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  1.  
  2. #include <iostream>
  3. #include <iomanip>
  4.  
  5. #include <boost/numeric/ublas/lu.hpp>
  6. #include <boost/numeric/ublas/matrix.hpp>
  7. #include <boost/numeric/ublas/vector.hpp>
  8. #include <boost/numeric/ublas/io.hpp>
  9.  
  10. #define EQUATIONS_COUNT 3
  11.  
  12. #define COEFFICIENTS \
  13. 3.0, -5.0, 1.0,\
  14. 2.0, 1.0, 2.0,\
  15. 1.0, -1.0, 1.0
  16.  
  17. #define CONSTANT_TERMS \
  18. 1.0,\
  19. 5.0,\
  20. 3.0
  21.  
  22. //#define DEBUG // uncomment to debug
  23.  
  24. using namespace boost::numeric::ublas;
  25.  
  26. #define DECL_VALUES_ARRAY(NAME, SIZE, ...)\
  27. double arr_##NAME[SIZE] = { __VA_ARGS__ };\
  28. std::vector<double> NAME;\
  29. NAME.assign(arr_##NAME, arr_##NAME + SIZE);
  30. typedef matrix<double, row_major, std::vector<double>> Matrix;
  31. typedef vector<double, std::vector<double>> Vector;
  32.  
  33. void printMatrix(const std::string & text, Matrix & printingMatrix){
  34.     std::cout << text << "[" << printingMatrix.size1() << "]" << "[" << printingMatrix.size2() << "](" <<std::endl;
  35.     for(unsigned int iIndex = 0; iIndex < printingMatrix.size1(); ++iIndex){
  36. 	std::cout << "( ";    	
  37. 	    for(unsigned int jIndex = 0; jIndex < printingMatrix.size2();  ++jIndex){ 
  38. 	        std::cout<<printingMatrix(iIndex, jIndex)<<" ";
  39. 		}
  40. 		std::cout << ")," << std::endl;
  41. 	}
  42.  
  43. 	std::cout << ")" << std::endl << std::endl;      
  44. }
  45.  
  46. void printEquationsSystem(const std::string & text, Matrix & printingMatrix, Vector& printingVector){
  47. 	std::cout << text << "{" << std::endl;
  48. 	for (unsigned int iIndex = 0; iIndex < printingMatrix.size1(); ++iIndex){
  49. 		unsigned char printedPrev = 0;
  50. 		for (unsigned int jIndex = 0; jIndex < printingMatrix.size2(); ++jIndex){
  51. 			double elementValue = printingMatrix(iIndex, jIndex);
  52. 			if (jIndex && printedPrev){
  53. 				if (elementValue > 0){
  54. 					std::cout << " + ";
  55. 				}
  56. 				else if (elementValue < 0){
  57. 					std::cout << " - ";
  58. 				}
  59. 				//else{} // nothing
  60. 			}
  61. 			if (elementValue > 0 || (!printedPrev && elementValue)){ // ( ... && ... ) - added for removing clang warning
  62. 				if (elementValue != -1. && elementValue != 1.) {
  63. 					std::cout << printingMatrix(iIndex, jIndex) << "*";
  64. 				}
  65. 				std::cout << "X" << jIndex + 1;// << " ";
  66. 				printedPrev = ~0;
  67. 			}
  68. 			else if (printingMatrix(iIndex, jIndex) < 0){	
  69. 				if (elementValue != -1.) {
  70. 					std::cout << -printingMatrix(iIndex, jIndex) << "*";				
  71. 				}
  72. 				std::cout << "X" << jIndex + 1;// << " ";
  73. 				printedPrev = ~0;
  74. 			}
  75. 			//else{} // nothing
  76. 		}
  77. 		std::cout << " = "  << printingVector(iIndex) << ";" << std::endl;
  78. 	}
  79.  
  80. 	std::cout << "}" << std::endl << std::endl;
  81. }
  82.  
  83. void printSolutionSet(const std::string & text, Vector & printingVector){
  84. 	std::cout << text << "{" << std::endl;
  85. 	for (unsigned int index = 0; index < printingVector.size(); ++index){
  86. 		unsigned char printedPrev = 0;
  87. 		std::cout << "X" << index + 1 << " = " << printingVector(index) << ";" << std::endl;
  88. 	}
  89.  
  90. 	std::cout << "}" << std::endl << std::endl;
  91. }
  92.  
  93. Matrix invertMatrix(const Matrix & matrixA){
  94.     Matrix copyMatrixA(matrixA);
  95.     //permutation_matrix<decltype(copyMatrixA)::size_type> permutationMatrixA(copyMatrixA.size1()); // ? // only for C++11	
  96. 	permutation_matrix<Matrix::size_type> permutationMatrixA(copyMatrixA.size1());
  97.     size_t res = lu_factorize(copyMatrixA, permutationMatrixA);
  98.     if(res != 0){
  99.         throw std::logic_error("lu_factorize error");
  100. 	}
  101.  
  102.     Matrix inverseMatrixA(identity_matrix<double>(copyMatrixA.size1())); // Identity matrix
  103.     lu_substitute(copyMatrixA, permutationMatrixA, inverseMatrixA);
  104.  
  105.     return inverseMatrixA;
  106. }
  107.  
  108. int main(int argc, char** argv){
  109.     try{
  110.         std::cout << std::fixed;
  111.  
  112. 		// A
  113. 		DECL_VALUES_ARRAY(matrixA_values, EQUATIONS_COUNT * EQUATIONS_COUNT, COEFFICIENTS);
  114. 		Matrix matrixA(EQUATIONS_COUNT, EQUATIONS_COUNT, matrixA_values);
  115.  
  116. 		// b
  117. 		DECL_VALUES_ARRAY(vectorB_values, EQUATIONS_COUNT, CONSTANT_TERMS);
  118. 		Vector vectorB(EQUATIONS_COUNT, vectorB_values);
  119.  
  120. 		// A^-1
  121. 		auto invertedMatrixA = invertMatrix(matrixA);
  122.  
  123. 		// x = A^-1 * b
  124. 		Vector vectorX = prod(invertedMatrixA, vectorB);
  125.  
  126. #ifdef DEBUG
  127. 		printMatrix("matrixA: ", matrixA);
  128. 		std::cout << "vectorB: " << vectorB << std::endl << std::endl;
  129. 		printMatrix("invertedMatrixA: ", invertedMatrixA);
  130. 		std::cout << "vectorX: " << vectorX << std::endl << std::endl;
  131. #endif
  132. 		printEquationsSystem("System of equations: ", matrixA, vectorB);
  133. 		printSolutionSet("Solving system of equations: ", vectorX);
  134.     }
  135.     catch(std::exception& ex){
  136.         std::cout << ex.what() << std::endl;
  137.     }
  138.  
  139. #ifdef __linux__ 
  140. 	std::cout << "Press any key to continue . . . " << std::endl;
  141. 	(void)getchar();
  142. #elif defined(_WIN32)    
  143. 	system("pause");
  144. #else
  145. #endif
  146.  
  147.     return 0;
  148. }
Success #stdin #stdout 0.01s 5484KB
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System of equations: {
3.000000*X1 - 5.000000*X2 + X3 = 1.000000;
2.000000*X1 + X2 + 2.000000*X3 = 5.000000;
X1 - X2 + X3 = 3.000000;
}

Solving system of equations: {
X1 = -1.666667;
X2 = -0.333333;
X3 = 4.333333;
}

Press any key to continue . . .
https://ideone.com/zNv0nS
language:
C++14 (gcc 8.3)
created:
333 days ago
visibility:
public

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