EigenvalueDecomposition(
Matrix Arg
)
{
double[][] A = Arg;
n = Arg.ColumnCount;
V = Matrix.CreateMatrixData(n, n);
d = new double[n];
e = new double[n];
isSymmetric = true;
for (int j = 0; (j < n) & isSymmetric; j++)
{
for (int i = 0; (i < n) & isSymmetric; i++)
{
isSymmetric &= (A[i][j] == A[j][i]);
}
}
if (isSymmetric)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
V[i][j] = A[i][j];
}
}
SymmetricTridiagonalize();
SymmetricDiagonalize();
}
else
{
H = new double[n][];
for (int i = 0; i < n; i++)
{
double[] Hi = new double[n];
double[] Ai = A[i];
for (int j = 0; j < n; j++)
{
Hi[j] = Ai[j];
}
H[i] = Hi;
}
NonsymmetricReduceToHessenberg();
NonsymmetricReduceHessenberToRealSchur();
}
_eigenValuesReal = new Vector(d);
_eigenValuesImag = new Vector(e);
_eigenValues = ComplexVector.Create(d, e);
InitOnDemandComputations();
}
EigenvalueDecomposition(
double[] d,
double[] e)
{
/* TODO: unit test missing for EigenvalueDecomposition constructor. */
_n = d.Length;
_v = Matrix.CreateMatrixData(_n, _n);
_d = new double[_n];
Array.Copy(d, 0, _d, 0, _n);
_e = new double[_n];
Array.Copy(e, 0, _e, 1, _n - 1);
for (int i = 0; i < _n; i++)
{
_v[i][i] = 1;
}
SymmetricDiagonalize();
_eigenValuesReal = new Vector(_d);
_eigenValuesImag = new Vector(_e);
_eigenValues = ComplexVector.Create(_d, _e);
InitOnDemandComputations();
}
AlmostEqual(
ComplexVector u,
ComplexVector v,
double maximumRelativeError)
{
return(Number.AlmostEqual(u, v, maximumRelativeError));
}
EigenvalueDecomposition(
double[] d,
double[] e
)
{
// TODO: unit test missing for EigenvalueDecomposition constructor.
n = d.Length;
V = Matrix.CreateMatrixData(n, n);
this.d = new double[n];
Array.Copy(d, 0, this.d, 0, n);
this.e = new double[n];
Array.Copy(e, 0, this.e, 1, n - 1);
for (int i = 0; i < n; i++)
{
V[i][i] = 1;
}
SymmetricDiagonalize();
_eigenValuesReal = new Vector(this.d);
_eigenValuesImag = new Vector(this.e);
_eigenValues = ComplexVector.Create(this.d, this.e);
InitOnDemandComputations();
}
EigenvalueDecomposition(Matrix arg)
{
double[][] a = arg;
_n = arg.ColumnCount;
_v = Matrix.CreateMatrixData(_n, _n);
_d = new double[_n];
_e = new double[_n];
_isSymmetric = true;
for (int j = 0; (j < _n) & _isSymmetric; j++)
{
for (int i = 0; (i < _n) & _isSymmetric; i++)
{
_isSymmetric &= (a[i][j] == a[j][i]);
}
}
if (_isSymmetric)
{
for (int i = 0; i < _n; i++)
{
for (int j = 0; j < _n; j++)
{
_v[i][j] = a[i][j];
}
}
SymmetricTridiagonalize();
SymmetricDiagonalize();
}
else
{
_h = new double[_n][];
for (int i = 0; i < _n; i++)
{
double[] hi = new double[_n];
double[] ai = a[i];
for (int j = 0; j < _n; j++)
{
hi[j] = ai[j];
}
_h[i] = hi;
}
NonsymmetricReduceToHessenberg();
NonsymmetricReduceHessenberToRealSchur();
}
_eigenValuesReal = new Vector(_d);
_eigenValuesImag = new Vector(_e);
_eigenValues = ComplexVector.Create(_d, _e);
InitOnDemandComputations();
}
AlmostEquals(ComplexVector other)
{
if (ReferenceEquals(other, null) ||
_length != other.Length)
{
return(false);
}
return(Number.AlmostEqualNorm(Norm1(), other.Norm1(), (this - other).Norm1()));
}
AlmostEquals(
ComplexVector other,
double maximumRelativeError)
{
if (ReferenceEquals(other, null) ||
_length != other.Length)
{
return(false);
}
return(Number.AlmostEqualNorm(Norm1(), other.Norm1(), (this - other).Norm1(), maximumRelativeError));
}
CrossProduct(
IVector <Complex> u,
IVector <Complex> v)
{
CheckMatchingVectorDimensions(u, v);
if (3 != u.Length)
{
throw new ArgumentOutOfRangeException("u", Properties.LocalStrings.ArgumentVectorThreeDimensional);
}
ComplexVector product = new ComplexVector(new Complex[] {
(u[1] * v[2]) - (u[2] * v[1]),
(u[2] * v[0]) - (u[0] * v[2]),
(u[0] * v[1]) - (u[1] * v[0])
});
return(product);
}
CrossProduct(
IVector <Complex> u,
IVector <Complex> v
)
{
CheckMatchingVectorDimensions(u, v);
if (3 != u.Length)
{
throw new ArgumentOutOfRangeException("u", Resources.ArgumentVectorThreeDimensional);
}
ComplexVector product = new ComplexVector(new Complex[] {
u[1] * v[2] - u[2] * v[1],
u[2] * v[0] - u[0] * v[2],
u[0] * v[1] - u[1] * v[0]
});
return(product);
}
Equals(ComplexVector other)
{
if (ReferenceEquals(other, null) ||
_length != other.Length)
{
return(false);
}
// compare all values
Complex[] otherData = other._data;
for (int i = 0; i < _data.Length; i++)
{
if (!_data[i].Equals(otherData[i]))
{
return(false);
}
}
return(true);
}
AlmostEqual(
ComplexVector u,
ComplexVector v)
{
return(Number.AlmostEqual(u, v));
}
Equals(object obj)
{
ComplexVector v = obj as ComplexVector;
return(ReferenceEquals(v, null) ? false : Equals(v));
}
