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cbd88fe5 | 1 | #include <stdlib.h> |
f47183de | 2 | //#include <omp.h> |
cbd88fe5 | 3 | |
d08fef42 | 4 | // Index matrix (by columns) |
9ac8ecc0 | 5 | #define mi(i, j, d1, d2) (j*d1 + i) |
cbd88fe5 | 6 | |
d08fef42 | 7 | // Index 3-tensor (by columns, matrices ordered by last dim) |
9ac8ecc0 | 8 | #define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i) |
cbd88fe5 | 9 | |
d08fef42 | 10 | // Empirical cross-moment of order 2 between X size nxd and Y size n |
cbd88fe5 BA |
11 | void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2) |
12 | { | |
6dd5c2ac BA |
13 | int n=*pn, d=*pd; |
14 | //double* M2 = (double*)calloc(d*d,sizeof(double)); | |
cbd88fe5 | 15 | |
6dd5c2ac BA |
16 | // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)] |
17 | for (int j=0; j<d; j++) | |
18 | { | |
19 | for (int i=0; i<n; i++) | |
20 | { | |
21 | M2[mi(j,j,d,d)] -= Y[i] / n; | |
22 | for (int k=0; k<d; k++) | |
23 | M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n; | |
24 | } | |
25 | } | |
cbd88fe5 BA |
26 | } |
27 | ||
d08fef42 | 28 | // Empirical cross-moment of order 3 between X size nxd and Y size n |
cbd88fe5 BA |
29 | void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3) |
30 | { | |
6dd5c2ac BA |
31 | int n=*pn, d=*pd; |
32 | //double* M3 = (double*)calloc(d*d*d,sizeof(double)); | |
cbd88fe5 | 33 | |
6dd5c2ac BA |
34 | // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e] |
35 | for (int j=0; j<d; j++) | |
36 | { | |
37 | for (int k=0; k<d; k++) | |
38 | { | |
39 | for (int i=0; i<n; i++) | |
40 | { | |
41 | double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n; | |
42 | M3[ti(j,k,j,d,d,d)] -= tensor_elt; | |
43 | M3[ti(j,j,k,d,d,d)] -= tensor_elt; | |
44 | M3[ti(k,j,j,d,d,d)] -= tensor_elt; | |
45 | for (int o=0; o<d; o++) | |
46 | M3[ti(j,k,o,d,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)]*X[mi(i,o,n,d)] / n; | |
47 | } | |
48 | } | |
49 | } | |
cbd88fe5 | 50 | } |
4263503b | 51 | |
d08fef42 BA |
52 | // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) ) |
53 | // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments | |
5af71d43 | 54 | void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W) |
4263503b | 55 | { |
f47183de | 56 | int n=*pn, d=*pd; //,nc=*pnc |
b389a46a | 57 | int dim = d + d*d + d*d*d; |
bbdcfe44 | 58 | //double* W = (double*)malloc(dim*dim*sizeof(double)); |
4bf8494d BA |
59 | |
60 | // (Re)Initialize W: | |
61 | for (int j=0; j<dim; j++) | |
62 | { | |
63 | for (int k=0; k<dim; k++) | |
64 | W[j*dim+k] = 0.0; | |
65 | } | |
4bf8494d | 66 | double* g = (double*)malloc(dim*sizeof(double)); |
a27d53c3 BA |
67 | // TODO: stabilize this (for now, random result) |
68 | // omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs()); | |
69 | // #pragma omp parallel for | |
7737c2fa BA |
70 | for (int i=0; i<n; i++) |
71 | { | |
bbdcfe44 | 72 | // g == gi: |
d08fef42 | 73 | for (int j=0; j<d; j++) |
19d893c4 | 74 | g[j] = Y[i] * X[mi(i,j,n,d)] - M[j]; |
d08fef42 BA |
75 | for (int j=d; j<d+(d*d); j++) |
76 | { | |
77 | int idx1 = (j-d) % d; //num row | |
78 | int idx2 = ((j-d) - idx1) / d; //num col | |
79 | g[j] = 0.0; | |
19d893c4 BA |
80 | if (idx1 == idx2) |
81 | g[j] -= Y[i]; | |
82 | g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j]; | |
d08fef42 BA |
83 | } |
84 | for (int j=d+d*d; j<dim; j++) | |
85 | { | |
86 | int idx1 = (j-d-d*d) % d; //num row | |
87 | int idx2 = ((j-d-d*d - idx1) / d) %d; //num col | |
88 | int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth" | |
89 | g[j] = 0.0; | |
19d893c4 BA |
90 | if (idx1 == idx2) |
91 | g[j] -= Y[i] * X[mi(i,idx3,n,d)]; | |
92 | if (idx1 == idx3) | |
93 | g[j] -= Y[i] * X[mi(i,idx2,n,d)]; | |
94 | if (idx2 == idx3) | |
95 | g[j] -= Y[i] * X[mi(i,idx1,n,d)]; | |
96 | g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j]; | |
d08fef42 BA |
97 | } |
98 | // Add 1/n t(gi) %*% gi to W | |
9fdd3e5f | 99 | for (int j=0; j<dim; j++) |
d08fef42 | 100 | { |
5af71d43 BA |
101 | // This final nested loop is very costly. Some basic optimisations: |
102 | double gj = g[j]; | |
103 | int baseIdx = j * dim; | |
f47183de | 104 | // #pragma GCC unroll 32 |
9fdd3e5f | 105 | for (int k=j; k>=0; k--) |
5af71d43 | 106 | W[baseIdx+k] += gj * g[k]; |
d08fef42 | 107 | } |
7737c2fa | 108 | } |
5af71d43 BA |
109 | // Normalize W: x 1/n |
110 | for (int j=0; j<dim; j++) | |
111 | { | |
ab35f610 | 112 | for (int k=j; k<dim; k++) |
5af71d43 BA |
113 | W[mi(j,k,dim,dim)] /= n; |
114 | } | |
ab35f610 | 115 | // Symmetrize W: W[k,j] = W[j,k] for k > j |
9fdd3e5f BA |
116 | for (int j=0; j<dim; j++) |
117 | { | |
de1a19fd | 118 | for (int k=j+1; k<dim; k++) |
ab35f610 | 119 | W[mi(k,j,dim,dim)] = W[mi(j,k,dim,dim)]; |
9fdd3e5f | 120 | } |
d08fef42 | 121 | free(g); |
4263503b | 122 | } |