public TqrEigenDecomposition(Vector diag, Vector sub, EigenVectorCalculation calc = EigenVectorCalculation.WithEigenVector,
ShiftStrategy strategy = ShiftStrategy.CloseEigenValue)
{
iter_ = 0;
d_ = new Vector(diag);
int row = calc == EigenVectorCalculation.WithEigenVector ? d_.size() :
calc == EigenVectorCalculation.WithoutEigenVector ? 0 : 1;
ev_ = new Matrix(row, d_.size(), 0.0);
int n = diag.size();
Utils.QL_REQUIRE(n == sub.size() + 1, () => "Wrong dimensions");
Vector e = new Vector(n, 0.0);
int i;
for (i = 1; i < e.Count; ++i)
{
e[i] = sub[i - 1];
}
for (i = 0; i < ev_.rows(); ++i)
{
ev_[i, i] = 1.0;
}
for (int k = n - 1; k >= 1; --k)
{
while (!offDiagIsZero(k, e))
{
int l = k;
while (--l > 0 && !offDiagIsZero(l, e))
{
;
}
iter_++;
double q = d_[l];
if (strategy != ShiftStrategy.NoShift)
{
// calculated eigenvalue of 2x2 sub matrix of
// [ d_[k-1] e_[k] ]
// [ e_[k] d_[k] ]
// which is closer to d_[k+1].
// FLOATING_POINT_EXCEPTION
double t1 = Math.Sqrt(
0.25 * (d_[k] * d_[k] + d_[k - 1] * d_[k - 1])
- 0.5 * d_[k - 1] * d_[k] + e[k] * e[k]);
double t2 = 0.5 * (d_[k] + d_[k - 1]);
double lambda = (Math.Abs(t2 + t1 - d_[k]) < Math.Abs(t2 - t1 - d_[k]))?
t2 + t1 : t2 - t1;
if (strategy == ShiftStrategy.CloseEigenValue)
{
q -= lambda;
}
else
{
q -= ((k == n - 1) ? 1.25 : 1.0) * lambda;
}
}
// the QR transformation
double sine = 1.0;
double cosine = 1.0;
double u = 0.0;
bool recoverUnderflow = false;
for (i = l + 1; i <= k && !recoverUnderflow; ++i)
{
double h = cosine * e[i];
double p = sine * e[i];
e[i - 1] = Math.Sqrt(p * p + q * q);
if (e[i - 1].IsNotEqual(0.0))
{
sine = p / e[i - 1];
cosine = q / e[i - 1];
double g = d_[i - 1] - u;
double t = (d_[i] - g) * sine + 2 * cosine * h;
u = sine * t;
d_[i - 1] = g + u;
q = cosine * t - h;
for (int j = 0; j < ev_.rows(); ++j)
{
double tmp = ev_[j, i - 1];
ev_[j, i - 1] = sine * ev_[j, i] + cosine * tmp;
ev_[j, i] = cosine * ev_[j, i] - sine * tmp;
}
}
else
{
// recover from underflow
d_[i - 1] -= u;
e[l] = 0.0;
recoverUnderflow = true;
}
}
if (!recoverUnderflow)
{
d_[k] -= u;
e[k] = q;
e[l] = 0.0;
}
}
}
// sort (eigenvalues, eigenvectors),
// code taken from symmetricSchureDecomposition.cpp
List <KeyValuePair <double, List <double> > > temp = new InitializedList <KeyValuePair <double, List <double> > >(n);
List <double> eigenVector = new InitializedList <double>(ev_.rows());
for (i = 0; i < n; i++)
{
if (ev_.rows() > 0)
{
eigenVector = ev_.column(i);
}
temp[i] = new KeyValuePair <double, List <double> >(d_[i], eigenVector);
}
temp.Sort(KeyValuePairCompare);
// first element is positive
for (i = 0; i < n; i++)
{
d_[i] = temp[i].Key;
double sign = 1.0;
if (ev_.rows() > 0 && temp[i].Value[0] < 0.0)
{
sign = -1.0;
}
for (int j = 0; j < ev_.rows(); ++j)
{
ev_[j, i] = sign * temp[i].Value[j];
}
}
}
public TqrEigenDecomposition(Vector diag, Vector sub, EigenVectorCalculation calc = EigenVectorCalculation.WithEigenVector,
ShiftStrategy strategy = ShiftStrategy.CloseEigenValue)
{
iter_ = 0;
d_ = new Vector(diag);
int row = calc == EigenVectorCalculation.WithEigenVector ? d_.size() :
calc == EigenVectorCalculation.WithoutEigenVector ? 0 : 1;
ev_ = new Matrix(row, d_.size(), 0.0);
int n = diag.size();
Utils.QL_REQUIRE( n == sub.size() + 1, () => "Wrong dimensions" );
Vector e = new Vector(sub);
int i;
for (i=0; i < ev_.rows(); ++i)
{
ev_[i,i] = 1.0;
}
for (int k=n-1; k >=1; --k)
{
while (!offDiagIsZero(k, e))
{
int l = k;
while (--l > 0 && !offDiagIsZero(l,e));
iter_++;
double q = d_[l];
if (strategy != ShiftStrategy.NoShift)
{
// calculated eigenvalue of 2x2 sub matrix of
// [ d_[k-1] e_[k] ]
// [ e_[k] d_[k] ]
// which is closer to d_[k+1].
// FLOATING_POINT_EXCEPTION
double t1 = Math.Sqrt(
0.25*(d_[k]*d_[k] + d_[k-1]*d_[k-1])
- 0.5*d_[k-1]*d_[k] + e[k]*e[k]);
double t2 = 0.5*(d_[k]+d_[k-1]);
double lambda = (Math.Abs(t2+t1 - d_[k]) < Math.Abs(t2-t1 - d_[k]))?
t2+t1 : t2-t1;
if (strategy == ShiftStrategy.CloseEigenValue)
{
q-=lambda;
}
else
{
q-=((k==n-1)? 1.25 : 1.0)*lambda;
}
}
// the QR transformation
double sine = 1.0;
double cosine = 1.0;
double u = 0.0;
bool recoverUnderflow = false;
for (i=l+1; i <= k && !recoverUnderflow; ++i)
{
double h = cosine*e[i];
double p = sine*e[i];
e[i-1] = Math.Sqrt(p*p+q*q);
if (e[i-1] != 0.0) {
sine = p/e[i-1];
cosine = q/e[i-1];
double g = d_[i-1]-u;
double t = (d_[i]-g)*sine+2*cosine*h;
u = sine*t;
d_[i-1] = g + u;
q = cosine*t - h;
for (int j=0; j < ev_.rows(); ++j)
{
double tmp = ev_[j,i-1];
ev_[j,i-1] = sine*ev_[j,i] + cosine*tmp;
ev_[j,i] = cosine*ev_[j,i] - sine*tmp;
}
}
else
{
// recover from underflow
d_[i-1] -= u;
e[l] = 0.0;
recoverUnderflow = true;
}
}
if (!recoverUnderflow) {
d_[k] -= u;
e[k] = q;
e[l] = 0.0;
}
}
}
// sort (eigenvalues, eigenvectors),
// code taken from symmetricSchureDecomposition.cpp
List<KeyValuePair<double, List<double> > > temp = new List<KeyValuePair<double,List<double>>>(n);
List<double> eigenVector = new List<double>(ev_.rows());
for (i=0; i<n; i++)
{
if (ev_.rows() > 0)
//std::copy(ev_.column_begin(i),ev_.column_end(i), eigenVector.begin());
eigenVector = ev_.column(i) ;
temp[i] = new KeyValuePair<double,List<double>>(d_[i], eigenVector);
}
//std::sort(temp.begin(), temp.end(), std::greater<std::pair<Real, std::vector<Real> > >());
temp.Sort();
// first element is positive
for (i=0; i<n; i++) {
d_[i] = temp[i].Key;
double sign = 1.0;
if (ev_.rows() > 0 && temp[i].Value[0]<0.0)
sign = -1.0;
for (int j=0; j<ev_.rows(); ++j) {
ev_[j,i] = sign * temp[i].Value[j];
}
}
}
