-
Notifications
You must be signed in to change notification settings - Fork 4
/
Copy pathlambda.c
235 lines (212 loc) · 7.75 KB
/
lambda.c
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
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
/*------------------------------------------------------------------------------
* lambda.c : integer ambiguity resolution
*-----------------------------------------------------------------------------*/
#include "gamp.h"
/* constants/macros ----------------------------------------------------------*/
#define LOOPMAX 10000 /* maximum count of search loop */
#define SGN(x) ((x)<=0.0?-1.0:1.0)
#define ROUND(x) (floor((x)+0.5))
#define SWAP(x,y) do {double tmp_; tmp_=x; x=y; y=tmp_;} while (0)
/* LD factorization (Q=L'*diag(D)*L) -----------------------------------------*/
static int LD(int n, const double *Q, double *L, double *D)
{
int i,j,k,info=0;
double a,*A=mat(n,n);
memcpy(A,Q,sizeof(double)*n*n);
for (i=n-1;i>=0;i--) {
if ((D[i]=A[i+i*n])<=0.0) {info=-1; break;}
a=sqrt(D[i]);
for (j=0;j<=i;j++) L[i+j*n]=A[i+j*n]/a;
for (j=0;j<=i-1;j++) for (k=0;k<=j;k++) A[j+k*n]-=L[i+k*n]*L[i+j*n];
for (j=0;j<=i;j++) L[i+j*n]/=L[i+i*n];
}
free(A);
if (info) fprintf(stderr,"%s : LD factorization error\n",__FILE__);
return info;
}
/* integer gauss transformation ----------------------------------------------*/
static void gauss(int n, double *L, double *Z, int i, int j)
{
int k,mu;
if ((mu=(int)ROUND(L[i+j*n]))!=0) {
for (k=i;k<n;k++) L[k+n*j]-=(double)mu*L[k+i*n];
for (k=0;k<n;k++) Z[k+n*j]-=(double)mu*Z[k+i*n];
}
}
/* permutations --------------------------------------------------------------*/
static void perm(int n, double *L, double *D, int j, double del, double *Z)
{
int k;
double eta,lam,a0,a1;
eta=D[j]/del;
lam=D[j+1]*L[j+1+j*n]/del;
D[j]=eta*D[j+1]; D[j+1]=del;
for (k=0;k<=j-1;k++) {
a0=L[j+k*n]; a1=L[j+1+k*n];
L[j+k*n]=-L[j+1+j*n]*a0+a1;
L[j+1+k*n]=eta*a0+lam*a1;
}
L[j+1+j*n]=lam;
for (k=j+2;k<n;k++) SWAP(L[k+j*n],L[k+(j+1)*n]);
for (k=0;k<n;k++) SWAP(Z[k+j*n],Z[k+(j+1)*n]);
}
/* lambda reduction (z=Z'*a, Qz=Z'*Q*Z=L'*diag(D)*L) (ref.[1]) ---------------*/
static void reduction(int n, double *L, double *D, double *Z)
{
int i,j,k;
double del;
j=n-2; k=n-2;
while (j>=0) {
if (j<=k) for (i=j+1;i<n;i++) gauss(n,L,Z,i,j);
del=D[j]+L[j+1+j*n]*L[j+1+j*n]*D[j+1];
if (del+1E-6<D[j+1]) { /* compared considering numerical error */
perm(n,L,D,j,del,Z);
k=j; j=n-2;
}
else j--;
}
}
/* modified lambda (mlambda) search (ref. [2]) -------------------------------*/
static int search(int n, int m, const double *L, const double *D,
const double *zs, double *zn, double *s)
{
int i,j,k,c,nn=0,imax=0;
double newdist,maxdist=1E99,y;
double *S=zeros(n,n),*dist=mat(n,1),*zb=mat(n,1),*z=mat(n,1),*step=mat(n,1);
k=n-1; dist[k]=0.0;
zb[k]=zs[k];
z[k]=ROUND(zb[k]); y=zb[k]-z[k]; step[k]=SGN(y);
for (c=0;c<LOOPMAX;c++) {
newdist=dist[k]+y*y/D[k];
if (newdist<maxdist) {
if (k!=0) {
dist[--k]=newdist;
for (i=0;i<=k;i++)
S[k+i*n]=S[k+1+i*n]+(z[k+1]-zb[k+1])*L[k+1+i*n];
zb[k]=zs[k]+S[k+k*n];
z[k]=ROUND(zb[k]); y=zb[k]-z[k]; step[k]=SGN(y);
}
else {
if (nn<m) {
if (nn==0||newdist>s[imax]) imax=nn;
for (i=0;i<n;i++) zn[i+nn*n]=z[i];
s[nn++]=newdist;
}
else {
if (newdist<s[imax]) {
for (i=0;i<n;i++) zn[i+imax*n]=z[i];
s[imax]=newdist;
for (i=imax=0;i<m;i++) if (s[imax]<s[i]) imax=i;
}
maxdist=s[imax];
}
z[0]+=step[0]; y=zb[0]-z[0]; step[0]=-step[0]-SGN(step[0]);
}
}
else {
if (k==n-1) break;
else {
k++;
z[k]+=step[k]; y=zb[k]-z[k]; step[k]=-step[k]-SGN(step[k]);
}
}
}
for (i=0;i<m-1;i++) { /* sort by s */
for (j=i+1;j<m;j++) {
if (s[i]<s[j]) continue;
SWAP(s[i],s[j]);
for (k=0;k<n;k++) SWAP(zn[k+i*n],zn[k+j*n]);
}
}
free(S); free(dist); free(zb); free(z); free(step);
if (c>=LOOPMAX) {
fprintf(stderr,"%s : search loop count overflow\n",__FILE__);
return -1;
}
return 0;
}
/* lambda/mlambda integer least-square estimation ------------------------------
* integer least-square estimation. reduction is performed by lambda (ref.[1]),
* and search by mlambda (ref.[2]).
* args : int n I number of float parameters
* int m I number of fixed solutions
* double *a I float parameters (n x 1)
* double *Q I covariance matrix of float parameters (n x n)
* double *F O fixed solutions (n x m)
* double *s O sum of squared residulas of fixed solutions (1 x m)
* return : status (0:ok,other:error)
* notes : matrix stored by column-major order (fortran convension)
*-----------------------------------------------------------------------------*/
extern int lambda(int n, int m, const double *a, const double *Q, double *F,
double *s)
{
int info;
double *L,*D,*Z,*z,*E;
if (n<=0||m<=0) return -1;
L=zeros(n,n); D=mat(n,1); Z=eye(n); z=mat(n,1); E=mat(n,m);
/* LD factorization */
if (!(info=LD(n,Q,L,D))) {
/* lambda reduction */
reduction(n,L,D,Z);
matmul("TN",n,1,n,1.0,Z,a,0.0,z); /* z=Z'*a */
/* mlambda search */
if (!(info=search(n,m,L,D,z,E,s))) {
info=solve("T",Z,E,n,m,F); /* F=Z'\E */
}
}
free(L); free(D); free(Z); free(z); free(E);
return info;
}
/* lambda reduction ------------------------------------------------------------
* reduction by lambda (ref [1]) for integer least square
* args : int n I number of float parameters
* double *Q I covariance matrix of float parameters (n x n)
* double *Z O lambda reduction matrix (n x n)
* return : status (0:ok,other:error)
*-----------------------------------------------------------------------------*/
extern int lambda_reduction(int n, const double *Q, double *Z)
{
double *L,*D;
int i,j,info;
if (n<=0) return -1;
L=zeros(n,n); D=mat(n,1);
for (i=0;i<n;i++) for (j=0;j<n;j++) {
Z[i+j*n]=i==j?1.0:0.0;
}
/* LD factorization */
if ((info=LD(n,Q,L,D))) {
free(L); free(D);
return info;
}
/* lambda reduction */
reduction(n,L,D,Z);
free(L); free(D);
return 0;
}
/* mlambda search --------------------------------------------------------------
* search by mlambda (ref [2]) for integer least square
* args : int n I number of float parameters
* int m I number of fixed solutions
* double *a I float parameters (n x 1)
* double *Q I covariance matrix of float parameters (n x n)
* double *F O fixed solutions (n x m)
* double *s O sum of squared residulas of fixed solutions (1 x m)
* return : status (0:ok,other:error)
*-----------------------------------------------------------------------------*/
extern int lambda_search(int n, int m, const double *a, const double *Q,
double *F, double *s)
{
double *L,*D;
int info;
if (n<=0||m<=0) return -1;
L=zeros(n,n); D=mat(n,1);
/* LD factorization */
if ((info=LD(n,Q,L,D))) {
free(L); free(D);
return info;
}
/* mlambda search */
info=search(n,m,L,D,a,F,s);
free(L); free(D);
return info;
}