lab1-octave

lab1/inlab1/input_inlab_task_A1.txt

+3 2

lab1/inlab1/output_inlab_task_01.txt

+1.57080

lab1/inlab1/readme.txt

+Group 11 - !nfinity
+
+(Kartik Singhal, 150050025) (Pranay Agrawal, 150050026) (Nilesh Gupta, 150050059)
+
+Student 1: 100%
+Student 2: 100%
+Student 3: 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Citations:
+http://stackoverflow.com
+www.gnu.org/software/octave/doc/v4.0.0
+http://in.mathworks.com/help/matlab/
+http://www.wolframalpha.com/
+http://en.flossmanuals.net/
+http://www.dm.unibo.it/~lenci/teaching/14/maa/octavetut.pdf
+http://www.gnu.org/software/octave/octave.pdf
+
+Reflections:
+1. Learnt Ocatave- taking input from text files
+					loading output in text files
+					finding roots of a equation
+2. Learnt process of Bi-Refringence
\ No newline at end of file

lab1/inlab1/refraction.m

+a=load('input_inlab_task_A1.txt');# takes input from text file and stores the numbers in an array
+nx=a(1);#assign nx the first element of a
+ny=a(2);#assign ny second element of a
+g=@(r)(nx*cos(r)+ny*sin(r))*sin(r/3)-sin(r);# define g as function of r 
+x0=[0 + 1e-5 pi/2];#range in which r should lie, 0 is a trivial solution irrespective of value of nx and ny
+r=fzero(g,x0);#computes zero of function g in range x0 and assign it to r
+fileID = fopen('output_inlab_task_01.txt','w');#opens the file in which output is to be loaded
+fprintf(fileID,'%4.5f\n',r);#writing the ouput in output file
+fclose(fileID);#closing the output file
\ No newline at end of file

lab1/inlab2/final_state_3.m

+function y=final_state_3(i,a)
+	b=[ 1 1 0 1 0 0 0 0 0;
+		1 1 1 0 1 0 0 0 0;
+		0 1 1 0 0 1 0 0 0;
+		1 0 0 1 1 0 1 0 0;
+		0 1 0 1 1 1 0 1 0;	# in matrix b, b(i,j)=1 iff button i is toggled on pressing button j
+		0 0 1 0 1 1 0 0 1;
+		0 0 0 1 0 0 1 1 0;
+		0 0 0 0 1 0 1 1 1;
+		0 0 0 0 0 1 0 1 1];
+
+	initial=i(:);			# converts initial matrix i of order 3*3 into order 9*1
+	action=a(:);			# converts action matrix a of order 3*3 into order 9*1
+	x=b*action+initial; 	
+	y=[ 0 0 0;
+		0 0 0;
+		0 0 0];
+	for i=1:9
+		y(i)=rem(x(i),2);	#converts back x of order 9*1 into y matrix of order 3*3 and takes modulo with 2
+	endfor
+
+	return;
+
+endfunction
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lab1/inlab2/lookup_solve_3.m

+function c=lookup_solve_3(a)
+
+	c=[ 0 0 0; 
+		0 0 0; #initialising the matrix c, which keep counts of which switch is pressed how many times
+		0 0 0];	
+
+	for x=0:2
+		if(a(x*3+1)==1)
+			a=toggle(a,x*3+2);	#turns off all the lights in the top row
+			c(x*3+2)++;
+		endif
+	endfor
+
+	for x=0:2
+		if(a(x*3+2)==1)
+			a=toggle(a,x*3+3);	#turns off all the lights in the middle row
+			c(x*3+3)++;
+		endif
+	endfor
+
+	# now checks the situation of bottom row and with the help of table presses the switches in top row
+
+	if(a(3,:)==[0 0 1])
+		a=toggle(a,4);
+		c(4)++;
+		a=toggle(a,7);
+		c(7)++;
+	endif
+
+	if(a(3,:)==[0 1 0])
+		a=toggle(a,1);
+		c(1)++;
+		a=toggle(a,4);
+		c(4)++;
+		a=toggle(a,7);
+		c(7)++;
+	endif
+
+	if(a(3,:)==[0 1 1])
+		a=toggle(a,1);
+		c(1)++;
+	endif
+
+	if(a(3,:)==[1 0 0])
+		a=toggle(a,1);
+		c(1)++;
+		a=toggle(a,4);
+		c(4)++;
+	endif
+
+	if(a(3,:)==[1 0 1])
+		a=toggle(a,1);
+		c(1)++;
+		a=toggle(a,7);
+		c(7)++;
+	endif
+
+	if(a(3,:)==[1 1 0])
+		a=toggle(a,7);
+		c(7)++;
+	endif
+
+	if(a(3,:)==[1 1 1])
+		a=toggle(a,4);
+		c(4)++;
+	endif
+
+	for x=0:2
+		if(a(x*3+1)==1)
+			a=toggle(a,x*3+2);	#repeat the same process, turns off the lights in toprow
+			c(x*3+2)++;
+		endif
+	endfor
+
+	for x=0:2
+		if(a(x*3+2)==1)
+			a=toggle(a,x*3+3);	# repeat the same process, turns off the lights in middle row
+			c(x*3+3)++;
+		endif
+	endfor
+
+	for x=1:9
+		c(x)=rem(c(x),2);		# if the button is pressed even number of times then, no need of it to be pressed and if it is pressed odd number of times then it should be pressed only once.
+	endfor
+
+	return;
+
+endfunction
\ No newline at end of file

lab1/inlab2/readme.txt

+Group 11 - !nfinity
+
+(Kartik Singhal, 150050025) (Pranay Agrawal, 150050026) (Nilesh Gupta, 150050059)
+
+Student 1: 100%
+Student 2: 100%
+Student 3: 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Citations:
+http://stackoverflow.com
+www.gnu.org/software/octave/doc/v4.0.0
+http://in.mathworks.com/help/matlab/
+http://www.wolframalpha.com/
+http://en.flossmanuals.net/
+http://www.dm.unibo.it/~lenci/teaching/14/maa/octavetut.pdf
+http://www.gnu.org/software/octave/octave.pdf
+
+Reflections:
+1. Learnt Octave-
+				Writing functions in octave
+				writing for and if loops
+			
+2. Learnt the mathematical reasoning behind lightsout problem
+3. Learnt Light Chasing algorithm for solving lightsout problem
+
+B1-lookup_solve_3.m
+The function takes a 3*3 matrix in initial state and returns a 3*3 matrix which denotes which switches are to be pressed.
+It uses another function toggle inside it which is defined separately.
+toggle(a,x) -> returns the matrix situation of matrix a of order 3*3 after switch x is pressed
+Switches: 1 4 7
+	  2 5 8
+	  3 6 9
+
+B2-final_state_3.m
+The function takes two 3*3 matrix i & a. i denotes the initial state of lights and a denotes the action matrix.
+It ouputs the final state of the matrix

lab1/inlab2/toggle.m

+function c=toggle(a,x)
+	if(rem(x,3)==0)
+		b=[x-3 x-1 x x+3];
+	elseif(rem(x,3)==1)
+		b=[x-3 x x+1 x+3];		# vector b stores the switch numbers which will be toggled by pressing the switch x;
+	else
+		b=[x-3 x-1 x x+1 x+3];
+	endif
+	for i=1:length(b)
+		if(b(i)>0 && b(i)<10)
+			a(b(i))=1-a(b(i)); 	# toggles the value of switch
+		endif
+	endfor
+	c=a;		# returns matrix c which is the state of matrix a after pressing switch x;
+endfunction
\ No newline at end of file

lab1/outlab/backward_solve.m

+function y=backward_solve(i)
+
+	rows=size(i,1);
+	columns=size(i,2);
+	c=0*ones (rows*columns, rows*columns); # initialise c matrix as NULL of order (rows*columns)*(rows*columns)
+	for j=1:rows*columns
+		if(rem(j,rows)==0)
+			b=[j-rows j-1 j j+rows];
+		elseif(rem(j,rows)==1)
+			b=[j-rows j j+1 j+rows];		# vector b stores the switch numbers which will be toggled by pressing the switch x;
+		else
+			b=[j-rows j-1 j j+1 j+rows];
+		endif
+		for k=1:length(b)
+			if(b(k)>0 && b(k)<rows*columns+1)
+				c(j,b(k))=1;					# in matrix c, c(i,j)=1 iff button i is toggled on pressing button j
+			endif
+		endfor
+	endfor
+	
+	initial=i(:);			# converts initial matrix i of order 3*3 into order 9*1
+	
+	x=det(c);
+	action=-x*inverse(c)*initial;	#computes the action matrix using matrix operations
+	w=int32(action);				#round off the action matrix into integer
+	y=0*ones (rows, columns);		#initialise c matrix as NULL of order rows*columns
+	for i=1:rows*columns
+		y(i)=mod(w(i),2);			# takes remainder with 2
+	endfor
+	return;
+
+endfunction
\ No newline at end of file

lab1/outlab/backward_solve_3.m

+function y=backward_solve_3(i)
+
+	b=[ 1 1 0 1 0 0 0 0 0;
+		1 1 1 0 1 0 0 0 0;
+		0 1 1 0 0 1 0 0 0;
+		1 0 0 1 1 0 1 0 0;
+		0 1 0 1 1 1 0 1 0;		# in matrix b, b(i,j)=1 iff button i is toggled on pressing button j
+		0 0 1 0 1 1 0 0 1;
+		0 0 1 0 1 1 0 0 1;
+		0 0 0 1 0 0 1 1 0;
+		0 0 0 0 1 0 1 1 1;
+		0 0 0 0 0 1 0 1 1];
+
+	initial=i(:);	# converts initial matrix i of order 3*3 into order 9*1
+	x=det(b);
+	action=-x*inverse(b)*initial;	#computes the action matrix using matrix operations
+	z=int32(action);				#round off the action matrix into integer
+	y=[ 0 0 0;
+		0 0 0;			
+		0 0 0];
+	for i=1:9
+		y(i)=mod(z(i),2);			# takes remainder with 2
+	endfor
+	return;
+
+endfunction
\ No newline at end of file

lab1/outlab/main_task_A1.m

+a=load('input_outlab_task_A1.txt'); # takes input from the file and store in vector
+
+global x1=a(1);
+global y1=a(2);
+global d=a(3);										#assign respective values in variables from the vector
+global w=a(4);
+global n=a(5);
+
+function y=f(x)
+	global x1;
+	global y1;
+	global d;										#variable declaration inside the function
+	global w;
+	global n;
+	y(1)=x(1)+x(2)+x(3)-x1;
+	y(2)=tan(x(4))*(y1-d-w)-x(1);
+	y(3)=tan(x(5))*w-x(2);							#equation which are to be solved
+	y(4)=tan(x(4))*d-x(3);
+	y(5)=sin(x(4))-n*sin(x(5));
+endfunction
+
+[x,info]=fsolve("f",[0;0;0;0;0]);					#solves the equation using fsolve
+fileID = fopen('output_outlab_task_A1.txt','w');	
+fprintf(fileID,'%4.1f\n',x(4)*180/pi);				#reads the output in file 
+fclose(fileID);
\ No newline at end of file

lab1/outlab/main_task_A2.m

+a=load('input_outlab_task_A2.txt'); # takes input from the file and store in vector
+
+global x0=a(1);
+global y0=a(2);
+global x1=a(3);
+global y1=a(4);
+global v2=a(5);
+global vl=a(6);						#assign respective values in variables from the vector
+global d=a(7);
+global w=a(8);
+global n=a(9);
+global t1=a(10);
+
+x1=x1-x0;
+y1=y1-y0;			#relative coordinate of x-wing with respect to TIE
+
+function y=f(x)
+	global x1;
+	global y1;
+	global v2;
+	global vl;						#variable declaration inside the function
+	global d;
+	global w;
+	global n;
+	global t1;
+	y(1)=(y1+v2*(x(3)+t1))*tan(x(1))+w*tan(x(2))-w*tan(x(1))-x1;
+	y(2)=(y1+v2*(x(3)+t1))*sec(x(1))-w*sec(x(1))+n*w*sec(x(2))-vl*x(3);			#equation which are to be solved
+	y(3)=n*sin(x(2))-sin(x(1));
+endfunction
+
+theta = 0;
+phi = 0;		#initialising the  variables as 0
+time = 0;
+[x,fval, info]=fsolve("f",[theta;phi;time]);	#solves the equation using fsolve
+while (info != 1)
+	theta = x(1);
+	phi = x(2);									#while loop till the value for the equations converges
+	time = x(3);	
+	[x,fval, info]=fsolve("f",[theta;phi;time]);
+endwhile
+
+fileID = fopen('output_outlab_task_A2.txt','w');
+fprintf(fileID,'%4.1f %4.1f %4.1f',x(1)*180/pi,x1,y1+v2*(x(3)+t1)); #reads the output in file 
+fclose(fileID);
\ No newline at end of file

lab1/outlab/readme.txt

+Group 11 - !nfinity
+
+(Kartik Singhal, 150050025) (Pranay Agrawal, 150050026) (Nilesh Gupta, 150050059)
+
+Student 1: 100%
+Student 2: 100%
+Student 3: 100%
+
+I pledge on my honour that I have not given or received any unauthorized assistance on this assignment or any previous task.
+
+Citations:
+http://stackoverflow.com
+www.gnu.org/software/octave/doc/v4.0.0
+http://in.mathworks.com/help/matlab/
+http://www.wolframalpha.com/
+http://en.flossmanuals.net/
+http://www.dm.unibo.it/~lenci/teaching/14/maa/octavetut.pdf
+http://www.gnu.org/software/octave/octave.pdf
+
+Reflections:
+1. Learnt Octave-
+				how fsolve function works
+				writing while loops
+			
+2. Learnt a fast and efficient way of solving lightsout problem for any order m*n
+3. Learnt Solving various equations simultaneously in octave
+
+
+