public static void invoke(
final ComplexNumber[] aData,
final Householder.Complex aHouseholder,
final ComplexNumber[] aWorker) {
final ComplexNumber[] tmpVector = aHouseholder.vector;
final int tmpFirst = aHouseholder.first;
final int tmpLength = tmpVector.length;
final ComplexNumber tmpBeta = aHouseholder.beta;
final int tmpCount = tmpLength - tmpFirst;
if (tmpCount > THRESHOLD) {
final DivideAndConquer tmpConqurer =
new DivideAndConquer() {
@Override
protected void conquer(final int aFirst, final int aLimit) {
MultiplyHermitianAndVector.invoke(
aWorker, aFirst, aLimit, aData, tmpVector, tmpFirst);
}
};
tmpConqurer.invoke(tmpFirst, tmpLength, THRESHOLD);
} else {
MultiplyHermitianAndVector.invoke(aWorker, tmpFirst, tmpLength, aData, tmpVector, tmpFirst);
}
ComplexNumber tmpVal = ComplexNumber.ZERO;
for (int c = tmpFirst; c < tmpLength; c++) {
// tmpVal += tmpVector[c] * aWorker[c];
tmpVal = tmpVal.add(tmpVector[c].conjugate().multiply(aWorker[c]));
}
// tmpVal *= (tmpBeta / TWO);
tmpVal = ComplexFunction.DIVIDE.invoke(tmpVal.multiply(tmpBeta), ComplexNumber.TWO);
for (int c = tmpFirst; c < tmpLength; c++) {
// aWorker[c] = tmpBeta * (aWorker[c] - (tmpVal * tmpVector[c]));
aWorker[c] = tmpBeta.multiply(aWorker[c].subtract(tmpVal.multiply(tmpVector[c])));
}
if (tmpCount > THRESHOLD) {
final DivideAndConquer tmpConqurer =
new DivideAndConquer() {
@Override
protected void conquer(final int aFirst, final int aLimit) {
HermitianRank2Update.invoke(aData, aFirst, aLimit, tmpVector, aWorker);
}
};
tmpConqurer.invoke(tmpFirst, tmpLength, THRESHOLD);
} else {
HermitianRank2Update.invoke(aData, tmpFirst, tmpLength, tmpVector, aWorker);
}
}
public void estimate(final Access1D<?> x, final Access1D<?> y) {
final int tmpRowDim = (int) Math.min(x.count(), y.count());
final int tmpColDim = this.size();
final PhysicalStore<ComplexNumber> tmpBody =
ComplexDenseStore.FACTORY.makeZero(tmpRowDim, tmpColDim);
final PhysicalStore<ComplexNumber> tmpRHS = ComplexDenseStore.FACTORY.makeZero(tmpRowDim, 1);
for (int i = 0; i < tmpRowDim; i++) {
ComplexNumber tmpX = ComplexNumber.ONE;
final ComplexNumber tmpXfactor = ComplexNumber.valueOf((Number) x.get(i));
final ComplexNumber tmpY = ComplexNumber.valueOf((Number) y.get(i));
for (int j = 0; j < tmpColDim; j++) {
tmpBody.set(i, j, tmpX);
tmpX = tmpX.multiply(tmpXfactor);
}
tmpRHS.set(i, 0, tmpY);
}
final QR<ComplexNumber> tmpQR = QR.makeComplex();
tmpQR.decompose(tmpBody);
this.set(tmpQR.solve(tmpRHS));
}
public ComplexNumber invoke(final ComplexNumber arg) {
int tmpPower = this.degree();
ComplexNumber retVal = this.get(tmpPower);
while (--tmpPower >= 0) {
retVal = this.get(tmpPower).add(arg.multiply(retVal));
}
return retVal;
}
@Override
protected Rotation<ComplexNumber>[] rotations(
final PhysicalStore<ComplexNumber> aStore,
final int aLowInd,
final int aHighInd,
final Rotation<ComplexNumber>[] retVal) {
final ComplexNumber a00 = aStore.get(aLowInd, aLowInd);
final ComplexNumber a01 = aStore.get(aLowInd, aHighInd);
final ComplexNumber a10 = aStore.get(aHighInd, aLowInd);
final ComplexNumber a11 = aStore.get(aHighInd, aHighInd);
final ComplexNumber x = a00.add(a11);
final ComplexNumber y = a10.subtract(a01);
ComplexNumber t; // tan, cot or something temporary
// Symmetrise - Givens
final ComplexNumber cg; // cos Givens
final ComplexNumber sg; // sin Givens
if (ComplexNumber.isSmall(PrimitiveMath.ONE, y)) {
cg = x.signum();
sg = ComplexNumber.ZERO;
} else if (ComplexNumber.isSmall(PrimitiveMath.ONE, x)) {
sg = y.signum();
cg = ComplexNumber.ZERO;
} else if (y.compareTo(x) == 1) {
t = x.divide(y); // cot
sg = y.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
cg = sg.multiply(t);
} else {
t = y.divide(x); // tan
cg = x.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
sg = cg.multiply(t);
}
final ComplexNumber b00 = cg.multiply(a00).add(sg.multiply(a10));
final ComplexNumber b11 = cg.multiply(a11).subtract(sg.multiply(a01));
final ComplexNumber b2 =
cg.multiply(a01.add(a10)).add(sg.multiply(a11.subtract(a00))); // b01 + b10
t = b11.subtract(b00).divide(b2);
t = t.signum().divide(ComplexFunction.SQRT1PX2.invoke(t).add(t.norm()));
// Annihilate - Jacobi
final ComplexNumber cj = ComplexFunction.SQRT1PX2.invoke(t).invert(); // Cos Jacobi
final ComplexNumber sj = cj.multiply(t); // Sin Jacobi
retVal[1] = new Rotation.Complex(aLowInd, aHighInd, cj, sj); // Jacobi
retVal[0] =
new Rotation.Complex(
aLowInd,
aHighInd,
cj.multiply(cg).add(sj.multiply(sg)),
cj.multiply(sg).subtract(sj.multiply(cg))); // Givens - Jacobi
return retVal;
}