Outlab 1

lab01_group23_final/Readme.txt

+
+Group number 23
+
+Group members: 
+(Harsh Depal, 150050010),(Tarun Verma, 150050021),(Bhavya Choudhary, 150050028)
+
+Honor code:- 
+I pledge on my honour that I have not given or received
+any unauthorized assistance on this assignment or any previous task.
+
+Individual Percentage : 
+Harsh Depal:100%, Tarun Verma:100%, Bhavya Choudhary:100%
+
+Citations:
+www.math.utah.edu
+stackoverflow.com
+gnu.org
+www.dm.unibo.it
+tutorialspoint.com
+http://www.ueda.info.waseda.ac.jp/~n-kato/lightsout/
+wikipedia.org
+
+
+
+Brief Reflection :
+We had study little bit of modular arithmatics for matrices to solve the Lights Out puzzle.
+As we couldn't find a function can do modular arithmatic in Octave we had to write our own functions using for loops.
+We learned how octave with its powerful built-in functions can be used to solve complicated mathematical equations.
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lab01_group23_final/backward_solve.m

+function action = backward_solve_3(cstate)
+	[row,col]=size(cstate);
+	M=[];  									# M will become the matrix where Mij = 1 ⇐⇒ button i is toggled on pressing button j
+	for x=1:row*col
+		for y=1:row*col
+			if(abs(y-x) == col | (abs(y-x)<=1 & floor((y-1)/col)==floor((x-1)/col)))
+				v(y)=1;
+			else 
+				v(y)=0;
+			endif
+		endfor
+	M=[M;v];  								# adding ith column as a row. we will transpose it later
+	endfor
+	for i=1:row
+		for j=1:col
+			w((i-1)*col+j)=cstate(i,j);     # converting cstate into vector 
+		endfor
+	endfor
+	M=[M;w];    							# making augmented matrix
+	M = M';
+	guassM=guass_elim(M);  					# last column is the answer, doing guass elimination  
+	action=[];
+	for l=1:row  							# converting last column as a matrix
+		for k=1:col
+			Arow(k)=guassM((l-1)*col+k,col*row+1);
+		endfor
+		action=[action;Arow];
+	endfor
+endfunction
+
+
+

lab01_group23_final/backward_solve_3.m

+function action = backward_solve_3(cstate)
+	[row,col]=size(cstate);
+	M=[];  									 # M will become the matrix where Mij = 1 ⇐⇒ button i is toggled on pressing button j
+	for x=1:row*col
+		for y=1:row*col
+			if(abs(y-x) == col | (abs(y-x)<=1 & floor((y-1)/col)==floor((x-1)/col)) )
+				v(y)=1;
+			else 
+				v(y)=0;
+			endif
+		endfor
+	M=[M;v]; 								 # adding ith column as a row. we will transpose it later
+	endfor
+	for i=1:row
+		for j=1:col
+			w((i-1)*col+j)=cstate(i,j);   	 # converting cstate into vector 
+		endfor
+	endfor
+	M=[M;w];    							 # making augmented matrix
+	M = M';
+	guassM=guass_elim(M);  					 # last column is the answer  
+	action=[];
+	for l=1:row  							 # converting last column as a matrix
+		for k=1:col
+			Arow(k)=guassM((l-1)*col+k,col*row+1);
+		endfor
+		action=[action;Arow];
+	endfor
+endfunction
+
+
+

lab01_group23_final/guass_elim.m

+# function to solve the matrix "augmented" by guassian elimination with modular arithematic and return the guass jordan form as the final "matrix"
+
+function final = guass_elim(augmented)
+		final = augmented;
+		n = size(final,1);						# n stores the number of rows in final
+		for i = 1 : n
+		    if (final(i,i)!=1)												
+		        
+        # for loop to make i,i position 1 by row operations
+
+			    for a = i : n
+				    if (final(a,i) == 1)
+					    final(i,:) = mod((final(i,:) + final(a,:)),2);
+					    break;
+				    endif
+			    endfor
+			 endif
+
+	 	# for loop to make all elements of column i 0 except i,i
+
+			for a = 1 : n
+				if (final(a,i) == 1 && a!=i)
+					final(a,:) = mod((final(i,:) + final(a,:)),2);
+				endif
+			endfor
+		endfor
+endfunction
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lab01_group23_final/main_task_A1.m

+filename = "input_outlab_task_A1.txt";
+[x1,y1,d,w,n] = textread(filename,"%f %f %f %f %f"); #reading data from input file
+f = @(x) [(y1-w)*tand(x(1)) + w*tand(x(2)) - x1;n*sind(x(2)) - sind(x(1))];
+x = fsolve(f,[0;0]); # using fsolve to find the required values
+csvwrite("output_outlab_task_A1.txt",x(1)); #writing the calculated answer in the output file
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lab01_group23_final/main_task_A2.m

+inputfile = "input_outlab_task_A2.txt";
+outputfile = "output_outlab_task_A2.txt";
+[xt,yt,xx,yx,v2,vl,d,w,n,t1] = textread(inputfile,"%f %f %f %f %f %f %f %f %f %f"); # reading data from input file
+x1 = xx - xt;
+y1 = yx - yt + t1*v2;
+f = @(x) [sind(x(1))-n*sind(x(2));(y1 + ((y1-w+w*n*cosd(x(1))/cosd(x(2)))/(vl*cosd(x(1))-v2))*v2)*tand(x(1)) + w*(tand(x(2))-tand(x(1))) - x1];
+x = fsolve(f,[0;0]); # using fsolve to find required vector x
+xf = xx;
+yf = yx + t1*v2 + ((y1-w+n*w*cosd(x(1))/cosd(x(2)))/(vl*cosd(x(1))-v2))*v2; # calculating final coordinates xf and yf
+ofile = fopen(outputfile,"w");
+fprintf(ofile,"%f %f %f",x(1),xx,yf); # writing the calculated answer in output file
+fclose(ofile);