In version 2 and 3, I used a superposition of 8 forbidden vectors for each clause. In this version, version 4, I used 0-8 forbidden vectors for each clause. I did this because this is the only way I will get true null vectors. My overall impression is that the results are pretty good. This is the version with: permutator, no repeating variable, true null vectors w/ 0 energy. This Version has the best freezing point so far: 1.429. But I am not sure that I am actually allowed to zero away some terms in the 8 term clause.
import java.io.*;
import static java.lang.Math.*;
import java.util.*;
public class QSATsolver4 {
private int clausesize = 3;
private int numvariable = 7;
private int numclause = 10;
private int numinstances = 50;
private ArrayList<Integer> temp2var = new ArrayList <Integer> ();
private ArrayList<ArrayList <Integer>> temp5var = new ArrayList <ArrayList<Integer>> ();
private ArrayList<String> chain = new ArrayList<String>();
private ArrayList<String> stack = new ArrayList<String>();
private ArrayList<double[][]> piMatrixStack = new ArrayList<double[][]>();
private ArrayList<double[][]> realStack = new ArrayList<double[][]>();
private ArrayList<ArrayList<Double>>temp2= new ArrayList<ArrayList<Double>>();
private ArrayList<ArrayList<ArrayList<Double>>> temp5 = new ArrayList<ArrayList<ArrayList<Double>>>();
private ArrayList<Double>temp = new ArrayList<Double>();
private int netCount = 0;
private int counter3=0;
private int nullcount=0;
private static final double Epsilon = 1e-10;
public static void main(String[] args) {
QSATsolver4 qs = new QSATsolver4();
qs.generate();
}
public void generate(){
double length = 0;
int max = (int)pow(2,numvariable);
boolean []taken = new boolean [numvariable];
for(int i=0; i<taken.length; i++){
taken[i] = false;
}
for (int k = 0; k < numinstances; k++) {
for (int j = 0; j < numclause; j++) {
int v;
for(int i = 0; i < clausesize; i++){
v = (int)(Math.random()*numvariable)+1;
while(taken[v-1] == true){
v = (int)(Math.random()*numvariable)+1;
}
taken[v-1] = true;
temp2var.add(new Integer(v));
}
for(int i = 0; i < taken.length; i++){
taken[i] = false;
}
int max5 = (int)pow(2,clausesize);
for (int i = 0; i < max5; i++){
int hasTerm =(int)(Math.random()*2);
if(hasTerm==1) {
double real = Math.random();
temp.add(new Double(real));
} else {
//nullcount++;
double real = 0;
temp.add(new Double(real));
}
temp2.add(temp);
temp = new ArrayList<Double>();
}
for (int i = 0; i < temp2.size(); i++){
ArrayList <Double> list = temp2.get(i);
for (int g = 0; g < list.size(); g++){
double a = Double.parseDouble(""+list.get(g));
length+=a;
}
}
if(length==0){
System.out.println("here");
length=1;
}
for (int i = 0; i < temp2.size(); i++){
ArrayList <Double> list = temp2.get(i);
for (int g = 0; g < list.size(); g++){
double c = Double.parseDouble(""+list.get(g));
c = c/length;
list.remove(g);
list.add(g, new Double(c));
}
}
temp5.add(temp2); //15 items in these
temp2 = new ArrayList<ArrayList<Double>>();
temp5var.add(temp2var);
temp2var = new ArrayList <Integer> ();
//chain = new ArrayList<String>();
length=0;
}
makeAllClauses();
if(calculateMatrix()){
netCount++;
}
piMatrixStack = new ArrayList<double[][]>();
realStack = new ArrayList<double[][]>();
temp5var = new ArrayList <ArrayList<Integer>> ();
temp5 = new ArrayList<ArrayList<ArrayList<Double>>>();
System.out.println(counter3);
//System.out.println(nullcount);
counter3=0;
}
System.out.println("netCount");
System.out.println(netCount);
}
public boolean calculateMatrix(){
double[][] temp1, temp2;
int max = (int)pow(2,numvariable);
double [][]sumtemp1 = new double [max][max];
temp1= new double[max][max];
boolean success = false;
for(int i=0; i<piMatrixStack.size(); i++){
double[][] one = piMatrixStack.get(i);
double[][] two = realStack.get(i);
double[][] invone = makeTranspose(one);
temp1 = matMultiply(matMultiply(one,two),invone);
for(int j = 0; j < temp1.length; j++){
for(int k = 0; k < temp1.length; k++){
sumtemp1[j][k] += temp1[j][k];
}
}
}
boolean [] x= gaussianElimination(sumtemp1,1);
success = nullvecExist(x);
return success;
}
public boolean nullvecExist(boolean [] x){
for(int i=0; i<x.length-1; i++){
if(x[i]==true){
//System.out.print(i+" ");
counter3++;
}
}
//if(counter3!=0)
//return true;
if(x[128]==false)
return true;
/*for(int i=0; i<x.length-1; i++){
if(x[i]==true){
return true;
}
}*/
return false;
}
public boolean [] gaussianElimination(double [][]matrix, int type){
//int zerocount = 0;
int max = matrix.length;
double [] temp;
int current = 0;
double ratio = 1;
boolean found = false;
boolean []sol = new boolean [matrix.length+1];
int counter5=0;
double [][]matrixcopy= new double[matrix.length][matrix.length];
for(int s=0; s<matrix.length; s++){
for (int t=0; t<matrix.length; t++){
matrixcopy[s][t]=matrix[s][t];
}
}
//current is the line number you have just fixed.
//i is all the line numbers that you are working on still.
//the point of this part is to order rows by increasing zero count.
/*for(int i=0; i<max; i++){
System.out.print(zeroCount2(matrix[i])+" ");
}*/
current=0;
int currentCount=0;
while(current<max){
for(int i = current; i < max; i++){
if(zeroCount2(matrix[i]) == currentCount){
temp = matrix[i];
matrix[i] = matrix[current];
matrix[current] = temp;
current++;
}
}
currentCount++;
}
//count is the number of zeros in the line you have
//just done working on. You stop working and you increase
//count when you get to a transition in the number of zeros
//in your rows of the matrix.
int count = zeroCount2(matrix[0]);
while(count<max){
for(int i = count+1; i<max; i++){
int c = zeroCount2(matrix[i]);
if(c==count) {
ratio = matrix[i][c]/matrix[count][c];
for(int w = 0; w < matrix.length; w++){
matrix[i][w]-=matrix[count][w]*ratio;
}
} else if(c>count){
break;
}
}
count++;
}
for(int i=0; i<sol.length; i++){
sol[i]=true;
}
for(int i=0; i<matrix.length; i++){
sol[zeroCount2(matrix[i])]=false;
}
/*for(int i=0; i<sol.length-1; i++){
if(sol[i]==true){
//System.out.print(i+" ");
counter5++;
}
}
if(counter5==127 && type==2){
System.out.println(sol[128]);
for(int i=0; i<matrix.length;i++){
for(int j=0; j<matrix.length; j++){
System.out.print(matrix[i][j]+" ");
}
System.out.println();
}
System.out.println();
System.out.println();
System.out.println();
for(int i=0; i<matrix.length;i++){
for(int j=0; j<matrix.length; j++){
System.out.print(matrixcopy[i][j]+" ");
}
System.out.println();
}
System.exit(0);
}*/
return sol;
}
public int zeroCount2 (double[] vec){
int temp = 0;
for(int i = 0; i < vec.length; i++){
if(vec[i]==0){
temp++;
} else {
break;
}
}
return temp;
}
public double[][] makeTranspose(double[][] mat){
double [][]temp = new double[mat.length][mat.length];
for(int i = 0; i < mat.length; i++){
for(int j = 0; j<mat[0].length; j++){
temp[i][j] = mat[j][i];
}
}
return temp;
}
public void makePi(){
int max = (int)pow(2,numvariable);
for(int j = 0; j<max; j++) {
String temp3 = Tobinary(j,"");
temp3 = reverseString(temp3);
if (temp3.length()<numvariable) {
temp3 = addZero(temp3, numvariable);
}
chain.add(temp3);
}
}
public void makeAllClauses(){
int max = (int)pow(2,numvariable);
int[] temp1 = new int[clausesize];
int[] temp3 = new int[numvariable-clausesize];
boolean[] taken = new boolean[numvariable];
int[] path = new int[numvariable];
for(int i = 0; i < taken.length; i++){
taken[i] = false;
}
int max2 = (int)pow(2,clausesize);
for(int i = 0; i<temp5var.size(); i++){
ArrayList<Integer> alist = temp5var.get(i);
ArrayList<ArrayList<Double>> blist = temp5.get(i);
for(int j = 0; j < alist.size(); j++){
int temp2 = (int)(Integer.parseInt(""+alist.get(j)))-1;
temp1[j] = temp2;
taken[temp2] = true;
}
int ind = 0;
for(int j = 0; j < (numvariable); j++){
if(!taken[j]){
temp3[ind] = j;
ind++;
}
}
for(int j = 0; j < taken.length; j++){
taken[j] = false;
}
for(int j = 0; j < numvariable; j++){
if(j<clausesize){
path[j] = temp1[j];
}else {
path[j] = temp3[j-clausesize];
}
}
double[][] onePi = makeProjector(path, i);
piMatrixStack.add(onePi);
double [][]oneClause=new double[max][max];
for(int u=0; u<max2; u++){
ArrayList<Double> list3= blist.get(u);
double factor= Double.parseDouble(""+list3.get(0));
String str2 = Tobinary(u,"");
str2 = reverseString(str2);
if (str2.length()<clausesize) {
str2 = addZero(str2, clausesize);
}
String str = getI()+""+reverseString(str2);
double[][]one = makeSig(str);
for(int l=0; l<one.length; l++){
for(int m=0; m<one.length; m++){
oneClause[l][m]+=factor*one[l][m];
}
}
}
double length=0;
for(int p=0; p<oneClause.length; p++){
length+=oneClause[p][p];
}
if(length==0){
length=1;
}
for(int p=0; p<oneClause.length; p++){
oneClause[p][p]=oneClause[p][p]/length;
}
realStack.add(oneClause);
}
}
public String getI(){
String temp = "";
for(int i = 0; i < numvariable-clausesize; i++){
temp = temp+"I";
}
return temp;
}
public double[][] makeSig (String path){
char next;
double a0 = 0;
double a1 = 0;
double a2 = 0;
double a3 = 0;
double[][]ul,ur,ll,lr;
double [][] orig = new double[2][2];
if(path.charAt(path.length()-1)=='I'){
orig[0][0] = 1;
orig[0][1] = 0;
orig[1][0] = 0;
orig[1][1] = 1;
}else {
if(path.charAt(path.length()-1)=='0'){
orig[0][0] = 1;
orig[0][1] = 0;
orig[1][0] = 0;
orig[1][1] = 0;
}else if(path.charAt(path.length()-1)=='1'){
orig[0][0] = 0;
orig[0][1] = 0;
orig[1][0] = 0;
orig[1][1] = 1;
}
}
for(int i = path.length()-2; i>=0; i--){
next = path.charAt(i);
if(next=='I'){
a0 = 1;
a1 = 0;
a2 = 0;
a3 = 1;
}else {
if(next=='0'){
a0 = 1;
a1 = 0;
a2 = 0;
a3 = 0;
}else if(next=='1'){
a0 = 0;
a1 = 0;
a2 = 0;
a3 = 1;
}
}
ul = multiply(a0, clone(orig));
ur = multiply(a1, clone(orig));
ll = multiply(a2, clone(orig));
lr = multiply(a3, clone(orig));
orig = makeLarge(ul, ur, ll, lr);
}
return orig;
}
public double[][] multiply(double c, double[][] mat){
double [][] temp = new double[mat.length][mat.length];
for (int i = 0; i<mat.length; i++){
for (int j = 0; j<mat[0].length; j++){
temp[i][j] = c*mat[i][j];
}
}
return temp;
}
public double[][] makeLarge(double[][] ul, double[][] ur, double[][] ll, double[][]lr){
double [][] temp = new double[ul.length*2][ul.length*2];
for(int i = 0; i<ul.length; i++){
for(int j = 0; j<ul.length; j++){
temp[i][j] = ul[i][j];
}
}
for(int i = 0; i<ul.length; i++){
for(int j = 0; j<ul.length; j++){
temp[i][j+ul.length] = ur[i][j];
}
}
for(int i = 0; i<ul.length; i++){
for(int j = 0; j<ul.length; j++){
temp[i+ul.length][j] = ll[i][j];
}
}
for(int i = 0; i<ul.length; i++){
for(int j = 0; j<ul.length; j++){
temp[i+ul.length][j+ul.length] = lr[i][j];
}
}
return temp;
}
public double[][] clone(double[][] mat){
double [][]temp = new double[mat.length][mat.length];
for (int i = 0; i<mat.length; i++){
for(int j = 0; j<mat[0].length; j++){
temp[i][j] = mat[i][j];
}
}
return temp;
}
public double[][] makeProjector(int [] path, int ind) {
String str = "";
int zeroCount = 0;
int max = (int)pow(2,numvariable);
double [] row = new double[max];
double[][] matrix= new double[max][max];
int [] bits= new int [numvariable];
chain = new ArrayList<String>();
makePi();
for(int i=0; i<chain.size(); i++){
String temp1 = chain.get(i);
for(int j = 0; j<path.length; j++){
bits[path[numvariable-1-j]]=Integer.parseInt(""+temp1.charAt(j));
}
for(int j=bits.length-1; j>=0; j--){
str=str+""+bits[j];
}
zeroCount = Todecimal(str);
for(int j = 0; j<max; j++){
if(j==zeroCount){
row[j] = 1;
}else {
row[j] = 0;
}
}
for(int j = 0; j<max; j++){
matrix[i][j] = row[j];
}
str = "";
}
/*for(int i=0; i<chain.size(); i++){
String temp1 = chain.get(i);
for(int j = path.length-1; j>=0; j--){
str = str+temp1.charAt(numvariable-path[j]-1);
}
zeroCount = Todecimal(str);
for(int j = 0; j<max; j++){
if(j==zeroCount){
row[j] = 1;
}else {
row[j] = 0;
}
}
for(int j = 0; j<max; j++){
matrix[i][j] = row[j];
//if(i==1)
//System.out.println(i);
}
str = "";
}*/
return matrix;
}
public double[][] matMultiply(double[][]mat1, double[][] mat2){
double[][]prod = new double[mat1.length][mat1.length];
for(int i = 0; i<prod.length; i++){
for(int j = 0; j<prod.length; j++) {
prod[i][j] = 0;
}
}
for(int i = 0; i<prod.length; i++){
for(int j = 0; j<prod.length; j++) {
for(int k = 0; k<prod.length; k++){
prod[i][j] += mat1[i][k]*mat2[k][j];
}
}
}
return prod;
}
public int Todecimal (String binary){
int sum=0;
for (int i=binary.length()-1; i>=0; i--){
String bit = ""+binary.charAt(i);
int bitval = Integer.parseInt(bit);
int factor = (int)pow(2, binary.length()-1-i);
sum += bitval*factor;
}
return sum;
}
public String reverseString(String st){
String temp = "";
for(int i = st.length()-1; i>=0; i--){
temp = temp+st.charAt(i);
}
return temp;
}
public String Tobinary(int decimal, String path){
int remainder;
if(decimal<=1){
path = path+decimal;
return path;
}
remainder = decimal % 2;
path = path+remainder;
return Tobinary(decimal>>1, path);
}
public String addZero(String s, int l){
int b = l-s.length();
for(int i = 0; i<b; i++){
s = "0"+""+s;
}
return s;
}
}
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