|
1 | 1 | #pragma once |
2 | 2 |
|
3 | 3 | #include "macros.hpp" |
| 4 | +#include "symmetricMatrix.hpp" |
4 | 5 | #include <cmath> |
5 | 6 |
|
6 | 7 | namespace hpcReact |
7 | 8 | { |
| 9 | + |
| 10 | +template< typename REAL_TYPE, int N > |
| 11 | +bool isPositiveDefinite( REAL_TYPE const (&A)[N][N] ) |
| 12 | +{ |
| 13 | + REAL_TYPE temp[N][N]; |
| 14 | + |
| 15 | + // Copy A into temp to avoid modifying original |
| 16 | + for( int i = 0; i < N; i++ ) |
| 17 | + { |
| 18 | + for( int j = 0; j < N; j++ ) |
| 19 | + { |
| 20 | + temp[i][j] = A[i][j]; |
| 21 | + } |
| 22 | + } |
| 23 | + |
| 24 | + for( int k = 0; k < N; k++ ) |
| 25 | + { |
| 26 | + // Compute determinant of k-th leading principal minor using Gaussian elimination |
| 27 | + if( temp[k][k] <= 0 ) |
| 28 | + return false; // Must be positive |
| 29 | + |
| 30 | + for( int i = k + 1; i < N; i++ ) |
| 31 | + { |
| 32 | + REAL_TYPE factor = temp[i][k] / temp[k][k]; |
| 33 | + for( int j = k; j < N; j++ ) |
| 34 | + { |
| 35 | + temp[i][j] -= factor * temp[k][j]; |
| 36 | + } |
| 37 | + } |
| 38 | + } |
| 39 | + return true; |
| 40 | +} |
| 41 | + |
| 42 | + |
| 43 | +template< typename REAL_TYPE, int N > |
| 44 | +void solveNxN_Cholesky( REAL_TYPE const (&A)[N][N], REAL_TYPE const (&b)[N], REAL_TYPE (& x)[N] ) |
| 45 | +{ |
| 46 | + REAL_TYPE L[N][N] = {{0}}; |
| 47 | + |
| 48 | + // **Cholesky Decomposition** |
| 49 | + for( int i = 0; i < N; i++ ) |
| 50 | + { |
| 51 | + for( int j = 0; j <= i; j++ ) |
| 52 | + { |
| 53 | + REAL_TYPE sum = 0; |
| 54 | + for( int k = 0; k < j; k++ ) |
| 55 | + { |
| 56 | + sum += L[i][k] * L[j][k]; |
| 57 | + } |
| 58 | + if( i == j ) |
| 59 | + L[i][j] = sqrt( A[i][i] - sum ); |
| 60 | + else |
| 61 | + L[i][j] = (A[i][j] - sum) / L[j][j]; |
| 62 | + } |
| 63 | + } |
| 64 | + |
| 65 | + // **Forward Substitution: Solve L y = b** |
| 66 | + //REAL_TYPE y[N]; |
| 67 | + for( int i = 0; i < N; i++ ) |
| 68 | + { |
| 69 | + x[i] = b[i]; |
| 70 | + for( int j = 0; j < i; j++ ) |
| 71 | + x[i] -= L[i][j] * x[j]; |
| 72 | + x[i] /= L[i][i]; |
| 73 | + } |
| 74 | + |
| 75 | + // **Backward Substitution: Solve L^T x = y** |
| 76 | + for( int i = N - 1; i >= 0; i-- ) |
| 77 | + { |
| 78 | +// x[i] = y[i]; |
| 79 | + for( int j = i + 1; j < N; j++ ) |
| 80 | + x[i] -= L[j][i] * x[j]; |
| 81 | + x[i] /= L[i][i]; |
| 82 | + } |
| 83 | +} |
| 84 | + |
| 85 | + |
| 86 | + |
| 87 | +template< typename REAL_TYPE, int N > |
| 88 | +void solveNxN_Cholesky( symmetricMatrix< REAL_TYPE, int, N > const & A, |
| 89 | + REAL_TYPE const (&b)[N], |
| 90 | + REAL_TYPE (& x)[N] ) |
| 91 | +{ |
| 92 | + symmetricMatrix< REAL_TYPE, int, N > L = {0}; |
| 93 | + |
| 94 | + // **Cholesky Decomposition** |
| 95 | + for( int i = 0; i < N; i++ ) |
| 96 | + { |
| 97 | + for( int j = 0; j <= i; j++ ) |
| 98 | + { |
| 99 | + REAL_TYPE sum = 0; |
| 100 | + for( int k = 0; k < j; k++ ) |
| 101 | + { |
| 102 | + sum += L( i, k ) * L( j, k ); |
| 103 | + } |
| 104 | + if( i == j ) |
| 105 | + { |
| 106 | + L( i, j ) = sqrt( A( i, i ) - sum ); |
| 107 | + } |
| 108 | + else |
| 109 | + { |
| 110 | + L( i, j ) = (A( i, j ) - sum) / L[j][j]; |
| 111 | + } |
| 112 | + } |
| 113 | + } |
| 114 | + |
| 115 | + // **Forward Substitution: Solve L y = b** |
| 116 | + REAL_TYPE y[N]; |
| 117 | + for( int i = 0; i < N; i++ ) |
| 118 | + { |
| 119 | + y[i] = b[i]; |
| 120 | + for( int j = 0; j < i; j++ ) |
| 121 | + { |
| 122 | + y[i] -= L( i, j ) * y[j]; |
| 123 | + } |
| 124 | + y[i] /= L( i, i ); |
| 125 | + } |
| 126 | + |
| 127 | + // **Backward Substitution: Solve L^T x = y** |
| 128 | + for( int i = N - 1; i >= 0; i-- ) |
| 129 | + { |
| 130 | + x[i] = y[i]; |
| 131 | + for( int j = i + 1; j < N; j++ ) |
| 132 | + { |
| 133 | + x[i] -= L( j, i ) * x[j]; |
| 134 | + } |
| 135 | + x[i] /= L( i, i ); |
| 136 | + } |
| 137 | +} |
| 138 | + |
| 139 | + |
8 | 140 | template< typename REAL_TYPE, int N > |
9 | 141 | HPCREACT_HOST_DEVICE |
10 | | -void solveNxN_pivoted( REAL_TYPE A[N][N], REAL_TYPE b[N], REAL_TYPE x[N] ) |
| 142 | +void solveNxN_pivoted( REAL_TYPE (& A)[N][N], REAL_TYPE (& b)[N], REAL_TYPE (& x)[N] ) |
11 | 143 | { |
12 | 144 |
|
13 | 145 |
|
|
0 commit comments