It's enough to compute half of W (complete by symmetry)
[morpheus.git] / pkg / src / functions.c
1 #include <stdlib.h>
2 #include <omp.h>
3
4 // Index matrix (by columns)
5 #define mi(i, j, d1, d2) (j*d1 + i)
6
7 // Index 3-tensor (by columns, matrices ordered by last dim)
8 #define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)
9
10 // Empirical cross-moment of order 2 between X size nxd and Y size n
11 void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
12 {
13 int n=*pn, d=*pd;
14 //double* M2 = (double*)calloc(d*d,sizeof(double));
15
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 }
26 }
27
28 // Empirical cross-moment of order 3 between X size nxd and Y size n
29 void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
30 {
31 int n=*pn, d=*pd;
32 //double* M3 = (double*)calloc(d*d*d,sizeof(double));
33
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 }
50 }
51
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
54 void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
55 {
56 int nc=*pnc, n=*pn, d=*pd;
57 int dim = d + d*d + d*d*d;
58 //double* W = (double*)malloc(dim*dim*sizeof(double));
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 }
66 double* g = (double*)malloc(dim*sizeof(double));
67 omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
68 #pragma omp parallel for
69 for (int i=0; i<n; i++)
70 {
71 // g == gi:
72 for (int j=0; j<d; j++)
73 g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
74 for (int j=d; j<d+(d*d); j++)
75 {
76 int idx1 = (j-d) % d; //num row
77 int idx2 = ((j-d) - idx1) / d; //num col
78 g[j] = 0.0;
79 if (idx1 == idx2)
80 g[j] -= Y[i];
81 g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
82 }
83 for (int j=d+d*d; j<dim; j++)
84 {
85 int idx1 = (j-d-d*d) % d; //num row
86 int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
87 int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
88 g[j] = 0.0;
89 if (idx1 == idx2)
90 g[j] -= Y[i] * X[mi(i,idx3,n,d)];
91 if (idx1 == idx3)
92 g[j] -= Y[i] * X[mi(i,idx2,n,d)];
93 if (idx2 == idx3)
94 g[j] -= Y[i] * X[mi(i,idx1,n,d)];
95 g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
96 }
97 // Add 1/n t(gi) %*% gi to W
98 for (int j=0; j<dim; j++)
99 {
100 // This final nested loop is very costly. Some basic optimisations:
101 double gj = g[j];
102 int baseIdx = j * dim;
103 #pragma GCC unroll 32
104 for (int k=j; k>=0; k--)
105 W[baseIdx+k] += gj * g[k];
106 }
107 }
108 // Normalize W: x 1/n
109 for (int j=0; j<dim; j++)
110 {
111 for (int k=0; k<=j; k++)
112 W[mi(j,k,dim,dim)] /= n;
113 }
114 // Symmetrize W: W[j,k] = W[k,j] for k > j
115 for (int j=0; j<dim; j++)
116 {
117 for (int k=j+1: k<dim; k++)
118 W[mi(j,k,dim,dim)] = W[mi(k,j,dim,dim)];
119 }
120 free(g);
121 }