First Lab added

Lab 1/Inlab/Citations

+Citations:
+https://www.gnu.org/software/octave/doc/v4.0.0/Simple-File-I_002fO.html  //textread 
+http://homepages.math.uic.edu/~hanson/Octave/OctaveNonlinearEG.html //example for fsolve and fzero
+
+http://stackoverflow.com/questions/12932052/what-is-the-fastest-way-to-write-a-matrix-to-a-text-file-in-octave // has an example for file i/o

Lab 1/Inlab/README

+Group member info:
+Team 16 : Invictus
+(Sreekar Garlapati ,150050065) , (Nagendra Reddy,150050067), (Sai Prakash , 150050075)
+Honor Code:
+We pledge on our honour that we have not given or received any unauthorized assistance on this assignment .
+Percentage : 150050065 :100% , 150050067 : 100% , 150050075 : 100% 
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Lab 1/Inlab/Task A1/reflection_essay_refraction

+The example nicely illustrates the basic use of GNU octave's I/O system and also the use of functions and how to solve non linear equations.
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Lab 1/Inlab/Task A1/refraction.m

+xx=fsolve(@test,pi/4);// storing output in a variable 
+file_id = fopen('output inlab task 01.txt', 'w+');//getting write file id
+fprintf(file_id, "%f",xx);//writing to the file
+fclose(file_id);//closing file id
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Lab 1/Inlab/Task A1/test.m

+function y=test(x)
+[a]=textread('input_inlab_task_A1.txt',"%f");//reading the input file
+c=a(1,1);//storing in
+d=a(2,1);//two variables as required
+y=c*cos(x)*sin(x/3)/sin(x)+d*sin(x/3)-1;// the function whose zero is to be computed
+endfunction
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Lab 1/Inlab/Task B1 and B2/ReadMe.txt

+Group Info:
+	Team Invictus (16)
+	(Sreekar Garlapati,150050065),(Nagendra Reddy,150050067),(Sai Prakash,150050075)
+
+Reflection Essay:
+	This set of problems teaches us to pass and return matrices to functions in octave and also highlights a few impressive applications of matrix multiplication .
+Citations :
+	https://en.wikibooks.org/wiki/Octave_Programming_Tutorial/Vectors_and_matrices // Introduces matrices well, with a few useful functions
+	https://en.wikibooks.org/wiki/Octave_Programming_Tutorial/Writing_functions  // Has a fairly detailed documentation of functions in octave
+Honor code:
+We pledge on our honour that we have not given or received any unauthorised on this assignment or the previous one.
+
+Percentage:
+	150050065:100%
+	150050067:100%
+	150050075:100%

Lab 1/Inlab/Task B1 and B2/action.txt

+0 0 0
+1 0 0
+0 0 1
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Lab 1/Inlab/Task B1 and B2/final_state_3.m

+function [final] = final_state_3(init,action)
+	final=zeros(3);
+	A =[1,1,0,1,0,0,0,0,0;   #conversion matrix
+		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;
+		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];
+	ini=zeros(9,1); #temporary row matrix for storing init values
+	act=zeros(9,1); #temporary row matrix for storing action values
+	fin=zeros(9,1); #temporary row matrix for storing final matrix values
+	for i=1:3
+		for j=1:3
+			ini(3*(i-1)+j,1)=init(i,j);    #converting 3x3 into 9x1 matrix
+			act(3*(i-1)+j,1)=action(i,j);  
+		endfor
+	endfor
+	fin=(A*act)+ini;  
+	fin=mod(fin,2);  #forming the final matrix in 9x1 format
+	for i=1:3
+		for j=1:3
+			final(i,j)=fin(3*(i-1)+j,1);  #conversion to 3x3
+		endfor
+	endfor
+endfunction
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Lab 1/Inlab/Task B1 and B2/input.txt

+1 1 0
+0 0 1
+0 0 0
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Lab 1/Inlab/Task B1 and B2/lookup_solve_3.m

+function [action] = lookup_solve_3(initial) 
+	action = zeros(3);
+	action(2,:)=initial(1,:);  #clearing the first row
+	final = final_state_3(initial,action);  #finding the resulting matrix
+	action(3,:)=final(2,:);   #clearing the second row
+	final = final_state_3(initial,action);  #finding the resulting matrix
+	check = zeros(3);
+	if final==check
+	else
+		action(1,:) = self_change(final(3,:));  #changing first row according to the last row
+		final = final_state_3(initial,action);
+		action = action+lookup_solve_3(final);  #repitition by recurrsion
+		action = mod(action,2);
+	endif
+endfunction
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Lab 1/Inlab/Task B1 and B2/main_B1.m

+A=zeros(3);
+[N]=textread('input.txt',"%f");
+for i=1:3
+	for j=1:3
+		A(i,j)=N(3*(i-1)+j);
+	endfor
+endfor
+#initial = [1,1,0;1,1,1;0,0,1]
+action = @lookup_solve_3(A)
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Lab 1/Inlab/Task B1 and B2/main_B2.m

+A=zeros(3);
+B=zeros(3);
+[N]=textread('input.txt',"%f");
+for i=1:3
+	for j=1:3
+		A(i,j)=N(3*(i-1)+j);
+	endfor
+endfor
+[N]=textread('action.txt',"%f");
+for i=1:3
+	for j=1:3
+		B(i,j)=N(3*(i-1)+j);
+	endfor
+endfor
+final = @final_state_3(A,B)
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Lab 1/Inlab/Task B1 and B2/self_change.m

+function [final] = self_change(action) #function forming the correspondence shown in the lookup table
+	final = zeros(1,3);
+	A = [1,1,0;1,1,1;0,1,1];  #conversion matrix for the mapping
+	final = mod(action*A,2);
+endfunction
+#the conversion using the lookup table can be conveniently done using matrix multiplication , in particular , multiplying the last row with A
+# gives the top row buttons to be pressed.
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Lab 1/Outlab/Readme.txt

+Group Info:
+	Team Invictus (16)
+	(Sreekar Garlapati,150050065),(Nagendra Reddy,150050067),(Sai Prakash,150050075)
+
+Reflection Essay:
+	Task A:
+		This task had the equation solving capability taken to the next level.The problem requires a careful analysis of the
+	situation and the answer can go wrong if one isn't careful enough.
+		Task A1 was relatively straightforward and had laid the foundation for the next task.
+		Task A2 was a tad tougher and the equation does get a bit messy. This checks scrupulous analysis on the solver's part.
+	Task B:
+		This was an extension of the inlab assignment, with the generalization of the earlier solution.One very interesting observation
+	which is incredibly crucial to this solution is that the conversion matrices have an odd determinant.The solution wouldn't have been
+	possible if this weren't so. Besides this observation , the problem has a good application of matrix inversion technique and also 
+	careful analysis of the situation ( as it will always be in our SSL assignments :-)  )
+Citations :
+	http://www.ueda.info.waseda.ac.jp/~n-kato/lightsout/   // the given link for testing various outputs for task B
+	New resources were not needed in attempting task A
+Honor code:
+	We pledge on our honour that we have not given or received any unauthorised on this assignment or the previous one.
+
+Percentage:
+	150050065:100%
+	150050067:100%
+	150050075:100%

Lab 1/Outlab/back_conv.m

+function [fin]=back_conv(C,m,n) 		#function to convert the column matrix back into the correct form
+	fin=zeros(m,n);#initializing empty array
+	if rows(C)*columns(C)==m*n   		#running a check
+	else
+		disp("error");
+		return;
+	endif  
+	for i=1:m
+		for j=1:n
+			fin(i,j)=C(n*(i-1)+j,1);  	#entering the values into the m X n matrix
+		endfor
+	endfor	
+endfunction
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Lab 1/Outlab/backward_solve.m

+function [root]=backward_solve(input)				#the main function which computes the answer
+	root=zeros(rows(input),columns(input));			#an initial zero matrix of the same size as input
+	A=get_conversion_matrix(input);					#the get_conversion_matrix call which gives us the matrix used to convert action vector to effect vector
+	B=col_conv(input);								#converting input into col matrix
+	x=det(A)*inv(A)*B;								#finding out the answer in column matirx form
+	root=back_conv(x,rows(input),columns(input));	#converting the answer column back into an m X n matrix form
+	root=int32(root);								#removing the ugly decimals
+	root=mod(root,2);								#returns the root
+endfunction
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Lab 1/Outlab/backward_solve_3.m

+function [root]=backward_solve_3(input)   #basically the backward_solve function but with a check for the input size
+	if rows(input)==3            
+	else return								# this block performs the check
+	endif
+	if columns(input)==3 
+	else return
+	endif
+	root=zeros(rows(input),columns(input));
+	A=get_conversion_matrix(input);
+	B=col_conv(input);
+	x=det(A)*inv(A)*B;
+	root=back_conv(x,rows(input),columns(input));
+	root=int32(root);
+	root=mod(root,2);
+endfunction
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Lab 1/Outlab/col_conv.m

+function [colm]=col_conv(mat) 					#converts into a column matrix
+	m=rows(mat);				
+	n=columns(mat);								#store the size
+	rowm=zeros(m*n,1);	
+	for i=1:m
+		for j=1:n
+			colm(n*(i-1)+j,1)=mat(i,j);			#the colm vector which is returned is storing the elements of the input in these loops
+		endfor
+	endfor
+endfunction
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Lab 1/Outlab/eqn.m

+function res= eqn(theta)
+	[N]=textread("input_outlab_task_A1.txt","%f");
+	x1=N(1);
+	y1=N(2);
+	d=N(3);
+	w=N(4);														#all these lines store
+	n=N(5);														#the input values
+	res=(y1-w)*tan(theta)+w*tan(get_alpha(theta,n))-x1;			#the equation needed to be solved for theta
+																# the get_alpha function calculates the angle of refraction in the smoke screen
+endfunction
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Lab 1/Outlab/eqn2.m

+function res=eqn2(theta)
+	[N]=textread("input_outlab_task_A2.txt","%f");
+	x0=N(1);
+	y0=N(2);
+	x1=N(3);
+	y1=N(4);
+	v2=N(5);
+	vl=N(6);
+	d=N(7);
+	w=N(8);
+	n=N(9);
+	t1=N(10);
+	x1ground=x1;
+	y1ground=y1;
+	x1=x1ground-x0;				  #   the input reading code lines
+	y1=y1ground-y0;               #		with the values x1 , y1 set to the relative values and the originals are stored in the ground suffixed values
+	
+	res  = ((x1-(w*tan(get_alpha(theta,n))))/(vl*sin(theta))+((w*n)/(vl*cos(get_alpha(theta,n)))))-((((x1-(w*tan(get_alpha(theta,n) ) ) )*cot(theta))-y1+w-(v2*t1))/v2);
+		# the above equation is the exact equation for getting the value of theta	
+endfunction
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Lab 1/Outlab/final_return.m

+function ans=final_return()    # a straightforward file with the purpose of returning the values of the various scattered functions
+theta=fsolve(@eqn2,pi/4);	   # gets the value of theta
+[x2,y2]=get_y(theta);		   # gets the final coordinates
+ans(1)=theta*180/pi;
+ans(2)=x2;
+ans(3)=y2;					   #answer stores the values
+endfunction
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Lab 1/Outlab/get_alpha.m

+function alpha = get_alpha (theta,n)
+	alpha=asin(sin(theta)/n);			# getting value of refraction inside smoke screen
+endfunction
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Lab 1/Outlab/get_conversion_matrix.m

+function [conv]=get_conversion_matrix(input)				#this forms the conversion matrix
+	m=rows(input);
+	n=columns(input);
+	conv=zeros(m*n);
+	for i=1:m
+		for j=1:n
+			conv((n*(i-1)+j),(n*(i-1)+j))=1;				#(i,i) is set to 1
+			if i==1
+			else
+				conv((n*(i-1)+j),(n*(i-2)+j))=1;			#the element on the top of it is set to 1 in the conversion matrix if it isnt in the first row
+			endif
+			if i==m
+			else
+				conv((n*(i-1)+j),(n*(i)+j))=1;				#the element on the bottom of it is set to 1 in the conversion matrix if it isnt in the last row
+			endif
+			if j==1
+			else
+				conv((n*(i-1)+j),(n*(i-1)+j-1))=1;			#the element on the left of it is set to 1 in the conversion matrix if it isnt in the leftmost column
+			endif
+			if j==n
+			else
+				conv((n*(i-1)+j),(n*(i-1)+j+1))=1;			#the element on the right of it is set to 1 in the conversion matrix if it isnt in the rightmost column
+			endif
+		endfor
+	endfor
+endfunction
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Lab 1/Outlab/get_y.m

+function [xfin,yfin]=get_y(theta)
+	[N]=textread("input_outlab_task_A2.txt","%f");
+	x0=N(1);
+	y0=N(2);
+	x1=N(3);
+	y1=N(4);
+	v2=N(5);
+	vl=N(6);
+	d=N(7);
+	w=N(8);
+	n=N(9);
+	t1=N(10);
+	x1ground=x1;
+	y1ground=y1;
+	x1=x1ground-x0;
+	y1=y1ground-y0;  # same as before , gets the relative coordinates
+	xfin=x1;
+	yfin=(((((x1-(w*tan(get_alpha(theta,n) ) ) )*cot(theta))-y1+w-(v2*t1))/v2)+t1)*v2+y1;   #finds the final y coordinate (relative)
+endfunction
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Lab 1/Outlab/input_outlab_task_A1.txt

+180.0 100 0.05 5 3.5
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Lab 1/Outlab/input_outlab_task_A2.txt

+0.0 0.0 76.63 27 0.027 0.0555 7 5 3.5 5
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Lab 1/Outlab/main_task_A1.m

+ans=fsolve("eqn",pi/4)*180/pi;						#getting the value of theta for A1 
+file_id=fopen("output_outlab_task_A1.txt",'w+');	#getting file id
+fprintf(file_id,"%f",ans);							#writing theta
+fclose(file_id);									#closing file id
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Lab 1/Outlab/main_task_A2.m

+ans=final_return();
+file_id=fopen("output_outlab_task_A2.txt",'w+');		#getting file id
+fprintf(file_id,"%f",ans(1));							#writing theta
+fprintf(file_id,"%s"," ");
+fprintf(file_id,"%f",ans(2));							#writing x final
+fprintf(file_id,"%s"," ");
+fprintf(file_id,"%f",ans(3));							#writing y final
+fclose(file_id);										#closing file id
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Lab 1/Outlab/output_outlab_task_A1.txt

+62.003645
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Lab 1/Outlab/output_outlab_task_A2.txt

+41.070191 76.630000 91.838433
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Lab 1/Outlab/sample_main_taskB.m

+A=[ 1 0 1 ;
+	1 1 1 ;
+	1 1 1 ;];							#sample test case
+backward_solve(A)						#running the general task B2
+disp("\n");
+backward_solve_3(A)						#running taskB1
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