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pprz_algebra_float.h
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20 
31 #ifndef PPRZ_ALGEBRA_FLOAT_H
32 #define PPRZ_ALGEBRA_FLOAT_H
33 
34 #ifdef __cplusplus
35 extern "C" {
36 #endif
37 
38 #include "pprz_algebra.h"
39 #include "message_pragmas.h"
40 
41 #include <math.h>
42 #include <float.h> // for FLT_MIN
43 
44 /* this seems to be missing for some arch */
45 #ifndef M_SQRT2
46 #define M_SQRT2 1.41421356237309504880
47 #endif
48 
49 struct FloatVect2 {
50  float x;
51  float y;
52 };
53 
54 struct FloatVect3 {
55  float x;
56  float y;
57  float z;
58 };
59 
63 struct FloatQuat {
64  float qi;
65  float qx;
66  float qy;
67  float qz;
68 };
69 
70 struct FloatMat33 {
71  float m[3 * 3];
72 };
73 
77 struct FloatRMat {
78  float m[3 * 3];
79 };
80 
84 struct FloatEulers {
85  float phi;
86  float theta;
87  float psi;
88 };
89 
93 struct FloatRates {
94  float p;
95  float q;
96  float r;
97 };
98 
99 #define FLOAT_ANGLE_NORMALIZE(_a) { \
100  while (_a > M_PI) _a -= (2.*M_PI); \
101  while (_a < -M_PI) _a += (2.*M_PI); \
102  }
103 
104 //
105 //
106 // Vector algebra
107 //
108 //
109 
110 
111 /*
112  * Dimension 2 Vectors
113  */
114 
115 #define FLOAT_VECT2_ZERO(_v) VECT2_ASSIGN(_v, 0., 0.)
116 
117 /* macros also usable if _v is not a FloatVect2, but a different struct with x,y members */
118 #define FLOAT_VECT2_NORM(_v) sqrtf(VECT2_NORM2(_v))
119 
120 static inline float float_vect2_norm2(struct FloatVect2 *v)
121 {
122  return v->x * v->x + v->y * v->y;
123 }
124 
125 static inline float float_vect2_norm(struct FloatVect2 *v)
126 {
127  return sqrtf(float_vect2_norm2(v));
128 }
129 
131 static inline void float_vect2_normalize(struct FloatVect2 *v)
132 {
133  const float n = float_vect2_norm(v);
134  if (n > 0) {
135  v->x /= n;
136  v->y /= n;
137  }
138 }
139 
140 #define FLOAT_VECT2_NORMALIZE(_v) float_vect2_normalize(&(_v))
141 
142 
143 /*
144  * Dimension 3 Vectors
145  */
146 
147 #define FLOAT_VECT3_ZERO(_v) VECT3_ASSIGN(_v, 0., 0., 0.)
148 
149 /* macros also usable if _v is not a FloatVect3, but a different struct with x,y,z members */
150 #define FLOAT_VECT3_NORM(_v) sqrtf(VECT3_NORM2(_v))
151 
152 static inline float float_vect3_norm2(struct FloatVect3 *v)
153 {
154  return v->x * v->x + v->y * v->y + v->z * v->z;
155 }
156 
157 static inline float float_vect3_norm(struct FloatVect3 *v)
158 {
159  return sqrtf(float_vect3_norm2(v));
160 }
161 
163 static inline void float_vect3_normalize(struct FloatVect3 *v)
164 {
165  const float n = float_vect3_norm(v);
166  if (n > 0) {
167  v->x /= n;
168  v->y /= n;
169  v->z /= n;
170  }
171 }
172 
173 #define FLOAT_VECT3_NORMALIZE(_v) float_vect3_normalize(&(_v))
174 
175 
176 
177 #define FLOAT_RATES_ZERO(_r) { \
178  RATES_ASSIGN(_r, 0., 0., 0.); \
179  }
180 
181 #define FLOAT_RATES_NORM(_v) (sqrtf((_v).p*(_v).p + (_v).q*(_v).q + (_v).r*(_v).r))
182 
183 #define FLOAT_RATES_LIN_CMB(_ro, _r1, _s1, _r2, _s2) { \
184  _ro.p = _s1 * _r1.p + _s2 * _r2.p; \
185  _ro.q = _s1 * _r1.q + _s2 * _r2.q; \
186  _ro.r = _s1 * _r1.r + _s2 * _r2.r; \
187  }
188 
189 
190 extern void float_vect3_integrate_fi(struct FloatVect3 *vec, struct FloatVect3 *dv,
191  float dt);
192 
193 extern void float_rates_integrate_fi(struct FloatRates *r, struct FloatRates *dr,
194  float dt);
195 
196 extern void float_rates_of_euler_dot(struct FloatRates *r, struct FloatEulers *e,
197  struct FloatEulers *edot);
198 
199 /* defines for backwards compatibility */
200 #define FLOAT_VECT3_INTEGRATE_FI(_vo, _dv, _dt) WARNING("FLOAT_VECT3_INTEGRATE_FI macro is deprecated, use the lower case function instead") float_vect3_integrate_fi(&(_vo), &(_dv), _dt)
201 #define FLOAT_RATES_INTEGRATE_FI(_ra, _racc, _dt) WARNING("FLOAT_RATES_INTEGRATE_FI macro is deprecated, use the lower case function instead") float_rates_integrate_fi(&(_ra), &(_racc), _dt)
202 #define FLOAT_RATES_OF_EULER_DOT(_ra, _e, _ed) WARNING("FLOAT_RATES_OF_EULER_DOT macro is deprecated, use the lower case function instead") float_rates_of_euler_dot(&(_ra), &(_e), &(_ed))
203 
204 
205 /*
206  * 3x3 matrices
207  */
208 #define FLOAT_MAT33_ZERO(_m) { \
209  MAT33_ELMT(_m, 0, 0) = 0.; \
210  MAT33_ELMT(_m, 0, 1) = 0.; \
211  MAT33_ELMT(_m, 0, 2) = 0.; \
212  MAT33_ELMT(_m, 1, 0) = 0.; \
213  MAT33_ELMT(_m, 1, 1) = 0.; \
214  MAT33_ELMT(_m, 1, 2) = 0.; \
215  MAT33_ELMT(_m, 2, 0) = 0.; \
216  MAT33_ELMT(_m, 2, 1) = 0.; \
217  MAT33_ELMT(_m, 2, 2) = 0.; \
218  }
219 
220 #define FLOAT_MAT33_DIAG(_m, _d00, _d11, _d22) { \
221  MAT33_ELMT(_m, 0, 0) = _d00; \
222  MAT33_ELMT(_m, 0, 1) = 0.; \
223  MAT33_ELMT(_m, 0, 2) = 0.; \
224  MAT33_ELMT(_m, 1, 0) = 0.; \
225  MAT33_ELMT(_m, 1, 1) = _d11; \
226  MAT33_ELMT(_m, 1, 2) = 0.; \
227  MAT33_ELMT(_m, 2, 0) = 0.; \
228  MAT33_ELMT(_m, 2, 1) = 0.; \
229  MAT33_ELMT(_m, 2, 2) = _d22; \
230  }
231 
232 
233 //
234 //
235 // Rotation Matrices
236 //
237 //
238 
239 
241 static inline void float_rmat_identity(struct FloatRMat *rm)
242 {
243  FLOAT_MAT33_DIAG(*rm, 1., 1., 1.);
244 }
245 
249 extern void float_rmat_inv(struct FloatRMat *m_b2a, struct FloatRMat *m_a2b);
250 
254 extern void float_rmat_comp(struct FloatRMat *m_a2c, struct FloatRMat *m_a2b,
255  struct FloatRMat *m_b2c);
256 
260 extern void float_rmat_comp_inv(struct FloatRMat *m_a2b, struct FloatRMat *m_a2c,
261  struct FloatRMat *m_b2c);
262 
264 extern float float_rmat_norm(struct FloatRMat *rm);
265 
269 extern void float_rmat_vmult(struct FloatVect3 *vb, struct FloatRMat *m_a2b,
270  struct FloatVect3 *va);
271 
275 extern void float_rmat_transp_vmult(struct FloatVect3 *vb, struct FloatRMat *m_b2a,
276  struct FloatVect3 *va);
277 
281 extern void float_rmat_ratemult(struct FloatRates *rb, struct FloatRMat *m_a2b,
282  struct FloatRates *ra);
283 
287 extern void float_rmat_transp_ratemult(struct FloatRates *rb, struct FloatRMat *m_b2a,
288  struct FloatRates *ra);
289 
291 extern void float_rmat_of_axis_angle(struct FloatRMat *rm, struct FloatVect3 *uv, float angle);
292 
305 extern void float_rmat_of_eulers_321(struct FloatRMat *rm, struct FloatEulers *e);
306 extern void float_rmat_of_eulers_312(struct FloatRMat *rm, struct FloatEulers *e);
307 #define float_rmat_of_eulers float_rmat_of_eulers_321
308 
309 extern void float_rmat_of_quat(struct FloatRMat *rm, struct FloatQuat *q);
311 extern void float_rmat_integrate_fi(struct FloatRMat *rm, struct FloatRates *omega, float dt);
312 extern float float_rmat_reorthogonalize(struct FloatRMat *rm);
313 
314 /* defines for backwards compatibility */
315 #define FLOAT_RMAT_INV(_m_b2a, _m_a2b) WARNING("FLOAT_RMAT_INV macro is deprecated, use the lower case function instead") float_rmat_inv(&(_m_b2a), &(_m_a2b))
316 #define FLOAT_RMAT_NORM(_m) WARNING("FLOAT_RMAT_NORM macro is deprecated, use the lower case function instead") float_rmat_norm(&(_m))
317 #define FLOAT_RMAT_COMP(_m_a2c, _m_a2b, _m_b2c) WARNING("FLOAT_RMAT_COMP macro is deprecated, use the lower case function instead") float_rmat_comp(&(_m_a2c), &(_m_a2b), &(_m_b2c))
318 #define FLOAT_RMAT_COMP_INV(_m_a2b, _m_a2c, _m_b2c) WARNING("FLOAT_RMAT_COMP_INV macro is deprecated, use the lower case function instead") float_rmat_comp_inv(&(_m_a2b), &(_m_a2c), &(_m_b2c))
319 #define FLOAT_RMAT_VMULT(_vb, _m_a2b, _va) WARNING("FLOAT_RMAT_VMULT macro is deprecated, use the lower case function instead") float_rmat_vmult(&(_vb), &(_m_a2b), &(_va))
320 #define FLOAT_RMAT_TRANSP_VMULT(_vb, _m_b2a, _va) WARNING("FLOAT_RMAT_TRANSP_VMULT macro is deprecated, use the lower case function instead") float_rmat_transp_vmult(&(_vb), &(_m_b2a), &(_va))
321 #define FLOAT_RMAT_RATEMULT(_rb, _m_a2b, _ra) WARNING("FLOAT_RMAT_RATEMULT macro is deprecated, use the lower case function instead") float_rmat_ratemult(&(_rb), &(_m_a2b), &(_ra))
322 #define FLOAT_RMAT_TRANSP_RATEMULT(_rb, _m_b2a, _ra) WARNING("FLOAT_RMAT_TRANSP_RATEMULT macro is deprecated, use the lower case function instead") float_rmat_ratemult(&(_rb), &(_m_b2a), &(_ra))
323 #define FLOAT_RMAT_OF_AXIS_ANGLE(_rm, _uv, _an) WARNING("FLOAT_RMAT_OF_AXIS_ANGLE macro is deprecated, use the lower case function instead") float_rmat_of_axis_angle(&(_rm), &(_uv), _an)
324 #define FLOAT_RMAT_OF_EULERS(_rm, _e) WARNING("FLOAT_RMAT_OF_EULERS macro is deprecated, use the lower case function instead") float_rmat_of_eulers_321(&(_rm), &(_e))
325 #define FLOAT_RMAT_OF_EULERS_321(_rm, _e) WARNING("FLOAT_RMAT_OF_EULERS_321 macro is deprecated, use the lower case function instead") float_rmat_of_eulers_321(&(_rm), &(_e))
326 #define FLOAT_RMAT_OF_EULERS_312(_rm, _e) WARNING("FLOAT_RMAT_OF_EULERS_312 macro is deprecated, use the lower case function instead") float_rmat_of_eulers_312(&(_rm), &(_e))
327 #define FLOAT_RMAT_OF_QUAT(_rm, _q) WARNING("FLOAT_RMAT_OF_QUAT macro is deprecated, use the lower case function instead") float_rmat_of_quat(&(_rm), &(_q))
328 #define FLOAT_RMAT_INTEGRATE_FI(_rm, _omega, _dt) WARNING("FLOAT_RMAT_INTEGRATE_FI macro is deprecated, use the lower case function instead") float_rmat_integrate_fi(&(_rm), &(_omega), &(_dt))
329 
330 
331 
332 //
333 //
334 // Quaternion algebras
335 //
336 //
337 
339 static inline void float_quat_identity(struct FloatQuat *q)
340 {
341  q->qi = 1.0;
342  q->qx = 0;
343  q->qy = 0;
344  q->qz = 0;
345 }
346 
347 #define FLOAT_QUAT_NORM2(_q) (SQUARE((_q).qi) + SQUARE((_q).qx) + SQUARE((_q).qy) + SQUARE((_q).qz))
348 
349 static inline float float_quat_norm(struct FloatQuat *q)
350 {
351  return sqrtf(SQUARE(q->qi) + SQUARE(q->qx) + SQUARE(q->qy) + SQUARE(q->qz));
352 }
353 
354 static inline void float_quat_normalize(struct FloatQuat *q)
355 {
356  float qnorm = float_quat_norm(q);
357  if (qnorm > FLT_MIN) {
358  q->qi = q->qi / qnorm;
359  q->qx = q->qx / qnorm;
360  q->qy = q->qy / qnorm;
361  q->qz = q->qz / qnorm;
362  }
363 }
364 
365 static inline void float_quat_invert(struct FloatQuat *qo, struct FloatQuat *qi)
366 {
367  QUAT_INVERT(*qo, *qi);
368 }
369 
370 static inline void float_quat_wrap_shortest(struct FloatQuat *q)
371 {
372  if (q->qi < 0.) {
373  QUAT_EXPLEMENTARY(*q, *q);
374  }
375 }
376 
377 #define FLOAT_QUAT_EXTRACT(_vo, _qi) QUAT_EXTRACT_Q(_vo, _qi)
378 
379 
383 extern void float_quat_comp(struct FloatQuat *a2c, struct FloatQuat *a2b, struct FloatQuat *b2c);
384 
388 extern void float_quat_comp_inv(struct FloatQuat *a2b, struct FloatQuat *a2c, struct FloatQuat *b2c);
389 
393 extern void float_quat_inv_comp(struct FloatQuat *b2c, struct FloatQuat *a2b, struct FloatQuat *a2c);
394 
398 extern void float_quat_comp_norm_shortest(struct FloatQuat *a2c, struct FloatQuat *a2b, struct FloatQuat *b2c);
399 
403 extern void float_quat_comp_inv_norm_shortest(struct FloatQuat *a2b, struct FloatQuat *a2c, struct FloatQuat *b2c);
404 
408 extern void float_quat_inv_comp_norm_shortest(struct FloatQuat *b2c, struct FloatQuat *a2b, struct FloatQuat *a2c);
409 
415 extern void float_quat_derivative(struct FloatQuat *qd, struct FloatRates *r, struct FloatQuat *q);
416 
422 extern void float_quat_derivative_lagrange(struct FloatQuat *qd, struct FloatRates *r, struct FloatQuat *q);
423 
426 extern void float_quat_differential(struct FloatQuat *q_out, struct FloatRates *w, float dt);
427 
429 extern void float_quat_integrate_fi(struct FloatQuat *q, struct FloatRates *omega, float dt);
430 
432 extern void float_quat_integrate(struct FloatQuat *q, struct FloatRates *omega, float dt);
433 
437 extern void float_quat_vmult(struct FloatVect3 *v_out, struct FloatQuat *q, const struct FloatVect3 *v_in);
438 
440 extern void float_quat_of_eulers(struct FloatQuat *q, struct FloatEulers *e);
441 
443 extern void float_quat_of_axis_angle(struct FloatQuat *q, const struct FloatVect3 *uv, float angle);
444 
448 extern void float_quat_of_orientation_vect(struct FloatQuat *q, const struct FloatVect3 *ov);
449 
451 extern void float_quat_of_rmat(struct FloatQuat *q, struct FloatRMat *rm);
452 
453 
454 /* defines for backwards compatibility */
455 #define FLOAT_QUAT_ZERO(_q) WARNING("FLOAT_QUAT_ZERO macro is deprecated, use the lower case function instead") float_quat_identity(&(_q))
456 #define FLOAT_QUAT_INVERT(_qo, _qi) WARNING("FLOAT_QUAT_INVERT macro is deprecated, use the lower case function instead") float_quat_invert(&(_qo), &(_qi))
457 #define FLOAT_QUAT_WRAP_SHORTEST(_q) WARNING("FLOAT_QUAT_WRAP_SHORTEST macro is deprecated, use the lower case function instead") float_quat_wrap_shortest(&(_q))
458 #define FLOAT_QUAT_NORM(_q) WARNING("FLOAT_QUAT_NORM macro is deprecated, use the lower case function instead") float_quat_norm(&(_q))
459 #define FLOAT_QUAT_NORMALIZE(_q) WARNING("FLOAT_QUAT_NORMALIZE macro is deprecated, use the lower case function instead") float_quat_normalize(&(_q))
460 #define FLOAT_QUAT_COMP(_a2c, _a2b, _b2c) WARNING("FLOAT_QUAT_COMP macro is deprecated, use the lower case function instead") float_quat_comp(&(_a2c), &(_a2b), &(_b2c))
461 #define FLOAT_QUAT_MULT(_a2c, _a2b, _b2c) WARNING("FLOAT_QUAT_MULT macro is deprecated, use the lower case function instead") float_quat_comp(&(_a2c), &(_a2b), &(_b2c))
462 #define FLOAT_QUAT_INV_COMP(_b2c, _a2b, _a2c) WARNING("FLOAT_QUAT_INV_COMP macro is deprecated, use the lower case function instead") float_quat_inv_comp(&(_b2c), &(_a2b), &(_a2c))
463 #define FLOAT_QUAT_COMP_INV(_a2b, _a2c, _b2c) WARNING("FLOAT_QUAT_COMP_INV macro is deprecated, use the lower case function instead") float_quat_comp_inv(&(_a2b), &(_a2c), &(_b2c))
464 #define FLOAT_QUAT_COMP_NORM_SHORTEST(_a2c, _a2b, _b2c) WARNING("FLOAT_QUAT_COMP_NORM_SHORTEST macro is deprecated, use the lower case function instead") float_quat_comp_norm_shortest(&(_a2c), &(_a2b), &(_b2c))
465 #define FLOAT_QUAT_COMP_INV_NORM_SHORTEST(_a2b, _a2c, _b2c) WARNING("FLOAT_QUAT_COMP_INV_NORM_SHORTEST macro is deprecated, use the lower case function instead") float_quat_comp_inv_norm_shortest(&(_a2b), &(_a2c), &(_b2c))
466 #define FLOAT_QUAT_INV_COMP_NORM_SHORTEST(_b2c, _a2b, _a2c) WARNING("FLOAT_QUAT_INV_COMP_NORM_SHORTEST macro is deprecated, use the lower case function instead") float_quat_inv_comp_norm_shortest(&(_b2c), &(_a2b), &(_a2c))
467 #define FLOAT_QUAT_DIFFERENTIAL(q_out, w, dt) WARNING("FLOAT_QUAT_DIFFERENTIAL macro is deprecated, use the lower case function instead") float_quat_differential(&(q_out), &(w), dt)
468 #define FLOAT_QUAT_INTEGRATE(_q, _omega, _dt) WARNING("FLOAT_QUAT_INTEGRATE macro is deprecated, use the lower case function instead") float_quat_integrate(&(_q), &(_omega), _dt)
469 #define FLOAT_QUAT_VMULT(v_out, q, v_in) WARNING("FLOAT_QUAT_VMULT macro is deprecated, use the lower case function instead") float_quat_vmult(&(v_out), &(q), &(v_in))
470 #define FLOAT_QUAT_DERIVATIVE(_qd, _r, _q) WARNING("FLOAT_QUAT_DERIVATIVE macro is deprecated, use the lower case function instead") float_quat_derivative(&(_qd), &(_r), &(_q))
471 #define FLOAT_QUAT_DERIVATIVE_LAGRANGE(_qd, _r, _q) WARNING("FLOAT_QUAT_DERIVATIVE_LAGRANGE macro is deprecated, use the lower case function instead") float_quat_derivative_lagrange(&(_qd), &(_r), &(_q))
472 #define FLOAT_QUAT_OF_EULERS(_q, _e) WARNING("FLOAT_QUAT_OF_EULERS macro is deprecated, use the lower case function instead") float_quat_of_eulers(&(_q), &(_e))
473 #define FLOAT_QUAT_OF_AXIS_ANGLE(_q, _uv, _an) WARNING("FLOAT_QUAT_OF_AXIS_ANGLE macro is deprecated, use the lower case function instead") float_quat_of_axis_angle(&(_q), &(_uv), _an)
474 #define FLOAT_QUAT_OF_ORIENTATION_VECT(_q, _ov) WARNING("FLOAT_QUAT_OF_ORIENTATION_VECT macro is deprecated, use the lower case function instead") float_quat_of_orientation_vect(&(_q), &(_ov))
475 #define FLOAT_QUAT_OF_RMAT(_q, _r) WARNING("FLOAT_QUAT_OF_RMAT macro is deprecated, use the lower case function instead") float_quat_of_rmat(&(_q), &(_r))
476 
477 
478 
479 //
480 //
481 // Euler angles
482 //
483 //
484 
485 #define FLOAT_EULERS_ZERO(_e) EULERS_ASSIGN(_e, 0., 0., 0.);
486 
487 static inline float float_eulers_norm(struct FloatEulers *e)
488 {
489  return sqrtf(SQUARE(e->phi) + SQUARE(e->theta) + SQUARE(e->psi));
490 }
491 extern void float_eulers_of_rmat(struct FloatEulers *e, struct FloatRMat *rm);
492 extern void float_eulers_of_quat(struct FloatEulers *e, struct FloatQuat *q);
493 
494 /* defines for backwards compatibility */
495 #define FLOAT_EULERS_OF_RMAT(_e, _rm) WARNING("FLOAT_EULERS_OF_RMAT macro is deprecated, use the lower case function instead") float_eulers_of_rmat(&(_e), &(_rm))
496 #define FLOAT_EULERS_OF_QUAT(_e, _q) WARNING("FLOAT_EULERS_OF_QUAT macro is deprecated, use the lower case function instead") float_eulers_of_quat(&(_e), &(_q))
497 #define FLOAT_EULERS_NORM(_e) WARNING("FLOAT_EULERS_NORM macro is deprecated, use the lower case function instead") float_eulers_norm(&(_e))
498 
499 //
500 //
501 // Generic vector algebra
502 //
503 //
504 
506 static inline void float_vect_zero(float *a, const int n)
507 {
508  int i;
509  for (i = 0; i < n; i++) { a[i] = 0.; }
510 }
511 
513 static inline void float_vect_copy(float *a, const float *b, const int n)
514 {
515  int i;
516  for (i = 0; i < n; i++) { a[i] = b[i]; }
517 }
518 
520 static inline void float_vect_sum(float *o, const float *a, const float *b, const int n)
521 {
522  int i;
523  for (i = 0; i < n; i++) { o[i] = a[i] + b[i]; }
524 }
525 
527 static inline void float_vect_diff(float *o, const float *a, const float *b, const int n)
528 {
529  int i;
530  for (i = 0; i < n; i++) { o[i] = a[i] - b[i]; }
531 }
532 
534 static inline void float_vect_mul(float *o, const float *a, const float *b, const int n)
535 {
536  int i;
537  for (i = 0; i < n; i++) { o[i] = a[i] * b[i]; }
538 }
539 
541 static inline void float_vect_add(float *a, const float *b, const int n)
542 {
543  int i;
544  for (i = 0; i < n; i++) { a[i] += b[i]; }
545 }
546 
548 static inline void float_vect_sub(float *a, const float *b, const int n)
549 {
550  int i;
551  for (i = 0; i < n; i++) { a[i] -= b[i]; }
552 }
553 
555 static inline void float_vect_smul(float *o, const float *a, const float s, const int n)
556 {
557  int i;
558  for (i = 0; i < n; i++) { o[i] = a[i] * s; }
559 }
560 
562 static inline void float_vect_sdiv(float *o, const float *a, const float s, const int n)
563 {
564  int i;
565  if (fabs(s) > 1e-5) {
566  for (i = 0; i < n; i++) { o[i] = a[i] / s; }
567  }
568 }
569 
571 static inline float float_vect_norm(const float *a, const int n)
572 {
573  int i;
574  float sum = 0;
575  for (i = 0; i < n; i++) { sum += a[i] * a[i]; }
576  return sqrtf(sum);
577 }
578 
579 //
580 //
581 // Generic matrix algebra
582 //
583 //
584 
586 #define MAKE_MATRIX_PTR(_ptr, _mat, _rows) \
587  float * _ptr[_rows]; \
588  { \
589  int __i; \
590  for (__i = 0; __i < _rows; __i++) { _ptr[__i] = &_mat[__i][0]; } \
591  }
592 
594 static inline void float_mat_zero(float **a, int m, int n)
595 {
596  int i, j;
597  for (i = 0; i < m; i++) {
598  for (j = 0; j < n; j++) { a[i][j] = 0.; }
599  }
600 }
601 
603 static inline void float_mat_copy(float **a, float **b, int m, int n)
604 {
605  int i, j;
606  for (i = 0; i < m; i++) {
607  for (j = 0; j < n; j++) { a[i][j] = b[i][j]; }
608  }
609 }
610 
612 static inline void float_mat_sum(float **o, float **a, float **b, int m, int n)
613 {
614  int i, j;
615  for (i = 0; i < m; i++) {
616  for (j = 0; j < n; j++) { o[i][j] = a[i][j] + b[i][j]; }
617  }
618 }
619 
621 static inline void float_mat_diff(float **o, float **a, float **b, int m, int n)
622 {
623  int i, j;
624  for (i = 0; i < m; i++) {
625  for (j = 0; j < n; j++) { o[i][j] = a[i][j] - b[i][j]; }
626  }
627 }
628 
630 static inline void float_mat_transpose(float **a, int n)
631 {
632  int i, j;
633  for (i = 0; i < n; i++) {
634  for (j = 0; j < i; j++) {
635  float t = a[i][j];
636  a[i][j] = a[j][i];
637  a[j][i] = t;
638  }
639  }
640 }
641 
648 static inline void float_mat_mul(float **o, float **a, float **b, int m, int n, int l)
649 {
650  int i, j, k;
651  for (i = 0; i < m; i++) {
652  for (j = 0; j < l; j++) {
653  o[i][j] = 0.;
654  for (k = 0; k < n; k++) {
655  o[i][j] += a[i][k] * b[k][j];
656  }
657  }
658  }
659 }
660 
667 static inline void float_mat_minor(float **o, float **a, int m, int n, int d)
668 {
669  int i, j;
670  float_mat_zero(o, m, n);
671  for (i = 0; i < d; i++) { o[i][i] = 1.0; }
672  for (i = d; i < m; i++) {
673  for (j = d; j < n; j++) {
674  o[i][j] = a[i][j];
675  }
676  }
677 }
678 
680 static inline void float_mat_vmul(float **o, float *v, int n)
681 {
682  int i, j;
683  for (i = 0; i < n; i++) {
684  for (j = 0; j < n; j++) {
685  o[i][j] = -2. * v[i] * v[j];
686  }
687  }
688  for (i = 0; i < n; i++) {
689  o[i][i] += 1.;
690  }
691 }
692 
694 static inline void float_mat_col(float *o, float **a, int m, int c)
695 {
696  int i;
697  for (i = 0; i < m; i++) {
698  o[i] = a[i][c];
699  }
700 }
701 
702 #ifdef __cplusplus
703 } /* extern "C" */
704 #endif
705 
706 #endif /* PPRZ_ALGEBRA_FLOAT_H */
707 
static float float_eulers_norm(struct FloatEulers *e)
void float_quat_comp_inv(struct FloatQuat *a2b, struct FloatQuat *a2c, struct FloatQuat *b2c)
Composition (multiplication) of two quaternions.
static void float_vect_sum(float *o, const float *a, const float *b, const int n)
o = a + b
static void float_mat_transpose(float **a, int n)
transpose square matrix
void float_rmat_inv(struct FloatRMat *m_b2a, struct FloatRMat *m_a2b)
Inverse/transpose of a rotation matrix.
static float float_vect_norm(const float *a, const int n)
||a||
void float_quat_of_eulers(struct FloatQuat *q, struct FloatEulers *e)
Quaternion from Euler angles.
float phi
in radians
void float_quat_comp(struct FloatQuat *a2c, struct FloatQuat *a2b, struct FloatQuat *b2c)
Composition (multiplication) of two quaternions.
void float_vect3_integrate_fi(struct FloatVect3 *vec, struct FloatVect3 *dv, float dt)
in place first order integration of a 3D-vector
static void float_mat_copy(float **a, float **b, int m, int n)
a = b
static void float_vect_add(float *a, const float *b, const int n)
a += b
void float_eulers_of_rmat(struct FloatEulers *e, struct FloatRMat *rm)
static void float_mat_col(float *o, float **a, int m, int c)
o = c-th column of matrix a[m x n]
static void float_quat_identity(struct FloatQuat *q)
initialises a quaternion to identity
#define QUAT_INVERT(_qo, _qi)
Definition: pprz_algebra.h:563
float r
in rad/s
static void float_vect2_normalize(struct FloatVect2 *v)
normalize 2D vector in place
float float_rmat_norm(struct FloatRMat *rm)
Norm of a rotation matrix.
#define QUAT_EXPLEMENTARY(b, a)
Definition: pprz_algebra.h:539
float psi
in radians
#define FLOAT_MAT33_DIAG(_m, _d00, _d11, _d22)
static void float_mat_diff(float **o, float **a, float **b, int m, int n)
o = a - b
void float_rmat_comp_inv(struct FloatRMat *m_a2b, struct FloatRMat *m_a2c, struct FloatRMat *m_b2c)
Composition (multiplication) of two rotation matrices.
static void float_vect_sub(float *a, const float *b, const int n)
a -= b
static void float_mat_vmul(float **o, float *v, int n)
o = I - v v^T
float dt
#define SQUARE(_a)
Definition: pprz_algebra.h:47
static void float_rmat_identity(struct FloatRMat *rm)
initialises a rotation matrix to identity
float q
in rad/s
float p
in rad/s
void float_quat_inv_comp(struct FloatQuat *b2c, struct FloatQuat *a2b, struct FloatQuat *a2c)
Composition (multiplication) of two quaternions.
static void float_vect_sdiv(float *o, const float *a, const float s, const int n)
o = a / s
static float float_vect3_norm2(struct FloatVect3 *v)
euler angles
static void float_mat_minor(float **o, float **a, int m, int n, int d)
matrix minor
static void float_vect3_normalize(struct FloatVect3 *v)
normalize 3D vector in place
Roation quaternion.
void float_rmat_integrate_fi(struct FloatRMat *rm, struct FloatRates *omega, float dt)
in place first order integration of a rotation matrix
static float float_vect3_norm(struct FloatVect3 *v)
void float_rmat_of_eulers_312(struct FloatRMat *rm, struct FloatEulers *e)
float theta
in radians
void float_rmat_vmult(struct FloatVect3 *vb, struct FloatRMat *m_a2b, struct FloatVect3 *va)
rotate 3D vector by rotation matrix.
void float_rmat_comp(struct FloatRMat *m_a2c, struct FloatRMat *m_a2b, struct FloatRMat *m_b2c)
Composition (multiplication) of two rotation matrices.
void float_rmat_transp_vmult(struct FloatVect3 *vb, struct FloatRMat *m_b2a, struct FloatVect3 *va)
rotate 3D vector by transposed rotation matrix.
static void float_vect_mul(float *o, const float *a, const float *b, const int n)
o = a * b (element wise)
static float float_vect2_norm(struct FloatVect2 *v)
void float_rates_integrate_fi(struct FloatRates *r, struct FloatRates *dr, float dt)
in place first order integration of angular rates
void float_rmat_of_quat(struct FloatRMat *rm, struct FloatQuat *q)
Paparazzi generic algebra macros.
void float_quat_integrate(struct FloatQuat *q, struct FloatRates *omega, float dt)
in place quaternion integration with constant rotational velocity
static void float_vect_zero(float *a, const int n)
a = 0
static void float_mat_zero(float **a, int m, int n)
a = 0
void float_quat_vmult(struct FloatVect3 *v_out, struct FloatQuat *q, const struct FloatVect3 *v_in)
rotate 3D vector by quaternion.
static void float_quat_normalize(struct FloatQuat *q)
void float_quat_comp_inv_norm_shortest(struct FloatQuat *a2b, struct FloatQuat *a2c, struct FloatQuat *b2c)
Composition (multiplication) of two quaternions with normalization.
static void float_quat_invert(struct FloatQuat *qo, struct FloatQuat *qi)
void float_quat_of_rmat(struct FloatQuat *q, struct FloatRMat *rm)
Quaternion from rotation matrix.
static void float_vect_smul(float *o, const float *a, const float s, const int n)
o = a * s
static void float_vect_diff(float *o, const float *a, const float *b, const int n)
o = a - b
void float_rates_of_euler_dot(struct FloatRates *r, struct FloatEulers *e, struct FloatEulers *edot)
void float_quat_derivative(struct FloatQuat *qd, struct FloatRates *r, struct FloatQuat *q)
Quaternion derivative from rotational velocity.
float m[3 *3]
float float_rmat_reorthogonalize(struct FloatRMat *rm)
void float_rmat_transp_ratemult(struct FloatRates *rb, struct FloatRMat *m_b2a, struct FloatRates *ra)
rotate anglular rates by transposed rotation matrix.
void float_rmat_of_eulers_321(struct FloatRMat *rm, struct FloatEulers *e)
Rotation matrix from 321 Euler angles (float).
void float_rmat_of_axis_angle(struct FloatRMat *rm, struct FloatVect3 *uv, float angle)
initialises a rotation matrix from unit vector axis and angle
void float_quat_of_orientation_vect(struct FloatQuat *q, const struct FloatVect3 *ov)
Quaternion from orientation vector.
void float_quat_of_axis_angle(struct FloatQuat *q, const struct FloatVect3 *uv, float angle)
Quaternion from unit vector and angle.
static void float_quat_wrap_shortest(struct FloatQuat *q)
void float_quat_comp_norm_shortest(struct FloatQuat *a2c, struct FloatQuat *a2b, struct FloatQuat *b2c)
Composition (multiplication) of two quaternions with normalization.
void float_quat_inv_comp_norm_shortest(struct FloatQuat *b2c, struct FloatQuat *a2b, struct FloatQuat *a2c)
Composition (multiplication) of two quaternions with normalization.
static void float_vect_copy(float *a, const float *b, const int n)
a = b
void float_quat_derivative_lagrange(struct FloatQuat *qd, struct FloatRates *r, struct FloatQuat *q)
Quaternion derivative from rotational velocity with Lagrange multiplier.
rotation matrix
static void float_mat_sum(float **o, float **a, float **b, int m, int n)
o = a + b
float m[3 *3]
static float float_quat_norm(struct FloatQuat *q)
void float_rmat_ratemult(struct FloatRates *rb, struct FloatRMat *m_a2b, struct FloatRates *ra)
rotate anglular rates by rotation matrix.
void float_quat_differential(struct FloatQuat *q_out, struct FloatRates *w, float dt)
Delta rotation quaternion with constant angular rates.
static float float_vect2_norm2(struct FloatVect2 *v)
void float_eulers_of_quat(struct FloatEulers *e, struct FloatQuat *q)
void float_quat_integrate_fi(struct FloatQuat *q, struct FloatRates *omega, float dt)
in place first order quaternion integration with constant rotational velocity
angular rates
static void float_mat_mul(float **o, float **a, float **b, int m, int n, int l)
o = a * b