public double valueAt(double[] param) {
double[] sdInv = new double[nVariables];
for (int i = 0; i < nVariables; i++) {
R.setEntry(i, i, 1.0 - param[i]);
sdInv[i] = 1.0 / Sinv.getEntry(i, i);
}
DiagonalMatrix diagSdInv = new DiagonalMatrix(sdInv);
EigenDecomposition eigen = new EigenDecomposition(R);
RealMatrix eigenVectors = eigen.getV().getSubMatrix(0, nVariables - 1, 0, nFactors - 1);
double[] ev = new double[nFactors];
for (int i = 0; i < nFactors; i++) {
ev[i] = Math.sqrt(eigen.getRealEigenvalue(i));
}
DiagonalMatrix evMatrix =
new DiagonalMatrix(
ev); // USE Apache version of Diagonal matrix when upgrade to version 3.2
RealMatrix LAMBDA = eigenVectors.multiply(evMatrix);
RealMatrix SIGMA = (LAMBDA.multiply(LAMBDA.transpose()));
double value = 0.0;
RealMatrix DIF = R.subtract(SIGMA);
for (int i = 0; i < DIF.getRowDimension(); i++) {
for (int j = 0; j < DIF.getColumnDimension(); j++) {
value = DIF.getEntry(i, j);
DIF.setEntry(i, j, Math.pow(value, 2));
}
}
RealMatrix RESID = diagSdInv.multiply(DIF).multiply(diagSdInv);
double sum = 0.0;
for (int i = 0; i < RESID.getRowDimension(); i++) {
for (int j = 0; j < RESID.getColumnDimension(); j++) {
sum += RESID.getEntry(i, j);
}
}
return sum;
}
private void computeFactorLoadings(double[] x) {
uniqueness = x;
communality = new double[nVariables];
for (int i = 0; i < nVariables; i++) {
R.setEntry(i, i, 1.0 - x[i]);
}
EigenDecomposition E = new EigenDecomposition(R);
RealMatrix L = E.getV().getSubMatrix(0, nVariables - 1, 0, nFactors - 1);
double[] ev = new double[nFactors];
for (int i = 0; i < nFactors; i++) {
ev[i] = Math.sqrt(E.getRealEigenvalue(i));
}
DiagonalMatrix M = new DiagonalMatrix(ev);
RealMatrix LOAD = L.multiply(M);
// rotate factor loadings
if (rotationMethod != RotationMethod.NONE) {
GPArotation gpa = new GPArotation();
RotationResults results = gpa.rotate(LOAD, rotationMethod);
LOAD = results.getFactorLoadings();
}
Sum[] colSums = new Sum[nFactors];
Sum[] colSumsSquares = new Sum[nFactors];
for (int j = 0; j < nFactors; j++) {
colSums[j] = new Sum();
colSumsSquares[j] = new Sum();
}
factorLoading = new double[nVariables][nFactors];
for (int i = 0; i < nVariables; i++) {
for (int j = 0; j < nFactors; j++) {
factorLoading[i][j] = LOAD.getEntry(i, j);
colSums[j].increment(factorLoading[i][j]);
colSumsSquares[j].increment(Math.pow(factorLoading[i][j], 2));
communality[i] += Math.pow(factorLoading[i][j], 2);
}
}
// check sign of factor
double sign = 1.0;
for (int i = 0; i < nVariables; i++) {
for (int j = 0; j < nFactors; j++) {
if (colSums[j].getResult() < 0) {
sign = -1.0;
} else {
sign = 1.0;
}
factorLoading[i][j] = factorLoading[i][j] * sign;
}
}
double totSumOfSquares = 0.0;
sumsOfSquares = new double[nFactors];
proportionOfExplainedVariance = new double[nFactors];
proportionOfVariance = new double[nFactors];
for (int j = 0; j < nFactors; j++) {
sumsOfSquares[j] = colSumsSquares[j].getResult();
totSumOfSquares += sumsOfSquares[j];
}
for (int j = 0; j < nFactors; j++) {
proportionOfExplainedVariance[j] = sumsOfSquares[j] / totSumOfSquares;
proportionOfVariance[j] = sumsOfSquares[j] / nVariables;
}
}