/**
* Calculates the variance-covariance matrix of the regression parameters.
*
* <p>Var(b) = (X<sup>T</sup>X)<sup>-1</sup>
*
* <p>Uses QR decomposition to reduce (X<sup>T</sup>X)<sup>-1</sup> to
* (R<sup>T</sup>R)<sup>-1</sup>, with only the top p rows of R included, where p = the length of
* the beta vector.
*
* @return The beta variance-covariance matrix
*/
@Override
protected RealMatrix calculateBetaVariance() {
int p = X.getColumnDimension();
RealMatrix Raug = qr.getR().getSubMatrix(0, p - 1, 0, p - 1);
RealMatrix Rinv = new LUDecompositionImpl(Raug).getSolver().getInverse();
return Rinv.multiply(Rinv.transpose());
}
public static void main(String[] args) {
RealMatrix coefficients2 =
new Array2DRowRealMatrix(
new double[][] {
{0.0D, 1.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.857D, 0.0D, 0.054D, 0.018D, 0.0D, 0.071D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.0D, 1.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.857D, 0.0D, 0.054D, 0.018D, 0.0D, 0.071D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 1.0D, 0.0D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 1.0D, 0.0D, 0.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 1.0D, 0.0D, 0.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.6D, 0.4D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 1.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 1.0D, 0.0D, 0.0D, 1.0D},
{0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D, 0.0D}
},
false);
for (int i = 0; i < 11; i++) {
coefficients2.setEntry(i, i, -1d);
}
coefficients2 = coefficients2.transpose();
DecompositionSolver solver = new LUDecompositionImpl(coefficients2).getSolver();
System.out.println("1 method my Value :");
RealVector constants =
new ArrayRealVector(new double[] {-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, false);
RealVector solution = solver.solve(constants);
double[] data = solution.getData();
DecimalFormat df = new DecimalFormat();
df.setRoundingMode(RoundingMode.DOWN);
System.out.println("Корни уравнения:");
for (double dd : data) {
System.out.print(df.format(dd) + " ");
}
System.out.println();
System.out.println(
"Среднее число процессорных операций, выполняемых при одном прогоне алгоритма: "
+ operationsByProcess(data, arr));
System.out.println("Среднее число обращений к файлам:");
for (int i = 1; i < 4; i++) {
System.out.println(" Файл " + i + " : " + fileMiddleRequest(data, arr, i));
}
System.out.println("Среднее количество информации передаваемой при одном обращении к файлам:");
for (int i = 1; i < 4; i++) {
System.out.println(" Файл " + i + " : " + bitsPerFileTransfer(data, arr, i));
}
System.out.println(
"Сумма среднего числа обращений к основным операторам: " + operatorExecute(data, arr));
System.out.println("Средняя трудоемкость этапа: " + middleWork(data, arr));
}
/**
* Compute the "hat" matrix.
*
* <p>The hat matrix is defined in terms of the design matrix X by
* X(X<sup>T</sup>X)<sup>-1</sup>X<sup>T</sup>
*
* <p>The implementation here uses the QR decomposition to compute the hat matrix as Q
* I<sub>p</sub>Q<sup>T</sup> where I<sub>p</sub> is the p-dimensional identity matrix augmented
* by 0's. This computational formula is from "The Hat Matrix in Regression and ANOVA", David C.
* Hoaglin and Roy E. Welsch, <i>The American Statistician</i>, Vol. 32, No. 1 (Feb., 1978), pp.
* 17-22.
*
* @return the hat matrix
*/
public RealMatrix calculateHat() {
// Create augmented identity matrix
RealMatrix Q = qr.getQ();
final int p = qr.getR().getColumnDimension();
final int n = Q.getColumnDimension();
Array2DRowRealMatrix augI = new Array2DRowRealMatrix(n, n);
double[][] augIData = augI.getDataRef();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j && i < p) {
augIData[i][j] = 1d;
} else {
augIData[i][j] = 0d;
}
}
}
// Compute and return Hat matrix
return Q.multiply(augI).multiply(Q.transpose());
}
/**
* Modifies this map through a single backpropagation iteration using the given error values on
* the output nodes.
*
* @param error
*/
public void train(List<Double> error, double learningRate) {
RealVector eOut = new ArrayRealVector(error.size());
for (int i : series(error.size())) eOut.setEntry(i, error.get(i));
// * gHidden: delta for the non-bias nodes of the hidden layer
gHidden.setSubVector(0, stateHidden.getSubVector(0, n)); // optimize
for (int i : Series.series(gHidden.getDimension()))
gHidden.setEntry(i, activation.derivative(gHidden.getEntry(i)));
eHiddenL = weights1.transpose().operate(eOut);
eHidden.setSubVector(0, eHiddenL.getSubVector(0, h));
for (int i : series(h)) eHidden.setEntry(i, eHidden.getEntry(i) * gHidden.getEntry(i));
weights1Delta = MatrixTools.outer(eOut, stateHidden);
weights1Delta = weights1Delta.scalarMultiply(-1.0 * learningRate); // optimize
weights0Delta = MatrixTools.outer(eHidden, stateIn);
weights0Delta = weights0Delta.scalarMultiply(-1.0 * learningRate);
weights0 = weights0.add(weights0Delta);
weights1 = weights1.add(weights1Delta);
}
