public static Counter ConstrainedEig(SparseMatrix mat, SparseMatrix orthogMat) {
double trimEps = 0;
int iterLimit = 10000;
long start;
long end;
Counter vector = new Counter();
int vecLen = mat.colDim;
for (int i = 0; i < vecLen; i++) {
// vector.add(i, 1.0/Math.sqrt(vecLen));
vector.add(i, Math.random() - 0.5);
}
Counter oldVector = new Counter();
// vector = mat.multiply(vector);
// for(int r: orthogMat.rows){
// Counter orthogRow = orthogMat.getRow(r);
// vector.orthogonalize(orthogRow);
//// System.out.println(vector.dot(orthogRow));
// }
double norm = 0;
double sim = 0;
double diff = 1.0;
double diffNeg = 1.0;
int t = 0;
start = System.currentTimeMillis();
while (diff > Math.pow(10.0, -16.0) && diffNeg > Math.pow(10.0, -16.0) && t < iterLimit) {
t += 1;
// vector.trimKeys(trimEps);
oldVector = new Counter(vector);
vector = mat.multiply(vector);
for (int r : orthogMat.rows) {
Counter orthogRow = orthogMat.getRow(r);
// System.out.println("before: "+vector.dot(orthogRow));
vector.orthogonalize(orthogRow);
// System.out.println("after: "+vector.dot(orthogRow));
}
norm = 0;
norm = vector.norm();
vector.multiply(1.0 / norm);
diff = 0;
diffNeg = 0;
Set<Integer> vecOldUnion = vector.concreteKeySet();
vecOldUnion.addAll(oldVector.concreteKeySet());
for (int i : vecOldUnion) {
// for(int i = 0; i < mat.colDim; i++){
diff += (oldVector.get(i) - vector.get(i)) * (oldVector.get(i) - vector.get(i));
diffNeg += (oldVector.get(i) + vector.get(i)) * (oldVector.get(i) + vector.get(i));
}
sim = vector.dot(oldVector);
// System.out.println(diff+" "+diffNeg+" "+sim+" "+norm+"
// "+vector.dot(orthogMat.getRow(0)));
// System.out.println(vector.toString());
// System.out.println(oldVector.toString());
}
System.out.println(norm + " " + orthogMat.rows.size() + " " + sim);
// System.out.println(mat.toStringValues());
end = System.currentTimeMillis();
System.out.println("Time: " + (end - start) + " iterations: " + t);
return vector;
}
public void removeEntries(SparseMatrix redundant) {
for (int r : redundant.getRows()) {
Counter row = redundant.getRow(r);
for (int c : row.keySet()) {
this.remove(r, c);
}
}
}
public SparseMatrix multiply(double f) {
SparseMatrix multMat = new SparseMatrix(this.rowDim, this.colDim);
for (int r : this.rows) {
Counter row = this.getRow(r);
multMat.addRow(r, row.multiplyImmutable(f));
}
return multMat;
}
public SparseMatrix add(SparseMatrix other) {
SparseMatrix sum = new SparseMatrix(this.rowDim, this.colDim);
sum = new SparseMatrix(this);
for (int r : other.rows) {
sum.addRow(r, other.getRow(r));
}
return sum;
}
public SparseMatrix symmetric() {
SparseMatrix symm = new SparseMatrix(this);
symm = symm.add(symm.transpose());
for (int r : rows) {
double v = this.get(r, r);
this.set(r, r, v / 2.0);
}
return symm;
}
public SparseMatrix transpose() {
SparseMatrix transp = new SparseMatrix(this.rowDim, this.colDim);
for (int r : rows) {
Counter row = this.getRow(r);
for (int c : row.keySet()) {
double v = row.get(c);
transp.set(c, r, v);
}
}
return transp;
}
public static Counter PersonalizedPageRank(Counter seedVector, SparseMatrix transitionMat) {
double trimEps = 0.0;
int iterLimit = 200;
transitionMat = transitionMat.stochasticizeRows();
double beta = 0.85;
long start;
long end;
Counter vector = new Counter(seedVector);
double svCard = 0;
for (int i : seedVector.keySet()) {
svCard += seedVector.get(i);
}
Counter oldVector = new Counter(vector);
vector = transitionMat.multiply(vector);
double diff = 1;
int t = 0;
start = System.currentTimeMillis();
while (diff > Math.pow(10.0, -10.0) && (diff < 3.99999 || diff > 4.00001) && t < iterLimit) {
t += 1;
vector.trimKeys(trimEps);
vector = transitionMat.multiply(vector);
Set<Integer> vecSeedUnion = vector.concreteKeySet();
vecSeedUnion.addAll(seedVector.concreteKeySet());
for (int i : vecSeedUnion) {
// vector.set(i,
// beta*vector.get(i)/norm+(1-beta)*seedVector.get(i));///Math.max(norm,1.0));
vector.set(
i,
beta * vector.get(i)
+ (1 - beta) * seedVector.get(i) / svCard); // /Math.max(norm,1.0));
}
double norm = 0;
for (int i : vector.keySet()) {
// norm += vector.get(i)*vector.get(i);
// norm += Math.abs(vector.get(i));
norm += vector.get(i);
}
// norm = Math.sqrt(norm);
diff = 0;
Set<Integer> vecOldUnion = vector.concreteKeySet();
vecOldUnion.addAll(oldVector.concreteKeySet());
for (int i : vecOldUnion) {
diff += (oldVector.get(i) - vector.get(i)) * (oldVector.get(i) - vector.get(i));
}
System.out.println(diff + " " + norm);
// System.out.println(vector.toString());
// System.out.println(oldVector.toString());
oldVector = new Counter(vector);
}
// System.out.println(transitionMat.toStringValues());
end = System.currentTimeMillis();
System.out.println("Time: " + (end - start) + " iterations: " + t);
return vector;
}
public SparseMatrix makeLaplacian() {
SparseMatrix laplacian = new SparseMatrix(this.rowDim, this.colDim);
for (int r : this.getRows()) {
Counter row = this.getRow(r);
laplacian.set(r, r, row.sum());
for (int c : row.keySet()) {
laplacian.set(r, c, -1 * row.get(c));
}
}
return laplacian;
}
public static Counter TopEig(SparseMatrix mat) {
double trimEps = 0.0;
int iterLimit = 1000;
long start;
long end;
Counter vector = new Counter();
int vecLen = mat.colDim;
// for(int i = 0; i < vecLen; i++){
// vector.add(i, Math.random()-0.5);
// }
for (int i = 0; i < vecLen; i++) {
vector.add(i, 1.0 / (double) vecLen);
}
Counter oldVector = new Counter(vector);
vector = mat.multiply(vector);
double diff = 1;
int t = 0;
start = System.currentTimeMillis();
while (diff > Math.pow(10.0, -10.0) && (diff < 3.99999 || diff > 4.00001) && t < iterLimit) {
t += 1;
vector.trimKeys(trimEps);
vector = mat.multiply(vector);
double norm = 0;
for (int i : vector.keySet()) {
norm += vector.get(i) * vector.get(i);
// norm += Math.abs(vector.get(i));
}
norm = Math.sqrt(norm);
vector.multiply(1.0 / norm);
diff = 0;
Set<Integer> vecOldUnion = vector.concreteKeySet();
vecOldUnion.addAll(oldVector.concreteKeySet());
for (int i : vecOldUnion) {
diff += (oldVector.get(i) - vector.get(i)) * (oldVector.get(i) - vector.get(i));
}
System.out.println(diff + " " + norm);
// System.out.println(vector.toString());
// System.out.println(oldVector.toString());
oldVector = new Counter(vector);
}
// System.out.println(mat.toStringValues());
end = System.currentTimeMillis();
System.out.println("Time: " + (end - start) + " iterations: " + t);
return vector;
}
public SparseMatrix multiply(SparseMatrix other) {
SparseMatrix mult = new SparseMatrix(this.rowDim, other.colDim);
for (int r : rows) {
// System.out.println("multiplying row: "+ r);
Counter row = this.getRow(r);
// for(int c: other.cols){
// Counter col = other.getCol(c);
// double dotProd = row.dot(col);
// System.out.println(row.toString()+" "+col.toString()+" "+dotProd);
// mult.set(r, c, dotProd);
// }
for (int c : row.keySet()) {
Counter oRow = other.getRow(c);
for (int oc : oRow.keySet()) {
mult.add(r, oc, row.get(c) * oRow.get(oc));
}
}
}
return mult;
}
public SparseMatrix stochasticizeRows() {
SparseMatrix stochasticMat = new SparseMatrix(this.rowDim, this.colDim);
double[] rowSums = new double[this.rowDim];
for (int r : this.rows) {
Counter row = this.getRow(r);
for (int c : row.keySet()) {
rowSums[r] += row.get(c);
}
}
for (int r : this.rows) {
Counter row = this.getRow(r);
for (int c : row.keySet()) {
double value = 0;
if (rowSums[r] != 0) {
// if(true){
value = this.get(r, c) / rowSums[r];
}
stochasticMat.set(r, c, value);
}
}
return stochasticMat;
}
public SparseMatrix getRedundant() {
SparseMatrix redMat = new SparseMatrix(this).multiply(this);
int oldCard = 0;
int card = redMat.cardinality();
int i = 0;
// for(int r = 0; r < rowDim; r++){
// if(true){//transMat.hasRow(r)){
// transMat.add(r, r, 1.0);
// }
// if(true){//tcMat.hasRow(r)){
// tcMat.add(r, r, 1.0);
// }
// }
while (card > oldCard) {
// System.out.println("iter: "+i);
i++;
oldCard = card;
redMat = redMat.add(redMat.multiply(this));
card = redMat.cardinality();
// System.out.println(tcMat.toString());
}
return redMat;
}
public SparseMatrix transitiveClosure() {
SparseMatrix tcMat = new SparseMatrix(this);
SparseMatrix transMat = new SparseMatrix(this);
int oldCard = 0;
int card = tcMat.cardinality();
int i = 0;
// for(int r = 0; r < rowDim; r++){
// if(true){//transMat.hasRow(r)){
// transMat.add(r, r, 1.0);
// }
// if(true){//tcMat.hasRow(r)){
// tcMat.add(r, r, 1.0);
// }
// }
while (card > oldCard) {
// System.out.println("iter: "+i);
i++;
oldCard = card;
tcMat = tcMat.add(tcMat.multiply(transMat));
card = tcMat.cardinality();
// System.out.println(tcMat.toString());
}
return tcMat;
}
public static void main(String[] args) {
long start;
long end;
int card;
double seconds;
double megaTEPs;
System.out.println("Working");
Random rand = new Random();
int dim = 16384;
int num = dim * 10;
SparseMatrix testMat = new SparseMatrix(dim, dim);
for (int i = 0; i < num; i++) {
if ((i % (1024 * 32 * 20) == 0)) System.out.println(i + " of " + num);
int r = rand.nextInt(dim);
int c = rand.nextInt(dim);
// int r = (i+2659)*3571%dim;
// int c = (i+2659)*2081%dim;
testMat.add(r, c, 1.0);
testMat.add(c, r, 1.0);
// testMat.add(r, r, 1.0);
// testMat.add(c, c, 1.0);
// testMat.set(r, c, 1.0);
// testMat.set(c, r, 1.0);
}
boolean isSymm = true;
int sum = 0;
for (int r = 0; r < dim; r++) {
for (int c = 0; c < dim; c++) {
double val = testMat.get(r, c);
sum += val;
if (val > 0.0) {
if (testMat.get(c, r) == 0) {
isSymm = false;
}
}
}
}
System.out.println(sum + " " + testMat.cardinality() + " " + isSymm);
// SparseMatrix testMat2 = new SparseMatrix(dim, dim);
// for (int i = 0; i < num; i++) {
// int r = rand.nextInt(dim);
// int c = rand.nextInt(dim);testMat
// testMat2.add(r, c, 1.0);
// }
// start = System.currentTimeMillis();
// SparseMatrix testMat3 = testMat.multiply(testMat2);
// end = System.currentTimeMillis();
// System.out.println("Time: "+(end-start));
// System.out.println(testMat.cardinality()+" "+testMat.add(testMat2).cardinality()+"
// "+testMat3.cardinality());
// start = System.currentTimeMillis();
// SparseMatrix apspRes = new SparseMatrix(testMat.rowDim, testMat.colDim);
// int T = 1;testMat
// for (int iter = 0; iter < T; iter++) {
// apspRes = testMat.apsp();
// }
// end = System.currentTimeMillis();
// System.out.println("Time: " + (end - start));
// card = testMat.cardinality();
// seconds = (double) (end - start) / 1000.0;
// megaTEPs = card / seconds * dim / 1000000.0;
// System.out.println("megaTEPs: " + megaTEPs);
// System.out.println(testMat.toString());
// System.out.println(apspRes.toString());
// start = System.currentTimeMillis();
// Counter bfsRes = new Counter();
// int iterMax = dim;
// for(int iter = 0; iter < iterMax; iter++){
// int init = iter;
// bfsRes = testMat.bfs(init);
// // System.out.println(bfsRes.toString());
// }
// end = System.currentTimeMillis();
// System.out.println("Time: "+(end-start));
// card = testMat.cardinality();
// seconds = (double)(end-start)/1000.0;
// megaTEPs = card/seconds*iterMax/1000000.0;
// System.out.println("megaTEPs: "+megaTEPs);
// System.out.println(init);
// System.out.println(testMat.toString());
// System.out.println(bfsRes.toString());
// SparseMatrix testMatStoch = testMat.stochasticizeRows();
// double beta = 0.85;
// ArrayList<Double> vector = new ArrayList<Double>();
// for(int i = 0; i < dim; i++){
// vector.add(0.0);
// if(i == 0) vector.set(i,1.0);
// }
// ArrayList<Double> seedVector = new ArrayList<Double>(vector);
// double svCard = 0;
// for(int i = 0; i < dim; i++){
// svCard += seedVector.get(i);
// }
// ArrayList<Double> oldVector = new ArrayList<Double>(vector);
// vector = (ArrayList<Double>) testMatStoch.multiply(vector);
// double diff = 1;
// int t = 0;
// start = System.currentTimeMillis();
// while(diff > Math.pow(10.0, -10.0) && (diff < 3.99999 || diff > 4.00001) && t < 200){
// t += 1;
// vector = (ArrayList<Double>) testMatStoch.multiply(vector);
// double norm = 0;
// for(int i = 0; i < dim; i++){
//// norm += vector.get(i)*vector.get(i);
// norm += Math.abs(vector.get(i));
// }
//// norm = Math.sqrt(norm);
// for(int i = 0; i < dim; i++){r
//// vector.set(i,
// beta*vector.get(i)/norm+(1-beta)*seedVector.get(i));///Math.max(norm,1.0));
// vector.set(i, beta*vector.get(i)+(1-beta)*seedVector.get(i));///Math.max(norm,1.0));
// }
// diff = 0;
// for(int i = 0; i < dim; i++){
// diff +=(oldVector.get(i)-vector.get(i))*(oldVector.get(i)-vector.get(i));
// }
// System.out.println(diff+" "+norm);
//// System.out.println(vector.toString());
// // System.out.println(oldVector.toString());
// oldVector = new ArrayList<Double>(vector);
// }
//// System.out.println(testMatStoch.toStringValues());
// end = System.currentTimeMillis();
// System.out.println("Time: "+(end-start)+" iterations: "+t);
// Counter sv = new Counter();
// sv.set(rand.nextInt(dim),1.0);
// sv.set(0, 1.0);
// SparseMatrix.PersonalizedPageRank(sv, testMat);
// SparseMatrix laplacian = testMat.makeLaplacian();
// SparseMatrix normedLap = laplacian.stochasticizeRows();
// for(int i = 0; i < testMat.rowDim; i++){
// testMat.add(i,i,100.0);
// }
// SparseMatrix normedTest = testMat.stochasticizeRows();
// testMat = testMat.symmetric();
SparseMatrix orthogMat = new SparseMatrix(0, testMat.colDim);
Counter topEig = SparseMatrix.ConstrainedEig(testMat, orthogMat);
// Counter topEig = SparseMatrix.TopEig(testMat);
// for(int i = 0; i < orthogMat.colDim; i++){
// orthogMat.set(0, i, 1.0);
// }
int topK = 10;
for (int j = 0; j < topK; j++) {
orthogMat.addRow(j, new Counter(topEig));
// double norm = testMat.multiply(topEig).norm();
// System.out.println("norm: "+norm);
topEig = SparseMatrix.ConstrainedEig(testMat, orthogMat);
}
// orthogMat.addRow(topK, new Counter(topEig));
// for(int i: orthogMat.rows){
// Counter eig = orthogMat.getRow(i);
// for(int j: orthogMat.rows){
// Counter eigOther = orthogMat.getRow(j);
// double sim = eig.dot(eigOther);
//// int sim = (int)(eig.dot(eigOther)+0.9999);
// System.out.print(sim+" ");
// }
// System.out.println();
// }
// SparseMatrix tcMin = testMat.minimize().transitiveClosure();
// SparseMatrix tcMat = testMat.transitiveClosure();
// System.out.println(tcMin.cardinality()+" "+tcMat.cardinality());
// testMat.add(0,0,1.0);
// testMat.add(0,1,1.0);
// testMat.add(1,1,1.0);
// testMat.add(1,2,1.0);
// testMat.add(2,2,1.0);
// System.out.println(testMat.cardinality());
// for(int t = 0; t < 1000; t++){
// testMat = testMat.multiply(testMat);
// System.out.println(testMat.cardinality());
// }
// System.out.println(testMat.toString());
}
public SparseMatrix minimize() {
SparseMatrix minMat = new SparseMatrix(this);
SparseMatrix redundant = this.getRedundant();
minMat.removeEntries(redundant);
return minMat;
}
/*
* Matrix mult but with min-plus, and iterative. Each min-plus operation
* that changes the path inserts it into a new queue
*/
public SparseMatrix apsp() {
SparseMatrix shortestPaths = new SparseMatrix(this);
SparseMatrix currentPairs = new SparseMatrix(this.rowDim, this.colDim);
SparseMatrix newPairs = new SparseMatrix(this.rowDim, this.colDim);
newPairs = new SparseMatrix(this);
for (int d = 0; d < this.rowDim; d++) {
shortestPaths.set(d, d, 0.0);
}
for (int d = 0; d < this.rowDim; d++) {
newPairs.set(d, d, 0.0);
}
while (!newPairs.isEmpty()) {
currentPairs = new SparseMatrix(newPairs);
newPairs = new SparseMatrix(this.rowDim, this.colDim);
for (int r : currentPairs.rows) {
Counter row = currentPairs.getRow(r);
for (int c : row.keySet()) {
Counter oRow = this.getRow(c);
for (int oc : oRow.keySet()) {
double pathLength = currentPairs.get(r, c) + oRow.get(oc);
if (pathLength < shortestPaths.getPath(r, oc)) {
newPairs.set(r, oc, pathLength);
shortestPaths.set(r, oc, pathLength);
}
}
}
}
}
return shortestPaths;
}
