		endfor
+	endfor
+
+
+	% A(i,j) = 1 if ith bulb is toggled with jth switch is pressed
+	
+
+	% initializing A
+
+	for i = 1 : rows
+		for j = 1 : cols
+			A(a(i,j), a(i,j)) = 1;
+			if (i + 1 <= rows)
+				A(a(i,j), a(i + 1, j)) = 1;
+			end
+			if (i - 1 >= 1)
+				A(a(i,j), a(i - 1, j)) = 1;
+			end
+			if (j + 1 <= cols)
+				A(a(i,j), a(i, j + 1)) = 1;
+			end
+			if (j - 1 >= 1)
+				A(a(i,j), a(i, j - 1)) = 1;
+			end
+		endfor
+	endfor
+
+	% vectorization of input as a column vector
+	input_col_vec = reshape(input', no_buttons, 1);
+	
+	% ith index of row_of_x contains row_number of A which has (i - 1) zeros before the first one
+	row_for_x = zeros(1,no_buttons);
+
+	% Gaussian elimination of A
+	for i = 1 : no_buttons
+		target_rows = find_rows(A, i - 1);
+		no_of_rows_to_be_added = size(target_rows)(2);
+		if (no_of_rows_to_be_added >= 2)
+			for j = 2 : no_of_rows_to_be_added
+				A(target_rows(j), :) = mod((A(target_rows(j), :) + A(target_rows(1), :)), 2);
+				input_col_vec(target_rows(j)) = input_col_vec(target_rows(j)) + input_col_vec(target_rows(1));
+			endfor
+		end
+		if (no_of_rows_to_be_added >= 1)
+			row_for_x(i) = target_rows(1);
+		end
+	endfor
+
+	
+	% x - vector form of solution
+	x = zeros(no_buttons, 1);
+	input_col_vec = mod(input_col_vec, 2);
+	for i = no_buttons : -1 : 1
+		if (row_for_x(i) != 0)
+			x(i) = mod((input_col_vec(row_for_x(i)) + A(row_for_x(i),:)*x), 2);
+		end
+	endfor
+	
+	% solution	
+	x = reshape(x, cols, rows)';
+	solution = x;
+endfunction

lab01/outlab/find_rows.m

+% finds rows which has 'no_of_zeros' zeros before the first one
+function found_rows = find_rows(A, no_of_zeros)
+	found_rows = zeros(1,0);
+	for i = 1 : size(A)(1)
+		if (isequal(A(i,1:no_of_zeros),zeros(1, no_of_zeros)) && isequal(A(i, no_of_zeros + 1), 1))
+			found_rows(end + 1) = i;
+		end
+	endfor	
+endfunction
\ No newline at end of file

lab01/outlab/main_task_A1.m

+
+% global variables
+global x1; 
+global y1; 
+global d; 
+global w;
+global mu;
+
+% reading values from file
+input_ptr = fopen("input_outlab_task_A1.txt", "r");
+[x1, y1, d, w, mu, count, errmsg] = fscanf(input_ptr, "%lf %lf %lf %lf %lf", "C");
+fclose(input_ptr);
+
+
+% function which gives value of expression at x(1) - incident angle on smoke screen
+% x(2) - refracted angle on smoke screen whose(expression's) value has to be made zero 
+function y = f(x)
+	global x1;
+	global y1;
+	global d;
+	global w;
+	global mu;
+	y = zeros(2,1);
+	y(1) = (y1 - w) * tand(x(1)) + w * tand(x(2)) - x1;
+	y(2) = sind(x(1)) - mu * sind(x(2));
+endfunction
+
+
+% solving equations using fsolve
+
+%initial values for fsolve
+i = atand(y1/x1);
+r = asind(sind(i)/mu);
+
+[x, fval, info] = fsolve("f", [i, r]);
+
+%writing angle at which the laser has to be shot to file
+output_ptr = fopen("output_outlab_task_A1.txt", "w");
+fprintf(output_ptr, "%.1f\n", x(1));
+fclose(output_ptr);
\ No newline at end of file

lab01/outlab/main_task_A2.m

+% global variables
+global xTIE;
+global yTIE;
+global xX_WING;
+global yX_WING;
+global v2;
+global vLaser;
+global d; 
+global w; 
+global mu;
+global t1;
+
+% reading values from file
+fid = fopen("input_outlab_task_A2.txt", "r");
+[xTIE, yTIE, xX_WING, yX_WING, v2, vLaser, d, w, mu, t1, count, errmsg] = fscanf(fid, "%lf %lf %lf %lf %lf %lf %lf %lf %lf %lf", "C");
+fclose(fid);
+
+
+%(x1, y1) - position of x-Xwing relative to xTIE
+global x1 = xX_WING - xTIE;
+global y1 = yX_WING - yTIE;
+
+
+% function which gives value of expression at x(1) - incident angle on smoke screen x(2) - refracted angle on smoke screen
+% x(3) - y coordinate of x-Xwing relative to xTIE at the time of impact whose(expression's) value has to be made zero
+function y = f(x)
+	global x1;
+	global y1;
+	global v2;
+	global vLaser;
+	global d;
+	global w;
+	global mu;
+	global t1;
+	y= zeros(3,1);
+	y(1) = (x(3) - w) * tand(x(1)) + w * tand(x(2)) - x1;
+	y(2) = (v2/vLaser)*((x(3) - w)/(cosd(x(1))) + w * mu/(cosd(x(2)))) - x(3) + y1 + v2 * t1;
+	y(3) = sind(x(1)) - mu * sind(x(2));
+endfunction
+
+% solving the equations using fsolve
+
+%initial values for fsolve
+yInitial = y1 + v2*t1;
+i = atand(yInitial/x1);
+r = asind(sind(i)/mu);
+
+[x, fval, info] = fsolve("f", [i, r, yInitial]);
+
+% writing (angle at which laser has to shot and the nearest position at which x-Xwing will get hit to the file )
+output_ptr = fopen("output_outab_task_A2.txt", "w");
+fprintf(output_ptr, "%.1f %.1f %.1f", x(1), x1, x(3));
+
+fclose(output_ptr);

lab01/outlab/readme.txt

+Group 33 : Lab01_outlab
+
+Tasks : A1, A2, B1, B2
+
+Group Members:
+(Vinayak K, 150050098), (Shriram S B, 150050099), (Anubhaw Kuntal Xess, 150050100)
+Vinayak K - 100%
+Shriram S B - 100%
+Anubhaw Kuntal Xess - 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Reflection essay (A1, A2) :
+	- Coverting a problem related to physics to mathematical equations and solving them using octave
+	- Learnt to solve simultaneous equations using fsolve
+
+Reflection essay (B1, B2) :
+	- appending to the end of vector
+	- reshape works in column major order but not row major order
+	- Gaussian elimination
+
+find_rows.m contains helper function required by backward_solve.m and backward_solve_3.m
+backward_solve.m works even with 3x3 matrix.
+So, for backward_solve_3.m is just the copy of backward_solve.m
+
+Citations: 
+	- Gnu octave Documentation
+	- http://www.ueda.info.waseda.ac.jp/~n-kato/lightsout/ for how Lights out work and how to solve it (Found Gaussian Elimination from here)