void OnStart()
{
matrix matrix_a =
{
{-3.474589, 1.106384, -9.091977,-3.925227 },
{-5.522139, 2.366887,-15.162351,-6.357512 },
{ 8.394926,-2.960067, 22.292115, 9.524129 },
{ 7.803242,-2.080287, 19.217706, 8.186645 }
};
matrix eigen_vectors;
vector eigen_values;
bool res=matrix_a.Eig(eigen_vectors, eigen_values);
Print("res=",res," error=",GetLastError());
Print("Eigen vectors:\n",eigen_vectors, "\nEigen Values:\n",eigen_values);
//--- 正しさを確認 A * v = lambda * v
int vectors=0;
for(ulong n=0; n<eigen_values.Size(); n++)
{
vector eigen_vector=eigen_vectors.Col(n);
vector vector_d1 =eigen_vector*eigen_values[n];
vector vector_d2 =matrix_a.MatMul(eigen_vector);
ulong errors=vector_d1.Compare(vector_d2,1e-13);
if(errors==0)
vectors++;
}
Print("vectors=",vectors);
//--- 複素数解
matrix<complex> eigen_vectors_c;
vector<complex> eigen_values_c;
ResetLastError();
res=matrix_a.Eig(eigen_vectors_c,eigen_values_c);
Print("res=",res," error=",GetLastError());
Print("Eigen vectors:\n",eigen_vectors_c, "\nEigen Values:\n",eigen_values_c);
//--- 正しさを確認 A * v = lambda * v
matrixc matrix_c;
matrix_c.Assign(matrix_a);
vectors=0;
for(ulong n=0; n<eigen_values_c.Size(); n++)
{
vectorc eigen_vector_c=eigen_vectors_c.Col(n);
vectorc vector_c1 =eigen_vector_c*eigen_values_c[n];
vectorc vector_c2 =matrix_c.MatMul(eigen_vector_c);
ulong errors=vector_c1.Compare(vector_c2,1e-13);
if(errors==0)
vectors++;
}
Print("vectors=",vectors);
}
/* Result
res=true error=4019
Eigen vectors:
[[0.2649667608713664]
[0.4488818803991876]
[-0.6527335897527492]
[-0.5497604331807768]]
Eigen Values:
[28.94158645962942]
vectors=1
res=true error=0
Eigen vectors:
[[(0.2649667608713664,0),(0.2227392219204762,0.3745470492013296),(0.403285439089771,-0.1345146135716524),(-0.2050778513598178,0)]
[(0.4488818803991876,0),(-0.2613452530342438,-0.3685707727819327),(-0.3968506126372395,0.5257002255533059),(0.8014703373356256,0)]
[(-0.6527335897527492,0),(-0.3418479634708521,-0.3299830378162041),(-0.3553021031180292,-0.03685418759727989),(-0.05618703726964112,0)]
[(-0.5497604331807768,0),(0.523227993452828,0.3262508584080381),(0.3512835596143666,0.3666300350184092),(0.558955624442244,0)]]
Eigen Values:
[(28.94158645962942,0),(0.01022501104810897,0.02954980822331488),(0.01022501104810897,-0.02954980822331488),(0.4090215182743634,0)]
vectors=3
*/
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