1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
|
#include "fff_gen_stats.h"
#include "fff_lapack.h"
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <errno.h>
#include <stdio.h>
/*
Generate a random permutation from [0..n-1].
*/
extern void fff_permutation(unsigned int* x, unsigned int n, unsigned long magic)
{
unsigned int* xi, i, ir, j, tmp, nc;
unsigned long int m = magic;
/* Initialize x as the identity permutation */
for(i=0, xi=x; i<n; i++, xi++)
*xi = i;
/* Draw numbers iteratively and rearrange the array */
for(i=0, nc=n; i<n; i++, nc--) {
/* Draw j in range [i..n[ */
ir = m % nc;
m = m / nc;
j = ir + i;
/* Move x[j] to i-th index and shift indices in range [i..j[ to
the right */
tmp = x[j];
xi = x + i;
memmove((void*)(xi+1), (void*)xi, ir*sizeof(unsigned int));
*xi = tmp;
}
return;
}
/*
Generate a random combination of k elements in [0..n-1].
x must be pre-allocated with size k.
*/
static unsigned long int _combinations(unsigned int k, unsigned int n)
{
unsigned long int c, i, aux;
/* Compute the total number of combinations: Cn,k */
aux = n - k;
for (i=1, c=1; i<=k; i++) {
c *= (aux+i);
c /= i;
}
return FFF_MAX(c, 1);
}
extern void fff_combination(unsigned int* x, unsigned int k, unsigned int n, unsigned long magic)
{
unsigned long int kk, nn, i;
unsigned long int m = magic;
unsigned int *bx = x;
unsigned long int c;
/* Ensure 0 <= magic < Cn,k */
c = _combinations(k, n);
m = magic % c;
/* Loop. At the beginning of each iteration, c == Cn-(i+1),k-(i+1). */
i = 0;
kk = k;
nn = n;
kk = k;
while( kk > 0 ) {
nn --;
c = _combinations(kk-1, nn);
/* If i is accepted, then store it and do: kk-- */
if ( m < c ) {
*bx = i;
bx ++;
kk --;
}
else
m = m - c;
/* Next candidate */
i ++;
}
return;
}
/*
Squared mahalanobis distance: d2 = x' S^-1 x
Beware: x is not const
*/
extern double fff_mahalanobis(fff_vector* x, fff_matrix* S, fff_matrix* Saux)
{
double d2;
double m = 0.0;
/* Cholesky decomposition: S = L L^t, L lower triangular */
fff_lapack_dpotrf(CblasLower, S, Saux);
/* Compute S^-1 x */
fff_blas_dtrsv(CblasLower, CblasNoTrans, CblasNonUnit, S, x); /* L^-1 x */
/* Compute x' S^-1 x */
d2 = (double) fff_vector_ssd(x, &m, 1);
return d2;
}
|
