/**
* Computes the correlation matrix for the columns of the input matrix.
*
* @param matrix matrix with columns representing variables to correlate
* @return correlation matrix
*/
public RealMatrix computeCorrelationMatrix(RealMatrix matrix) {
int nVars = matrix.getColumnDimension();
RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
for (int i = 0; i < nVars; i++) {
for (int j = 0; j < i; j++) {
double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
outMatrix.setEntry(i, j, corr);
outMatrix.setEntry(j, i, corr);
}
outMatrix.setEntry(i, i, 1d);
}
return outMatrix;
}
/**
* Derives a correlation matrix from a covariance matrix.
*
* <p>Uses the formula <br>
* <code>r(X,Y) = cov(X,Y)/s(X)s(Y)</code> where <code>r(·,·)</code> is the
* correlation coefficient and <code>s(·)</code> means standard deviation.
*
* @param covarianceMatrix the covariance matrix
* @return correlation matrix
*/
public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix) {
int nVars = covarianceMatrix.getColumnDimension();
RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
for (int i = 0; i < nVars; i++) {
double sigma = Math.sqrt(covarianceMatrix.getEntry(i, i));
outMatrix.setEntry(i, i, 1d);
for (int j = 0; j < i; j++) {
double entry =
covarianceMatrix.getEntry(i, j) / (sigma * Math.sqrt(covarianceMatrix.getEntry(j, j)));
outMatrix.setEntry(i, j, entry);
outMatrix.setEntry(j, i, entry);
}
}
return outMatrix;
}
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));
}
/**
* Solve an estimation problem using a least squares criterion.
*
* <p>This method set the unbound parameters of the given problem starting from their current
* values through several iterations. At each step, the unbound parameters are changed in order to
* minimize a weighted least square criterion based on the measurements of the problem.
*
* <p>The iterations are stopped either when the criterion goes below a physical threshold under
* which improvement are considered useless or when the algorithm is unable to improve it (even if
* it is still high). The first condition that is met stops the iterations. If the convergence it
* not reached before the maximum number of iterations, an {@link EstimationException} is thrown.
*
* @param problem estimation problem to solve
* @exception EstimationException if the problem cannot be solved
* @see EstimationProblem
*/
@Override
public void estimate(EstimationProblem problem) throws EstimationException {
initializeEstimate(problem);
// work matrices
double[] grad = new double[parameters.length];
ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);
double[] bDecrementData = bDecrement.getDataRef();
RealMatrix wGradGradT = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
// iterate until convergence is reached
double previous = Double.POSITIVE_INFINITY;
do {
// build the linear problem
incrementJacobianEvaluationsCounter();
RealVector b = new ArrayRealVector(parameters.length);
RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
for (int i = 0; i < measurements.length; ++i) {
if (!measurements[i].isIgnored()) {
double weight = measurements[i].getWeight();
double residual = measurements[i].getResidual();
// compute the normal equation
for (int j = 0; j < parameters.length; ++j) {
grad[j] = measurements[i].getPartial(parameters[j]);
bDecrementData[j] = weight * residual * grad[j];
}
// build the contribution matrix for measurement i
for (int k = 0; k < parameters.length; ++k) {
double gk = grad[k];
for (int l = 0; l < parameters.length; ++l) {
wGradGradT.setEntry(k, l, weight * gk * grad[l]);
}
}
// update the matrices
a = a.add(wGradGradT);
b = b.add(bDecrement);
}
}
try {
// solve the linearized least squares problem
RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
// update the estimated parameters
for (int i = 0; i < parameters.length; ++i) {
parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
}
} catch (InvalidMatrixException e) {
throw new EstimationException("unable to solve: singular problem");
}
previous = cost;
updateResidualsAndCost();
} while ((getCostEvaluations() < 2)
|| (Math.abs(previous - cost) > (cost * steadyStateThreshold)
&& (Math.abs(cost) > convergence)));
}
