/** Checks to see if all the real eigenvectors are linearly independent of each other. */
public void testVectorsLinearlyIndependent(SymmetricQRAlgorithmDecomposition alg) {
int N = alg.getNumberOfEigenvalues();
// create a matrix out of the eigenvectors
Matrix A = Matrix.create(N, N);
int off = 0;
for (int i = 0; i < N; i++) {
AVector v = alg.getEigenVector(i);
// it can only handle real eigenvectors
if (v == null) off++;
else {
for (int j = 0; j < N; j++) {
A.set(i - off, j, v.get(j));
}
}
}
// see if there are any real eigenvectors
if (N == off) return;
// A.reshape(N-off,N, false);
A = A.reshape(N - off, N);
AltLU lu = new AltLU();
lu._decompose(A);
assertFalse(lu.isSingular());
// assertTrue(MatrixFeatures.isRowsLinearIndependent(A));
}
@Override
public void setRow(int i, AVector row) {
int cc = checkColumnCount(row.length());
for (int j = 0; j < cc; i++) {
data[index(i, j)] = row.unsafeGet(i);
}
}
@Override
public AVector asVector() {
AVector v = Vector0.INSTANCE;
for (INDArray a : slices) {
v = v.join(a.asVector());
}
return v;
}
@Test
public void testOuterProducts() {
AVector v = Vectorz.createUniformRandomVector(5);
INDArray a = v.outerProduct(v);
assertTrue(a instanceof AMatrix);
AMatrix m = (AMatrix) a;
AVector v2 = v.clone();
v2.square();
assertEquals(v2, m.getLeadingDiagonal());
}
@Override
public void transformInPlace(AVector v) {
if (v instanceof AArrayVector) {
transformInPlace((AArrayVector) v);
return;
}
if (v.length() != dimensions)
throw new IllegalArgumentException(ErrorMessages.incompatibleShapes(this, v));
for (int i = 0; i < dimensions; i++) {
v.unsafeSet(i, v.unsafeGet(i) * unsafeGetDiagonalValue(i));
}
}
/**
* Get the rth threshold.
*
* @param thresholdIndex The index of the threshold
* @return the rth threshold.
*/
public double getThreshold(int thresholdIndex) {
double tr = t1;
if (thresholdIndex < 0) {
return Double.NEGATIVE_INFINITY;
} else if (thresholdIndex == 0) {
return tr;
} else if (thresholdIndex > beta.length()) {
return Double.POSITIVE_INFINITY;
} else {
for (int k = 0; k < thresholdIndex; k++) tr += Math.exp(beta.get(k));
return tr;
}
}
/**
* The constructor of OrdRecParameter. It use the quantized values of rating to initialize t1
* and beta. Each threshold is initialized as the mean of two contiguous rating values. Since
* the index of quantizer is always an successive non-negative integer begin from 0, so t1 will
* initialize as 0.5, and the interval between two thresholds will be 1.
*
* @param qtz The quantizer for ratings
*/
private OrdRecModel(Quantizer qtz) {
qtzValues = qtz.getValues();
levelCount = qtzValues.length();
t1 = (qtzValues.get(0) + qtzValues.get(1)) / 2;
beta = Vector.createLength(levelCount - 2);
double tr = t1;
for (int i = 1; i <= beta.length(); i++) {
double trnext = (qtzValues.get(i) + qtzValues.get(i + 1)) * 0.5;
beta.set(i - 1, Math.log(trnext - tr));
tr = trnext;
}
}
@Test
public void testNonZeroCount() {
AVector v = Vectorz.createUniformRandomVector(5);
v.add(1);
assertEquals(v.length(), v.nonZeroCount());
v.scale(0.0);
assertEquals(0, v.nonZeroCount());
}
/** Sees if the pair of eigenvalue and eigenvector was found in the decomposition. */
public void testForEigenpair(
SymmetricQRAlgorithmDecomposition alg, double valueReal, double valueImg, double... vector) {
int N = alg.getNumberOfEigenvalues();
int numMatched = 0;
for (int i = 0; i < N; i++) {
Vector2 c = alg.getEigenvalue(i);
if (Math.abs(c.x - valueReal) < 1e-4 && Math.abs(c.y - valueImg) < 1e-4) {
// if( c.isReal() ) {
if (Math.abs(c.y - 0) < 1e-8)
if (vector.length > 0) {
AVector v = alg.getEigenVector(i);
AMatrix e = Matrix.createFromRows(vector);
e = e.getTranspose();
Matrix t = Matrix.create(v.length(), 1);
t.setColumn(0, v);
double error = diffNormF(e, t);
// CommonOps.changeSign(e);
e.multiply(-1);
double error2 = diffNormF(e, t);
if (error < 1e-3 || error2 < 1e-3) numMatched++;
} else {
numMatched++;
}
else if (Math.abs(c.y - 0) > 1e-8) {
numMatched++;
}
}
}
assertEquals(1, numMatched);
}
/**
* Pushes an input vector through the LSTM and gets an output. Cell state and recurrent result
* value are updated.
*
* @param input The input vector to push through
* @return The result vector
*/
public AVector step(AVector input) {
// concatenate result vector onto the end of input vector, dimension zero as it is 1-dimensional
// AVector
// System.out.println(input);
// System.out.println(result);
input = input.join(result);
if (input.length() != weights[0].getShape(1)) {
throw new RuntimeException(
"Input was the wrong shape! Input ( + last out) was "
+ input.length()
+ "but weights were "
+ weights[0].getShape(1));
}
// System.out.println(input);
// System.out.println(input.rows());
/* There are 4 layers in LSTM, in order of sig(0) sig(1) sig(2) tanh(3) */
// For each sigmoid layer, multiply its weight matrix by the input vector, add its bias vector,
// and perform sigmoid operation on resultant vector
for (int i = 0; i < 3; i++) {
// System.out.println(weights[i].columns());
// The "columns" of the weights 3d matrix should represent the two-dimensional matrices for
// each of the activations.
sigmoidMult1[i] = weights[i].innerProduct(input);
// System.out.println(sigmoidMult1[i]);
sigmoidMult1[i].add(biases[i]);
// System.out.println(sigmoidMult1[i]);
sigmoidLayers[i] = Operations.Sigmoid.operate(sigmoidMult1[i]);
// System.out.println(sigmoidLayers[i]);
}
// Calculate tanh layer in same fashion as sigmoid layer, but with tanh activation function
tanhLayer = weights[3].innerProduct(input);
tanhLayer.add(biases[3]);
tanhLayer = Operations.Tanh.operate(tanhLayer);
// do the first element-wise multiplication: sigmoid layer 1 and the current cell state
sigmoidLayers[0].multiply(cellState);
// System.out.println("multiplication of forget and cell state: " + sigmoidLayers[0]);
// do the second element-wise multiplication: sigmoid layer 2 and the tanh layer
sigmoidLayers[1].multiply(tanhLayer);
// System.out.println("multiplication of input and activation layer: " + sigmoidLayers[1]);
sigmoidLayers[0].add(sigmoidLayers[1]);
// System.out.println("addition of " + sigmoidLayers[1]);
cellState = sigmoidLayers[0];
sigmoidLayers[0] = null;
sigmoidLayers[1] = null;
AVector tanhOp = Operations.Tanh.operate(cellState.copy());
sigmoidLayers[2].multiply(tanhOp);
result = sigmoidLayers[2];
sigmoidLayers[2] = null;
return result.copy();
}
@Override
public boolean load(INDArray data, String loadPath) {
boolean found = true;
switch (loadPath) {
case "activate_b":
activationBiases = (AVector) data;
break;
case "activate_w":
activationWeights = (AMatrix) data;
break;
case "forget_b":
forgetBiases = (AVector) data;
break;
case "forget_w":
forgetWeights = (AMatrix) data;
break;
case "input_b":
inputBiases = (AVector) data;
break;
case "input_w":
inputWeights = (AMatrix) data;
break;
case "out_b":
outputBiases = (AVector) data;
break;
case "out_w":
outputWeights = (AMatrix) data;
break;
case "initialstate":
AVector dataCast = (AVector) data;
cellState = dataCast.subVector(0, (dataCast.length() / 2)).dense();
// System.out.println(cellState);
result = dataCast.subVector(dataCast.length() / 2, dataCast.length() / 2).dense();
break;
default:
found = false;
break;
}
initWeights();
initBiases();
return found;
}
/** The train function of OrdRec. Get all parameters after learning process. */
@SuppressWarnings("ConstantConditions")
private void train(SparseVector ratings, MutableSparseVector scores) {
Vector dbeta = Vector.createLength(beta.length());
double dt1;
// n is the number of iteration;
for (int j = 0; j < iterationCount; j++) {
for (VectorEntry rating : ratings.fast()) {
long iid = rating.getKey();
double score = scores.get(iid);
int r = quantizer.index(rating.getValue());
double probEqualR = getProbEQ(score, r);
double probLessR = getProbLE(score, r);
double probLessR_1 = getProbLE(score, r - 1);
dt1 =
learningRate
/ probEqualR
* (probLessR * (1 - probLessR) * derivateOfBeta(r, 0, t1)
- probLessR_1 * (1 - probLessR_1) * derivateOfBeta(r - 1, 0, t1)
- regTerm * t1);
double dbetaK;
for (int k = 0; k < beta.length(); k++) {
dbetaK =
learningRate
/ probEqualR
* (probLessR * (1 - probLessR) * derivateOfBeta(r, k + 1, beta.get(k))
- probLessR_1
* (1 - probLessR_1)
* derivateOfBeta(r - 1, k + 1, beta.get(k))
- regTerm * beta.get(k));
dbeta.set(k, dbetaK);
}
t1 = t1 + dt1;
beta.add(dbeta);
}
}
}
@Override
public double elementSum() {
return vector.elementSum();
}
/**
* Checks to see if an eigenvalue is complex then the eigenvector is null. If it is real it then
* checks to see if the equation A*v = lambda*v holds true.
*/
public void testPairsConsistent(SymmetricQRAlgorithmDecomposition alg, Matrix A) {
//
// System.out.println("-------------------------------------------------------------------------");
int N = alg.getNumberOfEigenvalues();
for (int i = 0; i < N; i++) {
Vector2 c = alg.getEigenvalue(i);
AVector v = alg.getEigenVector(i);
if (Double.isInfinite(c.x)
|| Double.isNaN(c.x)
|| Double.isInfinite(c.y)
|| Double.isNaN(c.y)) fail("Uncountable eigenvalue");
if (Math.abs(c.y) > 1e-20) {
assertTrue(v == null);
} else {
assertTrue(v != null);
// if( MatrixFeatures.hasUncountable(v)) {
// throw new RuntimeException("Egads");
// }
assertFalse(v.hasUncountable());
// CommonOps.mult(A,v,tempA);
Matrix ta = Matrix.create(A.rowCount(), 1);
ta.setColumn(0, (v));
AMatrix tempA = Multiplications.multiply(A, ta);
// CommonOps.scale(c.real,v,tempB);
Matrix tb = Matrix.create(v.length(), 1);
tb.setColumn(0, v);
AMatrix tempB = tb.multiplyCopy(c.x);
// double max = NormOps.normPInf(A);
double max = normPInf(A);
if (max == 0) max = 1;
double error = diffNormF(tempA, tempB) / max;
if (error > 1e-12) {
// System.out.println("Original matrix:");
// System.out.println(A);
// A.print();
// System.out.println("Eigenvalue = "+c.x);
// Eigenpair p = EigenOps.computeEigenVector(A,c.real);
// p.vector.print();
// v.print();
//
//
// CommonOps.mult(A,p.vector,tempA);
// CommonOps.scale(c.real,p.vector,tempB);
//
// max = NormOps.normPInf(A);
//
// System.out.println("error before = "+error);
// error = SpecializedOps.diffNormF(tempA,tempB)/max;
// System.out.println("error after = "+error);
// A.print("%f");
// System.out.println();
fail("Error was too large");
}
assertTrue(error <= 1e-12);
}
}
}
@Override
public double dotProduct(AVector v) {
if (v.length() != length) throw new IllegalArgumentException("Different vector lengths");
return 0.0;
}
@Override
public RowMatrix exactClone() {
return new RowMatrix(vector.exactClone());
}
@Override
public double get(int row, int column) {
if (row != 0) throw new IndexOutOfBoundsException("Row: " + row);
return vector.get(column);
}
@Override
public void set(int row, int column, double value) {
if (row != 0) throw new IndexOutOfBoundsException("Row: " + row);
vector.set(column, value);
}
@Override
public double calculateElement(int i, AVector v) {
return v.unsafeGet(i) * unsafeGetDiagonalValue(i);
}
@Override
public Vector toVector() {
return vector.toVector();
}
@Override
public int columnCount() {
return vector.length();
}
@Override
public void applyOp(Op op) {
vector.applyOp(op);
}
@Override
public void multiply(double factor) {
vector.scale(factor);
}
@Override
public void setColumn(int j, AVector col) {
int rc = checkRowCount(col.length());
col.getElements(data, j * rc);
}
@Override
public long nonZeroCount() {
return vector.nonZeroCount();
}