e534c57200a1e1c0843f8a335a71bf6b395c02f7
[morpheus.git] / pkg / src / functions.c
1 #include <stdlib.h>
2
3 // Index matrix (by columns)
4 int mi(int i, int j, int d1, int d2)
5 {
6 return j*d1 + i;
7 }
8
9 // Index 3-tensor (by columns, matrices ordered by last dim)
10 int ti(int i, int j, int k, int d1, int d2, int d3)
11 {
12 return k*d1*d2 + j*d1 + i;
13 }
14
15 // Empirical cross-moment of order 2 between X size nxd and Y size n
16 void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
17 {
18 int n=*pn, d=*pd;
19 //double* M2 = (double*)calloc(d*d,sizeof(double));
20
21 // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
22 for (int j=0; j<d; j++)
23 {
24 for (int i=0; i<n; i++)
25 {
26 M2[mi(j,j,d,d)] -= Y[i] / n;
27 for (int k=0; k<d; k++)
28 M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
29 }
30 }
31 }
32
33 // Empirical cross-moment of order 3 between X size nxd and Y size n
34 void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
35 {
36 int n=*pn, d=*pd;
37 //double* M3 = (double*)calloc(d*d*d,sizeof(double));
38
39 // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
40 for (int j=0; j<d; j++)
41 {
42 for (int k=0; k<d; k++)
43 {
44 for (int i=0; i<n; i++)
45 {
46 double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
47 M3[ti(j,k,j,d,d,d)] -= tensor_elt;
48 M3[ti(j,j,k,d,d,d)] -= tensor_elt;
49 M3[ti(k,j,j,d,d,d)] -= tensor_elt;
50 for (int o=0; o<d; o++)
51 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;
52 }
53 }
54 }
55 }
56
57 // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
58 // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
59 void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
60 {
61 int n=*pn, d=*pd;
62 int dim = d + d*d + d*d*d;
63 //double* W = (double*)malloc(dim*dim*sizeof(double));
64
65 // (Re)Initialize W:
66 for (int j=0; j<dim; j++)
67 {
68 for (int k=0; k<dim; k++)
69 W[j*dim+k] = 0.0;
70 }
71 double* g = (double*)malloc(dim*sizeof(double));
72 for (int i=0; i<n; i++)
73 {
74 // g == gi:
75 for (int j=0; j<d; j++)
76 g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
77 for (int j=d; j<d+(d*d); j++)
78 {
79 int idx1 = (j-d) % d; //num row
80 int idx2 = ((j-d) - idx1) / d; //num col
81 g[j] = 0.0;
82 if (idx1 == idx2)
83 g[j] -= Y[i];
84 g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
85 }
86 for (int j=d+d*d; j<dim; j++)
87 {
88 int idx1 = (j-d-d*d) % d; //num row
89 int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
90 int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
91 g[j] = 0.0;
92 if (idx1 == idx2)
93 g[j] -= Y[i] * X[mi(i,idx3,n,d)];
94 if (idx1 == idx3)
95 g[j] -= Y[i] * X[mi(i,idx2,n,d)];
96 if (idx2 == idx3)
97 g[j] -= Y[i] * X[mi(i,idx1,n,d)];
98 g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
99 }
100 // Add 1/n t(gi) %*% gi to W
101 for (int j=0; j<dim; j++)
102 {
103 for (int k=0; k<dim; k++)
104 W[j*dim+k] += g[j] * g[k] / n;
105 }
106 }
107 free(g);
108 }