public static Vector operator -(Vector vector, double val)
{
EnsureValid(vector);
var v = new Vector(vector.NRows);
Parallel.For(0, v.NRows, i => v[i] = vector[i] - val);
return v;
}
public static Vector operator +(Vector target, Vector source)
{
EnsureValid(source, "Source vector");
EnsureValid(target, "Target vector");
EnsureCompatible(target, source);
var v = new Vector(target.NRows);
Parallel.For(0, v.NRows, i => v[i] = target[i] + source[i]);
return v;
}
public static bool AreCompatible(Vector v1, Vector v2)
{
EnsureValid(v1, "Vector 1");
EnsureValid(v2, "Vector 2");
return v1.NRows == v2.NRows;
}
private static void EnsureValid(Vector v, string name = "Vector")
{
if (!v.IsValid())
throw new ArgumentException($"{name} is not initialized");
}
private static void EnsureCompatible(Vector v1, Vector v2)
{
if (!AreCompatible(v1, v2))
throw new ArgumentException("Vectors are not compatible");
}
public Vector Sqrt()
{
EnsureValid(this);
var v = new Vector(NRows);
Parallel.For(0, NRows, i => v[i] = Math.Sqrt(this.Elements[i]));
return v;
}
public Vector ElementDiv(Vector target, Vector source)
{
EnsureValid(source, "Source vector");
EnsureValid(target, "Target vector");
EnsureCompatible(target, source);
var v = new Vector(target.NRows);
Parallel.For(0, NRows, i => v[i] = target[i] / source[i]);
return v;
}
public Vector Sqr()
{
EnsureValid(this);
var v = new Vector(NRows);
Parallel.For(0, this.NRows, i => v[i] = this.Elements[i] * this.Elements[i]);
return v;
}
public void MakeTridiagonal(Matrix a, Vector d, Vector e)
{
int num1 = a.m;
if (a.m != a.n)
throw new ArgumentException("Matrix to tridiagonalize must be square");
if (!a.IsSymmetric)
throw new ArgumentException("Can only tridiagonalise symmetric matrix");
var numArray1 = new double[this.M * this.N];
for (int index = 0; index < this.M * this.N; ++index)
numArray1[index] = a.Elements[index / this.M, index % this.N];
var elements1 = d.Elements;
var elements2 = e.Elements;
for (int index1 = num1 - 1; index1 > 0; --index1)
{
int num2 = index1 - 1;
double d1 = 0.0;
double num3 = 0.0;
if (num2 > 0)
{
for (int index2 = 0; index2 <= num2; ++index2)
num3 += Math.Abs(numArray1[index1 + index2 * num1]);
if (num3 == 0.0)
{
elements2[index1] = numArray1[index1 + num2 * num1];
}
else
{
for (int index2 = 0; index2 <= num2; ++index2)
{
numArray1[index1 + index2 * num1] /= num3;
d1 += numArray1[index1 + index2 * num1] * numArray1[index1 + index2 * num1];
}
double num4 = numArray1[index1 + num2 * num1];
double num5 = num4 < 0.0 ? Math.Sqrt(d1) : -Math.Sqrt(d1);
elements2[index1] = num3 * num5;
d1 -= num4 * num5;
numArray1[index1 + num2 * num1] = num4 - num5;
double num6 = 0.0;
for (int index2 = 0; index2 <= num2; ++index2)
{
numArray1[index2 + index1 * num1] = numArray1[index1 + index2 * num1] / d1;
double num7 = 0.0;
for (int index3 = 0; index3 <= index2; ++index3)
num7 += numArray1[index2 + index3 * num1] * numArray1[index1 + index3 * num1];
for (int index3 = index2 + 1; index3 <= num2; ++index3)
num7 += numArray1[index3 + index2 * num1] * numArray1[index1 + index3 * num1];
elements2[index2] = num7 / d1;
num6 += elements2[index2] * numArray1[index1 + index2 * num1];
}
double num8 = num6 / (d1 + d1);
for (int index2 = 0; index2 <= num2; ++index2)
{
double num7 = numArray1[index1 + index2 * num1];
double num9;
elements2[index2] = num9 = elements2[index2] - num8 * num7;
for (int index3 = 0; index3 <= index2; ++index3)
numArray1[index2 + index3 * num1] -= num7 * elements2[index3] + num9 * numArray1[index1 + index3 * num1];
}
}
}
else
elements2[index1] = numArray1[index1 + num2 * num1];
elements1[index1] = d1;
}
elements1[0] = 0.0;
elements2[0] = 0.0;
for (int index1 = 0; index1 < num1; ++index1)
{
int num2 = index1 - 1;
if (elements1[index1] != 0.0)
{
for (int index2 = 0; index2 <= num2; ++index2)
{
double num3 = 0.0;
for (int index3 = 0; index3 <= num2; ++index3)
num3 += numArray1[index1 + index3 * num1] * numArray1[index3 + index2 * num1];
for (int index3 = 0; index3 <= num2; ++index3)
numArray1[index3 + index2 * num1] -= num3 * numArray1[index3 + index1 * num1];
}
}
elements1[index1] = numArray1[index1 + index1 * num1];
numArray1[index1 + index1 * num1] = 1.0;
for (int index2 = 0; index2 <= num2; ++index2)
{
double[] numArray2 = numArray1;
int index3 = index2 + index1 * num1;
double[] numArray3 = numArray1;
int index4 = index1 + index2 * num1;
double num3 = 0.0;
double num4 = 0.0;
numArray3[index4] = num3;
double num5 = num4;
numArray2[index3] = num5;
}
}
for (int index = 0; index < this.M * this.N; ++index)
a.Elements[index / this.M, index % this.N] = numArray1[index];
}
public Matrix EigenVectors(Vector eigenValues)
{
if (!this.IsSymmetric)
throw new NotImplementedException("Not yet implemented for non-symmetric matrix");
var matrix = new Matrix(this.Rows, this.Cols);
for (int index1 = 0; index1 < this.Rows; ++index1)
for (int index2 = 0; index2 < this.Cols; ++index2)
matrix[index1, index2] = this[index1, index2];
eigenValues.ResizeTo(this.Rows);
var e = new Vector(this.Rows);
MakeTridiagonal(matrix, eigenValues, e);
MakeEigenVectors(eigenValues, e, matrix);
EigenSort(matrix, eigenValues);
return matrix;
}
public void EigenSort(Matrix eigenVectors, Vector eigenValues)
{
int rows = eigenVectors.Rows;
double[] numArray = new double[rows * rows];
for (int index = 0; index < rows * rows; ++index)
numArray[index] = eigenVectors.Elements[index / rows, index % rows];
double[] elements = eigenValues.Elements;
for (int index1 = 0; index1 < rows; ++index1)
{
int index2 = index1;
double num1 = elements[index1];
for (int index3 = index1 + 1; index3 < rows; ++index3)
{
if (elements[index3] >= num1)
{
index2 = index3;
num1 = elements[index3];
}
}
if (index2 != index1)
{
elements[index2] = elements[index1];
elements[index1] = num1;
for (int index3 = 0; index3 < rows; ++index3)
{
double num2 = numArray[index3 + index1 * rows];
numArray[index3 + index1 * rows] = numArray[index3 + index2 * rows];
numArray[index3 + index2 * rows] = num2;
}
}
}
for (int index = 0; index < rows * rows; ++index)
eigenVectors.Elements[index / rows, index % rows] = numArray[index];
}
public void MakeEigenVectors(Vector d, Vector e, Matrix z)
{
int rows = z.Rows;
double[] elements1 = d.Elements;
double[] elements2 = e.Elements;
double[] numArray = new double[rows * rows];
for (int index = 0; index < rows * rows; ++index)
numArray[index] = z.Elements[index / rows, index % rows];
for (int index = 1; index < rows; ++index)
elements2[index - 1] = elements2[index];
elements2[rows - 1] = 0.0;
for (int index1 = 0; index1 < rows; ++index1)
{
int num1 = 0;
int index2;
do
{
for (index2 = index1; index2 < rows - 1; ++index2)
{
double num2 = Math.Abs(elements1[index2]) + Math.Abs(elements1[index2 + 1]);
if (Math.Abs(elements2[index2]) + num2 == num2)
break;
}
if (index2 != index1)
{
if (num1++ != 30)
{
double num2 = (elements1[index1 + 1] - elements1[index1]) / (2.0 * elements2[index1]);
double num3 = Math.Sqrt(num2 * num2 + 1.0);
double num4 = elements1[index2] - elements1[index1] + elements2[index1] / (num2 + (num2 >= 0.0 ? Math.Abs(num3) : -Math.Abs(num3)));
double num5 = 1.0;
double num6 = 1.0;
double num7 = 0.0;
int index3;
for (index3 = index2 - 1; index3 >= index1; --index3)
{
double num8 = num5 * elements2[index3];
double num9 = num6 * elements2[index3];
num3 = Math.Sqrt(num8 * num8 + num4 * num4);
elements2[index3 + 1] = num3;
if (num3 != 0.0)
{
num5 = num8 / num3;
num6 = num4 / num3;
double num10 = elements1[index3 + 1] - num7;
num3 = (elements1[index3] - num10) * num5 + 2.0 * num6 * num9;
num7 = num5 * num3;
elements1[index3 + 1] = num10 + num7;
num4 = num6 * num3 - num9;
for (int index4 = 0; index4 < rows; ++index4)
{
double num11 = numArray[index4 + (index3 + 1) * rows];
numArray[index4 + (index3 + 1) * rows] = num5 * numArray[index4 + index3 * rows] + num6 * num11;
numArray[index4 + index3 * rows] = num6 * numArray[index4 + index3 * rows] - num5 * num11;
}
}
else
{
elements1[index3 + 1] -= num7;
elements2[index2] = 0.0;
break;
}
}
if (num3 != 0.0 || index3 < index1)
{
elements1[index1] -= num7;
elements2[index1] = num4;
elements2[index2] = 0.0;
}
}
else
goto label_31;
}
}
while (index2 != index1);
continue;
label_31:
Error("MakeEigenVectors", "too many iterationsn");
return;
}
for (int index = 0; index < rows * rows; ++index)
z.Elements[index / rows, index % rows] = numArray[index];
}