Delete backward_solve.m

backward_solve.m

-# function to solve a given initial lights out problem matrix
-# expects a single matrix as an argument
-# solves Ax + b = c for x
-# here, c is the vector describing final state of the matrix, consisting entirely of zeros
-function ret = backward_solve(input)
-	if(nargin ~= 1),
-		usage("The function backward_solve expects only one argument");
-	end;
-	b = mattovec(input);
-	sz = size(input);
-	m = sz(1); 
-	n = sz(2);
-	# constructing matrix A, where each entry aij contains whether the cell i is inverted or not by pressing the cell j 
-	A = zeros(m*n, m*n);
-	for x= 1:m*n,
-		for y= 1:m*n,
-			# pressing the button flips its own configuration
-			if x == y, 
-				A(x, y) = 1;
-			end;
-			# pressing the button flips the configuration of the button just before it, given it exists
-			if mod(x, n) ~= 1 && x - y == 1,
-				A(x, y) = 1;
-			end;
-			# pressing the button flips the configuration of the button just after it, given it exists
-			if mod(x, n) ~= 0 && y - x == 1,
-				A(x, y) = 1;
-			end;
-			# pressing the button flips the configuration of the button just above it, given it exists
-			if x > n && x - y == n,
-				A(x, y) = 1;
-			end;
-			# pressing the button flips the configuration of the button just below it, given it exists
-			if x < m*n - n + 1 && y - x == n,
-				A(x, y) = 1;
-			end;
-		end;
-	end;
-	de = det(A);
-	de = floor(de); 
-	if mod(de, 2) == 0,
-		de = de + 1;
-	end;
-	# multiplying by an odd number does not change the value of Ax modulo 2
-	A = floor(A);
-	# the process requires taking an inverse, in some cases a psuedo inverse is taken, which might not 
-	# have integral values, thus taking the floor 
-	b = b*de;
-	# the determinant value of inverse is reciprocal of the determinant value of given matrix
-	x = (A)\b;
-	x = mod(x + 0.01, 2);
-	# according to our observations, octave represents numbers very slightly less than two to two.
-	# in a few testcases that we tried, the mod function did the right thing, yet the display was misleading
-	x = floor(x);
-	# finally representing the strategy in matrix form
-	ret = vectomat(x,m,n);
-endfunction
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