private void hessenbergReduction(final RealMatrix matrixToReduce) {
final int n = matrixToReduce.getHeight();
final double[][] V = matrixToReduce.blank().toDoubleArray();
final double[][] H = matrixToReduce.toDoubleArray();
final double[] ort = new double[matrixToReduce.getHeight()];
// This is derived from the Algol procedures hessenbergReduction and ortran,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutines in EISPACK.
final int high = n - 1;
for (int m = 1; m <= high - 1; m++) {
// Scale column.
double scale = 0.0;
for (int i = m; i <= high; i++) scale = scale + Math.abs(H[i][m - 1]);
if (scale != 0.0) {
// Compute Householder transformation.
double h = 0.0;
for (int i = high; i >= m; i--) {
ort[i] = H[i][m - 1] / scale;
h += ort[i] * ort[i];
}
double g = Math.sqrt(h);
if (ort[m] > 0) g = -g;
h = h - ort[m] * g;
ort[m] = ort[m] - g;
// Apply Householder similarity transformation
// hessenbergMatrixElements = (I-u*u'/h)*hessenbergMatrixElements*(I-u*u')/h)
for (int j = m; j < n; j++) {
double f = 0.0;
for (int i = high; i >= m; i--) f += ort[i] * H[i][j];
f = f / h;
for (int i = m; i <= high; i++) H[i][j] -= f * ort[i];
}
for (int i = 0; i <= high; i++) {
double f = 0.0;
for (int j = high; j >= m; j--) f += ort[j] * H[i][j];
f = f / h;
for (int j = m; j <= high; j++) H[i][j] -= f * ort[j];
}
ort[m] = scale * ort[m];
H[m][m - 1] = scale * g;
}
}
// Accumulate transformations (Algol's ortran).
for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) V[i][j] = (i == j ? 1.0 : 0.0);
for (int m = high - 1; m >= 1; m--)
if (H[m][m - 1] != 0.0) {
for (int i = m + 1; i <= high; i++) ort[i] = H[i][m - 1];
for (int j = m; j <= high; j++) {
double g = 0.0;
for (int i = m; i <= high; i++) g += ort[i] * V[i][j];
// Double division avoids possible underflow
g = (g / ort[m]) / H[m][m - 1];
for (int i = m; i <= high; i++) V[i][j] += g * ort[i];
}
}
this.matrix = new SimpleRealMatrix(V);
this.hessenbergMatrix = new SimpleRealMatrix(H);
}
/**
* Check for symmetry, then construct the eigenvalue decomposition. Gives access to D and
* matrixElements.
*
* @param matrixToDecompose Elements Square matrix
*/
public NonsymetricHessenbergReduction(final RealMatrix matrixToDecompose) {
final int n = matrixToDecompose.getWidth();
// Reduce to Hessenberg form.
hessenbergReduction(matrixToDecompose.getSubmatrix(0, n, 0, n));
}