Example #1
0
		public static Vector operator -(Vector vector, double val)
		{
			if (!vector.IsValid())
				throw new ApplicationException("Vector is not initialized");
			Vector vector1 = new Vector(vector.nrows);
			for (int index = 0; index < vector.nrows; ++index)
				vector1[index] = vector[index] - val;
			return vector1;
		}
Example #2
0
		public static bool AreCompatible(Vector v1, Vector v2)
		{
			if (!v1.IsValid())
			{
				throw new ArgumentException("Vector 1 is not initialized");
			}
			if (!v2.IsValid())
			{
				throw new ArgumentException("Vector 2 is not initialized");
			}
			return v1.fNRows == v2.fNRows;
		}
Example #3
0
		public void MakeTridiagonal(Matrix a, Vector d, Vector e)
		{
			int num1 = a.rows;
			if (a.rows != a.cols)
				throw new ApplicationException("Matrix to tridiagonalize must be square");
			if (!a.IsSymmetric)
				throw new ApplicationException("Can only tridiagonalise symmetric matrix");
			double[] numArray = new double[this.M * this.N];
			for (int index = 0; index < this.M * this.N; ++index)
				numArray[index] = a.Elements[index / this.M, index % this.N];
			double[] elements1 = d.Elements;
			double[] 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(numArray[index1 + index2 * num1]);
					if (num3 == 0.0)
					{
						elements2[index1] = numArray[index1 + num2 * num1];
					}
					else
					{
						for (int index2 = 0; index2 <= num2; ++index2)
						{
							numArray[index1 + index2 * num1] /= num3;
							d1 += numArray[index1 + index2 * num1] * numArray[index1 + index2 * num1];
						}
						double num4 = numArray[index1 + num2 * num1];
						double num5 = num4 < 0.0 ? Math.Sqrt(d1) : -Math.Sqrt(d1);
						elements2[index1] = num3 * num5;
						d1 -= num4 * num5;
						numArray[index1 + num2 * num1] = num4 - num5;
						double num6 = 0.0;
						for (int index2 = 0; index2 <= num2; ++index2)
						{
							numArray[index2 + index1 * num1] = numArray[index1 + index2 * num1] / d1;
							double num7 = 0.0;
							for (int index3 = 0; index3 <= index2; ++index3)
								num7 += numArray[index2 + index3 * num1] * numArray[index1 + index3 * num1];
							for (int index3 = index2 + 1; index3 <= num2; ++index3)
								num7 += numArray[index3 + index2 * num1] * numArray[index1 + index3 * num1];
							elements2[index2] = num7 / d1;
							num6 += elements2[index2] * numArray[index1 + index2 * num1];
						}
						double num8 = num6 / (d1 + d1);
						for (int index2 = 0; index2 <= num2; ++index2)
						{
							double num7 = numArray[index1 + index2 * num1];
							double num9;
							elements2[index2] = num9 = elements2[index2] - num8 * num7;
							for (int index3 = 0; index3 <= index2; ++index3)
								numArray[index2 + index3 * num1] -= num7 * elements2[index3] + num9 * numArray[index1 + index3 * num1];
						}
					}
				}
				else
					elements2[index1] = numArray[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 += numArray[index1 + index3 * num1] * numArray[index3 + index2 * num1];
						for (int index3 = 0; index3 <= num2; ++index3)
							numArray[index3 + index2 * num1] -= num3 * numArray[index3 + index1 * num1];
					}
				}
				elements1[index1] = numArray[index1 + index1 * num1];
				numArray[index1 + index1 * num1] = 1.0;
				for (int index2 = 0; index2 <= num2; ++index2)
					numArray[index2 + index1 * num1] = numArray[index1 + index2 * num1] = 0.0;
			}
			for (int index = 0; index < this.M * this.N; ++index)
				a.Elements[index / this.M, index % this.N] = numArray[index];
		}
Example #4
0
		public Matrix EigenVectors(Vector eigenValues)
		{
			if (!this.IsSymmetric)
				throw new ApplicationException("Not yet implemented for non-symmetric matrix");
			Matrix 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);
			Vector e = new Vector(this.Rows);
			this.MakeTridiagonal(matrix, eigenValues, e);
			this.MakeEigenVectors(eigenValues, e, matrix);
			this.EigenSort(matrix, eigenValues);
			return matrix;
		}
Example #5
0
		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];
		}
Example #6
0
		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)
						{
							this.Error("MakeEigenVectors", "too many iterationsn");
							return;
						}
						else
						{
							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)
								{
									elements1[index3 + 1] -= num7;
									elements2[index2] = 0.0;
									break;
								}
								else
								{
									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;
									}
								}
							}
							if (num3 != 0.0 || index3 < index1)
							{
								elements1[index1] -= num7;
								elements2[index1] = num4;
								elements2[index2] = 0.0;
							}
						}
					}
				}
				while (index2 != index1);
			}
			for (int index = 0; index < rows * rows; ++index)
				z.Elements[index / rows, index % rows] = numArray[index];
		}
Example #7
0
		public static Vector operator +(Vector target, Vector source)
		{
			if (!source.IsValid())
				throw new ApplicationException("Source vector is not initialized");
			if (!target.IsValid())
				throw new ApplicationException("Target vector is not initialized");
			if (!Vector.AreCompatible(target, source))
				throw new ApplicationException("Vectors are not compatible");
			Vector vector = new Vector(target.nrows);
			for (int index = 0; index < target.nrows; ++index)
				vector[index] = target[index] + source[index];
			return vector;
		}
Example #8
0
		public Vector Sqrt()
		{
			if (!this.IsValid())
				throw new ApplicationException("Vector is not initialized");
			Vector vector = new Vector(this.nrows);
			for (int index = 0; index < this.nrows; ++index)
				vector[index] = Math.Sqrt(this.elements[index]);
			return vector;
		}
Example #9
0
		public void MakeTridiagonal(Matrix a, Vector d, Vector e)
		{
			int num = a.fRows;
			if (a.fRows != a.fCols)
			{
				throw new ApplicationException("Matrix to tridiagonalize must be square");
			}
			if (!a.IsSymmetric)
			{
				throw new ApplicationException("Can only tridiagonalise symmetric matrix");
			}
			double[] array = new double[this.M * this.N];
			for (int i = 0; i < this.M * this.N; i++)
			{
				array[i] = a.Elements[i / this.M, i % this.N];
			}
			double[] elements = d.Elements;
			double[] elements2 = e.Elements;
			for (int j = num - 1; j > 0; j--)
			{
				int num2 = j - 1;
				double num3 = 0.0;
				double num4 = 0.0;
				if (num2 > 0)
				{
					for (int k = 0; k <= num2; k++)
					{
						num4 += Math.Abs(array[j + k * num]);
					}
					if (num4 == 0.0)
					{
						elements2[j] = array[j + num2 * num];
					}
					else
					{
						for (int l = 0; l <= num2; l++)
						{
							array[j + l * num] /= num4;
							num3 += array[j + l * num] * array[j + l * num];
						}
						double num5 = array[j + num2 * num];
						double num6;
						if (num5 >= 0.0)
						{
							num6 = -Math.Sqrt(num3);
						}
						else
						{
							num6 = Math.Sqrt(num3);
						}
						elements2[j] = num4 * num6;
						num3 -= num5 * num6;
						array[j + num2 * num] = num5 - num6;
						num5 = 0.0;
						for (int m = 0; m <= num2; m++)
						{
							array[m + j * num] = array[j + m * num] / num3;
							num6 = 0.0;
							for (int l = 0; l <= m; l++)
							{
								num6 += array[m + l * num] * array[j + l * num];
							}
							for (int l = m + 1; l <= num2; l++)
							{
								num6 += array[l + m * num] * array[j + l * num];
							}
							elements2[m] = num6 / num3;
							num5 += elements2[m] * array[j + m * num];
						}
						double num7 = num5 / (num3 + num3);
						for (int m = 0; m <= num2; m++)
						{
							num5 = array[j + m * num];
							num6 = (elements2[m] -= num7 * num5);
							for (int l = 0; l <= m; l++)
							{
								array[m + l * num] -= num5 * elements2[l] + num6 * array[j + l * num];
							}
						}
					}
				}
				else
				{
					elements2[j] = array[j + num2 * num];
				}
				elements[j] = num3;
			}
			elements[0] = 0.0;
			elements2[0] = 0.0;
			for (int j = 0; j < num; j++)
			{
				int num8 = j - 1;
				if (elements[j] != 0.0)
				{
					for (int n = 0; n <= num8; n++)
					{
						double num9 = 0.0;
						for (int num10 = 0; num10 <= num8; num10++)
						{
							num9 += array[j + num10 * num] * array[num10 + n * num];
						}
						for (int num10 = 0; num10 <= num8; num10++)
						{
							array[num10 + n * num] -= num9 * array[num10 + j * num];
						}
					}
				}
				elements[j] = array[j + j * num];
				array[j + j * num] = 1.0;
				for (int num11 = 0; num11 <= num8; num11++)
				{
					array[num11 + j * num] = (array[j + num11 * num] = 0.0);
				}
			}
			for (int num12 = 0; num12 < this.M * this.N; num12++)
			{
				a.Elements[num12 / this.M, num12 % this.N] = array[num12];
			}
		}
Example #10
0
		public Matrix EigenVectors(Vector eigenValues)
		{
			if (this.IsSymmetric)
			{
				Matrix matrix = new Matrix(this.Rows, this.Cols);
				for (int i = 0; i < this.Rows; i++)
				{
					for (int j = 0; j < this.Cols; j++)
					{
						matrix[i, j] = this[i, j];
					}
				}
				eigenValues.ResizeTo(this.Rows);
				Vector e = new Vector(this.Rows);
				this.MakeTridiagonal(matrix, eigenValues, e);
				this.MakeEigenVectors(eigenValues, e, matrix);
				this.EigenSort(matrix, eigenValues);
				return matrix;
			}
			throw new ApplicationException("Not yet implemented for non-symmetric matrix");
		}
Example #11
0
		public void EigenSort(Matrix eigenVectors, Vector eigenValues)
		{
			int rows = eigenVectors.Rows;
			double[] array = new double[rows * rows];
			for (int i = 0; i < rows * rows; i++)
			{
				array[i] = eigenVectors.Elements[i / rows, i % rows];
			}
			double[] elements = eigenValues.Elements;
			for (int j = 0; j < rows; j++)
			{
				int num = j;
				double num2 = elements[j];
				for (int k = j + 1; k < rows; k++)
				{
					if (elements[k] >= num2)
					{
						num = k;
						num2 = elements[k];
					}
				}
				if (num != j)
				{
					elements[num] = elements[j];
					elements[j] = num2;
					for (int k = 0; k < rows; k++)
					{
						num2 = array[k + j * rows];
						array[k + j * rows] = array[k + num * rows];
						array[k + num * rows] = num2;
					}
				}
			}
			for (int l = 0; l < rows * rows; l++)
			{
				eigenVectors.Elements[l / rows, l % rows] = array[l];
			}
		}
Example #12
0
		public void MakeEigenVectors(Vector d, Vector e, Matrix z)
		{
			int rows = z.Rows;
			double[] elements = d.Elements;
			double[] elements2 = e.Elements;
			double[] array = new double[rows * rows];
			for (int i = 0; i < rows * rows; i++)
			{
				array[i] = z.Elements[i / rows, i % rows];
			}
			int j;
			for (j = 1; j < rows; j++)
			{
				elements2[j - 1] = elements2[j];
			}
			elements2[rows - 1] = 0.0;
			j = 0;
			while (j < rows)
			{
				int num = 0;
				int k;
				do
				{
					for (k = j; k < rows - 1; k++)
					{
						double num2 = Math.Abs(elements[k]) + Math.Abs(elements[k + 1]);
						if (Math.Abs(elements2[k]) + num2 == num2)
						{
							break;
						}
					}
					if (k != j)
					{
						if (num++ == 30)
						{
							goto Block_5;
						}
						double num3 = (elements[j + 1] - elements[j]) / (2.0 * elements2[j]);
						double num4 = Math.Sqrt(num3 * num3 + 1.0);
						num3 = elements[k] - elements[j] + elements2[j] / (num3 + ((num3 >= 0.0) ? Math.Abs(num4) : (-Math.Abs(num4))));
						double num5 = 1.0;
						double num6 = 1.0;
						double num7 = 0.0;
						int l;
						for (l = k - 1; l >= j; l--)
						{
							double num8 = num5 * elements2[l];
							double num9 = num6 * elements2[l];
							num4 = Math.Sqrt(num8 * num8 + num3 * num3);
							elements2[l + 1] = num4;
							if (num4 == 0.0)
							{
								elements[l + 1] -= num7;
								elements2[k] = 0.0;
								break;
							}
							num5 = num8 / num4;
							num6 = num3 / num4;
							num3 = elements[l + 1] - num7;
							num4 = (elements[l] - num3) * num5 + 2.0 * num6 * num9;
							num7 = num5 * num4;
							elements[l + 1] = num3 + num7;
							num3 = num6 * num4 - num9;
							for (int m = 0; m < rows; m++)
							{
								num8 = array[m + (l + 1) * rows];
								array[m + (l + 1) * rows] = num5 * array[m + l * rows] + num6 * num8;
								array[m + l * rows] = num6 * array[m + l * rows] - num5 * num8;
							}
						}
						if (num4 != 0.0 || l < j)
						{
							elements[j] -= num7;
							elements2[j] = num3;
							elements2[k] = 0.0;
						}
					}
				}
				while (k != j);
				j++;
				continue;
				Block_5:
				this.Error("MakeEigenVectors", "too many iterationsn");
				return;
			}
			for (int n = 0; n < rows * rows; n++)
			{
				z.Elements[n / rows, n % rows] = array[n];
			}
		}
Example #13
0
		public Vector ElementDiv(Vector target, Vector source)
		{
			if (!source.IsValid())
			{
				throw new ApplicationException("Source vector is not initialized");
			}
			if (!target.IsValid())
			{
				throw new ApplicationException("Target vector is not initialized");
			}
			if (!Vector.AreCompatible(target, source))
			{
				throw new ApplicationException("Vectors are not compatible");
			}
			Vector vector = new Vector(target.fNRows);
			for (int i = 0; i < this.fNRows; i++)
			{
				vector[i] = target[i] / source[i];
			}
			return vector;
		}
Example #14
0
		public Vector Sqrt()
		{
			if (!this.IsValid())
			{
				throw new ApplicationException("Vector is not initialized");
			}
			Vector vector = new Vector(this.fNRows);
			for (int i = 0; i < this.fNRows; i++)
			{
				vector[i] = Math.Sqrt(this.fElements[i]);
			}
			return vector;
		}
Example #15
0
		public static Vector operator -(Vector vector, double val)
		{
			if (!vector.IsValid())
			{
				throw new ApplicationException("Vector is not initialized");
			}
			Vector vector2 = new Vector(vector.fNRows);
			for (int i = 0; i < vector.fNRows; i++)
			{
				vector2[i] = vector[i] - val;
			}
			return vector2;
		}