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TheAlgorithms/C++: numerical_methods/qr_eigen_values.cpp File Reference

Compute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method. More...

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Compute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method.

Definition in file qr_eigen_values.cpp.

create a symmetric square matrix of given size with random elements. A symmetric square matrix will always have real eigen values.

Parameters

[out] A matrix to create (must be pre-allocated in memory)

Definition at line 28 of file qr_eigen_values.cpp.

28 {

i, j, tmp, lim2 =

>> 1;

30 int N = A->size();

31

32#ifdef _OPENMP

33#pragma omp for

34#endif

35 for (i = 0; i < N; i++) {

A[0][i][i] = (std::rand() %

) - lim2;

37 for (j = i + 1; j < N; j++) {

tmp = (std::rand() %

) - lim2;

39 A[0][i][j] = tmp;

40 A[0][j][i] = tmp;

41 }

42 }

43}

main function

Definition at line 243 of file qr_eigen_values.cpp.

243 {

245 if (argc == 2) {

247 } else {

250 std::cout << "Usage: ./qr_eigen_values [mat_size]\n";

251 return 0;

252 }

253

255 fprintf(stderr, "Matrix size should be > 2\n");

256 return -1;

257 }

258

259

260 std::srand(std::time(nullptr));

261

263

264 std::valarray<std::valarray<double>> A(rows);

265

266 for (int i = 0; i < rows; i++) {

267 A[i] = std::valarray<double>(columns);

268 }

269

270

272

273 std::cout << A << "\n";

274

275 clock_t t1 = clock();

277 double dtime = static_cast<double>(clock() - t1) / CLOCKS_PER_SEC;

278

279 std::cout << "Eigen vals: ";

(i = 0; i <

; i++) std::cout << eigen_vals[i] <<

;

281 std::cout << "\nTime taken to compute: " << dtime << " sec\n";

282

283 return 0;

284}

std::valarray< double > eigen_values(std::valarray< std::valarray< double > > *A, bool print_intermediates=false)

void create_matrix(std::valarray< std::valarray< double > > *A)

Perform multiplication of two matrices.

• R2 must be equal to C1
• Resultant matrix size should be R1xC2

  Parameters

  [in] A first matrix to multiply [in] B second matrix to multiply [out] OUT output matrix (must be pre-allocated)

  Returns

  pointer to resultant matrix

Definition at line 54 of file qr_eigen_values.cpp.

56 {

57 int R1 = A.size();

58 int C1 = A[0].size();

59 int R2 = B.size();

60 int C2 = B[0].size();

61 if (C1 != R2) {

62 perror("Matrix dimensions mismatch!");

63 return;

64 }

65

66 for (int i = 0; i < R1; i++) {

67 for (int j = 0; j < C2; j++) {

68 OUT[0][i][j] = 0.f;

(

k = 0;

< C1;

++) {

OUT[0][i][j] += A[i][

] * B[

][j];

71 }

72 }

73 }

74}

double k(double x)

Another test function.

template<typename T>

operator to print a matrix

Definition at line 33 of file qr_decompose.h.

34 {

35 const int width = 12;

36 const char separator = ' ';

37

38 out.precision(4);

39 for (size_t row = 0; row < v.size(); row++) {

40 for (size_t col = 0; col < v[row].size(); col++)

41 out << std::right << std::setw(width) << std::setfill(separator)

42 << v[row][col];

43 out << std::endl;

44 }

45

46 return out;

47}

test function to compute eigen values of a 2x2 matrix

\[\begin{bmatrix} 5 & 7\\ 7 & 11 \end{bmatrix}\]

which are approximately, {15.56158, 0.384227}

Definition at line 177 of file qr_eigen_values.cpp.

177 {

178 std::valarray<std::valarray<double>> X = {{5, 7}, {7, 11}};

179 double y[] = {15.56158, 0.384227};

180

181 std::cout << "------- Test 1 -------" << std::endl;

183

184 for (int i = 0; i < 2; i++) {

185 std::cout << i + 1 << "/2 Checking for " << y[i] << " --> ";

(

j = 0; j < 2 && !

; j++) {

188 if (std::abs(y[i] - eig_vals[j]) < 0.1) {

190 std::cout << "(" << eig_vals[j] << ") ";

191 }

192 }

193 assert(result);

194 std::cout << "found\n";

195 }

196 std::cout << "Test 1 Passed\n\n";

197}

uint64_t result(uint64_t n)

test function to compute eigen values of a 2x2 matrix

\[\begin{bmatrix} -4& 4& 2& 0& -3\\ 4& -4& 4& -3& -1\\ 2& 4& 4& 3& -3\\ 0& -3& 3& -1&-1\\ -3& -1& -3& -3& 0 \end{bmatrix}\]

which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994}

Definition at line 210 of file qr_eigen_values.cpp.

210 {

211 std::valarray<std::valarray<double>> X = {{-4, 4, 2, 0, -3},

212 {4, -4, 4, -3, -1},

213 {2, 4, 4, 3, -3},

214 {0, -3, 3, -1, -3},

215 {-3, -1, -3, -3, 0}};

216 double y[] = {9.27648, -9.26948, 2.0181, -1.03516,

217 -5.98994};

218

219 std::cout << "------- Test 2 -------" << std::endl;

221

222 std::cout << X << "\n"

223 << "Eigen values: " << eig_vals << "\n";

224

225 for (int i = 0; i < 5; i++) {

226 std::cout << i + 1 << "/5 Checking for " << y[i] << " --> ";

(

j = 0; j < 5 && !

; j++) {

229 if (std::abs(y[i] - eig_vals[j]) < 0.1) {

231 std::cout << "(" << eig_vals[j] << ") ";

232 }

233 }

234 assert(result);

235 std::cout << "found\n";

236 }

237 std::cout << "Test 2 Passed\n\n";

238}

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