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  1. #include <iostream>
  2. #include <vector>
  3. #include <stdlib.h>
  4. #include <string>
  5. #include <math.h> //fabs
  6.  
  7.  
  8. /* TO BE DONE
  9.  - need to check operations perform correctly
  10.  */
  11.  
  12. /*create a matrix input string of form [1,2,3][4,5,6][7,8,9] - or allow commas between brackets, [],[],[] (they are ignored) or add B vector - [1,2,3|1][4,5,6|2][7,8,9|3]
  13. take input in as string and convert it to a vector<T> A and vector<T> B inside of the mtx class
  14.  
  15. if the format works (implicitly) then the matrix should read it in - otherwise it should try a different form
  16. */
  17.  
  18. class line;
  19.  
  20. ////////////////////////////////////////////////////////////////////////////////
  21. //CLASS MTX DEFINITION
  22. template <class T>
  23. class mtx		
  24. {
  25. 	private:
  26. 	friend class line;
  27. 	std::vector<T> A;	//matrix
  28. 	std::vector<T> B;	//solution vector - size = number of rows for matrix - not necessary for some matrix operations
  29. 	std::size_t width;	
  30. 	std::size_t height;	
  31. 	std::size_t x, y;
  32. 	//PRIVATE FUNCTIONS
  33. 	bool isMatrixSquare();	//handles an error
  34. 	void swapRows (int first_in, int second_in);
  35. 	class line
  36. 	{
  37. 		mtx * p_mtx;
  38. 		public:
  39. 		line(mtx *p_mtx_in);
  40. 		T& operator [] (std::size_t y_in);
  41. 		const T& operator [] (std::size_t y_in) const;
  42. 	};
  43. 	public:
  44. 	//CONSTRUCTORS
  45. 	mtx ();
  46. 	mtx (std::vector<T>& Ain, std::vector<T>& Bin);
  47. 	//INDEX ACCESS OPERATOR OVERLOADS
  48. 	line& operator [] (std::size_t index);
  49. 	T& operator () (std::size_t x_in, std::size_t y_in);
  50. 	const T& operator () (std::size_t x_in, std::size_t y_in) const;
  51. 	//MATRIX PUBLIC FUNCTIONS
  52. 	mtx operator = (mtx& in);	//ASSIGNMENT OPERATOR
  53. 	T& at (int i, int j);
  54.  
  55. 	friend void swap(mtx<T>& first_in, mtx<T>& second_in);
  56. 	//UNARY FUNCTIONS
  57. 	mtx& operator += (const mtx& rhs);
  58. 	mtx& operator -= (const mtx& rhs);
  59. 	mtx& operator *= (const mtx& rhs);
  60. 	//BINARY FUNCTIONS
  61. 	mtx operator + (const mtx& rhs);
  62. 	mtx operator - (const mtx& rhs);
  63. 	mtx operator * (const mtx& rhs);
  64. 	mtx operator * (const T& rhs);	//scalar multiplication
  65.  
  66. 	//void Apush_back (double);
  67. 	//double Aat (int row, int col);													//reads element at row,col where 0,0 is the first element in the matrix
  68. 	//void Bpush_back (double);
  69. 	//double Bat (int x);
  70. 	//bool 
  71. 	//T determinant();	//calculates the determinant of square matrix
  72. 	mtx inverse();	//returns the inverse matrix
  73. 	void rref ();																//Reduce Row Echelon Form - basic solution for square matrix
  74. 	void print();
  75.  
  76. 	/*at some point more functions will be added but this should be enough for the beam calc
  77. 	void inverse (void);
  78. 	void eigen (void);
  79. 	mtx operator* (mtx const rhs&);	//A = B*C
  80. 	mtx& operator*= (mtx const rhs&);
  81.  
  82. 	*/
  83. 	private:
  84. 	line m_line;
  85. };
  86.  
  87. ////////////////////////////////////////////////////////////////////////////////
  88. //MATRIX CLASS DECLARATION
  89. //PRIVATE FUNCTIONS*************************************************************
  90. template <class T>
  91. bool mtx<T>::isMatrixSquare()
  92. {
  93. 	if (width == height)
  94. 	{
  95. 		return true;
  96. 	}
  97. 	std::cerr << "ERROR at bool mtx<T>::isMatrixSquare() - matrix is not square." << std::endl;
  98. 	return false;
  99. }
  100. template <class T>
  101. void mtx<T>::swapRows (int row1_in, int row2_in)
  102. {
  103. 	if (row1_in >= height || row2_in >= height)
  104. 	{
  105. 		std::cerr <<"Error - row parameters not within matrix and vector dimension";
  106. 		return;
  107. 	}
  108. 	T temp;
  109. 	for (int i; i < width; i++)
  110. 	{
  111. 		temp = A[i + row1_in * width];
  112. 		A[i + row1_in * width] = A[i + row2_in * width];
  113. 		A[i + row2_in * width] = temp;
  114. 	}
  115. 	temp = B.at(row1_in);	//swaps values in Bvector
  116. 	B.at(row1_in) = B.at(row2_in);
  117. 	B.at(row2_in) = temp;
  118. 	return;
  119. }
  120. template <class T>
  121. T& mtx<T>::line::operator [] (std::size_t y_in)
  122. {
  123. 	if (y_in >= p_mtx->height)
  124. 	{
  125. 		std::cerr << "row value is out of bounds and will be replaced with 0";
  126. 		p_mtx->y = 0;
  127. 	}
  128. 	else
  129. 	{
  130. 		p_mtx->y = y_in;
  131. 	}
  132. 	return p_mtx->A[p_mtx->x+p_mtx->y*p_mtx->width];
  133. }
  134. template <class T>
  135. const T& mtx<T>::line::operator [] (std::size_t y_in) const
  136. {
  137. 	if (y_in >= p_mtx->height)
  138. 	{
  139. 		std::cerr << "row value is out of bounds and will be replaced with 0";
  140. 		p_mtx->y = 0;
  141. 	}
  142. 	else
  143. 	{
  144. 		p_mtx->y = y_in;
  145. 	}
  146. 	return p_mtx->A[p_mtx->x+p_mtx->y*p_mtx->width];
  147. }
  148. //MATRIX CLASS CONSTRUCTORS*****************************************************
  149. template <class T>
  150. mtx<T>::mtx ():A(), B(), width(0), height(0), m_line(this)
  151. {
  152.  
  153. }
  154. template <class T>
  155. mtx<T>::mtx (std::vector<T>& Ain, std::vector<T>& Bin):A(Ain), B(Bin), m_line(this)
  156. {
  157. 	std::cout << "constructor started" <<std::endl;
  158. 	if(Ain.size() != 0 && Bin.size() != 0 && Ain.size() % Bin.size() == 0)
  159. 	{
  160. 		height = Bin.size();
  161. 		width = Ain.size()/height;
  162. 	}
  163. 	else
  164. 	{
  165. 		std::cerr << "Error - Matrix A and Vector B are of incompatible sizes - dummy matrix created";
  166. 		A.clear();
  167. 		B.clear();
  168. 	}
  169. }
  170. //MATRIX CLASS ACCESS OPERATOR OVERLOADS****************************************
  171. template <class T>
  172. typename mtx<T>::line& mtx<T>::operator [] (std::size_t x_in)
  173. {
  174. 	if (x_in >= width)
  175. 	{
  176. 		std::cerr << "row coordinate is out of bounds - setting to 0";
  177. 		x = 0;
  178. 	}
  179. 	else
  180. 	{
  181. 		x = x_in;
  182. 	}
  183. 	return m_line;
  184. }
  185. template <class T>
  186. T& mtx<T>::operator () (std::size_t x_in, std::size_t y_in)
  187. {
  188. 	return A[x_in + y_in * width];
  189. }
  190. template <class T>
  191. const T& mtx<T>::operator () (std::size_t x_in, std::size_t y_in) const
  192. {
  193. 	return A[x_in + y_in * width];
  194. }
  195. //MATRIX CLASS - UNARY FUNCTION OVERLOADS
  196. template <class T>
  197. mtx<T>& mtx<T>::operator += (const mtx& rhs)
  198. {
  199. 	if (height != rhs.height || width != rhs.width)
  200. 	{
  201. 		std::cerr << "ERROR at mtx& mtx<T>::operator += (const mtx& rhs) - matrix sizes do not match.  No addition performed." << std::endl;
  202. 		return *this;
  203. 	}
  204. 	for (int i = 0; i<= A.size(); i++)
  205. 	{
  206. 		A[i] += rhs.A[i];
  207. 	}
  208. 	return *this;
  209. }
  210. template <class T>
  211. mtx<T>& mtx<T>::operator -= (const mtx& rhs)
  212. {
  213. 	if (height != rhs.height || width != rhs.width)
  214. 	{
  215. 		std::cerr << "ERROR at mtx& mtx<T>::operator -= (const mtx& rhs) - matrix sizes do not match.  No subtraction performed." << std::endl;
  216. 		return *this;
  217. 	}
  218. 	for (int i = 0; i<= A.size(); i++)
  219. 	{
  220. 		A[i] -= rhs.A[i];
  221. 	}
  222. 	return *this;
  223. }
  224. template <class T>
  225. mtx<T>& mtx<T>::operator *= (const mtx& rhs)
  226. {
  227. 		if (width != rhs.height)
  228. 	{
  229. 		std::cout << "ERROR at mtx& mtx<T>::operator *= (const mtx& rhs) - matrix sizes are not compatible.  No multiplication performed." << std::endl;
  230. 		return *this;
  231. 	}
  232. 	//create new matrix then swap with this
  233. 	std::vector<T> Atemp;
  234. 	std::vector<T> Btemp(0,height);
  235. 	for (int j = 0; j < height; j++)//use j for height in this and width in rhs
  236. 	{
  237. 		for (int i = 0; i < rhs.width; i++)
  238. 		{
  239. 			T mtxValue = 0;
  240. 			for (int n = 0; n < width; n++)
  241. 			{
  242. 				mtxValue += A[n+j*width] * rhs(i,n); 
  243. 			}
  244. 			Atemp.push_back (mtxValue);
  245. 		}
  246. 	}
  247. 	mtx<T> temp(Atemp, Btemp);
  248. 	//swap(*this, temp);
  249. 	return temp;
  250. }
  251.  
  252.  
  253.  
  254.  
  255.  
  256. template <class T>
  257. T& mtx<T>::at (int x_in, int y_in)
  258. {
  259. 	return this->A.at(x_in + y_in * width);
  260. }
  261.  
  262.  
  263.  
  264. template <class T>
  265. void mtx<T>::rref ()
  266. {
  267. 	//WHAT HAPPENS WHEN WE HAVE MORE COLUMNS THAN ROWS?
  268. 	//MORE ROWS THAN COLUMNS?
  269. 	//WHEN A COLUMN DOESNT HAVE A 1 ON THE DIAGONAL
  270. 	if(A.size() == 0 || B.size() == 0 || A.size() % B.size() != 0)
  271. 	{
  272. 		std::cerr << "ERROR at [void mtx<T>::rref ()] - Matrix A and Vector B are of incompatible sizes - RREF not performed";
  273. 		return;
  274. 	}	
  275. 	T largest, coefficient;
  276. 	int largestRow, count;
  277. 	count = 0;
  278. 	for (int i = 0; i< width; i++)	//iterate through each column
  279. 	{
  280. 		largest = 0;
  281. 		for (int j = count; j < height; j++)	//find largest in each row
  282. 		{
  283. 			if (fabs(A[i + j * width]) > largest)
  284. 			{
  285. 				largest = fabs(A[i + j * width]);
  286. 				largestRow = j;
  287. 			}
  288. 		}
  289. 		if (largestRow != count)	//not on the diagonal then swap it onto the diagonal
  290. 		{
  291. 			this->swapRows(largestRow, count);
  292. 		}
  293. 		if (i != height && largest != 0)	//if largest is 0 then skip
  294. 		{
  295. 			for (int k = 0; k < height; k++)	//iterate through rows and 0 out column
  296. 			{
  297. 				if (k != count)	//skip over diagonal
  298. 				{
  299. 					coefficient = -A[i + k * width]/A[i + i * width];
  300. 					std::cout << "coefficient = " << coefficient << std::endl;
  301. 					A[i + k * width] = 0;	//first coefficient is 0 - no need to calc
  302. 					for (int m = i + 1; m < width; m++)	//iterate across width
  303. 					{
  304. 						A[m + k * width] += A[m + i * width] * coefficient; 
  305. 					}
  306. 					B[k] += B[i] * coefficient;	
  307. 				}
  308. 			}
  309. 			this->print();
  310. 		}
  311. 		if (A[i + i * width] != 0)	//set diagonal value to 1
  312. 		{
  313. 			coefficient = 1.0 / A[i + i * width];
  314. 			A[i + i * width] = 1.0;
  315. 			for (int n = i + 1; n < width; n++)
  316. 			{
  317. 				A[n + i * width] *= coefficient;
  318. 			}
  319. 			B[i] *= coefficient;
  320. 			count++;
  321. 			if (count == width || count == height)
  322. 			{
  323. 				return;
  324. 			}
  325. 		}
  326. 	}
  327. }
  328.  
  329. template <class T>
  330. mtx<T>::line::line (mtx * p_mtx_in):p_mtx(p_mtx_in)
  331. {
  332.  
  333. }
  334.  
  335. template <class T>
  336. void swap (mtx<T>& first_in, mtx<T>& second_in)
  337. {
  338. 	using std::swap;
  339. 	swap(first_in.A, second_in.A);
  340. 	swap(first_in.B, second_in.B);
  341. 	swap(first_in.width, second_in.width);
  342. 	swap(first_in.height, second_in.height);
  343. 	swap(first_in.x, second_in.x);
  344. 	swap(first_in.y, second_in.y);
  345. 	swap(first_in.m_line, second_in.m_line);
  346. 	return;
  347. }
  348.  
  349. template <class T>
  350. void mtx<T>::print ()
  351. {
  352. 	for (int j=0; j<height; j++)
  353. 	{
  354. 		for (int i = 0; i<width; i++)
  355. 		{
  356. 			std::cout << A[i + j * width] << " ";
  357. 		}
  358. 		std::cout << "| " << B[j] << std::endl;
  359. 	}
  360. }
  361.  
  362. int main() {
  363. 	// your code goes here
  364. 	std::vector<double> atemp, btemp;
  365.  
  366. 	for (int i = 0; i < 12; i++)
  367. 	{
  368. 		atemp.push_back(double(pow(i,3)/4.12785));
  369. 	}
  370.  
  371. 	for (int i = 0; i < 3; i++)
  372. 	{
  373. 		btemp.push_back(double(4.0-i));
  374. 	}
  375. 	mtx<double> M (atemp, btemp);
  376. 	M.print();
  377. 	M *= M;
  378. 	M.rref();
  379. 	M.print();
  380. 	double pi = 3.14159;
  381. 	M [1][2] = pi;
  382. 	M(0,1) = pi;
  383. 	M.print();
  384. 	M.rref();
  385. 	M.print();
  386.  
  387. 	return 0;
  388. }
  389.  
Success #stdin #stdout 0s 15248KB
comments (?)
stdin 
Standard input is empty
stdout 
constructor started
0 0.242257 1.93805 6.54094 | 4
15.5044 30.2821 52.3275 83.0941 | 3
124.036 176.605 242.257 322.444 | 2
ERROR at mtx& mtx<T>::operator *= (const mtx& rhs) - matrix sizes are not compatible.  No multiplication performed.
coefficient = -0.125
coefficient = -0
124.036 176.605 242.257 322.444 | 2
0 8.20645 22.0454 42.7886 | 2.75
0 0.242257 1.93805 6.54094 | 4
coefficient = -0.173501
coefficient = -0.0295203
1 0 -1.87177 -4.82426 | -0.461004
0 8.20645 22.0454 42.7886 | 2.75
0 0 1.28727 5.2778 | 3.91882
coefficient = 1.45406
coefficient = -2.08686
1 0 0 2.85 | 5.23721
0 1 0 -5.8 | -7.84291
0 0 1.28727 5.2778 | 3.91882
1 0 0 2.85 | 5.23721
0 1 0 -5.8 | -7.84291
0 0 1 4.1 | 3.04429
1 0 0 2.85 | 5.23721
3.14159 1 0 -5.8 | -7.84291
0 3.14159 1 4.1 | 3.04429
coefficient = -0.31831
coefficient = -0
3.14159 1 0 -5.8 | -7.84291
0 -0.31831 0 4.6962 | 7.73369
0 3.14159 1 4.1 | 3.04429
coefficient = -0.101321
coefficient = 0.101321
1 0 -0.101321 -2.26162 | -2.80493
0 3.14159 1 4.1 | 3.04429
0 0 0.101321 5.11162 | 8.04214
coefficient = 1
coefficient = -3.14159
1 0 0 2.85 | 5.23721
0 1 0 -14.7535 | -24.2961
0 0 0.101321 5.11162 | 8.04214
1 0 0 2.85 | 5.23721
0 1 0 -14.7535 | -24.2961
0 0 1 50.4495 | 79.3726
https://ideone.com/r63mKP
MATRIX STUFF
language:
C++14 (gcc 8.3)
created:
7 years ago
visibility:
public

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