Olivier Stasse committed May 12, 2020 1 ``````#include `````` Olivier Stasse committed May 12, 2020 2 3 4 ``````namespace eiquadprog { namespace solvers { `````` Olivier Stasse committed May 12, 2020 5 6 7 ``````using namespace Eigen; /* solve_quadprog is used for on-demand QP solving */ `````` Justin Carpentier committed Mar 30, 2022 8 `````` `````` Olivier Stasse committed May 12, 2020 9 10 ``````double solve_quadprog(MatrixXd& G, VectorXd& g0, const MatrixXd& CE, const VectorXd& ce0, const MatrixXd& CI, const VectorXd& ci0, VectorXd& x, VectorXi& activeSet, size_t& activeSetSize) { `````` Justin Carpentier committed Mar 30, 2022 11 12 13 14 15 16 17 18 19 20 21 `````` Eigen::DenseIndex p = CE.cols(); Eigen::DenseIndex m = CI.cols(); VectorXd y(p + m); return solve_quadprog(G, g0, CE, ce0, CI, ci0, x, y, activeSet, activeSetSize); } double solve_quadprog(MatrixXd& G, VectorXd& g0, const MatrixXd& CE, const VectorXd& ce0, const MatrixXd& CI, const VectorXd& ci0, VectorXd& x, VectorXd& y, VectorXi& activeSet, size_t& activeSetSize) { `````` Olivier Stasse committed May 12, 2020 22 23 24 25 26 27 28 29 `````` LLT chol(G.cols()); double c1; /* compute the trace of the original matrix G */ c1 = G.trace(); /* decompose the matrix G in the form LL^T */ chol.compute(G); `````` Justin Carpentier committed Mar 30, 2022 30 31 32 33 34 35 36 37 38 39 40 41 `````` return solve_quadprog(chol, c1, g0, CE, ce0, CI, ci0, x, y, activeSet, activeSetSize); } double solve_quadprog(LLT& chol, double c1, VectorXd& g0, const MatrixXd& CE, const VectorXd& ce0, const MatrixXd& CI, const VectorXd& ci0, VectorXd& x, VectorXi& activeSet, size_t& activeSetSize) { Eigen::DenseIndex p = CE.cols(); Eigen::DenseIndex m = CI.cols(); VectorXd y(p + m); return solve_quadprog(chol, c1, g0, CE, ce0, CI, ci0, x, y, activeSet, activeSetSize); `````` Olivier Stasse committed May 12, 2020 42 43 44 45 46 47 ``````} /* solve_quadprog2 is used for when the Cholesky decomposition of G is pre-computed * @param A Output vector containing the indexes of the active constraints. * @param q Output value representing the size of the active set. */ `````` Justin Carpentier committed Mar 30, 2022 48 49 ``````double solve_quadprog(LLT& chol, double c1, VectorXd& g0, const MatrixXd& CE, const VectorXd& ce0, const MatrixXd& CI, const VectorXd& ci0, VectorXd& x, VectorXd& u, VectorXi& A, size_t& q) { `````` Olivier Stasse committed May 12, 2020 50 51 52 53 54 55 56 `````` size_t i, k, l; /* indices */ size_t ip, me, mi; size_t n = g0.size(); size_t p = CE.cols(); size_t m = CI.cols(); MatrixXd R(g0.size(), g0.size()), J(g0.size(), g0.size()); `````` Justin Carpentier committed Mar 30, 2022 57 `````` VectorXd s(m + p), z(n), r(m + p), d(n), np(n); `````` Olivier Stasse committed May 12, 2020 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 `````` VectorXd x_old(n), u_old(m + p); double f_value, psi, c2, sum, ss, R_norm; const double inf = std::numeric_limits::infinity(); double t, t1, t2; /* t is the step length, which is the minimum of the partial step length t1 * and the full step length t2 */ // VectorXi A(m + p); // Del Prete: active set is now an output parameter if (static_cast(A.size()) != m + p) A.resize(m + p); VectorXi A_old(m + p), iai(m + p), iaexcl(m + p); // int q; size_t iq, iter = 0; me = p; /* number of equality constraints */ mi = m; /* number of inequality constraints */ q = 0; /* size of the active set A (containing the indices of the active constraints) */ /* * Preprocessing phase */ /* initialize the matrix R */ d.setZero(); R.setZero(); R_norm = 1.0; /* this variable will hold the norm of the matrix R */ /* compute the inverse of the factorized matrix G^-1, this is the initial value for H */ // J = L^-T J.setIdentity(); `````` Justin Carpentier committed Mar 30, 2022 85 `````` chol.matrixU().solveInPlace(J); `````` Olivier Stasse committed May 12, 2020 86 87 88 89 90 91 92 93 94 95 96 97 `````` c2 = J.trace(); #ifdef TRACE_SOLVER print_matrix("J", J, n); #endif /* c1 * c2 is an estimate for cond(G) */ /* * Find the unconstrained minimizer of the quadratic form 0.5 * x G x + g0 x * this is a feasible point in the dual space * x = G^-1 * g0 */ `````` Justin Carpentier committed Mar 30, 2022 98 99 `````` x = -g0; chol.solveInPlace(x); `````` Olivier Stasse committed May 12, 2020 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 `````` /* and compute the current solution value */ f_value = 0.5 * g0.dot(x); #ifdef TRACE_SOLVER std::cerr << "Unconstrained solution: " << f_value << std::endl; print_vector("x", x, n); #endif /* Add equality constraints to the working set A */ iq = 0; for (i = 0; i < me; i++) { np = CE.col(i); compute_d(d, J, np); update_z(z, J, d, iq); update_r(R, r, d, iq); #ifdef TRACE_SOLVER print_matrix("R", R, iq); print_vector("z", z, n); print_vector("r", r, iq); print_vector("d", d, n); #endif /* compute full step length t2: i.e., the minimum step in primal space s.t. the contraint becomes feasible */ t2 = 0.0; if (std::abs(z.dot(z)) > std::numeric_limits::epsilon()) // i.e. z != 0 t2 = (-np.dot(x) - ce0(i)) / z.dot(np); x += t2 * z; /* set u = u+ */ u(iq) = t2; u.head(iq) -= t2 * r.head(iq); /* compute the new solution value */ f_value += 0.5 * (t2 * t2) * z.dot(np); A(i) = static_cast(-i - 1); if (!add_constraint(R, J, d, iq, R_norm)) { // FIXME: it should raise an error // Equality constraints are linearly dependent return f_value; } } /* set iai = K \ A */ `````` Justin Carpentier committed Mar 30, 2022 145 146 `````` for (i = 0; i < mi; i++) iai(i) = static_cast(i); `````` Olivier Stasse committed May 12, 2020 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 `````` l1: iter++; #ifdef TRACE_SOLVER print_vector("x", x, n); #endif /* step 1: choose a violated constraint */ for (i = me; i < iq; i++) { ip = A(i); iai(ip) = -1; } /* compute s(x) = ci^T * x + ci0 for all elements of K \ A */ ss = 0.0; psi = 0.0; /* this value will contain the sum of all infeasibilities */ ip = 0; /* ip will be the index of the chosen violated constraint */ for (i = 0; i < mi; i++) { iaexcl(i) = 1; sum = CI.col(i).dot(x) + ci0(i); s(i) = sum; psi += std::min(0.0, sum); } #ifdef TRACE_SOLVER print_vector("s", s, mi); #endif if (std::abs(psi) <= static_cast(mi) * std::numeric_limits::epsilon() * c1 * c2 * 100.0) { /* numerically there are not infeasibilities anymore */ q = iq; return f_value; } /* save old values for u, x and A */ u_old.head(iq) = u.head(iq); A_old.head(iq) = A.head(iq); x_old = x; l2: /* Step 2: check for feasibility and determine a new S-pair */ for (i = 0; i < mi; i++) { if (s(i) < ss && iai(i) != -1 && iaexcl(i)) { ss = s(i); ip = i; } } if (ss >= 0.0) { q = iq; return f_value; } /* set np = n(ip) */ np = CI.col(ip); /* set u = (u 0)^T */ u(iq) = 0.0; /* add ip to the active set A */ A(iq) = static_cast(ip); #ifdef TRACE_SOLVER std::cerr << "Trying with constraint " << ip << std::endl; print_vector("np", np, n); #endif l2a: /* Step 2a: determine step direction */ /* compute z = H np: the step direction in the primal space (through J, see the paper) */ compute_d(d, J, np); update_z(z, J, d, iq); /* compute N* np (if q > 0): the negative of the step direction in the dual space */ update_r(R, r, d, iq); #ifdef TRACE_SOLVER std::cerr << "Step direction z" << std::endl; print_vector("z", z, n); print_vector("r", r, iq + 1); print_vector("u", u, iq + 1); print_vector("d", d, n); `````` Guilhem Saurel committed May 28, 2020 220 `````` print_vector("A", A, iq + 1); `````` Olivier Stasse committed May 12, 2020 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 ``````#endif /* Step 2b: compute step length */ l = 0; /* Compute t1: partial step length (maximum step in dual space without violating dual feasibility */ t1 = inf; /* +inf */ /* find the index l s.t. it reaches the minimum of u+(x) / r */ for (k = me; k < iq; k++) { double tmp; if (r(k) > 0.0 && ((tmp = u(k) / r(k)) < t1)) { t1 = tmp; l = A(k); } } /* Compute t2: full step length (minimum step in primal space such that the constraint ip becomes feasible */ if (std::abs(z.dot(z)) > std::numeric_limits::epsilon()) // i.e. z != 0 t2 = -s(ip) / z.dot(np); else t2 = inf; /* +inf */ /* the step is chosen as the minimum of t1 and t2 */ t = std::min(t1, t2); #ifdef TRACE_SOLVER std::cerr << "Step sizes: " << t << " (t1 = " << t1 << ", t2 = " << t2 << ") "; #endif /* Step 2c: determine new S-pair and take step: */ /* case (i): no step in primal or dual space */ if (t >= inf) { /* QPP is infeasible */ // FIXME: unbounded to raise q = iq; return inf; } /* case (ii): step in dual space */ if (t2 >= inf) { /* set u = u + t * [-r 1) and drop constraint l from the active set A */ u.head(iq) -= t * r.head(iq); u(iq) += t; iai(l) = static_cast(l); delete_constraint(R, J, A, u, p, iq, l); #ifdef TRACE_SOLVER std::cerr << " in dual space: " << f_value << std::endl; print_vector("x", x, n); print_vector("z", z, n); `````` Guilhem Saurel committed May 28, 2020 267 `````` print_vector("A", A, iq + 1); `````` Olivier Stasse committed May 12, 2020 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 ``````#endif goto l2a; } /* case (iii): step in primal and dual space */ x += t * z; /* update the solution value */ f_value += t * z.dot(np) * (0.5 * t + u(iq)); u.head(iq) -= t * r.head(iq); u(iq) += t; #ifdef TRACE_SOLVER std::cerr << " in both spaces: " << f_value << std::endl; print_vector("x", x, n); print_vector("u", u, iq + 1); print_vector("r", r, iq + 1); `````` Guilhem Saurel committed May 28, 2020 285 `````` print_vector("A", A, iq + 1); `````` Olivier Stasse committed May 12, 2020 286 287 288 289 290 291 292 293 294 295 296 297 298 299 ``````#endif if (t == t2) { #ifdef TRACE_SOLVER std::cerr << "Full step has taken " << t << std::endl; print_vector("x", x, n); #endif /* full step has taken */ /* add constraint ip to the active set*/ if (!add_constraint(R, J, d, iq, R_norm)) { iaexcl(ip) = 0; delete_constraint(R, J, A, u, p, iq, ip); #ifdef TRACE_SOLVER print_matrix("R", R, n); `````` Guilhem Saurel committed May 28, 2020 300 `````` print_vector("A", A, iq); `````` Olivier Stasse committed May 12, 2020 301 302 303 304 305 306 307 308 309 310 311 312 313 ``````#endif for (i = 0; i < m; i++) iai(i) = static_cast(i); for (i = 0; i < iq; i++) { A(i) = A_old(i); iai(A(i)) = -1; u(i) = u_old(i); } x = x_old; goto l2; /* go to step 2 */ } else iai(ip) = -1; #ifdef TRACE_SOLVER print_matrix("R", R, n); `````` Guilhem Saurel committed May 28, 2020 314 `````` print_vector("A", A, iq); `````` Olivier Stasse committed May 12, 2020 315 316 317 318 319 320 321 322 323 324 325 326 327 328 ``````#endif goto l1; } /* a patial step has taken */ #ifdef TRACE_SOLVER std::cerr << "Partial step has taken " << t << std::endl; print_vector("x", x, n); #endif /* drop constraint l */ iai(l) = static_cast(l); delete_constraint(R, J, A, u, p, iq, l); #ifdef TRACE_SOLVER print_matrix("R", R, n); `````` Guilhem Saurel committed May 28, 2020 329 `````` print_vector("A", A, iq); `````` Olivier Stasse committed May 12, 2020 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 ``````#endif s(ip) = CI.col(ip).dot(x) + ci0(ip); #ifdef TRACE_SOLVER print_vector("s", s, mi); #endif goto l2a; } bool add_constraint(MatrixXd& R, MatrixXd& J, VectorXd& d, size_t& iq, double& R_norm) { size_t n = J.rows(); #ifdef TRACE_SOLVER std::cerr << "Add constraint " << iq << '/'; #endif size_t j, k; double cc, ss, h, t1, t2, xny; /* we have to find the Givens rotation which will reduce the element d(j) to zero. if it is already zero we don't have to do anything, except of decreasing j */ for (j = n - 1; j >= iq + 1; j--) { /* The Givens rotation is done with the matrix (cc cs, cs -cc). If cc is one, then element (j) of d is zero compared with element (j - 1). Hence we don't have to do anything. If cc is zero, then we just have to switch column (j) and column (j - 1) of J. Since we only switch columns in J, we have to be careful how we update d depending on the sign of gs. Otherwise we have to apply the Givens rotation to these columns. The i - 1 element of d has to be updated to h. */ cc = d(j - 1); ss = d(j); h = distance(cc, ss); if (h == 0.0) continue; d(j) = 0.0; ss = ss / h; cc = cc / h; if (cc < 0.0) { cc = -cc; ss = -ss; d(j - 1) = -h; } else d(j - 1) = h; xny = ss / (1.0 + cc); for (k = 0; k < n; k++) { t1 = J(k, j - 1); t2 = J(k, j); J(k, j - 1) = t1 * cc + t2 * ss; J(k, j) = xny * (t1 + J(k, j - 1)) - t2; } } /* update the number of constraints added*/ iq++; /* To update R we have to put the iq components of the d vector into column iq - 1 of R */ R.col(iq - 1).head(iq) = d.head(iq); #ifdef TRACE_SOLVER std::cerr << iq << std::endl; #endif if (std::abs(d(iq - 1)) <= std::numeric_limits::epsilon() * R_norm) // problem degenerate return false; R_norm = std::max(R_norm, std::abs(d(iq - 1))); return true; } void delete_constraint(MatrixXd& R, MatrixXd& J, VectorXi& A, VectorXd& u, size_t p, size_t& iq, size_t l) { size_t n = R.rows(); #ifdef TRACE_SOLVER std::cerr << "Delete constraint " << l << ' ' << iq; #endif size_t i, j, k, qq = 0; double cc, ss, h, xny, t1, t2; /* Find the index qq for active constraint l to be removed */ for (i = p; i < iq; i++) if (static_cast(A(i)) == l) { qq = i; break; } /* remove the constraint from the active set and the duals */ for (i = qq; i < iq - 1; i++) { A(i) = A(i + 1); u(i) = u(i + 1); R.col(i) = R.col(i + 1); } A(iq - 1) = A(iq); u(iq - 1) = u(iq); A(iq) = 0; u(iq) = 0.0; for (j = 0; j < iq; j++) R(j, iq - 1) = 0.0; /* constraint has been fully removed */ iq--; #ifdef TRACE_SOLVER std::cerr << '/' << iq << std::endl; #endif if (iq == 0) return; for (j = qq; j < iq; j++) { cc = R(j, j); ss = R(j + 1, j); h = distance(cc, ss); if (h == 0.0) continue; cc = cc / h; ss = ss / h; R(j + 1, j) = 0.0; if (cc < 0.0) { R(j, j) = -h; cc = -cc; ss = -ss; } else R(j, j) = h; xny = ss / (1.0 + cc); for (k = j + 1; k < iq; k++) { t1 = R(j, k); t2 = R(j + 1, k); R(j, k) = t1 * cc + t2 * ss; R(j + 1, k) = xny * (t1 + R(j, k)) - t2; } for (k = 0; k < n; k++) { t1 = J(k, j); t2 = J(k, j + 1); J(k, j) = t1 * cc + t2 * ss; J(k, j + 1) = xny * (J(k, j) + t1) - t2; } } } `````` Olivier Stasse committed May 12, 2020 464 465 466 `````` } // namespace solvers } // namespace eiquadprog``````