make x column

2024-09-20 22:15:57 +03:00
parent 8e6024a01e
commit b073126348
4 changed files with 235 additions and 138 deletions
@@ -1,6 +1,7 @@
 # Prerequisites
 *.d
-
+CMakeLists.txt
+.idea
 # Compiled Object files
 *.slo
 *.lo
@@ -1,6 +1,18 @@
 #include <iostream>
+#include "tools/matrix.h"
+

 int main() {
-    std::cout << "Hello World!\n";
+    int n, m;
+    ColumnVector C(n);
+    Matrix A(n, m);
+    ColumnVector b(n);
+    double eps;
+    double eps_default;
+
+    std::cin >> C;
+    std::cin >> A;
+    std::cin >> b;
+    std::cin >> eps;
    return 0;
 }
@@ -1 +1,85 @@
-// implementation of simplex task
+#include <algorithm>
+#include <iostream>
+#include "tools/matrix.h"
+
+enum solver_state {
+	unbounded,
+	bounded
+};
+
+struct Result {
+	solver_state state;
+	ColumnVector *solution;
+	double objective_fucntion_value;
+};
+
+Result Simplex(ColumnVector C, Matrix A, ColumnVector b, double eps = 0.01, bool maximize) {
+	Result result;
+	std::vector<int> basicVars(A.getColumns() - A.getRows());
+	basicVars[0] = -1;
+
+	for (int i = 1; i < basicVars.size(); i++) {
+		basicVars[i] = static_cast<int>(basicVars.size()) + i;
+	}
+
+	int kc = 0;
+	double temp = A[0][0];
+	for (int j = 0; j< A.getColumns(); j++) {
+		if (A[0][j] < temp) {
+			temp = A[0][j];
+			kc = j;
+		}
+	}
+
+	if (A[0][kc] >= 0) {
+		result.state = unbounded;
+		result.solution = new ColumnVector(C.getRows());
+		for (int i = 0; i < C.getRows(); i++) {
+			result.solution->operator[](i) = 0;
+		}
+		for (int i = 1; i < basicVars.size(); i++) {
+			if (basicVars[i] <= C.getRows()) {
+				(*result.solution)[basicVars[i]] = b.getRows() - 1;
+			}
+		}
+		result.objective_fucntion_value = b[0];
+	}
+}
+
+/*
+Function_name(C, A, b, eps = eps_default)
+
+Input:
+- C: A vector of coefficients of the objective function
+- A: A matrix of coefficients of the constraint functions
+- b: A vector of right-hand side values
+- eps: Approximation accuracy (optional, default = eps_default)
+
+Steps:
+1. Print the optimization problem:
+   - max (or min) z = C[0] * x1 + C[1] * x2 + ... + C[n] * xn
+   - subject to the constraints:
+     - A[0] * x <= b[0]
+     - A[1] * x <= b[1]
+     - ...
+     - A[m] * x <= b[m]
+
+2. Initialize:
+   - Form the initial tableau by introducing slack variables to convert inequalities into equalities.
+
+3. Iteratively apply the Simplex method:
+   - Step 1: Identify the entering variable (most negative coefficient in the objective row).
+   - Step 2: Identify the leaving variable (smallest positive ratio of RHS to pivot column).
+   - Step 3: Perform pivot operations to update the tableau.
+
+4. Check for optimality or unboundedness:
+   - If all coefficients in the objective function row are non-negative, the solution is optimal.
+   - If no leaving variable exists, the problem is unbounded.
+
+5. Return:
+   - solver_state: {solved, unbounded}
+   - x*: Optimal vector of decision variables (if solved)
+   - z: Maximum (or minimum) value of the objective function (if solved)
+
+End Function
+*/
@@ -1,213 +1,213 @@
 #include "matrix.h"

 ColumnVector::ColumnVector(int n) {
-	rows = n;
-	columns = 1;
-	columnVector.resize(n);
+  rows = n;
+  columns = 1;
+  columnVector.resize(n);
 }

 ColumnVector::ColumnVector(const ColumnVector& other) {
-	rows = other.rows;
-	columns = other.columns;
-	columnVector = other.columnVector;
+  rows = other.rows;
+  columns = other.columns;
+  columnVector = other.columnVector;
 }

 int ColumnVector::getRows() const {
-	return rows;
+  return rows;
 }

 int ColumnVector::getColumns() const {
-	return columns;
+  return columns;
 }

 double& ColumnVector::operator[](int row) {
-	return columnVector[row];
+  return columnVector[row];
 }

 ColumnVector& ColumnVector::operator=(const ColumnVector& other) {
-	rows = other.rows;
-	columns = other.columns;
-	columnVector = other.columnVector;
-	return *this;
+  rows = other.rows;
+  columns = other.columns;
+  columnVector = other.columnVector;
+  return *this;
 }

 ColumnVector ColumnVector::operator+(ColumnVector& other) {
-	if (rows != other.rows) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
-	ColumnVector result(rows);
-	for (int i = 0; i < rows; ++i) {
-		result[i] = columnVector[i] + other[i];
-	}
+  if (rows != other.rows) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }
+  ColumnVector result(rows);
+  for (int i = 0; i < rows; ++i) {
+    result[i] = columnVector[i] + other[i];
+  }

-	return result;
+  return result;
 }

 ColumnVector ColumnVector::operator-(ColumnVector& other) {
-	if (rows != other.rows) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
-	ColumnVector result(rows);
-	for (int i = 0; i < rows; ++i) {
-		result[i] = columnVector[i] - other[i];
-	}
+  if (rows != other.rows) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }
+  ColumnVector result(rows);
+  for (int i = 0; i < rows; ++i) {
+    result[i] = columnVector[i] - other[i];
+  }

-	return result;
+  return result;
 }

 std::istream& operator>>(std::istream& cin, ColumnVector& vectorObj) {
-	for (int i = 0; i < vectorObj.rows; ++i) {
-		cin >> vectorObj[i];
-	}
-	return cin;
+  for (int i = 0; i < vectorObj.rows; ++i) {
+    cin >> vectorObj[i];
+  }
+  return cin;
 }

 std::ostream& operator<<(std::ostream& cout, ColumnVector& vectorObj) {
-	for (int i = 0; i < vectorObj.rows; ++i) {
-		if (i == vectorObj.rows - 1) {
-			cout << vectorObj[i] << std::endl;
-		}
-		else {
-			cout << vectorObj[i] << ' ';
-		}
-	}
-	return cout;
+  for (int i = 0; i < vectorObj.rows; ++i) {
+    if (i == vectorObj.rows - 1) {
+      cout << vectorObj[i] << std::endl;
+    }
+    else {
+      cout << vectorObj[i] << ' ';
+    }
+  }
+  return cout;
 }

 Matrix::Matrix(int n, int m) {
-	rows = n;
-	columns = m;
-	matrix.resize(n);
-	for (auto& row : matrix) {
-		row = ColumnVector(m);
-	}
+  rows = n;
+  columns = m;
+  matrix.resize(n);
+  for (auto& row : matrix) {
+    row = ColumnVector(m);
+  }
 }

 Matrix::Matrix(const Matrix& other) {
-	rows = other.rows;
-	columns = other.columns;
-	matrix = other.matrix;
+  rows = other.rows;
+  columns = other.columns;
+  matrix = other.matrix;
 }

 int Matrix::getRows() const {
-	return rows;
+  return rows;
 }

 int Matrix::getColumns() const {
-	return columns;
+  return columns;
 }

 ColumnVector& Matrix::operator[](int row) {
-	return matrix[row];
+  return matrix[row];
 }

 Matrix& Matrix::operator=(const Matrix& other) {
-	rows = other.rows;
-	columns = other.columns;
-	matrix = other.matrix;
-	return *this;
+  rows = other.rows;
+  columns = other.columns;
+  matrix = other.matrix;
+  return *this;
 }

 Matrix Matrix::operator+(Matrix& other) const {
-	if (rows != other.rows || columns != other.columns) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
-	Matrix result(rows, columns);
-	for (int i = 0; i < rows; ++i) {
-		for (int j = 0; j < columns; ++j) {
-			auto x = matrix[i];
-			auto y = other[i];
-			result[i][j] = x[j] + y[j];
-		}
-	}
+  if (rows != other.rows || columns != other.columns) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }
+  Matrix result(rows, columns);
+  for (int i = 0; i < rows; ++i) {
+    for (int j = 0; j < columns; ++j) {
+      auto x = matrix[i];
+      auto y = other[i];
+      result[i][j] = x[j] + y[j];
+    }
+  }

-	return result;
+  return result;
 }

 Matrix Matrix::operator-(Matrix& other) const {
-	if (rows != other.rows || columns != other.columns) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
-	Matrix result(rows, columns);
-	for (int i = 0; i < rows; ++i) {
-		for (int j = 0; j < columns; ++j) {
-			auto x = matrix[i];
-			auto y = other[i];
-			result[i][j] = x[j] - y[j];
-		}
-	}
+  if (rows != other.rows || columns != other.columns) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }
+  Matrix result(rows, columns);
+  for (int i = 0; i < rows; ++i) {
+    for (int j = 0; j < columns; ++j) {
+      auto x = matrix[i];
+      auto y = other[i];
+      result[i][j] = x[j] - y[j];
+    }
+  }

-	return result;
+  return result;
 }

 Matrix Matrix::operator*(Matrix& other) const {
-	if (columns != other.rows) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
+  if (columns != other.rows) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }

-	Matrix result(rows, other.columns);
-	for (int i = 0; i < rows; ++i) {
-		for (int j = 0; j < other.columns; ++j) {
-			result[i][j] = 0;
-			for (int k = 0; k < columns; ++k) {
-				auto x = matrix[i];
-				auto y = other[k];
-				result[i][j] += x[k] * y[j];
-			}
-		}
-	}
+  Matrix result(rows, other.columns);
+  for (int i = 0; i < rows; ++i) {
+    for (int j = 0; j < other.columns; ++j) {
+      result[i][j] = 0;
+      for (int k = 0; k < columns; ++k) {
+        auto x = matrix[i];
+        auto y = other[k];
+        result[i][j] += x[k] * y[j];
+      }
+    }
+  }

-	return result;
+  return result;
 }

 ColumnVector Matrix::operator*(ColumnVector other) const {
-	if (columns != other.getRows()) {
-		throw std::runtime_error("Error: the dimensional problem occurred");
-	}
+  if (columns != other.getRows()) {
+    throw std::runtime_error("Error: the dimensional problem occurred");
+  }

-	ColumnVector result(rows);
-	for (int i = 0; i < rows; ++i) {
-		result[i] = 0;
-		for (int k = 0; k < columns; ++k) {
-			auto x = matrix[i];
-			result[i] += x[k] * other[k];
-		}
-	}
+  ColumnVector result(rows);
+  for (int i = 0; i < rows; ++i) {
+    result[i] = 0;
+    for (int k = 0; k < columns; ++k) {
+      auto x = matrix[i];
+      result[i] += x[k] * other[k];
+    }
+  }

-	return result;
+  return result;
 }

 Matrix Matrix::transpose() const {
-	Matrix result(columns, rows);
-	for (int i = 0; i < rows; ++i) {
-		for (int j = 0; j < columns; ++j) {
-			auto x = matrix[i];
-			result[j][i] = x[j];
-		}
-	}
+  Matrix result(columns, rows);
+  for (int i = 0; i < rows; ++i) {
+    for (int j = 0; j < columns; ++j) {
+      auto x = matrix[i];
+      result[j][i] = x[j];
+    }
+  }

-	return result;
+  return result;
 }

 std::istream& operator>>(std::istream& cin, Matrix& matrixObj) {
-	for (int i = 0; i < matrixObj.rows; ++i) {
-		for (int j = 0; j < matrixObj.columns; ++j) {
-			cin >> matrixObj[i][j];
-		}
-	}
-	return cin;
+  for (int i = 0; i < matrixObj.rows; ++i) {
+    for (int j = 0; j < matrixObj.columns; ++j) {
+      cin >> matrixObj[i][j];
+    }
+  }
+  return cin;
 }

 std::ostream& operator<<(std::ostream& cout, Matrix& matrixObj) {
-	for (int i = 0; i < matrixObj.rows; ++i) {
-		for (int j = 0; j < matrixObj.columns; ++j) {
-			if (j == matrixObj.columns - 1) {
-				cout << matrixObj[i][j] << std::endl;
-			}
-			else {
-				cout << matrixObj[i][j] << ' ';
-			}
-		}
-	}
-	return cout;
+  for (int i = 0; i < matrixObj.rows; ++i) {
+    for (int j = 0; j < matrixObj.columns; ++j) {
+      if (j == matrixObj.columns - 1) {
+        cout << matrixObj[i][j] << std::endl;
+      }
+      else {
+        cout << matrixObj[i][j] << ' ';
+      }
+    }
+  }
+  return cout;
 }