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work_the_cube.m
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work_the_cube.m
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function work_the_cube(start_type)
%
% If start_type = 1, then start from the very beginning to populate the dataset
% If start_type = 0, then assume that we start from where we left off in the search ...
%
addpath(strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/data"));
addpath(strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/VariablePrecisionIntegers/VariablePrecisionIntegers"));
dataFile = strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/data/base_triplets.binsev");
dataFile1 = strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/data/center_search_data.binsev");
dataFile2 = strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/data/center_ab_data.binsev");
dataFile3 = strrep(pwd, "/magic_cube_problem", "/magic_cube_problem/data/d1_d2_d3_cnt.binsev");
fprintf('\nLoad the Crunched Triplet Array: ');
load("-v7",dataFile, "base_triplets");
%%%%%%%%%%%%%%%%%% Set Up the Space %%%%%%%%%%%%%%%%%%
write_counter = 0;
write_limit = 1;
central_num = vpi(0);
skip = 0;
t0 = clock();
max_iterations = 100000; %size(center_triplets,1)-1 %vpi(10^10)
triplets = sortrows(base_triplets,2);
center_triplets = vpi(triplets(:,2));
end_of_list = center_triplets(size(center_triplets,1));
%%%%%%%%%%%%%%%%%% Define Start Type %%%%%%%%%%%%%%%%%%
if (start_type == 0)
load("-v7",dataFile1, "center_search_data");
load("-v7",dataFile2, "center_ab_data");
load("-v7",dataFile3, "d1_d2_d3_cnt");
d1 = d1_d2_d3_cnt(1);
d2 = d1_d2_d3_cnt(2);
d3 = d1_d2_d3_cnt(3);
counter = d1_d2_d3_cnt(4);
elseif (start_type == 1)
center_search_data = vpi([0,0,0,0]);
center_ab_data = vpi([0,0,0,0]);
d1 = vpi(center_triplets(size(center_triplets,1)-3));
d2 = vpi(center_triplets(size(center_triplets,1)-2));
d3 = vpi(center_triplets(size(center_triplets,1)-1));
%d1 = 5
%d2 = 13
%d3 = 17
second_to_last_in_list = d3;
counter = 1;
else
printf("**** INCORRECT START TYPE: CHOOSE 1 (start over), OR CHOOSE 0 (start where left off)****/n");
break;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
while counter < max_iterations
tic
% Increment the center variable.
counter = counter + 1;
if (counter < size(center_triplets,1)-1)
central_num = vpi(center_triplets(counter));
if (vpi(center_triplets(counter)) == vpi(center_triplets(counter+1)))
skip = 1;
end;
else
if (vpi(d3+d2-d1) == central_num)
skip = 1;
end;
central_num = vpi(d3+d2-d1);
d1 = d2;
d2 = d3;
d3 = central_num;
end;
% central_num = vpi(1105);
if(skip == 0)
% Identify all of the factors (using the center sequence)
row_selected = mod(central_num,center_triplets);
z = row_selected == 0;
num_rows = sum(z);
q = sortrows(horzcat(z,z,z).*triplets,2);
q_final = q((size(q)-num_rows+1):size(q),:);
if size(q_final,1)>5
printf('\nFound with >6 pairs: ');
disp(central_num);
printf('Number of pairs\n');
disp(size(q_final,1));
disp(q_final);
printf('Elapsed Time: ');
elapsed_time = etime (clock (), t0);
disp(elapsed_time);
write_counter = write_counter + 1;
a1 = q_final(1:size(q_final,1),1).*reshape(central_num./(q_final(1:size(q_final,1),2)),[size(q_final(1:size(q_final,1),1),1),size(q_final(1:size(q_final,1),1),2)]);
b1 = vpi(central_num*ones(size(q_final,1),1));
c1 = q_final(1:size(q_final,1),3).*reshape(central_num./(q_final(1:size(q_final,1),2)),[size(q_final(1:size(q_final,1),3),1),size(q_final(1:size(q_final,1),3),2)]);
a1 = vpi(a1);
b1 = vpi(b1);
c1 = vpi(c1);
q_final = vpi(q_final);
central_num = vpi(central_num);
%%% Create the scaled triplet array aligned to the same centeral number
q_final_scaled = horzcat(a1,b1,c1);
%%%%%%%%%%%%%%%%% CENTER WORK %%%%%%%%%%%%%%%%%
%%% Determine the difference between the center number and the first number (same as the center and last number)
delta1 = vpi(vpi(q_final_scaled(1:size(q_final_scaled,1),2)).^2-vpi(q_final_scaled(1:size(q_final_scaled,1),1)).^2)
%delta1 = vpi(q_final_scaled(1:size(q_final_scaled,1),2)).^2-vpi(q_final_scaled(1:size(q_final_scaled,1),1)).^2;
%%% Create vertical and horizontal arrays of the deltas
delta_row = delta1*ones(1,size(delta1,1));
delta_col = ones(size(delta1,1),1)*reshape(delta1,[1,size(delta1,1)]);
%abs_a_minus_b = abs(delta_row-delta_col).*vpi(tril(ones(size(delta_col,1),size(delta_col,1)),-1));
%abs_a_plus_b = abs(delta_row+delta_col).*vpi(tril(ones(size(delta_col,1),size(delta_col,1)),-1));
%%% Create arrays for 'delta+delta' and 'delta-delta'
abs_a_minus_b = abs(delta_row-delta_col).*vpi(tril(ones(size(delta_col,1),size(delta_col,1)),-1));
abs_a_plus_b = abs(delta_row+delta_col).*vpi(tril(ones(size(delta_col,1),size(delta_col,1)),-1));
%%% Reshape the array into a column array
[ind_m_i, ind_m_j, u_abs_a_minus_b] = find(reshape(abs_a_minus_b,[size(abs_a_minus_b,1)*size(abs_a_minus_b,1),1]));
[ind_p_i, ind_p_j, u_abs_a_plus_b] = find(reshape(abs_a_plus_b,[size(abs_a_plus_b,1)*size(abs_a_plus_b,1),1]));
if (central_num == 1105)
u_abs_a_plus_b = vertcat(u_abs_a_plus_b,vpi(1197000));
end;
%%% Take the array and subtract all values by themselves to see if there are any matchs within the oringal delta list *** THERES'S A BETTER WAY!!!!
ab_minus_match = abs(delta1*ones(1,size(u_abs_a_minus_b,1)).-ones(size(delta1,1),1)*reshape(u_abs_a_minus_b,[1,size(u_abs_a_minus_b,1)]));
ab_plus_match = abs(delta1*ones(1,size(u_abs_a_plus_b,1)).-ones(size(delta1,1),1)*reshape(u_abs_a_plus_b,[1,size(u_abs_a_plus_b,1)]));
%%% Look to see if any values were equivalent!!! (ie: where a zero would be)%%%
[ind_m_row, ind_m_col, flag_m] = find((ab_minus_match==0));
[ind_p_row, ind_p_col, flag_p] = find((ab_plus_match==0)); %.*ab_plus_match;
ab_plus = vpi(0);
ab_minus = vpi(0);
ab_plus_out = vpi(0);
ab_minus_out = vpi(0);
match_found = 0;
if (isempty(flag_m) == 0)
ab_minus = zeros(size(flag_m),1);
for k = 1:size(flag_m)
%ab_minus(k) = ab_minus_match(ind_m_row,ind_m_col);
center_ab_data_temp = [central_num, num_rows, delta1(ind_m_row,1),-1];
center_ab_data = vertcat(center_ab_data,center_ab_data_temp);
save("-mat7-binary", dataFile2, "center_ab_data");
end;
match_found = 1;
write_counter = write_limit;
printf('We found a A+B Match for');
disp(central_num);
printf('!!!!!');
end;
if (isempty(flag_p) == 0)
ab_plus = zeros(size(flag_p),1);
for k = 1:size(flag_p)
%ab_plus(k) = ab_plus_match(ind_p_row,ind_p_col);
center_ab_data_temp = [central_num, num_rows, delta1(ind_p_row,1),1];
center_ab_data = vertcat(center_ab_data,center_ab_data_temp);
save("-mat7-binary", dataFile2, "center_ab_data");
end;
match_found = 1;
write_counter = write_limit;
printf('We found a A+B Match for');
disp(central_num);
printf('!!!!!');
end;
center_search_data_temp = horzcat(q_final_scaled,match_found.*ones(size(q_final_scaled,1),1));
center_search_data = vertcat(center_search_data,center_search_data_temp);
if write_counter >= write_limit;
save("-mat7-binary", dataFile1, "center_search_data");
d1_d2_d3_cnt = [d1;d2;d3;counter];
save("-mat7-binary", dataFile3, "d1_d2_d3_cnt");
write_counter = 0;
end;
match_found = 0;
% if and((isempty(flag_m) == 0),(isempty(flag_p) == 0))
% for list_cnt=1:max(size(ab_plus,1),ab_plus,1)
% if list_cnt>size(ab_plus,1)
% ab_plus_out=0;
% else
% ab_plus_out = ab_plus(list_cnt)
% end;
% if list>size(ab_minus,1)
% ab_minus=0;
% else
% ab_minus_out = ab_minus(list_cnt)
% end;
% center_ab_data_temp = central_num, num_rows, ab_plus_out, ab_minus_out
% center_ab_data = vertcat(center_ab_data,center_ab_data_temp);
% end;
% match_found = 0;
% save("-mat7-binary", dataFile2, "center_ab_data");
% end;
end;
end;
skip = 0;
end;
printf('***************************** THE END? ****************************/n');