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Functions associated with LU Decomposition of a square matrix. More...
#include <iostream>#include <valarray>#include <vector>
Go to the source code of this file.
template<typename T> using matrix = std::vector<std::valarray<T>>Functions associated with LU Decomposition of a square matrix.
Definition in file lu_decomposition.h.
◆ matrixtemplate<typename T>
using matrix = std::vector<std::valarray<T>>Define matrix type as a std::vector of std::valarray
Definition at line 19 of file lu_decomposition.h.
◆ determinant_lu()template<typename T>
double determinant_lu ( const matrix< T > & A )Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U.
Definition at line 90 of file lu_decomposition.h.
90 {
93
95 return 0;
96
98 for (size_t i = 0; i < A.size(); i++) {
99 result*= L[i][i] * U[i][i];
100 }
102}
uint64_t result(uint64_t n)
int lu_decomposition(const matrix< T > &A, matrix< double > *L, matrix< double > *U)
std::vector< std::valarray< T > > matrix
◆ lu_decomposition()template<typename T>
int lu_decomposition ( const matrix< T > & A, matrix< double > * L, matrix< double > * U )Perform LU decomposition on matrix
Definition at line 29 of file lu_decomposition.h.
29 {
30 int row, col, j;
32
34
35 std::cerr << "Not a square matrix!\n";
36 return -1;
37 }
38
39
40 for(row = 0; row <
mat_size; row++) {
41
42#ifdef _OPENMP
43#pragma omp for
44#endif
45 for(col = row; col <
mat_size; col++) {
46
47 double lu_sum = 0.;
48 for (j = 0; j < row; j++) {
49 lu_sum += L[0][row][j] * U[0][j][col];
50 }
51
52
53 U[0][row][col] = A[row][col] - lu_sum;
54 }
55
56
57#ifdef _OPENMP
58#pragma omp for
59#endif
60 for(col = row; col <
mat_size; col++) {
61 if (row == col) {
62 L[0][row][col] = 1.;
63 continue;
64 }
65
66
67 double lu_sum = 0.;
68 for (j = 0; j < row; j++) {
69 lu_sum += L[0][col][j] * U[0][j][row];
70 }
71
72
73 L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];
74 }
75 }
76
77 return 0;
78}
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