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Diffstat (limited to 'libraries/ode-0.9/ode/src/matrix.cpp')
-rw-r--r-- | libraries/ode-0.9/ode/src/matrix.cpp | 358 |
1 files changed, 0 insertions, 358 deletions
diff --git a/libraries/ode-0.9/ode/src/matrix.cpp b/libraries/ode-0.9/ode/src/matrix.cpp deleted file mode 100644 index 16afe91..0000000 --- a/libraries/ode-0.9/ode/src/matrix.cpp +++ /dev/null | |||
@@ -1,358 +0,0 @@ | |||
1 | /************************************************************************* | ||
2 | * * | ||
3 | * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. * | ||
4 | * All rights reserved. Email: russ@q12.org Web: www.q12.org * | ||
5 | * * | ||
6 | * This library is free software; you can redistribute it and/or * | ||
7 | * modify it under the terms of EITHER: * | ||
8 | * (1) The GNU Lesser General Public License as published by the Free * | ||
9 | * Software Foundation; either version 2.1 of the License, or (at * | ||
10 | * your option) any later version. The text of the GNU Lesser * | ||
11 | * General Public License is included with this library in the * | ||
12 | * file LICENSE.TXT. * | ||
13 | * (2) The BSD-style license that is included with this library in * | ||
14 | * the file LICENSE-BSD.TXT. * | ||
15 | * * | ||
16 | * This library is distributed in the hope that it will be useful, * | ||
17 | * but WITHOUT ANY WARRANTY; without even the implied warranty of * | ||
18 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files * | ||
19 | * LICENSE.TXT and LICENSE-BSD.TXT for more details. * | ||
20 | * * | ||
21 | *************************************************************************/ | ||
22 | |||
23 | #include <ode/common.h> | ||
24 | #include <ode/matrix.h> | ||
25 | |||
26 | // misc defines | ||
27 | #define ALLOCA dALLOCA16 | ||
28 | |||
29 | |||
30 | void dSetZero (dReal *a, int n) | ||
31 | { | ||
32 | dAASSERT (a && n >= 0); | ||
33 | while (n > 0) { | ||
34 | *(a++) = 0; | ||
35 | n--; | ||
36 | } | ||
37 | } | ||
38 | |||
39 | |||
40 | void dSetValue (dReal *a, int n, dReal value) | ||
41 | { | ||
42 | dAASSERT (a && n >= 0); | ||
43 | while (n > 0) { | ||
44 | *(a++) = value; | ||
45 | n--; | ||
46 | } | ||
47 | } | ||
48 | |||
49 | |||
50 | void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r) | ||
51 | { | ||
52 | int i,j,k,qskip,rskip,rpad; | ||
53 | dAASSERT (A && B && C && p>0 && q>0 && r>0); | ||
54 | qskip = dPAD(q); | ||
55 | rskip = dPAD(r); | ||
56 | rpad = rskip - r; | ||
57 | dReal sum; | ||
58 | const dReal *b,*c,*bb; | ||
59 | bb = B; | ||
60 | for (i=p; i; i--) { | ||
61 | for (j=0 ; j<r; j++) { | ||
62 | c = C + j; | ||
63 | b = bb; | ||
64 | sum = 0; | ||
65 | for (k=q; k; k--, c+=rskip) sum += (*(b++))*(*c); | ||
66 | *(A++) = sum; | ||
67 | } | ||
68 | A += rpad; | ||
69 | bb += qskip; | ||
70 | } | ||
71 | } | ||
72 | |||
73 | |||
74 | void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r) | ||
75 | { | ||
76 | int i,j,k,pskip,rskip; | ||
77 | dReal sum; | ||
78 | dAASSERT (A && B && C && p>0 && q>0 && r>0); | ||
79 | pskip = dPAD(p); | ||
80 | rskip = dPAD(r); | ||
81 | for (i=0; i<p; i++) { | ||
82 | for (j=0; j<r; j++) { | ||
83 | sum = 0; | ||
84 | for (k=0; k<q; k++) sum += B[i+k*pskip] * C[j+k*rskip]; | ||
85 | A[i*rskip+j] = sum; | ||
86 | } | ||
87 | } | ||
88 | } | ||
89 | |||
90 | |||
91 | void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r) | ||
92 | { | ||
93 | int i,j,k,z,rpad,qskip; | ||
94 | dReal sum; | ||
95 | const dReal *bb,*cc; | ||
96 | dAASSERT (A && B && C && p>0 && q>0 && r>0); | ||
97 | rpad = dPAD(r) - r; | ||
98 | qskip = dPAD(q); | ||
99 | bb = B; | ||
100 | for (i=p; i; i--) { | ||
101 | cc = C; | ||
102 | for (j=r; j; j--) { | ||
103 | z = 0; | ||
104 | sum = 0; | ||
105 | for (k=q; k; k--,z++) sum += bb[z] * cc[z]; | ||
106 | *(A++) = sum; | ||
107 | cc += qskip; | ||
108 | } | ||
109 | A += rpad; | ||
110 | bb += qskip; | ||
111 | } | ||
112 | } | ||
113 | |||
114 | |||
115 | int dFactorCholesky (dReal *A, int n) | ||
116 | { | ||
117 | int i,j,k,nskip; | ||
118 | dReal sum,*a,*b,*aa,*bb,*cc,*recip; | ||
119 | dAASSERT (n > 0 && A); | ||
120 | nskip = dPAD (n); | ||
121 | recip = (dReal*) ALLOCA (n * sizeof(dReal)); | ||
122 | aa = A; | ||
123 | for (i=0; i<n; i++) { | ||
124 | bb = A; | ||
125 | cc = A + i*nskip; | ||
126 | for (j=0; j<i; j++) { | ||
127 | sum = *cc; | ||
128 | a = aa; | ||
129 | b = bb; | ||
130 | for (k=j; k; k--) sum -= (*(a++))*(*(b++)); | ||
131 | *cc = sum * recip[j]; | ||
132 | bb += nskip; | ||
133 | cc++; | ||
134 | } | ||
135 | sum = *cc; | ||
136 | a = aa; | ||
137 | for (k=i; k; k--, a++) sum -= (*a)*(*a); | ||
138 | if (sum <= REAL(0.0)) return 0; | ||
139 | *cc = dSqrt(sum); | ||
140 | recip[i] = dRecip (*cc); | ||
141 | aa += nskip; | ||
142 | } | ||
143 | return 1; | ||
144 | } | ||
145 | |||
146 | |||
147 | void dSolveCholesky (const dReal *L, dReal *b, int n) | ||
148 | { | ||
149 | int i,k,nskip; | ||
150 | dReal sum,*y; | ||
151 | dAASSERT (n > 0 && L && b); | ||
152 | nskip = dPAD (n); | ||
153 | y = (dReal*) ALLOCA (n*sizeof(dReal)); | ||
154 | for (i=0; i<n; i++) { | ||
155 | sum = 0; | ||
156 | for (k=0; k < i; k++) sum += L[i*nskip+k]*y[k]; | ||
157 | y[i] = (b[i]-sum)/L[i*nskip+i]; | ||
158 | } | ||
159 | for (i=n-1; i >= 0; i--) { | ||
160 | sum = 0; | ||
161 | for (k=i+1; k < n; k++) sum += L[k*nskip+i]*b[k]; | ||
162 | b[i] = (y[i]-sum)/L[i*nskip+i]; | ||
163 | } | ||
164 | } | ||
165 | |||
166 | |||
167 | int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n) | ||
168 | { | ||
169 | int i,j,nskip; | ||
170 | dReal *L,*x; | ||
171 | dAASSERT (n > 0 && A && Ainv); | ||
172 | nskip = dPAD (n); | ||
173 | L = (dReal*) ALLOCA (nskip*n*sizeof(dReal)); | ||
174 | memcpy (L,A,nskip*n*sizeof(dReal)); | ||
175 | x = (dReal*) ALLOCA (n*sizeof(dReal)); | ||
176 | if (dFactorCholesky (L,n)==0) return 0; | ||
177 | dSetZero (Ainv,n*nskip); // make sure all padding elements set to 0 | ||
178 | for (i=0; i<n; i++) { | ||
179 | for (j=0; j<n; j++) x[j] = 0; | ||
180 | x[i] = 1; | ||
181 | dSolveCholesky (L,x,n); | ||
182 | for (j=0; j<n; j++) Ainv[j*nskip+i] = x[j]; | ||
183 | } | ||
184 | return 1; | ||
185 | } | ||
186 | |||
187 | |||
188 | int dIsPositiveDefinite (const dReal *A, int n) | ||
189 | { | ||
190 | dReal *Acopy; | ||
191 | dAASSERT (n > 0 && A); | ||
192 | int nskip = dPAD (n); | ||
193 | Acopy = (dReal*) ALLOCA (nskip*n * sizeof(dReal)); | ||
194 | memcpy (Acopy,A,nskip*n * sizeof(dReal)); | ||
195 | return dFactorCholesky (Acopy,n); | ||
196 | } | ||
197 | |||
198 | |||
199 | /***** this has been replaced by a faster version | ||
200 | void dSolveL1T (const dReal *L, dReal *b, int n, int nskip) | ||
201 | { | ||
202 | int i,j; | ||
203 | dAASSERT (L && b && n >= 0 && nskip >= n); | ||
204 | dReal sum; | ||
205 | for (i=n-2; i>=0; i--) { | ||
206 | sum = 0; | ||
207 | for (j=i+1; j<n; j++) sum += L[j*nskip+i]*b[j]; | ||
208 | b[i] -= sum; | ||
209 | } | ||
210 | } | ||
211 | */ | ||
212 | |||
213 | |||
214 | void dVectorScale (dReal *a, const dReal *d, int n) | ||
215 | { | ||
216 | dAASSERT (a && d && n >= 0); | ||
217 | for (int i=0; i<n; i++) a[i] *= d[i]; | ||
218 | } | ||
219 | |||
220 | |||
221 | void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip) | ||
222 | { | ||
223 | dAASSERT (L && d && b && n > 0 && nskip >= n); | ||
224 | dSolveL1 (L,b,n,nskip); | ||
225 | dVectorScale (b,d,n); | ||
226 | dSolveL1T (L,b,n,nskip); | ||
227 | } | ||
228 | |||
229 | |||
230 | void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip) | ||
231 | { | ||
232 | int j,p; | ||
233 | dReal *W1,*W2,W11,W21,alpha1,alpha2,alphanew,gamma1,gamma2,k1,k2,Wp,ell,dee; | ||
234 | dAASSERT (L && d && a && n > 0 && nskip >= n); | ||
235 | |||
236 | if (n < 2) return; | ||
237 | W1 = (dReal*) ALLOCA (n*sizeof(dReal)); | ||
238 | W2 = (dReal*) ALLOCA (n*sizeof(dReal)); | ||
239 | |||
240 | W1[0] = 0; | ||
241 | W2[0] = 0; | ||
242 | for (j=1; j<n; j++) W1[j] = W2[j] = a[j] * M_SQRT1_2; | ||
243 | W11 = (REAL(0.5)*a[0]+1)*M_SQRT1_2; | ||
244 | W21 = (REAL(0.5)*a[0]-1)*M_SQRT1_2; | ||
245 | |||
246 | alpha1=1; | ||
247 | alpha2=1; | ||
248 | |||
249 | dee = d[0]; | ||
250 | alphanew = alpha1 + (W11*W11)*dee; | ||
251 | dee /= alphanew; | ||
252 | gamma1 = W11 * dee; | ||
253 | dee *= alpha1; | ||
254 | alpha1 = alphanew; | ||
255 | alphanew = alpha2 - (W21*W21)*dee; | ||
256 | dee /= alphanew; | ||
257 | gamma2 = W21 * dee; | ||
258 | alpha2 = alphanew; | ||
259 | k1 = REAL(1.0) - W21*gamma1; | ||
260 | k2 = W21*gamma1*W11 - W21; | ||
261 | for (p=1; p<n; p++) { | ||
262 | Wp = W1[p]; | ||
263 | ell = L[p*nskip]; | ||
264 | W1[p] = Wp - W11*ell; | ||
265 | W2[p] = k1*Wp + k2*ell; | ||
266 | } | ||
267 | |||
268 | for (j=1; j<n; j++) { | ||
269 | dee = d[j]; | ||
270 | alphanew = alpha1 + (W1[j]*W1[j])*dee; | ||
271 | dee /= alphanew; | ||
272 | gamma1 = W1[j] * dee; | ||
273 | dee *= alpha1; | ||
274 | alpha1 = alphanew; | ||
275 | alphanew = alpha2 - (W2[j]*W2[j])*dee; | ||
276 | dee /= alphanew; | ||
277 | gamma2 = W2[j] * dee; | ||
278 | dee *= alpha2; | ||
279 | d[j] = dee; | ||
280 | alpha2 = alphanew; | ||
281 | |||
282 | k1 = W1[j]; | ||
283 | k2 = W2[j]; | ||
284 | for (p=j+1; p<n; p++) { | ||
285 | ell = L[p*nskip+j]; | ||
286 | Wp = W1[p] - k1 * ell; | ||
287 | ell += gamma1 * Wp; | ||
288 | W1[p] = Wp; | ||
289 | Wp = W2[p] - k2 * ell; | ||
290 | ell -= gamma2 * Wp; | ||
291 | W2[p] = Wp; | ||
292 | L[p*nskip+j] = ell; | ||
293 | } | ||
294 | } | ||
295 | } | ||
296 | |||
297 | |||
298 | // macros for dLDLTRemove() for accessing A - either access the matrix | ||
299 | // directly or access it via row pointers. we are only supposed to reference | ||
300 | // the lower triangle of A (it is symmetric), but indexes i and j come from | ||
301 | // permutation vectors so they are not predictable. so do a test on the | ||
302 | // indexes - this should not slow things down too much, as we don't do this | ||
303 | // in an inner loop. | ||
304 | |||
305 | #define _GETA(i,j) (A[i][j]) | ||
306 | //#define _GETA(i,j) (A[(i)*nskip+(j)]) | ||
307 | #define GETA(i,j) ((i > j) ? _GETA(i,j) : _GETA(j,i)) | ||
308 | |||
309 | |||
310 | void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d, | ||
311 | int n1, int n2, int r, int nskip) | ||
312 | { | ||
313 | int i; | ||
314 | dAASSERT(A && p && L && d && n1 > 0 && n2 > 0 && r >= 0 && r < n2 && | ||
315 | n1 >= n2 && nskip >= n1); | ||
316 | #ifndef dNODEBUG | ||
317 | for (i=0; i<n2; i++) dIASSERT(p[i] >= 0 && p[i] < n1); | ||
318 | #endif | ||
319 | |||
320 | if (r==n2-1) { | ||
321 | return; // deleting last row/col is easy | ||
322 | } | ||
323 | else if (r==0) { | ||
324 | dReal *a = (dReal*) ALLOCA (n2 * sizeof(dReal)); | ||
325 | for (i=0; i<n2; i++) a[i] = -GETA(p[i],p[0]); | ||
326 | a[0] += REAL(1.0); | ||
327 | dLDLTAddTL (L,d,a,n2,nskip); | ||
328 | } | ||
329 | else { | ||
330 | dReal *t = (dReal*) ALLOCA (r * sizeof(dReal)); | ||
331 | dReal *a = (dReal*) ALLOCA ((n2-r) * sizeof(dReal)); | ||
332 | for (i=0; i<r; i++) t[i] = L[r*nskip+i] / d[i]; | ||
333 | for (i=0; i<(n2-r); i++) | ||
334 | a[i] = dDot(L+(r+i)*nskip,t,r) - GETA(p[r+i],p[r]); | ||
335 | a[0] += REAL(1.0); | ||
336 | dLDLTAddTL (L + r*nskip+r, d+r, a, n2-r, nskip); | ||
337 | } | ||
338 | |||
339 | // snip out row/column r from L and d | ||
340 | dRemoveRowCol (L,n2,nskip,r); | ||
341 | if (r < (n2-1)) memmove (d+r,d+r+1,(n2-r-1)*sizeof(dReal)); | ||
342 | } | ||
343 | |||
344 | |||
345 | void dRemoveRowCol (dReal *A, int n, int nskip, int r) | ||
346 | { | ||
347 | int i; | ||
348 | dAASSERT(A && n > 0 && nskip >= n && r >= 0 && r < n); | ||
349 | if (r >= n-1) return; | ||
350 | if (r > 0) { | ||
351 | for (i=0; i<r; i++) | ||
352 | memmove (A+i*nskip+r,A+i*nskip+r+1,(n-r-1)*sizeof(dReal)); | ||
353 | for (i=r; i<(n-1); i++) | ||
354 | memcpy (A+i*nskip,A+i*nskip+nskip,r*sizeof(dReal)); | ||
355 | } | ||
356 | for (i=r; i<(n-1); i++) | ||
357 | memcpy (A+i*nskip+r,A+i*nskip+nskip+r+1,(n-r-1)*sizeof(dReal)); | ||
358 | } | ||