/// <summary>
/// Multiplies two maricies together
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns>The product of the matrices</returns>
public static Matrix Multiply(this Matrix A, Matrix B)
{
var matrix = new Matrix(A.Rows, B.Columns);
for (int i = 0; i < A.Rows; i++)
{
for (int j = 0; j < B.Columns; j++)
{
matrix[i, j] = DotProduct(A.GetRow(i), B.GetColumn(j));
}
}
/*
* for (int i = 0; i < A.Rows; i++)
* {
* for (int k = 0; k < A.Columns; k++)
* {
* for (int j = 0; j < B.Columns; j++)
* {
* array[i * A.Columns + j] += A.internalArray[i * A.Columns + k]
* B.internalArray[k * B.Columns + j];
* }
* }
* } */
return(matrix);
}
public static Matrix MultiplyMatrices(Matrix matrix1, Matrix matrix2)
{
int matrix1ColumnsCount = matrix1.GetColumnsCount();
int matrix2RowsCount = matrix2.GetRowsCount();
if (matrix1ColumnsCount != matrix2RowsCount)
{
throw new ArgumentException($"Матрицы {nameof(matrix1)} и {nameof(matrix2)} не согласованы.", nameof(matrix2));
}
int matrix1RowsCount = matrix1.GetRowsCount();
int matrix2ColumnsCount = matrix2.GetColumnsCount();
Matrix newMatrix = new Matrix(matrix2ColumnsCount, matrix1RowsCount);
for (int i = 0; i < matrix1RowsCount; i++)
{
for (int j = 0; j < matrix2ColumnsCount; j++)
{
newMatrix.rows[i].SetComponent(j, Vector.MultiplyVectors(matrix1.rows[i], matrix2.GetColumn(j)));
}
}
return(newMatrix);
}
static void Main(string[] args)
{
Matrix matrix1 = new Matrix(5, 7);
Matrix matrix2 = new Matrix(matrix1);
Matrix matrix3 = new Matrix(new double[, ] {
{ 5, 6 }, { 3, 2 }, { 5, 6 }
});
Matrix matrix4 = new Matrix(new Vector[] { new Vector(new double[] { 5.6, 6.4 }),
new Vector(new double[] { 3.7, 6.5, 7.8 }) });
Matrix matrix5 = new Matrix(matrix4);
Console.WriteLine("Размер матрицы {0} = {1} на {2}", matrix1, matrix1.GetColumnsCount(), matrix1.GetRowsCount());
Console.WriteLine();
Console.WriteLine("Размер матрицы {0} = {1} на {2}", matrix2, matrix2.GetColumnsCount(), matrix2.GetRowsCount());
Console.WriteLine();
Console.WriteLine("Размер матрицы {0} = {1} на {2}", matrix3, matrix3.GetColumnsCount(), matrix3.GetRowsCount());
Console.WriteLine();
Console.WriteLine("Размер матрицы {0} = {1} на {2}", matrix4, matrix4.GetColumnsCount(), matrix4.GetRowsCount());
Console.WriteLine();
Console.WriteLine();
int index = 1;
Console.WriteLine("Горизонтальный вектор номер {0} = {1}", index, matrix3.GetRow(index));
Console.WriteLine();
matrix3.SetRow(1, new Vector(new double[] { 2, 3 }));
Console.WriteLine("Теперь горизонтальный вектор номер {0} = {1}", index, matrix3.GetRow(index));
Console.WriteLine();
Console.WriteLine("Вертикальный вектор номер {0} = {1}", index, matrix3.GetColumn(index));
Console.WriteLine();
Console.WriteLine();
Console.Write("Результат транспонирования матрицы {0} = ", matrix4);
matrix4.Transpose();
Console.WriteLine(matrix4);
Console.WriteLine();
Console.Write("Результат умножения матрицы {0} на 10 = ", matrix3);
matrix3.MultiplyByScalar(10);
Console.WriteLine(matrix3);
Console.WriteLine();
Matrix matrix6 = new Matrix(new double[, ] {
{ 5, 6 }, { 3, 2 }
});
Console.WriteLine("Определитель матрицы {0} = {1}", matrix6, matrix6.GetDeterminant());
Console.WriteLine();
Vector vector = new Vector(new double[] { -1, -10 });
Console.Write("Результат умножения матрицы {0} на вектор {1} = {2}", matrix3, vector, matrix3.MultiplyByVector(vector));
Console.WriteLine();
Console.Write("Результат сложения матриц {0} и {1} = ", matrix3, matrix4);
matrix3.AddMatrix(matrix4);
Console.WriteLine(matrix3);
Console.WriteLine();
Console.Write("Разность матриц {0} и {1} = ", matrix3, matrix4);
matrix3.SubtractMatrix(matrix4);
Console.WriteLine(matrix3);
Console.WriteLine();
Console.WriteLine("Результат сложения матриц {0} и {1} = {2}", matrix4, matrix3, Matrix.AddMatrices(matrix4, matrix3));
Console.WriteLine();
Console.WriteLine("Разность матриц {0} и {1} = {2}", matrix4, matrix3, Matrix.SubtractMatrices(matrix4, matrix3));
Console.WriteLine();
Console.WriteLine("Результат умножения матриц {0} и {1} = {2}", matrix6, matrix5, Matrix.MultiplyMatrices(matrix6, matrix5));
Console.ReadKey();
}
/// <summary>
/// Performs gaussian elimination on the given matrix.
/// </summary>
/// <param name="matrix"></param>
/// <returns></returns>
public static Matrix GaussianElimination(Matrix matrix)
{
// Derived from ref [1] Theorem 3.5
// identify the row with the first non zero element
int nonZeroRowIndex = 0;
bool run = true;
int nonZeroColumnIndex = 0;
while (run && nonZeroColumnIndex < matrix.Columns)
{
// Check if columns has non-zero entry
var col = matrix.GetColumn(nonZeroColumnIndex);
for (int j = 0; j < col.Length; j++)
{
if (Math.Abs(col[j]) > TOLERANCE)
{
nonZeroRowIndex = j;
run = false;
break;
}
}
if (run)
{
nonZeroColumnIndex++;
}
}
// Move this row into the top position
if (nonZeroRowIndex != 0)
{
matrix = SwapRows(matrix, nonZeroRowIndex, 0);
}
// If the first non zero row does not equal 1 then normalize the
if (Math.Abs(matrix[0, nonZeroColumnIndex] - 1.0) > TOLERANCE)
{
matrix = MultiplyRowByScalar(matrix, 0, 1.0 / matrix[0, nonZeroColumnIndex]);
}
int iMax = Math.Min(matrix.Columns, matrix.Rows);
// Zero-wise columns
for (int i = 0, currentCol = 0; i < iMax && currentCol < matrix.Columns; i++, currentCol++)
{
var currentStartElement = matrix[i, currentCol];
if (Math.Abs(currentStartElement) > TOLERANCE)
{
for (int j = i + 1; j < iMax; j++)
{
var modifiedRow =
matrix.GetRow(i)
.Select(m => - 1 * m * (matrix[j, currentCol] / currentStartElement))
.ToArray();
matrix = AddRows(matrix, modifiedRow, j);
}
}
else
{
i--; // The test element was zero, do not increment the row
}
}
return(matrix);
}
