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[morpheus.git] / pkg / src / functions.c
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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
11void 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
29void 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
54void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
55{
56 int n=*pn, d=*pd; //,nc=*pnc
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 // TODO: stabilize this (for now, random result)
68// omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
69// #pragma omp parallel for
70 for (int i=0; i<n; i++)
71 {
72 // g == gi:
73 for (int j=0; j<d; j++)
74 g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
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;
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];
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;
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];
97 }
98 // Add 1/n t(gi) %*% gi to W
99 for (int j=0; j<dim; j++)
100 {
101 // This final nested loop is very costly. Some basic optimisations:
102 double gj = g[j];
103 int baseIdx = j * dim;
104// #pragma GCC unroll 32
105 for (int k=j; k>=0; k--)
106 W[baseIdx+k] += gj * g[k];
107 }
108 }
109 // Normalize W: x 1/n
110 for (int j=0; j<dim; j++)
111 {
112 for (int k=j; k<dim; k++)
113 W[mi(j,k,dim,dim)] /= n;
114 }
115 // Symmetrize W: W[k,j] = W[j,k] for k > j
116 for (int j=0; j<dim; j++)
117 {
118 for (int k=j+1; k<dim; k++)
119 W[mi(k,j,dim,dim)] = W[mi(j,k,dim,dim)];
120 }
121 free(g);
122}