public void random3Partition(DataSet p1, DataSet p2, DataSet p3, double f1, double f2) {
int size1 = (int) (f1 * x.rows());
int size2 = (int) (f2 * x.rows());
int size3 = x.rows() - size1 - size2;
Random random = new Random(new Date().getTime());
p1.x = newFromTemplate(p1.x, size1, x.columns());
p1.y = new double[size1];
p2.x = newFromTemplate(p2.x, size2, x.columns());
p2.y = new double[size2];
p3.x = newFromTemplate(p3.x, size3, x.columns());
p3.y = new double[size3];
// FIXME: Verify the uniformity of the partitioning scheme.
int r1 = 0;
int r2 = 0;
int r3 = 0;
for (int r = 0; r < x.rows(); r++) {
double p = random.nextDouble();
if (p < f1 && r1 < size1) {
p1.copyInstanceTo(r1, this, r);
r1++;
} else if (p < f1 + f2 && r2 < size2) {
p2.copyInstanceTo(r2, this, r);
r2++;
} else if (r3 < size3) {
p3.copyInstanceTo(r3, this, r);
r3++;
} else {
r--;
}
}
}
/**
* Splits recursively the points of the graph while the value of the best cut found is less of a
* specified limit (the alpha star factor).
*
* @param W the weight matrix of the graph
* @param alpha_star the alpha star factor
* @return an array of sets of points (partitions)
*/
protected int[][] partition(DoubleMatrix2D W, double alpha_star) {
numPartitions++;
// System.out.println("!");
// If the graph contains only one point
if (W.columns() == 1) {
int[][] p = new int[1][1];
p[0][0] = 0;
return p;
// Otherwise
} else {
// Computes the best cut
int[][] cut = bestCut(W);
// Computes the value of the found cut
double cutVal = Ncut(W, cut[0], cut[1], null);
// System.out.println("cutVal = "+cutVal +"\tnumPartitions = "+numPartitions);
// If the value is less than alpha star
if (cutVal < alpha_star && numPartitions < 2) {
// Recursively partitions the first one found ...
DoubleMatrix2D W0 = W.viewSelection(cut[0], cut[0]);
int[][] p0 = partition(W0, alpha_star);
// ... and the second one
DoubleMatrix2D W1 = W.viewSelection(cut[1], cut[1]);
int[][] p1 = partition(W1, alpha_star);
// Merges the partitions found in the previous recursive steps
int[][] p = new int[p0.length + p1.length][];
for (int i = 0; i < p0.length; i++) {
p[i] = new int[p0[i].length];
for (int j = 0; j < p0[i].length; j++) p[i][j] = cut[0][p0[i][j]];
}
for (int i = 0; i < p1.length; i++) {
p[i + p0.length] = new int[p1[i].length];
for (int j = 0; j < p1[i].length; j++) p[i + p0.length][j] = cut[1][p1[i][j]];
}
return p;
} else {
// Otherwise returns the partitions found in current step
// w/o recursive invocation
int[][] p = new int[1][W.columns()];
for (int i = 0; i < p[0].length; i++) p[0][i] = i;
return p;
}
}
}
/**
* Save factorisation machine in a compressed, human readable file.
*
* @param out output
* @throws IOException when I/O error
*/
public void save(OutputStream out) throws IOException {
int N = m.rows();
int K = m.columns();
try (ZipOutputStream zip = new ZipOutputStream(out)) {
zip.putNextEntry(new ZipEntry("info"));
PrintStream ps = new PrintStream(zip);
ps.println(N);
ps.println(K);
ps.flush();
zip.closeEntry();
zip.putNextEntry(new ZipEntry("b"));
ps = new PrintStream(zip);
ps.println(b);
ps.flush();
zip.closeEntry();
zip.putNextEntry(new ZipEntry("w"));
saveDenseDoubleMatrix1D(zip, w);
zip.closeEntry();
zip.putNextEntry(new ZipEntry("m"));
saveDenseDoubleMatrix2D(zip, m);
zip.closeEntry();
}
}
@Override
public DoubleMatrix getEigenvectors() {
DoubleMatrix2D V = myDecomposition.getV();
int nrows = V.rows();
int ncols = V.columns();
DoubleMatrix dm = DoubleMatrixFactory.DEFAULT.make(nrows, ncols);
for (int r = 0; r < nrows; r++) {
for (int c = 0; c < ncols; c++) {
dm.set(r, c, V.getQuick(r, c));
}
}
return dm;
}
static boolean computeLogMi(
FeatureGenerator featureGen,
double lambda[],
DoubleMatrix2D Mi_YY,
DoubleMatrix1D Ri_Y,
boolean takeExp,
boolean reuseM,
boolean initMDone) {
if (reuseM && initMDone) {
Mi_YY = null;
} else initMDone = false;
if (Mi_YY != null) Mi_YY.assign(0);
Ri_Y.assign(0);
while (featureGen.hasNext()) {
Feature feature = featureGen.next();
int f = feature.index();
int yp = feature.y();
int yprev = feature.yprev();
float val = feature.value();
// System.out.println(feature.toString());
if (yprev < 0) {
// this is a single state feature.
double oldVal = Ri_Y.getQuick(yp);
Ri_Y.setQuick(yp, oldVal + lambda[f] * val);
} else if (Mi_YY != null) {
Mi_YY.setQuick(yprev, yp, Mi_YY.getQuick(yprev, yp) + lambda[f] * val);
initMDone = true;
}
}
if (takeExp) {
for (int r = Ri_Y.size() - 1; r >= 0; r--) {
Ri_Y.setQuick(r, expE(Ri_Y.getQuick(r)));
if (Mi_YY != null)
for (int c = Mi_YY.columns() - 1; c >= 0; c--) {
Mi_YY.setQuick(r, c, expE(Mi_YY.getQuick(r, c)));
}
}
}
return initMDone;
}
/**
* Predict the value of an instance.
*
* @param x instance
* @return value of prediction
*/
public double prediction(I x) {
double pred = b;
DoubleMatrix1D xm = new DenseDoubleMatrix1D(m.columns());
pred +=
x.operate(
(i, xi) -> {
double wi = w.getQuick(i);
DoubleMatrix1D mi = m.viewRow(i);
xm.assign(mi, (r, s) -> r + xi * s);
return xi * wi - 0.5 * xi * xi * mi.zDotProduct(mi);
},
(v1, v2) -> v1 + v2);
pred += 0.5 * xm.zDotProduct(xm);
return pred;
}
/**
* Constructs a new time series data contains for the given row-major data array and the given
* list of variables. Each row of the data, data[i], contains a measured for each variable (in
* order) for a particular time. The series of times is in increasing order.
*/
public TimeSeriesData(DoubleMatrix2D matrix, List<String> varNames) {
if (matrix == null) {
throw new NullPointerException("Data must not be null.");
}
if (varNames == null) {
throw new NullPointerException("Variables must not be null.");
}
for (int i = 0; i < varNames.size(); i++) {
if (varNames.get(i) == null) {
throw new NullPointerException("Variable at index " + i + "is null.");
}
}
this.data2 = matrix;
if (varNames.size() != matrix.columns()) {
throw new IllegalArgumentException(
"Number of columns in the data " + "must match the number of variables.");
}
this.varNames = varNames;
this.name = "Time Series Data";
}
/**
* Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be
* retrieved via instance methods of the returned decomposition object. Checks for symmetry, then
* constructs the eigenvalue decomposition.
*
* @param A A square matrix.
* @return A decomposition object to access <tt>D</tt> and <tt>V</tt>.
* @throws IllegalArgumentException if <tt>A</tt> is not square.
*/
public EigenvalueDecomposition(DoubleMatrix2D A) {
Property.DEFAULT.checkSquare(A);
n = A.columns();
V = new double[n][n];
d = new double[n];
e = new double[n];
issymmetric = Property.DEFAULT.isSymmetric(A);
if (issymmetric) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
V[i][j] = A.getQuick(i, j);
}
}
// Tridiagonalize.
tred2();
// Diagonalize.
tql2();
} else {
H = new double[n][n];
ort = new double[n];
for (int j = 0; j < n; j++) {
for (int i = 0; i < n; i++) {
H[i][j] = A.getQuick(i, j);
}
}
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
}
}
/**
* Returns the best cut of a graph w.r.t. the degree of dissimilarity between points of different
* partitions and the degree of similarity between points of the same partition.
*
* @param W the weight matrix of the graph
* @return an array of two elements, each of these contains the points of a partition
*/
protected static int[][] bestCut(DoubleMatrix2D W) {
int n = W.columns();
// Builds the diagonal matrices D and D^(-1/2) (represented as their diagonals)
DoubleMatrix1D d = DoubleFactory1D.dense.make(n);
DoubleMatrix1D d_minus_1_2 = DoubleFactory1D.dense.make(n);
for (int i = 0; i < n; i++) {
double d_i = W.viewRow(i).zSum();
d.set(i, d_i);
d_minus_1_2.set(i, 1 / Math.sqrt(d_i));
}
DoubleMatrix2D D = DoubleFactory2D.sparse.diagonal(d);
// System.out.println("DoubleMatrix2D :\n"+D.toString());
DoubleMatrix2D X = D.copy();
// System.out.println("DoubleMatrix2D copy :\n"+X.toString());
// X = D^(-1/2) * (D - W) * D^(-1/2)
X.assign(W, Functions.minus);
// System.out.println("DoubleMatrix2D X: (D-W) :\n"+X.toString());
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
X.set(i, j, X.get(i, j) * d_minus_1_2.get(i) * d_minus_1_2.get(j));
// Computes the eigenvalues and the eigenvectors of X
EigenvalueDecomposition e = new EigenvalueDecomposition(X);
DoubleMatrix1D lambda = e.getRealEigenvalues();
// Selects the eigenvector z_2 associated with the second smallest eigenvalue
// Creates a map that contains the pairs <index, eigenvalue>
AbstractIntDoubleMap map = new OpenIntDoubleHashMap(n);
for (int i = 0; i < n; i++) map.put(i, Math.abs(lambda.get(i)));
IntArrayList list = new IntArrayList();
// Sorts the map on the value
map.keysSortedByValue(list);
// Gets the index of the second smallest element
int i_2 = list.get(1);
// y_2 = D^(-1/2) * z_2
DoubleMatrix1D y_2 = e.getV().viewColumn(i_2).copy();
y_2.assign(d_minus_1_2, Functions.mult);
// Creates a map that contains the pairs <i, y_2[i]>
map.clear();
for (int i = 0; i < n; i++) map.put(i, y_2.get(i));
// Sorts the map on the value
map.keysSortedByValue(list);
// Search the element in the map previuosly ordered that minimizes the cut
// of the partition
double best_cut = Double.POSITIVE_INFINITY;
int[][] partition = new int[2][];
// The array v contains all the elements of the graph ordered by their
// projection on vector y_2
int[] v = list.elements();
// For each admissible splitting point i
for (int i = 1; i < n; i++) {
// The array a contains all the elements that have a projection on vector
// y_2 less or equal to the one of i-th element
// The array b contains the remaining elements
int[] a = new int[i];
int[] b = new int[n - i];
System.arraycopy(v, 0, a, 0, i);
System.arraycopy(v, i, b, 0, n - i);
double cut = Ncut(W, a, b, v);
if (cut < best_cut) {
best_cut = cut;
partition[0] = a;
partition[1] = b;
}
}
// System.out.println("Partition:");
// UtilsJS.printMatrix(partition);
return partition;
}
/**
* Gibt die Lösung x des Gleichungssystems zurück: nur eindeutige (d.h. parameterunabhängige xi)
* werden zurückgegeben. index 0: Wert = 0 bedeutet xi unbestimmt, Wert = 1 bedeutet xi bestimmt
* index 1: eigentlicher Wert (nur wenn xi bestimmt, dh index 0 = 1, sonst Wert 0)
*/
public final double[][] solve() throws ArithmeticException {
// --------------------------------------------------------------------------
// EIGENTLICHER SOLVER für bestimmte Lösungsvariablen in unbestimmen Systemen
// --------------------------------------------------------------------------
int gebrauchteUnbestParam = 0;
x =
new double[A.columns()]
[2 + anzUnbestParam]; // Status 1 (bestimmt), kN, alpha, beta (Parameter)
int z = A.rows() - 1; // Zeilenvariable, beginnt zuunterst
// Gleichungen mit lauter Nullen
while (R.viewRow(z).cardinality() == 0 // nachfolgende Tests massgebend, dieser jedoch schnell
|| (Fkt.max(R.viewRow(z).toArray()) < TOL && Fkt.min(R.viewRow(z).toArray()) > -TOL)) {
double cwert;
if (z < c.rows()) cwert = c.get(z, 0);
else cwert = 0;
if (Math.abs(cwert) > TOL) {
System.out.println("widersprüchliche Gleichungen im System! Zeile " + z);
throw new ArithmeticException("Widerspruch im Gleichungssystem!");
}
z--;
if (z <= 0) {
System.out.println("lauter Nullen im GLS");
break;
}
}
// Verarbeiten der Gleichungen (von unten her)
for (z = z; z >= 0; z--) {
// finde erste nicht-Null in Zeile (Pivot)
int p = -1; // Pivot: erste Zahl welche nicht null ist
pivotfinden:
for (int i = 0; i < R.columns(); i++) {
if (Math.abs(R.get(z, i))
> TOL) { // Versuch, numerische Probleme (Überbestimmtheit) zu vermeiden
p = i;
break pivotfinden;
}
}
// Fall Kein Pivot gefunden (d.h. linker Teil der Gleichung aus lauter Nullen)
if (p < 0) {
if (debug) System.out.println("Warnung: kein Pivot gefunden in Zeile " + z);
// Kontrolle, ob rechte Seite (c) auch null --> ok, sonst Widerspruch im GLS
if (Math.abs(c.get(z, 0)) > TOL) {
System.out.println("widersprüchliche Gleichungen im System! Zeile " + z);
throw new ArithmeticException("Widerspruch im Gleichungssystem!");
} else {
if (debug)
System.out.println("Entwarnung: Zeile " + z + " besteht aus lauter Nullen (ok)");
continue;
}
}
// kontrollieren, ob es in der Gleichung (Zeile) eine neue Unbestimmte Variable (i.d.R. Pivot)
// hat.
boolean alleVarBestimmt = true;
int effPivot = p; // effektiver Pivot (1. Unbestimmte Variable der Zeile), i.d.R. Pivot
for (int i = p; i < R.columns(); i++) {
if (x[i][0] == 0 && Math.abs(R.viewRow(z).get(i)) > TOL) {
alleVarBestimmt = false;
effPivot = i; // i.d.R. effPivot=p, aber nicht immer.
break;
}
}
if (alleVarBestimmt) { // alle Variablen (inkl.Pivot) schon bestimmt!
// CHECKEN, ob (Zeile "+z+") nicht widersprüchlich
double[] kontrolle = new double[1 + anzUnbestParam];
for (int j = 0; j < kontrolle.length; j++) kontrolle[j] = 0;
for (int i = p; i < R.columns(); i++) {
for (int j = 0; j < kontrolle.length; j++) {
kontrolle[j] += R.viewRow(z).get(i) * x[i][j + 1];
}
}
kontrolle[0] -= c.get(z, 0);
// TODO TESTEN!
boolean alleParamNull = true;
int bekParam = -1; // Parameter der aus der Gleichung bestimmt werden kann.
for (int j = kontrolle.length - 1; j > 0; j--) {
if (Math.abs(kontrolle[j]) > TOL) {
alleParamNull = false;
if (bekParam < 0) bekParam = j;
}
}
// Überprüfen, ob Gleichung widersprüchlich ist
if (alleParamNull) { // TODO ev. nochmals prüfen ob alle 0 mit geringerer Toleranz (Problem
// fastNull*Param ≠ 0 könnte bedeuten dass Param = 0). Zumindestens
// wenn noch Parameter zu vergeben.
double obnull = Math.abs(kontrolle[0]);
if (obnull > TOL) {
System.out.println("");
System.out.println(
"Widerspruch im Gleichungssystem! (Zeile "
+ z
+ ") "
+ obnull
+ " ungleich 0"); // TODO: URSPRÜNGLICH ZEILE (piv) ANGEBEN!
System.out.println("eventuell numerisches Problem");
throw new ArithmeticException("Widerspruch im Gleichungssystem!");
} else continue; // nächste Gleichung
}
// else
// Ein schon vergebener Parameter kann ausgerechnet werden
// Schlaufe über bisherige Lösung
assert bekParam > 0;
for (int xi = 0; xi < x.length; xi++) {
double faktor = x[xi][1 + bekParam];
if (Math.abs(faktor) < TOL) continue;
// Einsetzen
assert x[xi][0] > 0; // bestimmt
for (int j = 0; j < kontrolle.length; j++) {
if (j != bekParam) {
x[xi][j + 1] += -kontrolle[j] * faktor / kontrolle[bekParam];
}
}
}
for (int xi = 0; xi < x.length; xi++) {
// Parameter nachrutschen
if (bekParam < anzUnbestParam) { // d.h. nicht der letzte zu vergebende Parameter.
for (int j = bekParam; j < anzUnbestParam; j++) {
x[xi][j + 1] = x[xi][j + 2];
x[xi][j + 2] = 0;
}
} else x[xi][bekParam + 1] = 0;
}
if (debug)
System.err.println(
"VORSICHT, wenig GETESTETES Modul des Solvers im Einsatz."); // TODO Warnung
// entfernen, da
// vermutlich i.O.
gebrauchteUnbestParam--;
}
// Normalfall, unbestimmter (effektiver) Pivot vorhanden
else {
// unbekannte
x[effPivot][1] = c.get(z, 0) / R.viewRow(z).get(effPivot);
for (int i = R.columns() - 1; i >= p; i--) { // R.Spalten, da dies AnzUnbek x entspricht
if (i == effPivot) continue;
if (x[i][0] == 0) { // unbestimmt, aber nicht Pivot
if (Math.abs(R.viewRow(z).get(i)) > TOL) { // TODO testen!!!
if (gebrauchteUnbestParam >= anzUnbestParam) {
System.err.println(
"Programmfehler in solver: gebrauchteUnbestParam >= anzUnbestParam");
throw new AssertionError(
"Programmfehler in solver: gebrauchteUnbestParam >= anzUnbestParam");
}
x[i][gebrauchteUnbestParam + 2] = 1; // neuer Parameter (alpha, beta) setzen
x[i][0] = 1; // bestimmt (auch wenn von Parameter abhängig).
gebrauchteUnbestParam++;
}
}
x[effPivot][1] += -R.viewRow(z).get(i) * x[i][1] / R.viewRow(z).get(effPivot);
for (int j = 0; j < gebrauchteUnbestParam; j++) {
x[effPivot][2 + j] += -R.viewRow(z).get(i) * x[i][2 + j] / R.viewRow(z).get(effPivot);
}
}
x[effPivot][0] = 1;
}
}
if (debug) {
System.out.println("");
for (int i = 0; i < x.length; i++) {
System.out.print("x" + i + " = " + Fkt.nf(x[i][1], 3));
for (int j = 2; j < x[i].length; j++) {
System.out.print(", P" + (j - 1) + " = " + Fkt.nf(x[i][j], 3));
}
System.out.println("");
}
}
// ------------------
// Lösung zurückgeben
// ------------------
// Lösung x: nur eindeutige (d.h. parameterunabhängige xi) werden zurückgegeben
// index 0: Wert = 0 bedeutet xi unbestimmt, Wert = 1 bedeutet xi bestimmt
// index 1: eigentlicher Wert (nur wenn xi bestimmt, dh index 0 = 1, sonst Wert 0)
xLsg = new double[R.columns()][2];
for (int i = 0; i < x.length; i++) {
boolean bestimmt;
if (x[i][0] > 0) {
bestimmt = true;
// schauen, ob Lösungsvariable xi bestimmt, dh unabhängig von überzähligen Parametern
for (int j = 2; j < x[i].length; j++) {
if (Math.abs(x[i][j]) > TOL) bestimmt = false;
}
} else bestimmt = false;
if (bestimmt) {
xLsg[i][0] = 1;
xLsg[i][1] = x[i][1];
} else xLsg[i][0] = 0;
}
solved = true;
return xLsg;
}