/* primal-dual interior-point method, hard constraints, time variant matrices (mpc version) ; version with A diagonal and nu & nx time-variant*/
int d_ip2_diag_mpc(int *kk, int k_max, double mu0, double mu_tol, double alpha_min, int warm_start, double *sigma_par, double *stat, int N, int *nx, int *nu, int *nb, int **idxb, double **dA, double **pBt, double **pR, double **pSt, double **pQ, double **b, double **d, double **rq, double **ux, int compute_mult, double **pi, double **lam, double **t, double *work_memory)
{
// indeces
int jj, ll, ii, bs0, idx;
// constants
const int bs = D_MR; //d_get_mr();
const int ncl = D_NCL;
const int nal = D_MR*D_NCL; // number of doubles per cache line
// const int nz = nx+nu+1;
// const int nxu = nx+nu;
// const int pnz = bs*((nz+bs-1)/bs);
// const int pnx = bs*((nx+bs-1)/bs);
// const int pnb = bs*((nb+bs-1)/bs); // simd aligned number of two-sided box constraints !!!!!!!!!!!!!!!!!!
// const int cnz = ncl*((nz+ncl-1)/ncl);
// const int cnx = ncl*((nx+ncl-1)/ncl);
// const int anz = nal*((nz+nal-1)/nal);
// const int anx = nal*((nx+nal-1)/nal);
// const int anb = nal*((2*nb+nal-1)/nal); // cache aligned number of box constraints
//const int anb = nal*((nb+nal-1)/nal); // cache aligned number of two-sided box constraints !!!!!!!!!!!!!!!!!!
// const int pad = (ncl-nx%ncl)%ncl; // packing between BAbtL & P
//const int cnl = cnz<cnx+ncl ? nx+pad+cnx+ncl : nx+pad+cnz;
// const int cnl = cnz<cnx+ncl ? cnx+ncl : cnz;
//printf("\n%d %d %d %d %d\n", N, nx, nu, nb, ng);
//d_print_pmat(nz, nx, bs, pBAbt[0], cnx);
//d_print_pmat(nz, nx, bs, pBAbt[1], cnx);
//d_print_pmat(nz, nx, bs, pBAbt[N-1], cnx);
//d_print_pmat(nz, nz, bs, pQ[0], cnz);
//d_print_pmat(nz, nz, bs, pQ[1], cnz);
//d_print_pmat(nz, nz, bs, pQ[N], cnz);
//d_print_pmat(nx+nu, ng, bs, pDCt[0], cng);
//d_print_pmat(nx+nu, ng, bs, pDCt[1], cng);
//d_print_pmat(nx+nu, ng, bs, pDCt[N], cng);
//d_print_mat(1, 2*pnb+2*png, d[0], 1);
//d_print_mat(1, 2*pnb+2*png, d[1], 1);
//d_print_mat(1, 2*pnb+2*png, d[N], 1);
//d_print_mat(1, nx+nu, ux[0], 1);
//d_print_mat(1, nx+nu, ux[1], 1);
//d_print_mat(1, nx+nu, ux[N], 1);
//exit(1);
double *ptr;
ptr = work_memory;
int *ptr_int, *anu, *anx, *pnu, *pnx, *pnb, *cnu, *cnx;
ptr_int = (int *) ptr;
anu = ptr_int; ptr_int += (N+1);
anx = ptr_int; ptr_int += (N+1);
pnu = ptr_int; ptr_int += (N+1);
pnx = ptr_int; ptr_int += (N+1);
pnb = ptr_int; ptr_int += (N+1);
cnu = ptr_int; ptr_int += (N+1);
cnx = ptr_int; ptr_int += (N+1);
for(jj=0; jj<=N; jj++)
{
anu[jj] = (nu[jj]+nal-1)/nal*nal;
anx[jj] = (nx[jj]+nal-1)/nal*nal;
pnu[jj] = (nu[jj]+bs-1)/bs*bs;
pnx[jj] = (nx[jj]+bs-1)/bs*bs;
pnb[jj] = (nb[jj]+bs-1)/bs*bs;
cnu[jj] = (nu[jj]+ncl-1)/ncl*ncl;
cnx[jj] = (nx[jj]+ncl-1)/ncl*ncl;
}
int pnxM = 0; for(jj=0; jj<=N; jj++) pnxM = pnx[jj]>pnxM ? pnx[jj] : pnxM;
int pnuM = 0; for(jj=0; jj<=N; jj++) pnuM = pnu[jj]>pnuM ? pnu[jj] : pnuM;
int cnuM = 0; for(jj=0; jj<=N; jj++) cnuM = cnu[jj]>cnuM ? cnu[jj] : cnuM;
/* align work space */
size_t align = 64;
size_t addr = (size_t) ptr_int;
size_t offset = addr % align;
ptr_int = ptr_int + offset / sizeof(int);
ptr = (double *) ptr_int;
// initialize work space
double *(pL[N]);
double *pK;
double *(pP[N+1]);
double *(dux[N+1]);
double *(dpi[N+1]);
double *(Pb[N]);
double *(pd[N+1]);
double *(pl[N+1]);
double *(bd[N+1]);
double *(bl[N+1]);
double *(dlam[N+1]);
double *(dt[N+1]);
double *(lamt[N+1]);
double *(t_inv[N+1]);
double *work;
// ptr += (N+1)*(pnx + pnz*cnl + 12*pnz) + 3*pnz;
// hpL
for(jj=0; jj<N; jj++)
{
pL[jj] = ptr;
ptr += (pnu[jj]+pnx[jj])*cnu[jj];
}
// pK
pK = ptr;
ptr += pnxM*cnuM;
// hpP
for(jj=0; jj<=N; jj++)
{
pP[jj] = ptr;
ptr += pnx[jj]*cnx[jj];
}
// inputs and states
for(jj=0; jj<=N; jj++)
{
dux[jj] = ptr;
ptr += anu[jj]+anx[jj];
}
// equality constr multipliers
for(jj=0; jj<=N; jj++)
{
dpi[jj] = ptr;
ptr += anx[jj];
}
// backup of P*b
for(jj=0; jj<N; jj++)
{
Pb[jj] = ptr;
ptr += anx[jj+1];
}
// Hessian
for(jj=0; jj<=N; jj++)
{
pd[jj] = ptr; //pQ[jj];
pl[jj] = ptr + 1*(pnb[jj]);
bd[jj] = ptr + 2*(pnb[jj]);
bl[jj] = ptr + 3*(pnb[jj]);
ptr += 4*(pnb[jj]);
// backup
//for(ll=0; ll<nu[jj]; ll++)
// bd[jj][ll] = pR[jj][(ll/bs)*bs*cnu[jj]+ll%bs+ll*bs];
//for(ll=0; ll<nx[jj]; ll++)
// bd[jj][nu[jj]+ll] = pQ[jj][(ll/bs)*bs*cnx[jj]+ll%bs+ll*bs];
for(ll=0; ll<nb[jj] && idxb[jj][ll]<nu[jj]; ll++)
{
idx = idxb[jj][ll];
bd[jj][ll] = pR[jj][idx/bs*bs*cnu[jj]+idx%bs+idx*bs];
bl[jj][ll] = rq[jj][idx];
}
for(; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll] - nu[jj];
bd[jj][ll] = pQ[jj][idx/bs*bs*cnx[jj]+idx%bs+idx*bs];
bl[jj][ll] = rq[jj][idx];
}
//d_print_mat(1, nb[jj], bd[jj], 1);
}
//exit(1);
// slack variables, Lagrangian multipliers for inequality constraints and work space
for(jj=0; jj<=N; jj++)
{
dlam[jj] = ptr;
dt[jj] = ptr + 2*pnb[jj];
ptr += 4*pnb[jj];
}
for(jj=0; jj<=N; jj++)
{
lamt[jj] = ptr;
ptr += 2*pnb[jj];
}
for(jj=0; jj<=N; jj++)
{
t_inv[jj] = ptr;
ptr += 2*pnb[jj];
}
work = ptr;
ptr += pnxM + pnuM;
double temp0, temp1;
double alpha, mu, mu_aff;
double mu_scal = 0.0;
for(jj=0; jj<=N; jj++) mu_scal += nb[jj];
mu_scal = 0.5/mu_scal;
double sigma, sigma_decay, sigma_min;
sigma = sigma_par[0]; //0.4;
sigma_decay = sigma_par[1]; //0.3;
sigma_min = sigma_par[2]; //0.01;
// initialize ux & t>0 (slack variable)
d_init_var_diag_mpc(N, nx, nu, nb, idxb, ux, pi, d, t, lam, mu0, warm_start);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], ux[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], lam[ii], 1);
exit(1);
#endif
// initialize pi
for(jj=0; jj<=N; jj++)
for(ll=0; ll<nx[jj]; ll++)
dpi[jj][ll] = 0.0;
// initialize dux
for(ll=0; ll<nx[0]; ll++)
dux[0][nu[0]+ll] = ux[0][nu[0]+ll];
// compute the duality gap
//alpha = 0.0; // needed to compute mu !!!!!
//d_compute_mu_hard_mpc(N, nx, nu, nb, &mu, mu_scal, alpha, lam, dlam, t, dt);
mu = mu0;
// set to zero iteration count
*kk = 0;
// larger than minimum accepted step size
alpha = 1.0;
// update hessian in Riccati routine
const int update_hessian = 1;
//int fast_rsqrt = 0;
// IP loop
while( *kk<k_max && mu>mu_tol && alpha>=alpha_min )
{
//update cost function matrices and vectors (box constraints)
d_update_hessian_diag_mpc(N, nx, nu, nb, 0.0, t, t_inv, lam, lamt, dlam, bd, bl, pd, pl, d);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t_inv[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], lam[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], lamt[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], dlam[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], bd[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pd[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], bl[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
if(*kk==1)
exit(1);
#endif
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pd[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
//if(*kk==1)
exit(1);
#endif
// update hessian & jacobian
for(jj=0; jj<=N; jj++)
{
for(ll=0; ll<nb[jj] && idxb[jj][ll]<nu[jj]; ll++)
{
idx = idxb[jj][ll];
pR[jj][idx/bs*bs*cnu[jj]+idx%bs+idx*bs] = pd[jj][ll];
rq[jj][idx] = pl[jj][ll];
}
for(; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll] - nu[jj];
pQ[jj][idx/bs*bs*cnx[jj]+idx%bs+idx*bs] = pd[jj][ll];
idx = idxb[jj][ll];
rq[jj][idx] = pl[jj][ll];
}
}
#if 0
for(ii=0; ii<N; ii++)
d_print_pmat(nu[ii], nu[ii], bs, pR[ii], cnu[ii]);
for(ii=0; ii<=N; ii++)
d_print_pmat(nx[ii], nx[ii], bs, pQ[ii], cnx[ii]);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], rq[ii], 1);
exit(1);
#endif
// compute the search direction: factorize and solve the KKT system
//printf("\n%d %f\n", fast_rsqrt, mu);
d_ric_diag_trf_mpc(N, nx, nu, dA, pBt, pR, pSt, pQ, pL, pK, pP, work);
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(nx[ii], nx[ii], bs, pP[ii], cnx[ii]);
#endif
d_ric_diag_trs_mpc(N, nx, nu, dA, pBt, pL, pP, b, rq, dux, 1, Pb, compute_mult, dpi, work);
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(pnu[ii]+pnx[ii], cnu[ii], bs, pL[ii], cnu[ii]);
exit(1);
#endif
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], dux[ii], 1);
if(*kk==1)
exit(1);
#endif
#if 1
// compute t_aff & dlam_aff & dt_aff & alpha
for(jj=0; jj<=N; jj++)
for(ll=0; ll<2*nb[jj]; ll++)
dlam[jj][ll] = 0.0;
alpha = 1.0;
d_compute_alpha_diag_mpc(N, nx, nu, nb, idxb, &alpha, t, dt, lam, dlam, lamt, dux, d);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+1] = alpha;
alpha *= 0.995;
//printf("\nalpha = %f\n", alpha);
// compute the affine duality gap
d_compute_mu_diag_mpc(N, nx, nu, nb, &mu_aff, mu_scal, alpha, lam, dlam, t, dt);
stat[5*(*kk)+2] = mu_aff;
//printf("\nmu = %f\n", mu_aff);
//mu_aff = 1.346982; // TODO remove !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// compute sigma
sigma = mu_aff/mu;
sigma = sigma*sigma*sigma;
// if(sigma<sigma_min)
// sigma = sigma_min;
//printf("\n%f %f %f %f\n", mu_aff, mu, sigma, mu_scal);
//exit(1);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], dt[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], dlam[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t_inv[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
//exit(1);
#endif
d_update_gradient_diag_mpc(N, nx, nu, nb, sigma*mu, dt, dlam, t_inv, pl);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
if(*kk==1)
exit(1);
#endif
// update jacobian
for(jj=0; jj<=N; jj++)
{
for(ll=0; ll<nb[jj] && idxb[jj][ll]<nu[jj]; ll++)
{
idx = idxb[jj][ll];
rq[jj][idx] = pl[jj][ll];
}
for(; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll];
rq[jj][idx] = pl[jj][ll];
}
}
// solve the system
d_ric_diag_trs_mpc(N, nx, nu, dA, pBt, pL, pP, b, rq, dux, 0, Pb, compute_mult, dpi, work);
//d_ric_trs_mpc(nx, nu, N, pBAbt, pL, pl, dux, work, 1, Pb, compute_mult, dpi, nb, ng, ngN, pDCt, qx);
#endif
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], dux[ii], 1);
if(*kk==1)
exit(1);
#endif
// compute t & dlam & dt & alpha
alpha = 1.0;
d_compute_alpha_diag_mpc(N, nx, nu, nb, idxb, &alpha, t, dt, lam, dlam, lamt, dux, d);
//printf("\n%f\n", alpha);
//exit(1);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+3] = alpha;
alpha *= 0.995;
// update x, u, lam, t & compute the duality gap mu
d_update_var_diag_mpc(N, nx, nu, nb, &mu, mu_scal, alpha, ux, dux, t, dt, lam, dlam, pi, dpi);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], ux[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], lam[ii], 1);
exit(1);
#endif
stat[5*(*kk)+4] = mu;
// update sigma
// sigma *= sigma_decay;
// if(sigma<sigma_min)
// sigma = sigma_min;
// if(alpha<0.3)
// sigma = sigma_par[0];
#if 0
d_print_mat(1, 2*pnb+2*png, lam[0], 1);
d_print_mat(1, 2*pnb+2*png, lam[1], 1);
d_print_mat(1, 2*pnb+2*png, lam[N], 1);
d_print_mat(1, 2*pnb+2*png, t[0], 1);
d_print_mat(1, 2*pnb+2*png, t[1], 1);
d_print_mat(1, 2*pnb+2*png, t[N], 1);
printf("\n%f\n", mu);
exit(1);
#endif
//mu = 13.438997;
// increment loop index
(*kk)++;
} // end of IP loop
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], rq[ii], 1);
#endif
// restore Hessian
//for(jj=0; jj<=N; jj++)
// {
// for(ll=0; ll<nu[jj]; ll++)
// pR[jj][(ll/bs)*bs*cnu[jj]+ll%bs+ll*bs] = bd[jj][ll];
// for(ll=0; ll<nx[jj]; ll++)
// pQ[jj][(ll/bs)*bs*cnx[jj]+ll%bs+ll*bs] = bd[jj][nu[jj]+ll];
// }
for(jj=0; jj<=N; jj++)
{
for(ll=0; ll<nb[jj] && idxb[jj][ll]<nu[jj]; ll++)
{
idx = idxb[jj][ll];
pR[jj][idx/bs*bs*cnu[jj]+idx%bs+idx*bs] = bd[jj][ll];
rq[jj][idx] = bl[jj][ll];
}
for(; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll] - nu[jj];
pQ[jj][idx/bs*bs*cnx[jj]+idx%bs+idx*bs] = bd[jj][ll];
idx = idxb[jj][ll];
rq[jj][idx] = bl[jj][ll];
}
}
#if 0
for(ii=0; ii<N; ii++)
d_print_pmat(nu[ii], nu[ii], bs, pR[ii], cnu[ii]);
for(ii=0; ii<=N; ii++)
d_print_pmat(nx[ii], nx[ii], bs, pQ[ii], cnx[ii]);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], bl[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], rq[ii], 1);
exit(1);
#endif
// successful exit
if(mu<=mu_tol)
return 0;
// max number of iterations reached
if(*kk>=k_max)
return 1;
// no improvement
if(alpha<alpha_min)
return 2;
// impossible
return -1;
} // end of ipsolver
/* primal-dual interior-point method, hard constraints, time variant matrices, time variant size (mpc version) */
int d_ip2_hard_mpc_tv(int *kk, int k_max, double mu0, double mu_tol, double alpha_min, int warm_start, double *sigma_par, double *stat, int N, int *nx, int *nu, int *nb, int **idxb, int *ng, double **pBAbt, double **pQ, double **pDCt, double **d, double **ux, int compute_mult, double **pi, double **lam, double **t, double *double_work_memory, int *int_work_memory)
{
// indeces
int jj, ll, ii, bs0;
// constants
const int bs = D_MR;
const int ncl = D_NCL;
const int nal = bs*ncl; // number of doubles per cache line
// matrices size
// work_space_int_size_per_stage = 7
int idx;
int nxM = 0;
int nzM = 0;
int ngM = 0;
int *ptr_int, *anx, *anz, *pnz, *pnb, *png, *cnx, *cnz;
ptr_int = int_work_memory; // no alignmenr requirements
anx = ptr_int; ptr_int += N+1;
anz = ptr_int; ptr_int += N+1;
pnz = ptr_int; ptr_int += N+1;
pnb = ptr_int; ptr_int += N+1;
png = ptr_int; ptr_int += N+1;
cnx = ptr_int; ptr_int += N+1;
cnz = ptr_int; ptr_int += N+1;
for(jj=0; jj<=N; jj++)
{
anx[jj] = (nx[jj]+nal-1)/nal*nal;
anz[jj] = (nu[jj]+nx[jj]+1+nal-1)/nal*nal;
pnz[jj] = (nu[jj]+nx[jj]+1+bs-1)/bs*bs;
pnb[jj] = (nb[jj]+bs-1)/bs*bs;
png[jj] = (ng[jj]+bs-1)/bs*bs;
cnx[jj] = (nx[jj]+ncl-1)/ncl*ncl;
cnz[jj] = (nu[jj]+nx[jj]+1+ncl-1)/ncl*ncl;
if(nx[jj]>nxM) nxM = nx[jj];
if(nu[jj]+nx[jj]+1>nzM) nzM = nu[jj]+nx[jj]+1;
if(ng[jj]>ngM) ngM = ng[jj];
}
// initialize work space
// work_space_double_size_per_stage = pnz*cnl + 2*anz + 2*anx + 14*pnb + 10*png
// work_space_double_size_const_max = pnz*cnxg + pnz
double *ptr;
ptr = double_work_memory; // supposed to be aligned to cache line boundaries
double *(pL[N+1]);
double *(l[N+1]);
double *work;
double *(q[N+1]);
double *(dux[N+1]);
double *(dpi[N+1]);
double *(pd[N+1]); // pointer to diagonal of Hessian
double *(pl[N+1]); // pointer to linear part of Hessian
double *(bd[N+1]); // backup diagonal of Hessian
double *(bl[N+1]); // backup linear part of Hessian
double *diag;
double *(dlam[N+1]);
double *(dt[N+1]);
double *(lamt[N+1]);
double *(t_inv[N+1]);
double *(Qx[N+1]);
double *(qx[N+1]);
double *(qx2[N+1]);
double *(Pb[N]);
// work space
for(jj=0; jj<=N; jj++)
{
pL[jj] = ptr;
ptr += pnz[jj] * ( cnx[jj]+ncl>cnz[jj] ? cnx[jj]+ncl : cnz[jj] ); // pnz*cnl
}
for(jj=0; jj<=N; jj++)
{
l[jj] = ptr;
ptr += anz[jj];
}
work = ptr;
ptr += ((nzM+bs-1)/bs*bs) * ((nxM+ngM+ncl-1)/ncl*ncl); // pnzM*cnxgM
// inputs and states
for(jj=0; jj<=N; jj++)
{
dux[jj] = ptr;
ptr += anz[jj];
}
// equality constr multipliers
for(jj=0; jj<=N; jj++)
{
dpi[jj] = ptr;
ptr += anx[jj];
}
// backup of P*b
for(jj=0; jj<N; jj++)
{
Pb[jj] = ptr;
ptr += anx[jj+1];
}
// linear part of cost function
for(jj=0; jj<=N; jj++)
{
q[jj] = ptr;
ptr += anz[jj];
for(ll=0; ll<nu[jj]+nx[jj]; ll++) q[jj][ll] = pQ[jj][(nu[jj]+nx[jj])/bs*bs*cnz[jj]+(nu[jj]+nx[jj])%bs+ll*bs];
}
// Hessian backup
for(jj=0; jj<=N; jj++)
{
pd[jj] = ptr;
pl[jj] = ptr + pnb[jj];
bd[jj] = ptr + 2*pnb[jj];
bl[jj] = ptr + 3*pnb[jj];
ptr += 4*pnb[jj];
// backup
for(ll=0; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll];
bd[jj][ll] = pQ[jj][idx/bs*bs*cnz[jj]+idx%bs+idx*bs];
bl[jj][ll] = q[jj][idx];
}
}
diag = ptr;
ptr += (nzM+bs-1)/bs*bs; // pnzM
// slack variables, Lagrangian multipliers for inequality constraints and work space
for(jj=0; jj<=N; jj++)
{
dlam[jj] = ptr;
dt[jj] = ptr + 2*pnb[jj]+2*png[jj];
ptr += 4*pnb[jj]+4*png[jj];
}
for(jj=0; jj<=N; jj++)
{
lamt[jj] = ptr;
ptr += 2*pnb[jj]+2*png[jj];
}
for(jj=0; jj<=N; jj++)
{
t_inv[jj] = ptr;
ptr += 2*pnb[jj]+2*png[jj];
}
for(jj=0; jj<=N; jj++)
{
Qx[jj] = ptr;
qx[jj] = ptr+pnb[jj]+png[jj];
qx2[jj] = ptr+2*pnb[jj]+2*png[jj];
ptr += 3*pnb[jj]+3*png[jj];
}
double temp0, temp1;
double alpha, mu, mu_aff;
double mu_scal = 0.0;
for(jj=0; jj<=N; jj++) mu_scal += 2*nb[jj] + 2*ng[jj];
//printf("\nmu_scal = %f\n", mu_scal);
mu_scal = 1.0 / mu_scal;
//printf("\nmu_scal = %f\n", mu_scal);
double sigma, sigma_decay, sigma_min;
//for(ii=0; ii<=N; ii++)
// printf("\n%d %d\n", nb[ii], ng[ii]);
//exit(1);
sigma = sigma_par[0]; //0.4;
sigma_decay = sigma_par[1]; //0.3;
sigma_min = sigma_par[2]; //0.01;
// initialize ux & t>0 (slack variable)
d_init_var_hard_mpc_tv(N, nx, nu, nb, idxb, ng, ux, pi, pDCt, d, t, lam, mu0, warm_start);
// initialize pi
for(jj=0; jj<=N; jj++)
for(ll=0; ll<nx[jj]; ll++)
dpi[jj][ll] = 0.0;
// initialize dux
for(ll=0; ll<nx[0]; ll++)
dux[0][nu[0]+ll] = ux[0][nu[0]+ll];
// compute the duality gap
//alpha = 0.0; // needed to compute mu !!!!!
//d_compute_mu_hard_mpc(N, nx, nu, nb, &mu, mu_scal, alpha, lam, dlam, t, dt);
mu = mu0;
// set to zero iteration count
*kk = 0;
// larger than minimum accepted step size
alpha = 1.0;
// update hessian in Riccati routine
const int update_hessian = 1;
int fast_rsqrt = 0;
// IP loop
while( *kk<k_max && mu>mu_tol && alpha>=alpha_min )
{
//update cost function matrices and vectors (box constraints)
d_update_hessian_hard_mpc_tv(N, nx, nu, nb, ng, 0.0, t, t_inv, lam, lamt, dlam, Qx, qx, qx2, bd, bl, pd, pl, d);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pd[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, ng[ii], Qx[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, ng[ii], qx[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, ng[ii], qx2[ii], 1);
if(*kk==1)
exit(1);
#endif
// compute the search direction: factorize and solve the KKT system
#if defined(FAST_RSQRT)
if(mu>1e-2)
fast_rsqrt = 2;
else
{
if(mu>1e-4)
fast_rsqrt = 1;
else
fast_rsqrt = 0;
}
#else
fast_rsqrt = 0;
#endif
//printf("\n%d %f\n", fast_rsqrt, mu);
d_ric_sv_mpc_tv(N, nx, nu, pBAbt, pQ, dux, pL, work, diag, 1, Pb, compute_mult, dpi, nb, idxb, pd, pl, ng, pDCt, Qx, qx2, fast_rsqrt);
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(nu[ii]+nx[ii]+1, nu[ii]+nx[ii]+1, bs, pQ[ii], cnz[ii]);
//exit(1);
#endif
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(pnz[ii], cnz[ii], bs, pL[ii], cnz[ii]);
//exit(1);
#endif
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], dux[ii], 1);
if(*kk==1)
exit(1);
#endif
#if 1
// compute t_aff & dlam_aff & dt_aff & alpha
alpha = 1.0;
d_compute_alpha_hard_mpc_tv(N, nx, nu, nb, idxb, ng, &alpha, t, dt, lam, dlam, lamt, dux, pDCt, d);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+1] = alpha;
alpha *= 0.995;
//printf("\nalpha = %f\n", alpha);
// compute the affine duality gap
d_compute_mu_hard_mpc_tv(N, nx, nu, nb, ng, &mu_aff, mu_scal, alpha, lam, dlam, t, dt);
stat[5*(*kk)+2] = mu_aff;
//printf("\nmu = %f\n", mu_aff);
// compute sigma
sigma = mu_aff/mu;
sigma = sigma*sigma*sigma;
// if(sigma<sigma_min)
// sigma = sigma_min;
//printf("\n%f %f %f %f\n", mu_aff, mu, sigma, mu_scal);
//exit(1);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], dt[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], dlam[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, 2*pnb[ii], t_inv[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
//exit(1);
#endif
d_update_gradient_hard_mpc_tv(N, nx, nu, nb, ng, sigma*mu, dt, dlam, t_inv, pl, qx);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nb[ii], pl[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, ng[ii], qx[ii], 1);
if(*kk==1)
exit(1);
#endif
// copy b into x
for(ii=0; ii<N; ii++)
for(jj=0; jj<nx[ii+1]; jj++)
dux[ii+1][nu[ii+1]+jj] = pBAbt[ii][(nu[ii]+nx[ii])/bs*bs*cnx[ii+1]+(nu[ii]+nx[ii])%bs+bs*jj]; // copy b
// solve the system
d_ric_trs_mpc_tv(N, nx, nu, pBAbt, pL, q, l, dux, work, 0, Pb, compute_mult, dpi, nb, idxb, pl, ng, pDCt, qx);
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu[ii]+nx[ii], dux[ii], 1);
if(*kk==1)
exit(1);
#endif
#endif
// compute t & dlam & dt & alpha
alpha = 1.0;
d_compute_alpha_hard_mpc_tv(N, nx, nu, nb, idxb, ng, &alpha, t, dt, lam, dlam, lamt, dux, pDCt, d);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+3] = alpha;
alpha *= 0.995;
// update x, u, lam, t & compute the duality gap mu
d_update_var_hard_mpc_tv(N, nx, nu, nb, ng, &mu, mu_scal, alpha, ux, dux, t, dt, lam, dlam, pi, dpi);
stat[5*(*kk)+4] = mu;
// update sigma
/* sigma *= sigma_decay;*/
/* if(sigma<sigma_min)*/
/* sigma = sigma_min;*/
/* if(alpha<0.3)*/
/* sigma = sigma_par[0];*/
// increment loop index
(*kk)++;
} // end of IP loop
// restore Hessian
for(jj=0; jj<=N; jj++)
{
for(ll=0; ll<nb[jj]; ll++)
{
idx = idxb[jj][ll];
pQ[jj][idx/bs*bs*cnz[jj]+idx%bs+idx*bs] = bd[jj][ll];
pQ[jj][(nu[jj]+nx[jj])/bs*bs*cnz[jj]+(nu[jj]+nx[jj])%bs+idx*bs] = bl[jj][ll];
}
}
// successful exit
if(mu<=mu_tol)
return 0;
// max number of iterations reached
if(*kk>=k_max)
return 1;
// no improvement
if(alpha<alpha_min)
return 2;
// impossible
return -1;
} // end of ipsolver
int main()
{
printf("\n");
printf("\n");
printf("\n");
printf(" HPMPC -- Library for High-Performance implementation of solvers for MPC.\n");
printf(" Copyright (C) 2014-2015 by Technical University of Denmark. All rights reserved.\n");
printf("\n");
printf(" HPMPC is distributed in the hope that it will be useful,\n");
printf(" but WITHOUT ANY WARRANTY; without even the implied warranty of\n");
printf(" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n");
printf(" See the GNU Lesser General Public License for more details.\n");
printf("\n");
printf("\n");
printf("\n");
int ii, jj, ll;
double **dummy;
int ** int_dummy;
const int bs = D_MR; //d_get_mr();
const int ncl = D_NCL;
const int nal = bs*ncl; // number of doubles per cache line
int nx, nu, N, nrep;
// timing variables
float time_ric_diag, time_ric_full, time_ric_full_tv, time_ip_diag, time_ip_full, time_ip_full_tv;
/************************************************
* test of riccati eye/diag & size-variant
************************************************/
#if 1
// horizon length
N = 11;
// base nx and nu
int nx0 = 2;
int nu0 = 1;
// size-varing
int nxx[N+1];
for(ii=0; ii<=N; ii++) nxx[ii] = (N+1-ii)*nx0 + nu0;
int pnxx[N+1];
for(ii=0; ii<=N; ii++) pnxx[ii] = (nxx[ii]+bs-1)/bs*bs;
int cnxx[N+1];
for(ii=0; ii<=N; ii++) cnxx[ii] = (nxx[ii]+ncl-1)/ncl*ncl;
int nuu[N+1];
for(ii=0; ii<N; ii++) nuu[ii] = nu0;
nuu[N] = 0; // !!!!!
int pnuu[N+1];
for(ii=0; ii<N; ii++) pnuu[ii] = (nuu[ii]+bs-1)/bs*bs;
pnuu[N] = 0; // !!!!!
int cnuu[N+1];
for(ii=0; ii<N; ii++) cnuu[ii] = (nuu[ii]+ncl-1)/ncl*ncl;
cnuu[N] = 0; // !!!!!
//for(ii=0; ii<=N; ii++) printf("\n%d %d %d\n", nxx[ii], pnxx[ii], cnxx[ii]);
//for(ii=0; ii<N; ii++) printf("\n%d %d %d\n", nuu[ii], pnuu[ii], cnuu[ii]);
// factorization
printf("\nRiccati diag\n\n");
// data memory space
double *hdA[N];
double *hpBt[N];
double *hpR[N];
double *hpS[N];
double *hpQ[N+1];
double *hpLK[N];
double *hpP[N+1];
double *pK;
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hdA[ii], pnxx[ii], 1);
d_zeros_align(&hpBt[ii], pnuu[ii], cnxx[ii+1]);
d_zeros_align(&hpR[ii], pnuu[ii], cnuu[ii]);
d_zeros_align(&hpS[ii], pnxx[ii], cnuu[ii]);
d_zeros_align(&hpQ[ii], pnxx[ii], cnxx[ii]);
d_zeros_align(&hpLK[ii], pnuu[ii]+pnxx[ii], cnuu[ii]);
d_zeros_align(&hpP[ii], pnxx[ii], cnxx[ii]);
}
d_zeros_align(&hpQ[N], pnxx[N], cnxx[N]);
d_zeros_align(&hpP[N], pnxx[N], cnxx[N]);
d_zeros_align(&pK, pnxx[0], cnuu[0]); // max(nx) x nax(nu)
// dA
for(ii=0; ii<N; ii++)
for(jj=0; jj<nxx[ii+1]; jj++)
hdA[ii][jj] = 1.0;
//d_print_mat(1, cnxx[1], hdA[0], 1);
// B
double *eye_nu0; d_zeros(&eye_nu0, nu0, nu0);
for(jj=0; jj<nu0; jj++) eye_nu0[jj*(nu0+1)] = 1.0;
double *ptrB = BBB;
for(ii=0; ii<N; ii++)
{
d_cvt_mat2pmat(nuu[ii], nuu[ii], eye_nu0, nuu[ii], 0, hpBt[ii], cnxx[ii+1]);
d_cvt_tran_mat2pmat(nxx[ii+1]-nuu[ii], nuu[ii], ptrB, nxx[ii+1]-nuu[ii], 0, hpBt[ii]+nuu[ii]*bs, cnxx[ii+1]);
ptrB += nxx[ii+1] - nuu[ii];
}
free(eye_nu0);
//d_print_pmat(pnuu[0], cnxx[1], bs, hpBt[0], cnxx[0]);
//d_print_pmat(pnuu[1], cnxx[2], bs, hpBt[1], cnxx[1]);
//d_print_pmat(pnuu[2], cnxx[3], bs, hpBt[2], cnxx[2]);
//d_print_pmat(pnuu[N-1], cnxx[N-1], bs, hpBt[N-2], cnxx[N-2]);
//d_print_pmat(pnuu[N-1], cnxx[N], bs, hpBt[N-1], cnxx[N-1]);
// R
// penalty on du
for(ii=0; ii<N; ii++)
for(jj=0; jj<nuu[ii]; jj++)
hpR[ii][jj/bs*bs*cnuu[ii]+jj%bs+jj*bs] = 0.0;
//for(ii=0; ii<N; ii++)
// d_print_pmat(pnuu[ii], cnuu[ii], bs, hpR[ii], pnuu[ii]);
//d_print_pmat(pnuu[0], cnuu[0], bs, hpR[0], pnuu[0]);
// S (zero)
// Q
for(ii=0; ii<=N; ii++)
{
// penalty on u
for(jj=0; jj<nu0; jj++)
hpQ[ii][jj/bs*bs*cnxx[ii]+jj%bs+jj*bs] = 1.0;
// penalty on x
// for(jj==1; jj<nxx[ii]-nx0; jj++)
// hpQ[ii][jj/bs*bs*cnxx[ii]+jj%bs+jj*bs] = 0.0002;
for(jj=nxx[ii]-nx0; jj<nxx[ii]; jj++)
hpQ[ii][jj/bs*bs*cnxx[ii]+jj%bs+jj*bs] = 1.0;
}
//for(ii=0; ii<=N; ii++)
// d_print_pmat(pnxx[ii], cnxx[ii], bs, hpQ2[ii], cnxx[ii]);
//d_print_pmat(pnxx[0], cnxx[0], bs, hpQ2[0], cnxx[0]);
//d_print_pmat(pnxx[1], cnxx[1], bs, hpQ2[1], cnxx[1]);
//d_print_pmat(pnxx[N-1], cnxx[N-1], bs, hpQ2[N-1], cnxx[N-1]);
//d_print_pmat(pnxx[N], cnxx[N], bs, hpQ2[N], cnxx[N]);
//exit(1);
// work space
double *diag; d_zeros_align(&diag, pnxx[0]+pnuu[0], 1);
// factorization
printf("\nfactorization ...\n");
d_ric_diag_trf_mpc(N, nxx, nuu, hdA, hpBt, hpR, hpS, hpQ, hpLK, pK, hpP, diag);
printf("\nfactorization done\n\n");
#if 1
//d_print_pmat(nxx[0], nxx[0], bs, hpP[0], cnxx[0]);
//d_print_pmat(nxx[1], nxx[1], bs, hpP[1], cnxx[1]);
//d_print_pmat(nxx[N-2], nxx[N-2], bs, hpP[N-2], cnxx[N-2]);
//d_print_pmat(nxx[N-1], nxx[N-1], bs, hpP[N-1], cnxx[N-1]);
//d_print_pmat(nxx[N], nxx[N], bs, hpP[N], cnxx[N]);
//for(ii=0; ii<=N; ii++)
// d_print_pmat(pnuu[ii]+nxx[ii], nuu[ii], bs, hpLK[ii], cnuu[ii]);
//d_print_pmat(pnuu[0]+nxx[0], nuu[0], bs, hpLK[0], cnuu[0]);
//d_print_pmat(pnuu[1]+nxx[1], nuu[1], bs, hpLK[1], cnuu[1]);
//d_print_pmat(pnuu[2]+nxx[2], nuu[2], bs, hpLK[2], cnuu[2]);
//d_print_pmat(pnuu[N-3]+nxx[N-3], nuu[N-3], bs, hpLK[N-3], cnuu[N-3]);
//d_print_pmat(pnuu[N-2]+nxx[N-2], nuu[N-2], bs, hpLK[N-2], cnuu[N-2]);
//d_print_pmat(pnuu[N-1]+nxx[N-1], nuu[N-1], bs, hpLK[N-1], cnuu[N-1]);
#endif
// backward-forward solution
// data memory space
double *hrq[N+1];
double *hux[N+1];
double *hpi[N+1];
double *hPb[N];
double *hb[N];
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hrq[ii], pnuu[ii]+pnxx[ii], 1);
d_zeros_align(&hux[ii], pnuu[ii]+pnxx[ii], 1);
d_zeros_align(&hpi[ii], pnxx[ii], 1);
d_zeros_align(&hPb[ii], pnxx[ii+1], 1);
d_zeros_align(&hb[ii], pnxx[ii+1], 1);
}
d_zeros_align(&hrq[N], pnuu[N]+pnxx[N], 1);
d_zeros_align(&hux[N], pnuu[N]+pnxx[N], 1);
d_zeros_align(&hpi[N], pnxx[N], 1);
double *work_diag; d_zeros_align(&work_diag, pnxx[0], 1);
for(ii=0; ii<=N; ii++)
for(jj=0; jj<nuu[ii]; jj++)
hrq[ii][jj] = 0.0;
for(ii=0; ii<=N; ii++)
for(jj=0; jj<nxx[ii]; jj++)
hrq[ii][nuu[ii]+jj] = 0.0;
for(ii=0; ii<N; ii++)
for(jj=0; jj<nxx[ii+1]; jj++)
hb[ii][jj] = 0.0;
// x0
for(jj=0; jj<nuu[0]; jj++)
{
hux[0][jj] = 0.0;
}
for(; jj<nuu[0]+nu0; jj++)
{
hux[0][jj] = 7.5097;
}
for(; jj<nxx[0]; jj+=2)
{
hux[0][jj+0] = 15.01940;
hux[0][jj+1] = 0.0;
}
//d_print_mat(1, nuu[0]+nxx[0], hux2[0], 1);
printf("\nbackward-forward solution ...\n");
d_ric_diag_trs_mpc(N, nxx, nuu, hdA, hpBt, hpLK, hpP, hb, hrq, hux, 1, hPb, 1, hpi, work_diag);
printf("\nbackward-forward solution done\n\n");
#if 1
printf("\nux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hux[ii], 1);
#endif
// residuals
// data memory space
double *hres_rq[N+1];
double *hres_b[N];
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hres_rq[ii], pnuu[ii]+pnxx[ii], 1);
d_zeros_align(&hres_b[ii], pnxx[ii+1], 1);
}
d_zeros_align(&hres_rq[N], pnuu[N]+pnxx[N], 1);
printf("\nresuduals ...\n");
d_res_diag_mpc(N, nxx, nuu, hdA, hpBt, hpR, hpS, hpQ, hb, hrq, hux, hpi, hres_rq, hres_b, work_diag);
printf("\nresiduals done\n\n");
#if 1
printf("\nres_q\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hres_rq[ii], 1);
printf("\nres_b\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nxx[ii+1], hres_b[ii], 1);
#endif
// timing
struct timeval tv20, tv21;
#if 1
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 10000;
for(ii=0; ii<nrep; ii++)
{
d_ric_diag_trf_mpc(N, nxx, nuu, hdA, hpBt, hpR, hpS, hpQ, hpLK, pK, hpP, diag);
d_ric_diag_trs_mpc(N, nxx, nuu, hdA, hpBt, hpLK, hpP, hb, hrq, hux, 1, hPb, 1, hpi, work_diag);
}
gettimeofday(&tv21, NULL); // start
time_ric_diag = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
printf("\ntiming done\n\n");
#endif
#if 1
printf("\nRiccati full\n\n");
// size-variant full
int nzz[N+1];
for(ii=0; ii<=N; ii++) nzz[ii] = nuu[ii] + nxx[ii] + 1;
int pnzz[N+1];
for(ii=0; ii<=N; ii++) pnzz[ii] = (nzz[ii]+bs-1)/bs*bs;
int cnzz[N+1];
for(ii=0; ii<=N; ii++) cnzz[ii] = (nzz[ii]+ncl-1)/ncl*ncl;
int anzz[N+1];
for(ii=0; ii<=N; ii++) anzz[ii] = (nzz[ii]+nal-1)/nal*nal;
int cnll[N+1];
for(ii=0; ii<=N; ii++) cnll[ii] = cnzz[ll]<cnxx[ll]+ncl ? cnxx[ll]+ncl : cnzz[ll];
int nzero[N+1];
for(ii=0; ii<=N; ii++) nzero[ii] = 0;
double *hpBAbt_tv[N];
double *hpRSQ_tv[N+1];
double *hpL_tv[N+1];
double *hl[N+1];
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hpBAbt_tv[ii], pnzz[ii], cnxx[ii+1]);
d_zeros_align(&hpRSQ_tv[ii], pnzz[ii], cnzz[ii]);
d_zeros_align(&hpL_tv[ii], pnzz[ii], cnll[ii]);
d_zeros_align(&hl[ii], anzz[ii], 1);
}
d_zeros_align(&hpRSQ_tv[N], pnzz[N], cnzz[N]);
d_zeros_align(&hpL_tv[N], pnzz[N], cnll[N]);
d_zeros_align(&hl[N], anzz[ii], 1);
double *work_ric_tv; d_zeros_align(&work_ric_tv, pnzz[0], cnxx[0]);
for(ii=0; ii<N; ii++)
{
d_copy_pmat(nuu[ii], nxx[ii+1], bs, hpBt[ii], cnxx[ii], hpBAbt_tv[ii], cnxx[ii+1]);
for(jj=0; jj<nxx[ii+1]; jj++) hpBAbt_tv[ii][(nuu[ii]+jj)/bs*bs*cnxx[ii+1]+(nuu[ii]+jj)%bs+jj*bs] = 1.0;
for(jj=0; jj<nxx[ii+1]; jj++) hpBAbt_tv[ii][(nuu[ii]+nxx[ii])/bs*bs*cnxx[ii+1]+(nuu[ii]+nxx[ii])%bs+jj*bs] = hb[ii][jj];
//d_print_pmat(nzz[ii], nxx[ii+1], bs, hpBAbt_tv[ii], cnxx[ii+1]);
}
for(ii=0; ii<=N; ii++)
{
// R
// penalty on du
for(jj=0; jj<nuu[ii]; jj++)
hpRSQ_tv[ii][jj/bs*bs*cnzz[ii]+jj%bs+jj*bs] = 0.0;
// Q
// penalty on u
for(; jj<nuu[ii]+nu0; jj++)
hpRSQ_tv[ii][jj/bs*bs*cnzz[ii]+jj%bs+jj*bs] = 1.0;
// penalty on x
for(jj=nuu[ii]+nxx[ii]-nx0; jj<nuu[ii]+nxx[ii]; jj++)
hpRSQ_tv[ii][jj/bs*bs*cnzz[ii]+jj%bs+jj*bs] = 1.0;
// r q
for(jj=0; jj<nuu[ii]+nxx[ii]; jj++) hpRSQ_tv[ii][(nuu[ii]+nxx[ii])/bs*bs*cnzz[ii]+(nuu[ii]+nxx[ii])%bs+jj*bs] = hrq[ii][jj];
//d_print_pmat(nzz[ii], nzz[ii], bs, hpRSQ_tv[ii], cnzz[ii]);
}
printf("\nfactorization and backward-forward solution ...\n");
d_ric_sv_mpc_tv(N, nxx, nuu, hpBAbt_tv, hpRSQ_tv, hux, hpL_tv, work_ric_tv, diag, COMPUTE_MULT, hpi, nzero, int_dummy, dummy, dummy, nzero, dummy, dummy, dummy, 0);
printf("\nfactorization and backward-forward solution done\n\n");
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(nzz[ii], nzz[ii], bs, hpL_tv[ii], cnzz[ii]);
#endif
printf("\nux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hux[ii], 1);
for(ii=0; ii<N; ii++)
for(jj=0; jj<nxx[ii+1]; jj++)
hux[ii+1][nuu[ii+1]+jj] = hb[ii][jj];
printf("\nbackward-forward solution ...\n");
d_ric_trs_mpc_tv(N, nxx, nuu, hpBAbt_tv, hpL_tv, hrq, hl, hux, work_ric_tv, 1, hPb, COMPUTE_MULT, hpi, nzero, int_dummy, dummy, nzero, dummy, dummy);
printf("\nbackward-forward solution done\n\n");
printf("\nux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hux[ii], 1);
//exit(1);
printf("\nresuduals ...\n");
d_res_diag_mpc(N, nxx, nuu, hdA, hpBt, hpR, hpS, hpQ, hb, hrq, hux, hpi, hres_rq, hres_b, work_diag);
printf("\nresiduals done\n\n");
#if 1
printf("\nres_q\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hres_rq[ii], 1);
printf("\nres_b\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nxx[ii+1], hres_b[ii], 1);
#endif
#if 1
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 10000;
for(ii=0; ii<nrep; ii++)
{
d_ric_sv_mpc_tv(N, nxx, nuu, hpBAbt_tv, hpRSQ_tv, hux, hpL_tv, work_ric_tv, diag, COMPUTE_MULT, hpi, nzero, int_dummy, dummy, dummy, nzero, dummy, dummy, dummy, 0);
}
gettimeofday(&tv21, NULL); // start
time_ric_full_tv = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
printf("\ntiming done\n\n");
#endif
#endif
#if 1
// IPM
printf("\nIPM diag\n\n");
int kk = -1;
int kmax = 50;
double mu0 = 1;
double mu_tol = 1e-8;
double alpha_min = 1e-12;
double sigma_par[] = {0.4, 0.3, 0.01};
double stat[5*50] = {};
int nbb[N+1];
nbb[0] = nu0;//nuu[0]; // XXX !!!!!!!!!!!!!!
for(ii=1; ii<N; ii++) nbb[ii] = 2*nu0 + nx0; //nuu[ii] + nxx[ii];
nbb[N] = nu0 + nx0;
int *(idxb[N+1]);
for(ii=0; ii<=N; ii++)
{
idxb[ii] = (int *) malloc(nbb[ii]*sizeof(int));
}
int pnbb[N+1];
for(ii=0; ii<=N; ii++) pnbb[ii] = (nbb[ii]+bs-1)/bs*bs;
// data memory space
double *hd[N+1];
double *hlam[N+1];
double *ht[N+1];
double *hres_d[N+1];
for(ii=0; ii<=N; ii++)
{
d_zeros_align(&hd[ii], 2*pnbb[ii], 1);
d_zeros_align(&hlam[ii], 2*pnbb[ii], 1);
d_zeros_align(&ht[ii], 2*pnbb[ii], 1);
d_zeros_align(&hres_d[ii], 2*pnbb[ii], 1);
}
double mu = -1;
//printf("\nbounds\n");
ii = 0; // initial stage
ll = 0;
for(jj=0; jj<nuu[ii]; jj++)
{
hd[ii][ll] = -20.5;
hd[ii][pnbb[ii]+ll] = -20.5;
idxb[ii][ll] = jj;
ll++;
}
//d_print_mat(1, 2*pnbb[ii], hd[ii], 1);
for(ii=1; ii<=N; ii++)
{
ll = 0;
for(jj=0; jj<nuu[ii]; jj++)
{
hd[ii][ll] = -20.5;
hd[ii][pnbb[ii]+ll] = -20.5;
idxb[ii][ll] = jj;
ll++;
}
for(; jj<nuu[ii]+nu0; jj++)
{
hd[ii][ll] = - 2.5; // -2.5
hd[ii][pnbb[ii]+ll] = -10.0; // -10
idxb[ii][ll] = jj;
ll++;
}
//for(; jj<nbb[ii]-nx0; jj++)
//for(; jj<nbb[ii]; jj++)
//{
//hd[ii][jj] = -100.0;
//hd[ii][pnbb[ii]+jj] = -100.0;
//idxb[ii][ll] = jj;
//ll++;
//}
jj += nx0*(N-ii);
hd[ii][ll+0] = - 0.0; // 0
hd[ii][pnbb[ii]+ll+0] = -20.0; // -20
idxb[ii][ll] = jj;
ll++;
jj++;
hd[ii][ll+0] = -10.0; // -10
hd[ii][pnbb[ii]+ll+0] = -10.0; // -10
idxb[ii][ll] = jj;
ll++;
jj++;
//d_print_mat(1, 2*pnbb[ii], hd[ii], 1);
}
#if 0
for(ii=0; ii<=N; ii++)
{
for(jj=0; jj<nbb[ii]; jj++)
printf("%d\t", idxb[ii][jj]);
printf("\n");
}
exit(1);
#endif
for(jj=0; jj<nuu[0]; jj++)
{
hux[0][jj] = 0.0;
}
for(; jj<nuu[0]+nu0; jj++)
{
hux[0][jj] = 7.5097;
}
for(; jj<nxx[0]; jj+=2)
{
hux[0][jj+0] = 15.01940;
hux[0][jj+1] = 0.0;
}
//d_print_mat(1, nuu[0]+nxx[0], hux2[0], 1);
int pnxM = pnxx[0];
int pnuM = pnuu[0];
int cnuM = cnuu[0];
int anxx[N+1];
for(ii=0; ii<=N; ii++) anxx[ii] = (nxx[ii]+nal-1)/nal*nal;
int anuu[N+1];
for(ii=0; ii<=N; ii++) anuu[ii] = (nuu[ii]+nal-1)/nal*nal;
int work_space_ip_double = 0;
for(ii=0; ii<=N; ii++)
work_space_ip_double += anuu[ii] + 3*anxx[ii] + (pnuu[ii]+pnxx[ii])*cnuu[ii] + pnxx[ii]*cnxx[ii] + 12*pnbb[ii];
work_space_ip_double += pnxM*cnuM + pnxM + pnuM;
int work_space_ip_int = (N+1)*7*sizeof(int);
work_space_ip_int = (work_space_ip_int+63)/64*64;
work_space_ip_int /= sizeof(int);
printf("\nIPM diag work space size: %d double + %d int\n\n", work_space_ip_double, work_space_ip_int);
double *work_space_ip; d_zeros_align(&work_space_ip, work_space_ip_double+(work_space_ip_int+1)/2, 1); // XXX assume sizeof(double) = 2 * sizeof(int) !!!!!
printf("\nIPM solution ...\n");
d_ip2_diag_mpc(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, N, nxx, nuu, nbb, idxb, hdA, hpBt, hpR, hpS, hpQ, hb, hd, hrq, hux, 1, hpi, hlam, ht, work_space_ip);
printf("\nIPM solution done\n");
printf("\nux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hux[ii], 1);
printf("\nlam\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], hlam[ii], 1);
d_print_mat(1, nbb[ii], hlam[ii]+pnbb[ii], 1);
}
printf("\nt\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], ht[ii], 1);
d_print_mat(1, nbb[ii], ht[ii]+pnbb[ii], 1);
}
printf("\nstatistics\n\n");
for(ii=0; ii<kk; ii++)
printf("%d\t%f\t%f\t%f\t%e\t%f\t%f\t%e\n", ii+1, stat[5*ii+0], stat[5*ii+1], stat[5*ii+2], stat[5*ii+2], stat[5*ii+3], stat[5*ii+4], stat[5*ii+4]);
printf("\n\n");
// residuals
printf("\nresuduals IPM ...\n");
d_res_ip_diag_mpc(N, nxx, nuu, nbb, idxb, hdA, hpBt, hpR, hpS, hpQ, hb, hrq, hd, hux, hpi, hlam, ht, hres_rq, hres_b, hres_d, &mu, work_diag);
printf("\nresiduals IPM done\n");
printf("\nres_rq\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hres_rq[ii], 1);
printf("\nres_b\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nxx[ii+1], hres_b[ii], 1);
printf("\nres_d\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], hres_d[ii], 1);
d_print_mat(1, nbb[ii], hres_d[ii]+pnbb[ii], 1);
}
printf("\nres_mu\n");
d_print_mat(1, 1, &mu, 1);
// timing
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 1000;
for(ii=0; ii<nrep; ii++)
{
d_ip2_diag_mpc(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, N, nxx, nuu, nbb, idxb, hdA, hpBt, hpR, hpS, hpQ, hb, hd, hrq, hux, 1, hpi, hlam, ht, work_space_ip);
}
gettimeofday(&tv21, NULL); // start
printf("\ntiming done\n\n");
time_ip_diag = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
// simulation
printf("\nsimulation ...\n\n");
nrep = 15;
for(ii=0; ii<nrep; ii++)
{
d_ip2_diag_mpc(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, N, nxx, nuu, nbb, idxb, hdA, hpBt, hpR, hpS, hpQ, hb, hd, hrq, hux, 1, hpi, hlam, ht, work_space_ip);
dgemv_t_lib(nuu[0], nxx[0], hpBt[0], cnxx[0], hux[0], hux[0]+nuu[0], 1);
for(jj=0; jj<nxx[0]-nx0-nu0; jj++) hux[0][nuu[0]+nxx[0]-jj-1] = hux[0][nuu[0]+nxx[0]-jj-1-nx0];
printf("\nsimulation step = %d, IPM iterations = %d, mu = %e\n\n", ii, kk, stat[5*(kk-1)+4]);
d_print_mat(1, nuu[0]+nxx[0], hux[0], 1);
}
printf("\nsimulation done\n\n");
//exit(1);
#if 1
// IPM
printf("\nIPM full\n\n");
int ngg[N+1];
for(ii=0; ii<=N; ii++) ngg[ii] = 0;
int pngg[N+1];
for(ii=0; ii<=N; ii++) pngg[ii] = (ngg[ii]+bs-1)/bs*bs;
//int pnzM = pnzz[0]; // max
//int cnxgM = cnxx[0]; // max
//int work_space_int_size = 7*(N+1);
//int work_space_double_size = pnzM*cnxgM + pnzM;
//for(ii=0; ii<=N; ii++)
// work_space_double_size += pnzz[ii]*cnll[ii] + 3*anzz[ii] + 2*anxx[ii] + 14*pnbb[ii] + 10*pngg[ii];
//printf("\nIPM diag work space size: %d double + %d int\n\n", work_space_double_size, work_space_int_size);
//double *work_ipm_tv_double; d_zeros_align(&work_ipm_tv_double, work_space_double_size, 1);
double *work_ipm_tv_double; d_zeros_align(&work_ipm_tv_double, d_ip2_hard_mpc_tv_work_space_size_double(N, nxx, nuu, nbb, ngg), 1);
//int *work_ipm_tv_int = (int *) malloc(work_space_int_size*sizeof(int));
int *work_ipm_tv_int = (int *) malloc(d_ip2_hard_mpc_tv_work_space_size_int(N, nxx, nuu, nbb, ngg)*sizeof(int));
for(jj=0; jj<nuu[0]; jj++)
{
hux[0][jj] = 0.0;
}
for(; jj<nuu[0]+nu0; jj++)
{
hux[0][jj] = 7.5097;
}
for(; jj<nxx[0]; jj+=2)
{
hux[0][jj+0] = 15.01940;
hux[0][jj+1] = 0.0;
}
//d_print_mat(1, nuu[0]+nxx[0], hux2[0], 1);
printf("\nIPM solution ...\n");
d_ip2_hard_mpc_tv(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, N, nxx, nuu, nbb, idxb, ngg, hpBAbt_tv, hpRSQ_tv, dummy, hd, hux, 1, hpi, hlam, ht, work_ipm_tv_double, work_ipm_tv_int);
printf("\nIPM solution done\n");
printf("\nux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hux[ii], 1);
printf("\nlam\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], hlam[ii], 1);
d_print_mat(1, nbb[ii], hlam[ii]+pnbb[ii], 1);
}
printf("\nt\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], ht[ii], 1);
d_print_mat(1, nbb[ii], ht[ii]+pnbb[ii], 1);
}
printf("\nstatistics\n\n");
for(ii=0; ii<kk; ii++)
printf("%d\t%f\t%f\t%f\t%e\t%f\t%f\t%e\n", ii+1, stat[5*ii+0], stat[5*ii+1], stat[5*ii+2], stat[5*ii+2], stat[5*ii+3], stat[5*ii+4], stat[5*ii+4]);
printf("\n\n");
printf("\nresiduals ...\n\n");
d_res_ip_hard_mpc_tv(N, nxx, nuu, nbb, idxb, ngg, hpBAbt_tv, hpRSQ_tv, hrq, hux, dummy, hd, hpi, hlam, ht, hres_rq, hres_b, hres_d, &mu);
printf("\nresiduals dones\n\n");
printf("\nres_rq\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nuu[ii]+nxx[ii], hres_rq[ii], 1);
printf("\nres_b\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nxx[ii+1], hres_b[ii], 1);
printf("\nres_d\n");
for(ii=0; ii<=N; ii++)
{
d_print_mat(1, nbb[ii], hres_d[ii], 1);
d_print_mat(1, nbb[ii], hres_d[ii]+pnbb[ii], 1);
}
printf("\nres_mu\n");
d_print_mat(1, 1, &mu, 1);
// timing
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 1000;
for(ii=0; ii<nrep; ii++)
{
d_ip2_hard_mpc_tv(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, N, nxx, nuu, nbb, idxb, ngg, hpBAbt_tv, hpRSQ_tv, dummy, hd, hux, 1, hpi, hlam, ht, work_ipm_tv_double, work_ipm_tv_int);
}
gettimeofday(&tv21, NULL); // start
printf("\ntiming done\n\n");
time_ip_full_tv = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
free(work_ric_tv);
free(work_ipm_tv_double);
free(work_ipm_tv_int);
for(ii=0; ii<N; ii++)
{
free(hpBAbt_tv[ii]);
free(hpRSQ_tv[ii]);
free(hpL_tv[ii]);
free(hl[ii]);
}
free(hpRSQ_tv[N]);
free(hpL_tv[N]);
free(hl[N]);
//exit(1);
#endif
// free memory
for(ii=0; ii<=N; ii++)
{
free(idxb[ii]);
free(hd[ii]);
free(hlam[ii]);
free(ht[ii]);
}
free(work_space_ip);
#endif
for(ii=0; ii<N; ii++)
{
free(hdA[ii]);
free(hpBt[ii]);
free(hpR[ii]);
free(hpS[ii]);
free(hpQ[ii]);
free(hpLK[ii]);
free(hpP[ii]);
free(hrq[ii]);
free(hux[ii]);
free(hpi[ii]);
free(hPb[ii]);
free(hb[ii]);
free(hres_rq[ii]);
free(hres_b[ii]);
}
free(hpQ[N]);
free(hpP[N]);
free(pK);
free(hrq[N]);
free(hux[N]);
free(hpi[N]);
free(work_diag);
free(hres_rq[N]);
/************************************************
* test of normal riccati & IPM
************************************************/
printf("\nRiccati full\n\n");
nx = 25;
nu = 1;
N = 11;
int rep;
int nz = nx+nu+1;
int anz = nal*((nz+nal-1)/nal);
int anx = nal*((nx+nal-1)/nal);
int pnz = bs*((nz+bs-1)/bs);
int pnx = bs*((nx+bs-1)/bs);
int pnu = bs*((nu+bs-1)/bs);
int cnz = ncl*((nx+nu+1+ncl-1)/ncl);
int cnx = ncl*((nx+ncl-1)/ncl);
int cnu = ncl*((nu+ncl-1)/ncl);
int cnl = cnz<cnx+ncl ? cnx+ncl : cnz;
const int ncx = nx;
#if 1
double *BAb_temp; d_zeros(&BAb_temp, nx, nu+nx+1);
double *hpBAbt2[N];
ptrB = BBB;
for(ii=0; ii<N; ii++)
{
//printf("\n%d\n", ii);
d_zeros_align(&hpBAbt2[ii], pnz, cnx);
for(jj=0; jj<nx*(nx+nu+1); jj++) BAb_temp[jj] = 0.0;
for(jj=0; jj<nu; jj++) BAb_temp[jj*(nx+1)] = 1.0;
d_copy_mat(nxx[ii+1]-1, nuu[ii], ptrB, nxx[ii+1]-1, BAb_temp+1, nx);
ptrB += nxx[ii+1]-1;
for(jj=0; jj<nxx[ii+1]; jj++) BAb_temp[nuu[ii]*nx+jj*(nx+1)] = 1.0;
//for(jj=0; jj<nxx[ii+1]; jj++) BAb_temp[(nuu[ii]+nxx[ii+1])*nx+jj] = 1.0;
//d_print_mat(nx, nu+nx+1, BAb_temp, nx);
d_cvt_tran_mat2pmat(nx, nx+nu+1, BAb_temp, nx, 0, hpBAbt2[ii], cnx);
//d_print_pmat(nx+nu+1, nx, bs, hpBAbt2[ii], cnx);
}
double *RSQ; d_zeros(&RSQ, nz, nz);
double *hpRSQ[N+1];
for(ii=0; ii<=N; ii++)
{
//printf("\n%d\n", ii);
d_zeros_align(&hpRSQ[ii], pnz, cnz);
for(jj=0; jj<nz*nz; jj++) RSQ[jj] = 0.0;
for(jj=nu; jj<2*nu; jj++) RSQ[jj*(nz+1)] = 1.0;
for(jj=nu+nxx[ii]-nx0; jj<nu+nxx[ii]; jj++) RSQ[jj*(nz+1)] = 1.0;
d_cvt_mat2pmat(nz, nz, RSQ, nz, 0, hpRSQ[ii], cnz);
//d_print_pmat(nz, nz, bs, hpRSQ[ii], cnz);
}
double *hpL[N+1];
double *hq2[N+1];
double *hux2[N+1];
double *hpi2[N+1];
double *hPb2[N];
for(jj=0; jj<N; jj++)
{
d_zeros_align(&hq2[jj], pnz, 1); // it has to be pnz !!!
d_zeros_align(&hpL[jj], pnz, cnl);
d_zeros_align(&hux2[jj], pnz, 1); // it has to be pnz !!!
d_zeros_align(&hpi2[jj], pnx, 1);
d_zeros_align(&hPb2[jj], pnx, 1);
}
d_zeros_align(&hpL[N], pnz, cnl);
d_zeros_align(&hq2[N], pnz, 1); // it has to be pnz !!!
d_zeros_align(&hux2[N], pnz, 1); // it has to be pnz !!!
d_zeros_align(&hpi2[N], pnx, 1);
//double *work; d_zeros_align(&work, 2*anz, 1);
double *work; d_zeros_align(&work, pnz, cnx);
for(jj=0; jj<nx+nu; jj++) hux2[0][jj] = 0.0;
for(jj=0; jj<nu; jj++)
{
hux2[0][nu+jj] = 7.5097;
}
for(; jj<nx; jj+=2)
{
hux2[0][nu+jj+0] = 15.01940;
hux2[0][nu+jj+1] = 0.0;
}
printf("\nfactorization and backward-forward solution ...\n");
d_ric_sv_mpc(nx, nu, N, hpBAbt2, hpRSQ, 0, dummy, dummy, hux2, hpL, work, diag, COMPUTE_MULT, hpi2, 0, 0, 0, dummy, dummy, dummy, 0);
printf("\nfactorization and backward-forward solution done\n\n");
//for(ii=0; ii<=N; ii++)
// d_print_pmat(pnz, cnl-3, bs, hpL[ii], cnl);
//d_print_pmat(pnz, nu, bs, hpL[0], cnl);
//d_print_pmat(pnz, cnl-3, bs, hpL[1], cnl);
//d_print_pmat(pnz, cnl-3, bs, hpL[2], cnl);
//d_print_pmat(pnz, cnl-3, bs, hpL[N-3], cnl);
//d_print_pmat(pnz, cnl-3, bs, hpL[N-2], cnl);
//d_print_pmat(pnz, cnl-3, bs, hpL[N-1], cnl);
//d_print_pmat(pnz, cnl, bs, hpL[N], cnl);
#if 1
printf("\nux Riccati full\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx+nu, hux2[ii], 1);
#endif
// residuals
double *hres_rq2[N+1];
double *hres_b2[N];
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hres_rq2[ii], pnz, 1);
d_zeros_align(&hres_b2[ii], pnx, 1);
}
d_zeros_align(&hres_rq2[N], pnz, 1);
printf("\nresuduals ...\n");
d_res_mpc(nx, nu, N, hpBAbt2, hpRSQ, hq2, hux2, hpi2, hres_rq2, hres_b2);
printf("\nresiduals done\n\n");
printf("\nres_q full\n");
d_print_mat(1, nu, hres_rq2[ii], 1);
for(ii=0; ii<N; ii++)
d_print_mat(1, nx+nu, hres_rq2[ii], 1);
printf("\nres_b full\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nx, hres_b2[ii], 1);
// timing
//struct timeval tv20, tv21;
#if 1
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 10000;
for(ii=0; ii<nrep; ii++)
{
d_ric_sv_mpc(nx, nu, N, hpBAbt2, hpRSQ, 0, dummy, dummy, hux2, hpL, work, diag, COMPUTE_MULT, hpi2, 0, 0, 0, dummy, dummy, dummy, 0);
}
gettimeofday(&tv21, NULL); // start
time_ric_full = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
printf("\ntiming done\n\n");
#endif
printf("\nIPM full\n\n");
int nb = nu+nx;
int ng = 0;
int ngN = 0;
int pnb = (nb+bs-1)/bs*bs;
int png = (ng+bs-1)/bs*bs;
int pngN = (ngN+bs-1)/bs*bs;
double *hd2[N+1];
double *hlam2[N+1];
double *ht2[N+1];
for(ii=0; ii<N; ii++)
{
d_zeros_align(&hd2[ii], 2*pnb+2*png, 1);
d_zeros_align(&hlam2[ii],2*pnb+2*png, 1);
d_zeros_align(&ht2[ii], 2*pnb+2*png, 1);
}
d_zeros_align(&hd2[N], 2*pnb+2*pngN, 1);
d_zeros_align(&hlam2[N],2*pnb+2*pngN, 1);
d_zeros_align(&ht2[N], 2*pnb+2*pngN, 1);
// work space // more than enought !!!!!
double *work_ipm_full; d_zeros_align(&work_ipm_full, hpmpc_ip_hard_mpc_dp_work_space(N, nx, nu, nb, ng, ngN), 1);
// bounds
for(ii=0; ii<=N; ii++)
{
for(jj=0; jj<nu; jj++)
{
hd2[ii][jj] = -20.5;
hd2[ii][pnb+jj] = -20.5;
}
for(; jj<2*nu; jj++)
{
hd2[ii][jj] = - 2.5;
hd2[ii][pnb+jj] = -10.0;
}
for(; jj<2*nu+(N-ii)*nx0; jj++)
{
hd2[ii][jj] = -100.0;
hd2[ii][pnb+jj] = -100.0;
}
hd2[ii][jj+0] = 0.0;
hd2[ii][pnb+jj+0] = -20.0;
hd2[ii][jj+1] = -10.0;
hd2[ii][pnb+jj+1] = -10.0;
jj += 2;
for(; jj<nu+nx; jj++)
{
hd2[ii][jj] = -100.0;
hd2[ii][pnb+jj] = -100.0;
}
//d_print_mat(1, nb, hd2[ii], 1);
//d_print_mat(1, nb, hd2[ii]+pnb, 1);
}
//exit(1);
printf("\nIPM full solve ...\n\n");
d_ip2_hard_mpc(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, nx, nu, N, nb, ng, ngN, hpBAbt2, hpRSQ, dummy, hd2, hux2, 1, hpi2, hlam2, ht2, work_ipm_full);
printf("\nIPM full solve done\n\n");
#if 1
printf("\nux IPM full\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx+nu, hux2[ii], 1);
#endif
printf("\nstatistics\n\n");
for(ii=0; ii<kk; ii++)
printf("%d\t%f\t%f\t%f\t%e\t%f\t%f\t%e\n", ii+1, stat[5*ii+0], stat[5*ii+1], stat[5*ii+2], stat[5*ii+2], stat[5*ii+3], stat[5*ii+4], stat[5*ii+4]);
printf("\n\n");
// timing
printf("\ntiming ...\n\n");
gettimeofday(&tv20, NULL); // start
nrep = 1000;
for(ii=0; ii<nrep; ii++)
{
d_ip2_hard_mpc(&kk, kmax, mu0, mu_tol, alpha_min, 0, sigma_par, stat, nx, nu, N, nb, ng, ngN, hpBAbt2, hpRSQ, dummy, hd2, hux2, 1, hpi2, hlam2, ht2, work_ipm_full);
}
gettimeofday(&tv21, NULL); // start
printf("\ntiming done\n\n");
time_ip_full = (float) (tv21.tv_sec-tv20.tv_sec)/(nrep+0.0)+(tv21.tv_usec-tv20.tv_usec)/(nrep*1e6);
// free memory
free(work_ipm_full);
for(ii=0; ii<N; ii++)
{
free(hd2[ii]);
free(hlam2[ii]);
free(ht2[ii]);
}
free(hd2[N]);
free(hlam2[N]);
free(ht2[N]);
// free memory
free(work);
free(RSQ);
free(BAb_temp);
for(ii=0; ii<N; ii++)
{
free(hpBAbt2[ii]);
free(hpRSQ[ii]);
free(hpL[ii]);
free(hux2[ii]);
free(hpi2[ii]);
free(hq2[ii]);
free(hPb2[ii]);
free(hres_rq2[ii]);
free(hres_b2[ii]);
}
free(hpRSQ[N]);
free(hpL[N]);
free(hux2[N]);
free(hpi2[N]);
free(hq2[N]);
free(hres_rq2[N]);
#endif
printf("\nric diag time = %e\t\tric full time = %e\t\tric full tv time = %e\t\tip diag time = %e\t\tip full time = %e\t\tip full tv time = %e\n\n", time_ric_diag, time_ric_full, time_ric_full_tv, time_ip_diag, time_ip_full, time_ip_full_tv);
#endif
}
/* primal-dual interior-point method, hard constraints, time variant matrices (mpc version) */
int d_ip2_hard_mpc(int *kk, int k_max, double mu0, double mu_tol, double alpha_min, int warm_start, double *sigma_par, double *stat, int nx, int nu, int N, int nb, int ng, int ngN, double **pBAbt, double **pQ, double **pDCt, double **d, double **ux, int compute_mult, double **pi, double **lam, double **t, double *work_memory)
{
int nbu = nu<nb ? nu : nb ;
// indeces
int jj, ll, ii, bs0;
// constants
const int bs = D_MR; //d_get_mr();
const int ncl = D_NCL;
const int nal = bs*ncl; // number of doubles per cache line
const int nz = nx+nu+1;
const int nxu = nx+nu;
const int pnz = bs*((nz+bs-1)/bs);
const int pnx = bs*((nx+bs-1)/bs);
const int pnb = bs*((nb+bs-1)/bs); // simd aligned number of two-sided box constraints !!!!!!!!!!!!!!!!!!
const int png = bs*((ng+bs-1)/bs); // simd aligned number of two-sided general constraints !!!!!!!!!!!!!!!!!!
const int pngN = bs*((ngN+bs-1)/bs); // simd aligned number of two-sided general constraints at stage N !!!!!!!!!!!!!!!!!!
const int cnz = ncl*((nz+ncl-1)/ncl);
const int cnx = ncl*((nx+ncl-1)/ncl);
// const int cng = ncl*((ng+ncl-1)/ncl);
const int cngN = ncl*((ngN+ncl-1)/ncl);
const int cnxg = ncl*((ng+nx+ncl-1)/ncl);
const int anz = nal*((nz+nal-1)/nal);
const int anx = nal*((nx+nal-1)/nal);
// const int anb = nal*((2*nb+nal-1)/nal); // cache aligned number of box constraints
//const int anb = nal*((nb+nal-1)/nal); // cache aligned number of two-sided box constraints !!!!!!!!!!!!!!!!!!
// const int pad = (ncl-nx%ncl)%ncl; // packing between BAbtL & P
//const int cnl = cnz<cnx+ncl ? nx+pad+cnx+ncl : nx+pad+cnz;
const int cnl = cnz<cnx+ncl ? cnx+ncl : cnz;
//printf("\n%d %d %d %d %d\n", N, nx, nu, nb, ng);
//d_print_pmat(nz, nx, bs, pBAbt[0], cnx);
//d_print_pmat(nz, nx, bs, pBAbt[1], cnx);
//d_print_pmat(nz, nx, bs, pBAbt[N-1], cnx);
//d_print_pmat(nz, nz, bs, pQ[0], cnz);
//d_print_pmat(nz, nz, bs, pQ[1], cnz);
//d_print_pmat(nz, nz, bs, pQ[N], cnz);
//d_print_pmat(nx+nu, ng, bs, pDCt[0], cng);
//d_print_pmat(nx+nu, ng, bs, pDCt[1], cng);
//d_print_pmat(nx+nu, ng, bs, pDCt[N], cng);
//d_print_mat(1, 2*pnb+2*png, d[0], 1);
//d_print_mat(1, 2*pnb+2*png, d[1], 1);
//d_print_mat(1, 2*pnb+2*png, d[N], 1);
//d_print_mat(1, nx+nu, ux[0], 1);
//d_print_mat(1, nx+nu, ux[1], 1);
//d_print_mat(1, nx+nu, ux[N], 1);
//exit(1);
// initialize work space
double *ptr;
ptr = work_memory;
double *(dux[N+1]);
double *(dpi[N+1]);
double *(pL[N+1]);
double *(pd[N+1]); // pointer to diagonal of Hessian
double *(pl[N+1]); // pointer to linear part of Hessian
double *(bd[N+1]); // backup diagonal of Hessian
double *(bl[N+1]); // backup linear part of Hessian
double *work;
double *diag;
double *(dlam[N+1]);
double *(dt[N+1]);
double *(lamt[N+1]);
double *(t_inv[N+1]);
double *(Qx[N+1]);
double *(qx[N+1]);
double *(Pb[N]);
// ptr += (N+1)*(pnx + pnz*cnl + 12*pnz) + 3*pnz;
// inputs and states
for(jj=0; jj<=N; jj++)
{
dux[jj] = ptr;
ptr += anz;
}
// equality constr multipliers
for(jj=0; jj<=N; jj++)
{
dpi[jj] = ptr;
ptr += anx;
}
// Hessian
for(jj=0; jj<=N; jj++)
{
pd[jj] = ptr; //pQ[jj];
pl[jj] = ptr + anz; //pQ[jj] + ((nu+nx)/bs)*bs*cnz + (nu+nx)%bs;
bd[jj] = ptr + 2*anz;
bl[jj] = ptr + 3*anz;
ptr += 4*anz;
// backup
for(ll=0; ll<nx+nu; ll++)
{
bd[jj][ll] = pQ[jj][(ll/bs)*bs*cnz+ll%bs+ll*bs];
bl[jj][ll] = pQ[jj][((nx+nu)/bs)*bs*cnz+(nx+nu)%bs+ll*bs];
}
}
// work space
for(jj=0; jj<=N; jj++)
{
pL[jj] = ptr;
ptr += pnz*cnl;
}
work = ptr;
//ptr += 2*anz;
if(cngN<=cnxg)
ptr += pnz*cnxg;
else
ptr += pnz*cngN;
diag = ptr;
ptr += anz;
// slack variables, Lagrangian multipliers for inequality constraints and work space (assume # box constraints <= 2*(nx+nu) < 2*pnz)
for(jj=0; jj<N; jj++)
{
dlam[jj] = ptr;
dt[jj] = ptr + 2*pnb+2*png;
ptr += 4*pnb+4*png;
}
dlam[N] = ptr;
dt[N] = ptr + 2*pnb+2*pngN;
ptr += 4*pnb+4*pngN;
for(jj=0; jj<N; jj++)
{
lamt[jj] = ptr;
ptr += 2*pnb+2*png;
}
lamt[N] = ptr;
ptr += 2*pnb+2*pngN;
for(jj=0; jj<N; jj++)
{
t_inv[jj] = ptr;
ptr += 2*pnb+2*png;
}
t_inv[N] = ptr;
ptr += 2*pnb+2*pngN;
for(jj=0; jj<N; jj++)
{
Qx[jj] = ptr;
qx[jj] = ptr+png;
ptr += 2*pnb+2*png;
}
Qx[N] = ptr;
qx[N] = ptr+pngN;
ptr += 2*pnb+2*pngN;
// backup of P*b
for(jj=0; jj<N; jj++)
{
Pb[jj] = ptr;
ptr += anx;
}
double temp0, temp1;
double alpha, mu, mu_aff;
double mu_scal = N*2*(nb+ng)+2*ngN;
//printf("\nmu_scal = %f\n", mu_scal);
mu_scal = 1.0/mu_scal;
//printf("\nmu_scal = %f\n", mu_scal);
double sigma, sigma_decay, sigma_min;
//printf("\n%d %d %d\n", ng, ngN, N*2*ng+2*ngN);
//exit(1);
sigma = sigma_par[0]; //0.4;
sigma_decay = sigma_par[1]; //0.3;
sigma_min = sigma_par[2]; //0.01;
// initialize ux & t>0 (slack variable)
d_init_var_hard_mpc(N, nx, nu, nb, ng, ngN, ux, pi, pDCt, d, t, lam, mu0, warm_start);
#if 0
d_print_mat(1, 2*pnb+2*png, t[0], 1);
d_print_mat(1, 2*pnb+2*png, t[1], 1);
d_print_mat(1, 2*pnb+2*pngN, t[N], 1);
d_print_mat(1, 2*pnb+2*png, lam[0], 1);
d_print_mat(1, 2*pnb+2*png, lam[1], 1);
d_print_mat(1, 2*pnb+2*pngN, lam[N], 1);
exit(1);
#endif
// initialize pi
for(jj=0; jj<=N; jj++)
for(ll=0; ll<nx; ll++)
dpi[jj][ll] = 0.0;
// initialize dux
for(ll=0; ll<nx; ll++)
dux[0][nu+ll] = ux[0][nu+ll];
// compute the duality gap
//alpha = 0.0; // needed to compute mu !!!!!
//d_compute_mu_hard_mpc(N, nx, nu, nb, &mu, mu_scal, alpha, lam, dlam, t, dt);
mu = mu0;
// set to zero iteration count
*kk = 0;
// larger than minimum accepted step size
alpha = 1.0;
// update hessian in Riccati routine
const int update_hessian = 1;
int fast_rsqrt = 0;
// IP loop
while( *kk<k_max && mu>mu_tol && alpha>=alpha_min )
{
//update cost function matrices and vectors (box constraints)
d_update_hessian_hard_mpc(N, nx, nu, nb, ng, ngN, cnz, 0.0, t, t_inv, lam, lamt, dlam, Qx, qx, bd, bl, pd, pl, d);
#if 0
d_print_mat(1, 2*pnb+2*png, pd[0], 1);
d_print_mat(1, 2*pnb+2*png, pd[1], 1);
d_print_mat(1, 2*pnb+2*png, pd[N], 1);
d_print_mat(1, 2*pnb+2*png, pl[0], 1);
d_print_mat(1, 2*pnb+2*png, pl[1], 1);
d_print_mat(1, 2*pnb+2*png, pl[N], 1);
#if 0
d_print_mat(1, 2*pnb+2*png, Qx[0], 1);
d_print_mat(1, 2*pnb+2*png, Qx[1], 1);
d_print_mat(1, 2*pnb+2*pngN, Qx[N], 1);
d_print_mat(1, 2*pnb+2*png, qx[0], 1);
d_print_mat(1, 2*pnb+2*png, qx[1], 1);
d_print_mat(1, 2*pnb+2*pngN, qx[N], 1);
#endif
exit(1);
#endif
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu+nx, pd[ii], 1);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu+nx, pl[ii], 1);
for(ii=0; ii<N; ii++)
d_print_mat(1, ng, Qx[ii], 1);
d_print_mat(1, ngN, Qx[N], 1);
for(ii=0; ii<N; ii++)
d_print_mat(1, ng, qx[ii], 1);
d_print_mat(1, ngN, qx[N], 1);
if(*kk==1)
exit(1);
#endif
// compute the search direction: factorize and solve the KKT system
#if defined(FAST_RSQRT)
if(mu>1e-2)
fast_rsqrt = 2;
else
{
if(mu>1e-4)
fast_rsqrt = 1;
else
fast_rsqrt = 0;
}
#else
fast_rsqrt = 0;
#endif
//printf("\n%d %f\n", fast_rsqrt, mu);
d_back_ric_sv(N, nx, nu, pBAbt, pQ, update_hessian, pd, pl, 1, dux, pL, work, diag, 1, Pb, compute_mult, dpi, nb, ng, ngN, pDCt, Qx, qx);
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(nz, nz, bs, pL[ii], cnl);
exit(1);
#endif
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx+nu, dux[ii], 1);
if(*kk==1)
exit(1);
#endif
#if 1
// compute t_aff & dlam_aff & dt_aff & alpha
for(jj=0; jj<=N; jj++)
for(ll=0; ll<2*nb; ll++)
dlam[jj][ll] = 0.0;
alpha = 1.0;
d_compute_alpha_hard_mpc(N, nx, nu, nb, ng, ngN, &alpha, t, dt, lam, dlam, lamt, dux, pDCt, d);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+1] = alpha;
alpha *= 0.995;
// compute the affine duality gap
d_compute_mu_hard_mpc(N, nx, nu, nb, ng, ngN, &mu_aff, mu_scal, alpha, lam, dlam, t, dt);
stat[5*(*kk)+2] = mu_aff;
//mu_aff = 1.346982; // TODO remove !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// compute sigma
sigma = mu_aff/mu;
sigma = sigma*sigma*sigma;
// if(sigma<sigma_min)
// sigma = sigma_min;
d_update_gradient_hard_mpc(N, nx, nu, nb, ng, ngN, sigma*mu, dt, dlam, t_inv, pl, qx);
#if 0
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu+nx, pl[ii], 1);
//for(ii=0; ii<N; ii++)
// d_print_mat(1, ng, qx[ii], 1);
//d_print_mat(1, ngN, qx[N], 1);
if(*kk==1)
exit(1);
#endif
#if 0
// first stage
for(ii=0; ii<2*nbu; ii+=2)
{
dlam[0][ii+0] = t_inv[0][ii+0]*(sigma*mu - dlam[0][ii+0]*dt[0][ii+0]); // !!!!!
dlam[0][ii+1] = t_inv[0][ii+1]*(sigma*mu - dlam[0][ii+1]*dt[0][ii+1]); // !!!!!
pl[0][ii/2] += dlam[0][ii+1] - dlam[0][ii+0];
}
// middle stages
for(jj=1; jj<N; jj++)
{
for(ii=0; ii<2*nb; ii+=2)
{
dlam[jj][ii+0] = t_inv[jj][ii+0]*(sigma*mu - dlam[jj][ii+0]*dt[jj][ii+0]); // !!!!!
dlam[jj][ii+1] = t_inv[jj][ii+1]*(sigma*mu - dlam[jj][ii+1]*dt[jj][ii+1]); // !!!!!
pl[jj][ii/2] += dlam[jj][ii+1] - dlam[jj][ii+0];
}
}
// last stages
for(ii=2*nu; ii<2*nb; ii+=2)
{
dlam[jj][ii+0] = t_inv[jj][ii+0]*(sigma*mu - dlam[jj][ii+0]*dt[jj][ii+0]); // !!!!!
dlam[jj][ii+1] = t_inv[jj][ii+1]*(sigma*mu - dlam[jj][ii+1]*dt[jj][ii+1]); // !!!!!
pl[jj][ii/2] += dlam[jj][ii+1] - dlam[jj][ii+0];
}
#endif
// copy b into x
for(ii=0; ii<N; ii++)
for(jj=0; jj<nx; jj++)
dux[ii+1][nu+jj] = pBAbt[ii][((nu+nx)/bs)*bs*cnx+(nu+nx)%bs+bs*jj]; // copy b
// solve the system
d_ric_trs_mpc(nx, nu, N, pBAbt, pL, pl, dux, work, 0, Pb, compute_mult, dpi, nb, ng, ngN, pDCt, qx);
#if 0
printf("\ndux\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx+nu, dux[ii], 1);
if(*kk==1)
exit(1);
#endif
#endif
// compute t & dlam & dt & alpha
alpha = 1.0;
d_compute_alpha_hard_mpc(N, nx, nu, nb, ng, ngN, &alpha, t, dt, lam, dlam, lamt, dux, pDCt, d);
stat[5*(*kk)] = sigma;
stat[5*(*kk)+3] = alpha;
alpha *= 0.995;
// update x, u, lam, t & compute the duality gap mu
d_update_var_hard_mpc(N, nx, nu, nb, ng, ngN, &mu, mu_scal, alpha, ux, dux, t, dt, lam, dlam, pi, dpi);
stat[5*(*kk)+4] = mu;
// update sigma
/* sigma *= sigma_decay;*/
/* if(sigma<sigma_min)*/
/* sigma = sigma_min;*/
/* if(alpha<0.3)*/
/* sigma = sigma_par[0];*/
#if 0
d_print_mat(1, 2*pnb+2*png, lam[0], 1);
d_print_mat(1, 2*pnb+2*png, lam[1], 1);
d_print_mat(1, 2*pnb+2*png, lam[N], 1);
d_print_mat(1, 2*pnb+2*png, t[0], 1);
d_print_mat(1, 2*pnb+2*png, t[1], 1);
d_print_mat(1, 2*pnb+2*png, t[N], 1);
printf("\n%f\n", mu);
exit(1);
#endif
//mu = 13.438997;
// increment loop index
(*kk)++;
} // end of IP loop
// restore Hessian
for(jj=0; jj<=N; jj++)
{
for(ll=0; ll<nx+nu; ll++)
{
pQ[jj][(ll/bs)*bs*cnz+ll%bs+ll*bs] = bd[jj][ll];
pQ[jj][((nx+nu)/bs)*bs*cnz+(nx+nu)%bs+ll*bs] = bl[jj][ll];
}
}
// successful exit
if(mu<=mu_tol)
return 0;
// max number of iterations reached
if(*kk>=k_max)
return 1;
// no improvement
if(alpha<alpha_min)
return 2;
// impossible
return -1;
} // end of ipsolver
int main()
{
printf("\n");
printf("\n");
printf("\n");
printf(" HPMPC -- Library for High-Performance implementation of solvers for MPC.\n");
printf(" Copyright (C) 2014-2015 by Technical University of Denmark. All rights reserved.\n");
printf("\n");
printf(" HPMPC is distributed in the hope that it will be useful,\n");
printf(" but WITHOUT ANY WARRANTY; without even the implied warranty of\n");
printf(" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n");
printf(" See the GNU Lesser General Public License for more details.\n");
printf("\n");
printf("\n");
printf("\n");
#if defined(TARGET_X64_AVX2) || defined(TARGET_X64_AVX) || defined(TARGET_X64_SSE3) || defined(TARGET_X86_ATOM) || defined(TARGET_AMD_SSE3)
_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON); // flush to zero subnormals !!! works only with one thread !!!
#endif
int ii, jj;
int rep, nrep=1000;//NREP;
int nx = NX; // number of states (it has to be even for the mass-spring system test problem)
int nu = NU; // number of inputs (controllers) (it has to be at least 1 and at most nx/2 for the mass-spring system test problem)
int N = NN; // horizon lenght
int nb = nu+nx; // number of box constrained inputs and states
int ng = nx; //4; // number of general constraints
int ngN = nx; // number of general constraints at the last stage
# define USE_IPM_RES 1
// int M = 32; // where the equality constraint hold
int nbu = nu<nb ? nu : nb ;
int nbx = nb-nu>0 ? nb-nu : 0;
#define KEEP_X0 0
// stage-wise variant size
int nx_v[N+1];
#if KEEP_X0
nx_v[0] = nx;
#else
nx_v[0] = 0;
#endif
for(ii=1; ii<=N; ii++)
nx_v[ii] = nx;
int nu_v[N+1];
for(ii=0; ii<N; ii++)
nu_v[ii] = nu;
nu_v[N] = 0;
int nb_v[N+1];
#if KEEP_X0
nb_v[0] = nb;
#else
nb_v[0] = nbu;
#endif
for(ii=1; ii<N; ii++)
nb_v[ii] = nb;
nb_v[N] = nbx;
int ng_v[N+1];
for(ii=0; ii<N; ii++)
ng_v[ii] = ng;
ng_v[N] = ngN;
// ng_v[M] = nx; // XXX
printf(" Test problem: mass-spring system with %d masses and %d controls.\n", nx/2, nu);
printf("\n");
printf(" MPC problem size: %d states, %d inputs, %d horizon length, %d two-sided box constraints, %d two-sided general constraints.\n", nx, nu, N, nb, ng);
printf("\n");
#if IP == 1
printf(" IP method parameters: primal-dual IP, double precision, %d maximum iterations, %5.1e exit tolerance in duality measure (edit file test_param.c to change them).\n", K_MAX, MU_TOL);
#elif IP == 2
printf(" IP method parameters: predictor-corrector IP, double precision, %d maximum iterations, %5.1e exit tolerance in duality measure (edit file test_param.c to change them).\n", K_MAX, MU_TOL);
#else
printf(" Wrong value for IP solver choice: %d\n", IP);
#endif
int info = 0;
const int bs = D_MR; //d_get_mr();
const int ncl = D_NCL;
int pnz = (nu+nx+1+bs-1)/bs*bs;
int pnu = (nu+bs-1)/bs*bs;
int pnu1 = (nu+1+bs-1)/bs*bs;
int pnx = (nx+bs-1)/bs*bs;
int pnx1 = (nx+1+bs-1)/bs*bs;
int pnux = (nu+nx+bs-1)/bs*bs;
int cnx = (nx+ncl-1)/ncl*ncl;
int cnu = (nu+ncl-1)/ncl*ncl;
int cnux = (nu+nx+ncl-1)/ncl*ncl;
int pnb_v[N+1];
int png_v[N+1];
int pnx_v[N+1];
int pnz_v[N+1];
int pnux_v[N+1];
int cnx_v[N+1];
int cnux_v[N+1];
int cng_v[N+1];
for(ii=0; ii<N; ii++)
{
pnb_v[ii] = (nb_v[ii]+bs-1)/bs*bs;
png_v[ii] = (ng_v[ii]+bs-1)/bs*bs;
pnx_v[ii] = (nx_v[ii]+bs-1)/bs*bs;
pnz_v[ii] = (nu_v[ii]+nx_v[ii]+1+bs-1)/bs*bs;
pnux_v[ii] = (nu_v[ii]+nx_v[ii]+bs-1)/bs*bs;
cnx_v[ii] = (nx_v[ii]+ncl-1)/ncl*ncl;
cnux_v[ii] = (nu_v[ii]+nx_v[ii]+ncl-1)/ncl*ncl;
cng_v[ii] = (ng_v[ii]+ncl-1)/ncl*ncl;
}
ii = N;
pnb_v[ii] = (nb_v[ii]+bs-1)/bs*bs;
png_v[ii] = (ng_v[ii]+bs-1)/bs*bs;
pnx_v[ii] = (nx_v[ii]+bs-1)/bs*bs;
pnz_v[ii] = (nx_v[ii]+1+bs-1)/bs*bs;
pnux_v[ii] = (nx_v[ii]+bs-1)/bs*bs;
cnx_v[ii] = (nx_v[ii]+ncl-1)/ncl*ncl;
cnux_v[ii] = (nx_v[ii]+ncl-1)/ncl*ncl;
cng_v[ii] = (ng_v[ii]+ncl-1)/ncl*ncl;
/************************************************
* dynamical system
************************************************/
double *A; d_zeros(&A, nx, nx); // states update matrix
double *B; d_zeros(&B, nx, nu); // inputs matrix
double *b; d_zeros_align(&b, nx, 1); // states offset
double *x0; d_zeros_align(&x0, nx, 1); // initial state
double Ts = 0.5; // sampling time
mass_spring_system(Ts, nx, nu, N, A, B, b, x0);
for(jj=0; jj<nx; jj++)
b[jj] = 0.1;
for(jj=0; jj<nx; jj++)
x0[jj] = 0;
x0[0] = 2.5;
x0[1] = 2.5;
double *pA; d_zeros_align(&pA, pnx, cnx);
d_cvt_mat2pmat(nx, nx, A, nx, 0, pA, cnx);
double *b0; d_zeros_align(&b0, pnx, 1);
for(ii=0; ii<nx; ii++) b0[ii] = b[ii];
#if ! KEEP_X0
dgemv_n_lib(nx, nx, pA, cnx, x0, 1, b0, b0);
#endif
double *pBAbt0;
d_zeros_align(&pBAbt0, pnz_v[0], cnx_v[1]);
d_cvt_tran_mat2pmat(nx_v[1], nu_v[0], B, nx_v[1], 0, pBAbt0, cnx_v[1]);
d_cvt_tran_mat2pmat(nx_v[1], nx_v[0], A, nx_v[1], nu_v[0], pBAbt0+nu_v[0]/bs*bs*cnx_v[1]+nu_v[0]%bs, cnx_v[1]);
d_cvt_tran_mat2pmat(nx_v[1], 1, b0, nx_v[1], nu_v[0]+nx_v[0], pBAbt0+(nu_v[0]+nx_v[0])/bs*bs*cnx_v[1]+(nu_v[0]+nx_v[0])%bs, cnx_v[1]);
double *pBAbt1;
if(N>1)
{
d_zeros_align(&pBAbt1, pnz_v[1], cnx_v[2]);
d_cvt_tran_mat2pmat(nx_v[2], nu_v[1], B, nx_v[2], 0, pBAbt1, cnx_v[2]);
d_cvt_tran_mat2pmat(nx_v[2], nx_v[1], A, nx_v[2], nu_v[1], pBAbt1+nu_v[1]/bs*bs*cnx_v[2]+nu_v[1]%bs, cnx_v[2]);
d_cvt_tran_mat2pmat(nx_v[2], 1, b, nx_v[2], nu_v[1]+nx_v[1], pBAbt1+(nu_v[1]+nx_v[1])/bs*bs*cnx_v[2]+(nu_v[1]+nx_v[1])%bs, cnx_v[2]);
}
#if 0
d_print_pmat(nu_v[0]+nx_v[0]+1, nx_v[1], bs, pBAbt0, cnx_v[1]);
d_print_pmat(nu_v[1]+nx_v[1]+1, nx_v[2], bs, pBAbt1, cnx_v[2]);
exit(2);
#endif
/************************************************
* box & general constraints
************************************************/
int *idx0; i_zeros(&idx0, nb_v[0], 1);
double *d0; d_zeros_align(&d0, 2*pnb_v[0]+2*png_v[0], 1);
#if KEEP_X0
for(jj=0; jj<nbu; jj++)
{
d0[jj] = - 0.5; // umin
d0[pnb_v[0]+jj] = 0.5; // umax
idx0[jj] = jj;
}
for(; jj<nb; jj++)
{
d0[jj] = x0[jj-nu]; // xmin
d0[pnb_v[0]+jj] = x0[jj-nu]; // xmax
idx0[jj] = jj;
}
#else
for(jj=0; jj<nbu; jj++)
{
d0[jj] = - 0.5; // umin
d0[pnb_v[0]+jj] = 0.5; // umax
idx0[jj] = jj;
}
#endif
for(jj=0; jj<ng_v[0]; jj++)
{
d0[2*pnb_v[0]+jj] = - 100.0; // xmin
d0[2*pnb_v[0]+png_v[0]+jj] = 100.0; // xmax
}
#if 0
i_print_mat(1, nb_v[0], idx0, 1);
d_print_mat(1, 2*pnb_v[0]+2*png_v[0], d0, 1);
exit(2);
#endif
int *idx1; i_zeros(&idx1, nb_v[1], 1);
double *d1; d_zeros_align(&d1, 2*pnb_v[1]+2*png_v[1], 1);
for(jj=0; jj<nbu; jj++)
{
d1[jj] = - 0.5; // umin
d1[pnb_v[1]+jj] = 0.5; // umax
idx1[jj] = jj;
}
for(; jj<nb; jj++)
{
d1[jj] = - 10.0; // xmin
d1[pnb_v[1]+jj] = 10.0; // xmax
idx1[jj] = jj;
}
for(jj=0; jj<ng_v[1]; jj++)
{
d1[2*pnb_v[1]+jj] = - 100.0; // xmin
d1[2*pnb_v[1]+png_v[1]+jj] = 100.0; // xmax
}
// i_print_mat(nb, 1, idx1, nb);
int *idxN; i_zeros(&idxN, nb_v[N], 1);
double *dN; d_zeros_align(&dN, 2*pnb_v[N]+2*png_v[N], 1);
for(jj=0; jj<nbx; jj++)
{
dN[jj] = - 10.0; // xmin
dN[pnb_v[N]+jj] = 10.0; // xmax
idxN[jj] = jj;
}
for(jj=0; jj<ng_v[N]; jj++)
{
dN[2*pnb_v[N]+jj] = - 0.0; // xmin
dN[2*pnb_v[N]+png_v[N]+jj] = 0.0; // xmax
}
// d_print_mat(1, 2*pnb+2*png, d, 1);
// d_print_mat(1, 2*pnb_v[N]+2*png_v[N], dN, 1);
// exit(1);
// double *dM; d_zeros_align(&dM, 2*pnb_v[M]+2*png_v[M], 1);
// for(jj=0; jj<nbu; jj++)
// {
// dM[jj] = - 0.5; // umin
// dM[pnb_v[1]+jj] = 0.5; // umax
// }
// for(; jj<nb; jj++)
// {
// dM[jj] = - 4.0; // xmin
// dM[pnb_v[1]+jj] = 4.0; // xmax
// }
// for(jj=0; jj<ng_v[M]; jj++)
// {
// dM[2*pnb_v[M]+jj] = - 0.5; // xmin
// dM[2*pnb_v[M]+png_v[M]+jj] = - 0.5; // xmax
// }
double *C; d_zeros(&C, ng, nx);
for(ii=0; ii<ng; ii++)
C[ii*(ng+1)] = 1.0;
double *D; d_zeros(&D, ng, nu);
// first stage
double *pDCt0; d_zeros_align(&pDCt0, pnux_v[0], cng_v[0]);
// middle stage
double *DC1; d_zeros(&DC1, ng_v[1], nu_v[1]+nx_v[1]);
for(jj=0; jj<ng_v[1]; jj++) DC1[jj+(nu_v[1]+jj)*ng_v[1]] = 1.0;
// d_print_mat(ng_v[1], nu_v[1]+nx_v[1], DC1, ng_v[1]);
double *pDCt1; d_zeros_align(&pDCt1, pnux_v[1], cng_v[1]);
d_cvt_tran_mat2pmat(ng_v[1], nu_v[1]+nx_v[1], DC1, ng_v[1], 0, pDCt1, cng_v[1]);
// d_print_pmat(nu_v[1]+nx_v[1], ng_v[1], bs, pDCt1, cng_v[1]);
// exit(2);
// last stage
double *DCN; d_zeros(&DCN, ng_v[N], nx_v[N]);
for(jj=0; jj<ng_v[N]; jj++) DCN[jj*(ng_v[N]+1)] = 1.0;
// d_print_mat(ng_v[N], nx_v[N], DCN, ng_v[N]);
double *pDCtN; d_zeros_align(&pDCtN, pnx_v[N], cng_v[N]);
d_cvt_tran_mat2pmat(ng_v[N], nx_v[N], DCN, ng_v[N], 0, pDCtN, cng_v[N]);
// d_print_pmat(nx_v[N], ng_v[N], bs, pDCtN, cng_v[N]);
// constrained stage
// double *DCM; d_zeros(&DCM, ng_v[M], nu_v[M]+nx_v[M]);
// for(jj=0; jj<ng_v[M]; jj++) DCM[jj+(jj+nu_v[M])*ng_v[M]] = 1.0;
// d_print_mat(ng_v[M], nu_v[M]+nx_v[M], DCM, ng_v[M]);
// double *pDCtM; d_zeros_align(&pDCtM, pnux_v[M], cng_v[M]);
// d_cvt_tran_mat2pmat(ng_v[M], nu_v[M]+nx_v[M], DCM, ng_v[M], 0, pDCtM, cng_v[M]);
// d_print_pmat(nu_v[M]+nx_v[M], ng_v[M], bs, pDCtM, cng_v[M]);
// exit(2);
/************************************************
* cost function
************************************************/
double *Q; d_zeros(&Q, nx, nx);
for(ii=0; ii<nx; ii++) Q[ii*(nx+1)] = 1.0;
double *R; d_zeros(&R, nu, nu);
for(ii=0; ii<nu; ii++) R[ii*(nu+1)] = 2.0;
double *S; d_zeros(&S, nu, nx); // S=0, so no need to update r0
double *q; d_zeros(&q, nx, 1);
for(ii=0; ii<nx; ii++) q[ii] = 0.1;
double *r; d_zeros(&r, nu, 1);
for(ii=0; ii<nu; ii++) r[ii] = 0.2;
#if KEEP_X0
double *pRSQ0; d_zeros_align(&pRSQ0, pnz, cnux);
d_cvt_mat2pmat(nu, nu, R, nu, 0, pRSQ0, cnux);
d_cvt_tran_mat2pmat(nu, nx, S, nu, nu, pRSQ0+nu/bs*bs*cnux+nu%bs, cnux);
d_cvt_tran_mat2pmat(nu, 1, r, nu, nu+nx, pRSQ0+(nu+nx)/bs*bs*cnux+(nu+nx)%bs, cnux);
d_cvt_mat2pmat(nx, nx, Q, nx, nu, pRSQ0+nu/bs*bs*cnux+nu%bs+nu*bs, cnux);
d_cvt_tran_mat2pmat(nx, 1, q, nx, nu+nx, pRSQ0+(nu+nx)/bs*bs*cnux+(nu+nx)%bs+nu*bs, cnux);
// d_print_pmat(nu+nx+1, nu+nx, bs, pRSQ0, cnux);
double *rq0; d_zeros_align(&rq0, pnux, 1);
d_copy_mat(nu, 1, r, nu, rq0, pnux);
d_copy_mat(nx, 1, q, nx, rq0+nu, pnux);
#else
double *pRSQ0; d_zeros_align(&pRSQ0, pnu1, cnu);
d_cvt_mat2pmat(nu, nu, R, nu, 0, pRSQ0, cnu);
d_cvt_tran_mat2pmat(nu, 1, r, nu, nu, pRSQ0+nu/bs*bs*cnu+nu%bs, cnu);
// d_print_pmat(nu+1, nu, bs, pRSQ0, cnu);
double *rq0; d_zeros_align(&rq0, pnu, 1);
d_copy_mat(nu, 1, r, nu, rq0, pnu);
#endif
double *pRSQ1; d_zeros_align(&pRSQ1, pnz, cnux);
d_cvt_mat2pmat(nu, nu, R, nu, 0, pRSQ1, cnux);
d_cvt_tran_mat2pmat(nu, nx, S, nu, nu, pRSQ1+nu/bs*bs*cnux+nu%bs, cnux);
d_cvt_tran_mat2pmat(nu, 1, r, nu, nu+nx, pRSQ1+(nu+nx)/bs*bs*cnux+(nu+nx)%bs, cnux);
d_cvt_mat2pmat(nx, nx, Q, nx, nu, pRSQ1+nu/bs*bs*cnux+nu%bs+nu*bs, cnux);
d_cvt_tran_mat2pmat(nx, 1, q, nx, nu+nx, pRSQ1+(nu+nx)/bs*bs*cnux+(nu+nx)%bs+nu*bs, cnux);
// d_print_pmat(nu+nx+1, nu+nx, bs, pRSQ1, cnux);
double *rq1; d_zeros_align(&rq1, pnux, 1);
d_copy_mat(nu, 1, r, nu, rq1, pnux);
d_copy_mat(nx, 1, q, nx, rq1+nu, pnux);
double *pRSQN; d_zeros_align(&pRSQN, pnx1, cnx);
d_cvt_mat2pmat(nx, nx, Q, nx, 0, pRSQN, cnx);
d_cvt_tran_mat2pmat(nx, 1, q, nx, nx, pRSQN+(nx)/bs*bs*cnx+(nx)%bs, cnx);
// d_print_pmat(nx+1, nx, bs, pRSQN, cnx);
double *rqN; d_zeros_align(&rqN, pnx, 1);
d_copy_mat(nx, 1, q, nx, rqN, pnx);
// maximum element in cost functions
double mu0 = 2.0;
/************************************************
* high level interface work space
************************************************/
#if 0
double *rA; d_zeros(&rA, nx, N*nx);
d_rep_mat(N, nx, nx, A, nx, rA, nx);
double *rB; d_zeros(&rB, nx, N*nu);
d_rep_mat(N, nx, nu, B, nx, rB, nx);
double *rC; d_zeros(&rC, ng, (N+1)*nx);
d_rep_mat(N, ng, nx, C, ng, rC+nx*ng, ng);
double *CN = DCN;
double *rD; d_zeros(&rD, ng, N*nu);
d_rep_mat(N, ng, nu, D, ng, rD, ng);
double *rb; d_zeros(&rb, nx, N*1);
d_rep_mat(N, nx, 1, b, nx, rb, nx);
double *rQ; d_zeros(&rQ, nx, N*nx);
d_rep_mat(N, nx, nx, Q, nx, rQ, nx);
double *rQf; d_zeros(&rQf, nx, nx);
d_copy_mat(nx, nx, Q, nx, rQf, nx);
double *rS; d_zeros(&rS, nu, N*nx);
d_rep_mat(N, nu, nx, S, nu, rS, nu);
double *rR; d_zeros(&rR, nu, N*nu);
d_rep_mat(N, nu, nu, R, nu, rR, nu);
double *rq; d_zeros(&rq, nx, N);
d_rep_mat(N, nx, 1, q, nx, rq, nx);
double *rqf; d_zeros(&rqf, nx, 1);
d_copy_mat(nx, 1, q, nx, rqf, nx);
double *rr; d_zeros(&rr, nu, N);
d_rep_mat(N, nu, 1, r, nu, rr, nu);
double *lb; d_zeros(&lb, nb, 1);
for(ii=0; ii<nb; ii++)
lb[ii] = d1[ii];
double *rlb; d_zeros(&rlb, nb, N+1);
d_rep_mat(N+1, nb, 1, lb, nb, rlb, nb);
// d_print_mat(nb, N+1, rlb, nb);
double *lg; d_zeros(&lg, ng, 1);
for(ii=0; ii<ng; ii++)
lg[ii] = d1[2*pnb_v[1]+ii];
double *rlg; d_zeros(&rlg, ng, N);
d_rep_mat(N, ng, 1, lg, ng, rlg, ng);
// d_print_mat(ng, N, rlg, ng);
double *lgN; d_zeros(&lgN, ngN, 1);
for(ii=0; ii<ngN; ii++)
lgN[ii] = dN[2*pnb_v[N]+ii];
// d_print_mat(ngN, 1, lgN, ngN);
double *ub; d_zeros(&ub, nb, 1);
for(ii=0; ii<nb; ii++)
ub[ii] = d1[pnb_v[1]+ii];
double *rub; d_zeros(&rub, nb, N+1);
d_rep_mat(N+1, nb, 1, ub, nb, rub, nb);
// d_print_mat(nb, N+1, rub, nb);
double *ug; d_zeros(&ug, ng, 1);
for(ii=0; ii<ng; ii++)
ug[ii] = d1[2*pnb_v[1]+png_v[1]+ii];
double *rug; d_zeros(&rug, ng, N);
d_rep_mat(N, ng, 1, ug, ng, rug, ng);
// d_print_mat(ng, N, rug, ng);
double *ugN; d_zeros(&ugN, ngN, 1);
for(ii=0; ii<ngN; ii++)
ugN[ii] = dN[2*pnb_v[N]+png_v[N]+ii];
// d_print_mat(ngN, 1, ugN, ngN);
double *rx; d_zeros(&rx, nx, N+1);
d_copy_mat(nx, 1, x0, nx, rx, nx);
double *ru; d_zeros(&ru, nu, N);
double *rpi; d_zeros(&rpi, nx, N);
double *rlam; d_zeros(&rlam, N*2*(nb+ng)+2*(nb+ngN), 1);
double *rt; d_zeros(&rt, N*2*(nb+ng)+2*(nb+ngN), 1);
double *rwork = (double *) malloc(hpmpc_d_ip_mpc_hard_tv_work_space_size_bytes(N, nx, nu, nb, ng, ngN));
double inf_norm_res[4] = {}; // infinity norm of residuals: rq, rb, rd, mu
#endif
/************************************************
* low level interface work space
************************************************/
double *hpBAbt[N];
double *hpDCt[N+1];
double *hb[N];
double *hpRSQ[N+1];
double *hrq[N+1];
double *hd[N+1];
int *idx[N+1];
double *hux[N+1];
double *hpi[N];
double *hlam[N+1];
double *ht[N+1];
double *hrb[N];
double *hrrq[N+1];
double *hrd[N+1];
hpBAbt[0] = pBAbt0;
hpDCt[0] = pDCt0;
hb[0] = b0;
hpRSQ[0] = pRSQ0;
hrq[0] = rq0;
hd[0] = d0;
idx[0] = idx0;
d_zeros_align(&hux[0], pnux_v[0], 1);
d_zeros_align(&hpi[0], pnx_v[1], 1);
d_zeros_align(&hlam[0], 2*pnb_v[0]+2*png_v[0], 1);
d_zeros_align(&ht[0], 2*pnb_v[0]+2*png_v[0], 1);
d_zeros_align(&hrb[0], pnx_v[1], 1);
d_zeros_align(&hrrq[0], pnz_v[0], 1);
d_zeros_align(&hrd[0], 2*pnb_v[0]+2*png_v[0], 1);
for(ii=1; ii<N; ii++)
{
hpBAbt[ii] = pBAbt1;
// d_zeros_align(&hpBAbt[ii], pnz_v[ii], cnx_v[ii+1]); for(jj=0; jj<pnz_v[ii]*cnx_v[ii+1]; jj++) hpBAbt[ii][jj] = pBAbt1[jj];
hpDCt[ii] = pDCt1;
hb[ii] = b;
hpRSQ[ii] = pRSQ1;
// d_zeros_align(&hpRSQ[ii], pnz_v[ii], cnux_v[ii]); for(jj=0; jj<pnz_v[ii]*cnux_v[ii]; jj++) hpRSQ[ii][jj] = pRSQ1[jj];
hrq[ii] = rq1;
hd[ii] = d1;
idx[ii] = idx1;
d_zeros_align(&hux[ii], pnux_v[ii], 1);
d_zeros_align(&hpi[ii], pnx_v[ii+1], 1);
d_zeros_align(&hlam[ii], 2*pnb_v[ii]+2*png_v[ii], 1);
d_zeros_align(&ht[ii], 2*pnb_v[ii]+2*png_v[ii], 1);
d_zeros_align(&hrb[ii], pnx_v[ii+1], 1);
d_zeros_align(&hrrq[ii], pnz_v[ii], 1);
d_zeros_align(&hrd[ii], 2*pnb_v[ii]+2*png_v[ii], 1);
}
hpDCt[N] = pDCtN;
hpRSQ[N] = pRSQN;
hrq[N] = rqN;
hd[N] = dN;
idx[N] = idxN;
d_zeros_align(&hux[N], pnx, 1);
d_zeros_align(&hlam[N], 2*pnb_v[N]+2*png_v[N], 1);
d_zeros_align(&ht[N], 2*pnb_v[N]+2*png_v[N], 1);
d_zeros_align(&hrrq[N], pnz_v[N], 1);
d_zeros_align(&hrd[N], 2*pnb_v[N]+2*png_v[N], 1);
// hpDCt[M] = pDCtM;
// hd[M] = dM;
double mu = 0.0;
#if USE_IPM_RES
double *work; d_zeros_align(&work, d_ip2_res_mpc_hard_tv_work_space_size_bytes(N, nx_v, nu_v, nb_v, ng_v)/sizeof(double), 1);
#else
double *work; d_zeros_align(&work, d_ip2_mpc_hard_tv_work_space_size_bytes(N, nx_v, nu_v, nb_v, ng_v)/sizeof(double), 1);
#endif
/************************************************
* (new) high level interface work space
************************************************/
// box constraints
double *lb0; d_zeros(&lb0, nb_v[0], 1);
for(ii=0; ii<nb_v[0]; ii++)
lb0[ii] = d0[ii];
double *ub0; d_zeros(&ub0, nb_v[0], 1);
for(ii=0; ii<nb_v[0]; ii++)
ub0[ii] = d0[pnb_v[0]+ii];
double *lb1; d_zeros(&lb1, nb_v[1], 1);
for(ii=0; ii<nb_v[1]; ii++)
lb1[ii] = d1[ii];
double *ub1; d_zeros(&ub1, nb_v[1], 1);
for(ii=0; ii<nb_v[1]; ii++)
ub1[ii] = d1[pnb_v[1]+ii];
double *lbN; d_zeros(&lbN, nb_v[N], 1);
for(ii=0; ii<nb_v[N]; ii++)
lbN[ii] = dN[ii];
double *ubN; d_zeros(&ubN, nb_v[N], 1);
for(ii=0; ii<nb_v[N]; ii++)
ubN[ii] = dN[pnb_v[N]+ii];
// general constraints
double *lg0; d_zeros(&lg0, ng_v[0], 1);
for(ii=0; ii<ng_v[0]; ii++)
lg0[ii] = d0[2*pnb_v[0]+ii];
double *ug0; d_zeros(&ug0, ng_v[0], 1);
for(ii=0; ii<ng_v[0]; ii++)
ug0[ii] = d0[2*pnb_v[0]+png_v[0]+ii];
double *lg1; d_zeros(&lg1, ng_v[1], 1);
for(ii=0; ii<ng_v[1]; ii++)
lg1[ii] = d1[2*pnb_v[1]+ii];
double *ug1; d_zeros(&ug1, ng_v[1], 1);
for(ii=0; ii<ng_v[1]; ii++)
ug1[ii] = d1[2*pnb_v[1]+png_v[1]+ii];
double *lgN; d_zeros(&lgN, ng_v[N], 1);
for(ii=0; ii<ng_v[N]; ii++)
lgN[ii] = dN[2*pnb_v[N]+ii];
double *ugN; d_zeros(&ugN, ng_v[N], 1);
for(ii=0; ii<ng_v[N]; ii++)
ugN[ii] = dN[2*pnb_v[N]+png_v[N]+ii];
// data matrices
double *hA[N];
double *hB[N];
double *hC[N+1];
double *hD[N];
double *hQ[N+1];
double *hS[N];
double *hR[N];
double *hq[N+1];
double *hr[N];
double *hlb[N+1];
double *hub[N+1];
double *hlg[N+1];
double *hug[N+1];
double *hx[N+1];
double *hu[N];
double *hpi1[N];
double *hlam1[N+1];
double *ht1[N+1];
double inf_norm_res[4] = {}; // infinity norm of residuals: rq, rb, rd, mu
ii = 0;
hA[0] = A;
hB[0] = B;
hC[0] = C;
hD[0] = D;
hQ[0] = Q;
hS[0] = S;
hR[0] = R;
hq[0] = q;
hr[0] = r;
hlb[0] = lb0;
hub[0] = ub0;
hlg[0] = lg0;
hug[0] = ug0;
d_zeros(&hx[0], nx_v[0], 1);
d_zeros(&hu[0], nu_v[0], 1);
d_zeros(&hpi1[0], nx_v[1], 1);
d_zeros(&hlam1[0], 2*nb_v[0]+2*ng_v[0], 1);
d_zeros(&ht1[0], 2*nb_v[0]+2*ng_v[0], 1);
for(ii=1; ii<N; ii++)
{
hA[ii] = A;
hB[ii] = B;
hC[ii] = C;
hD[ii] = D;
hQ[ii] = Q;
hS[ii] = S;
hR[ii] = R;
hq[ii] = q;
hr[ii] = r;
hlb[ii] = lb1;
hub[ii] = ub1;
hlg[ii] = lg1;
hug[ii] = ug1;
d_zeros(&hx[ii], nx_v[ii], 1);
d_zeros(&hu[ii], nu_v[ii], 1);
d_zeros(&hpi1[ii], nx_v[ii+1], 1);
d_zeros(&hlam1[ii], 2*nb_v[ii]+2*ng_v[ii], 1);
d_zeros(&ht1[ii], 2*nb_v[ii]+2*ng_v[ii], 1);
}
ii = N;
hC[N] = C;
hQ[N] = Q;
hq[N] = q;
hlb[N] = lbN;
hub[N] = ubN;
hlg[N] = lgN;
hug[N] = ugN;
d_zeros(&hx[N], nx_v[N], 1);
d_zeros(&hlam1[N], 2*nb_v[N]+2*ng_v[N], 1);
d_zeros(&ht1[N], 2*nb_v[N]+2*ng_v[N], 1);
// work space
#if 0
printf("work space in bytes: %d\n", hpmpc_d_ip_ocp_hard_tv_work_space_size_bytes(N, nx_v, nu_v, nb_v, ng_v));
exit(3);
#endif
void *work1 = malloc(hpmpc_d_ip_ocp_hard_tv_work_space_size_bytes(N, nx_v, nu_v, nb_v, ng_v));
double *ptr_work1 = (double *) work1;
/************************************************
* solvers common stuff
************************************************/
int hpmpc_status;
int kk, kk_avg;
int k_max = 10;
double mu_tol = 1e-20;
double alpha_min = 1e-8;
int warm_start = 0; // read initial guess from x and u
double *stat; d_zeros(&stat, k_max, 5);
int compute_res = 1;
int compute_mult = 1;
struct timeval tv0, tv1, tv2, tv3;
double time;
double **dummy;
/************************************************
* call the solver (high-level interface)
************************************************/
#if 1
int time_invariant = 0; // assume the problem to be time invariant
int free_x0 = 0; // assume x0 as optimization variable
gettimeofday(&tv0, NULL); // stop
kk_avg = 0;
for(rep=0; rep<nrep; rep++)
{
// hpmpc_status = fortran_order_d_ip_mpc_hard_tv(&kk, k_max, mu0, mu_tol, N, nx, nu, nb, ng, ngN, time_invariant, free_x0, warm_start, rA, rB, rb, rQ, rQf, rS, rR, rq, rqf, rr, rlb, rub, rC, rD, rlg, rug, CN, lgN, ugN, rx, ru, rpi, rlam, rt, inf_norm_res, rwork, stat);
hpmpc_status = fortran_order_d_ip_ocp_hard_tv(&kk, k_max, mu0, mu_tol, N, nx_v, nu_v, nb_v, ng_v, warm_start, hA, hB, hb, hQ, hS, hR, hq, hr, hlb, hub, hC, hD, hlg, hug, hx, hu, hpi1, hlam1, ht1, inf_norm_res, work1, stat);
kk_avg += kk;
}
gettimeofday(&tv1, NULL); // stop
printf("\nsolution from high-level interface\n\n");
// d_print_mat(nx, N+1, rx, nx);
// d_print_mat(nu, N, ru, nu);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx_v[ii], hx[ii], 1);
for(ii=0; ii<N; ii++)
d_print_mat(1, nu_v[ii], hu[ii], 1);
printf("\ninfinity norm of residuals\n\n");
d_print_mat_e(1, 4, inf_norm_res, 1);
time = (tv1.tv_sec-tv0.tv_sec)/(nrep+0.0)+(tv1.tv_usec-tv0.tv_usec)/(nrep*1e6);
printf("\nstatistics from last run\n\n");
for(jj=0; jj<kk; jj++)
printf("k = %d\tsigma = %f\talpha = %f\tmu = %f\t\tmu = %e\talpha = %f\tmu = %f\tmu = %e\n", jj, stat[5*jj], stat[5*jj+1], stat[5*jj+2], stat[5*jj+2], stat[5*jj+3], stat[5*jj+4], stat[5*jj+4]);
printf("\n");
printf("\n");
printf(" Average number of iterations over %d runs: %5.1f\n", nrep, kk_avg / (double) nrep);
printf(" Average solution time over %d runs: %5.2e seconds\n", nrep, time);
printf("\n\n");
gettimeofday(&tv0, NULL); // stop
kk_avg = 0;
for(rep=0; rep<nrep; rep++)
{
// fortran_order_d_solve_kkt_new_rhs_mpc_hard_tv(N, nx, nu, nb, ng, ngN, time_invariant, free_x0, rA, rB, rb, rQ, rQf, rS, rR, rq, rqf, rr, rlb, rub, rC, rD, rlg, rug, CN, lgN, ugN, rx, ru, rpi, rlam, rt, inf_norm_res, rwork);
fortran_order_d_solve_kkt_new_rhs_ocp_hard_tv(N, nx_v, nu_v, nb_v, ng_v, hA, hB, hb, hQ, hS, hR, hq, hr, hlb, hub, hC, hD, hlg, hug, hx, hu, hpi1, hlam1, ht1, inf_norm_res, work1);
kk_avg += kk;
}
gettimeofday(&tv1, NULL); // stop
printf("\nsolution from high-level interface (resolve final kkt)\n\n");
// d_print_mat(nx, N+1, rx, nx);
// d_print_mat(nu, N, ru, nu);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nx_v[ii], hx[ii], 1);
for(ii=0; ii<N; ii++)
d_print_mat(1, nu_v[ii], hu[ii], 1);
printf("\ninfinity norm of residuals\n\n");
d_print_mat_e(1, 4, inf_norm_res, 1);
time = (tv1.tv_sec-tv0.tv_sec)/(nrep+0.0)+(tv1.tv_usec-tv0.tv_usec)/(nrep*1e6);
printf(" Average solution time over %d runs: %5.2e seconds\n", nrep, time);
#endif
/************************************************
* call the solver (low-level interface)
************************************************/
// for(ii=0; ii<N; ii++)
// d_print_pmat(nu_v[ii]+nx_v[ii]+1, nx_v[ii+1], bs, hpBAbt[ii], cnx_v[ii+1]);
// exit(3);
gettimeofday(&tv0, NULL); // stop
kk_avg = 0;
printf("\nsolution...\n");
for(rep=0; rep<nrep; rep++)
{
#if USE_IPM_RES
hpmpc_status = d_ip2_res_mpc_hard_tv(&kk, k_max, mu0, mu_tol, alpha_min, warm_start, stat, N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hpRSQ, hpDCt, hd, hux, compute_mult, hpi, hlam, ht, work);
#else
hpmpc_status = d_ip2_mpc_hard_tv(&kk, k_max, mu0, mu_tol, alpha_min, warm_start, stat, N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hpRSQ, hpDCt, hd, hux, compute_mult, hpi, hlam, ht, work);
#endif
kk_avg += kk;
}
printf("\ndone\n");
gettimeofday(&tv1, NULL); // stop
printf("\nsolution from low-level interface (original problem)\n\n");
printf("\nux\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu_v[ii]+nx_v[ii], hux[ii], 1);
printf("\npi\n\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nx_v[ii+1], hpi[ii], 1);
// printf("\nux\n\n");
// for(ii=0; ii<=N; ii++)
// d_print_mat(1, 2*pnb_v[ii]+2*png_v[ii], hlam[ii], 1);
// printf("\nux\n\n");
// for(ii=0; ii<=N; ii++)
// d_print_mat(1, 2*pnb_v[ii]+2*png_v[ii], ht[ii], 1);
// residuals
if(compute_res)
{
// compute residuals
d_res_mpc_hard_tv(N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hb, hpRSQ, hrq, hux, hpDCt, hd, hpi, hlam, ht, hrrq, hrb, hrd, &mu);
// print residuals
printf("\nhrrq\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nu_v[ii]+nx_v[ii], hrrq[ii], 1);
printf("\nhrb\n\n");
for(ii=0; ii<N; ii++)
d_print_mat_e(1, nx_v[ii+1], hrb[ii], 1);
printf("\nhrd low\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nb_v[ii], hrd[ii], 1);
printf("\nhrd up\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nb_v[ii], hrd[ii]+pnb_v[ii], 1);
}
// zero the solution again
for(ii=0; ii<=N; ii++)
for(jj=0; jj<nu_v[ii]+nx_v[ii]; jj++) hux[ii][jj] = 0.0;
// modify constraints
#if 0
for(jj=0; jj<nbx; jj++)
{
dN[jj] = - 4.0; // xmin
dN[pnb_v[N]+jj] = 4.0; // xmax
idxN[jj] = jj;
}
for(jj=0; jj<ng_v[N]; jj++)
{
dN[2*pnb_v[N]+jj] = 0.1; // xmin
dN[2*pnb_v[N]+png_v[N]+jj] = 0.1; // xmax
}
#endif
#if 0
for(ii=0; ii<=N; ii++)
d_print_pmat(nu_v[ii]+nx_v[ii]+1, nu_v[ii]+nx_v[ii], bs, hpRSQ[ii], cnux_v[ii]);
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu_v[ii]+nx_v[ii], hrq[ii], 1);
exit(1);
#endif
gettimeofday(&tv2, NULL); // stop
printf("\nsolution...\n");
for(rep=0; rep<nrep; rep++)
{
#if USE_IPM_RES
d_kkt_solve_new_rhs_res_mpc_hard_tv(N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hb, hpRSQ, hrq, hpDCt, hd, hux, compute_mult, hpi, hlam, ht, work);
#else
d_kkt_solve_new_rhs_mpc_hard_tv(N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hb, hpRSQ, hrq, hpDCt, hd, hux, compute_mult, hpi, hlam, ht, work);
#endif
}
printf("\ndone\n");
gettimeofday(&tv3, NULL); // stop
printf("\nsolution from low-level interface (resolve final kkt)\n\n");
printf("\nux\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat(1, nu_v[ii]+nx_v[ii], hux[ii], 1);
printf("\npi\n\n");
for(ii=0; ii<N; ii++)
d_print_mat(1, nx_v[ii+1], hpi[ii], 1);
// printf("\nux\n\n");
// for(ii=0; ii<=N; ii++)
// d_print_mat(1, 2*pnb_v[ii]+2*png_v[ii], hlam[ii], 1);
// printf("\nux\n\n");
// for(ii=0; ii<=N; ii++)
// d_print_mat(1, 2*pnb_v[ii]+2*png_v[ii], ht[ii], 1);
// residuals
if(compute_res)
{
// compute residuals
d_res_mpc_hard_tv(N, nx_v, nu_v, nb_v, idx, ng_v, hpBAbt, hb, hpRSQ, hrq, hux, hpDCt, hd, hpi, hlam, ht, hrrq, hrb, hrd, &mu);
// print residuals
printf("\nhrrq\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nu_v[ii]+nx_v[ii], hrrq[ii], 1);
printf("\nhrb\n\n");
for(ii=0; ii<N; ii++)
d_print_mat_e(1, nx_v[ii+1], hrb[ii], 1);
printf("\nhrd low\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nb_v[ii], hrd[ii], 1);
printf("\nhrd up\n\n");
for(ii=0; ii<=N; ii++)
d_print_mat_e(1, nb_v[ii], hrd[ii]+pnb_v[ii], 1);
}
double time_ipm = (tv1.tv_sec-tv0.tv_sec)/(nrep+0.0)+(tv1.tv_usec-tv0.tv_usec)/(nrep*1e6);
double time_final = (tv3.tv_sec-tv2.tv_sec)/(nrep+0.0)+(tv3.tv_usec-tv2.tv_usec)/(nrep*1e6);
printf("\nstatistics from last run\n\n");
for(jj=0; jj<kk; jj++)
printf("k = %d\tsigma = %f\talpha = %f\tmu = %f\t\tmu = %e\talpha = %f\tmu = %f\tmu = %e\n", jj, stat[5*jj], stat[5*jj+1], stat[5*jj+2], stat[5*jj+2], stat[5*jj+3], stat[5*jj+4], stat[5*jj+4]);
printf("\n");
printf("\n");
printf(" Average number of iterations over %d runs: %5.1f\n", nrep, kk_avg / (double) nrep);
printf(" Average solution time over %d runs: %5.2e seconds (IPM)\n", nrep, time_ipm);
printf(" Average solution time over %d runs: %5.2e seconds (resolve final kkt)\n", nrep, time_final);
printf("\n\n");
/************************************************
* compute residuals
************************************************/
/************************************************
* free memory
************************************************/
// problem data
free(A);
free(B);
d_free_align(b);
d_free_align(x0);
free(C);
free(D);
free(Q);
free(S);
free(R);
free(q);
free(r);
// low level interface
d_free_align(pA);
d_free_align(b0);
d_free_align(pBAbt0);
d_free_align(pBAbt1);
d_free_align(d0);
d_free_align(d1);
d_free_align(dN);
d_free_align(pDCt0);
d_free_align(pDCt1);
free(DCN);
d_free_align(pDCtN);
free(idx0);
free(idx1);
free(idxN);
d_free_align(pRSQ0);
d_free_align(pRSQ1);
d_free_align(pRSQN);
d_free_align(rq0);
d_free_align(rq1);
d_free_align(rqN);
d_free_align(work);
free(stat);
for(ii=0; ii<N; ii++)
{
d_free_align(hux[ii]);
d_free_align(hpi[ii]);
d_free_align(hlam[ii]);
d_free_align(ht[ii]);
d_free_align(hrb[ii]);
d_free_align(hrrq[ii]);
d_free_align(hrd[ii]);
}
d_free_align(hux[N]);
d_free_align(hlam[N]);
d_free_align(ht[N]);
d_free_align(hrrq[N]);
d_free_align(hrd[N]);
#if 0
// high level interface
free(rA);
free(rB);
free(rC);
free(rD);
free(rb);
free(rQ);
free(rQf);
free(rS);
free(rR);
free(rq);
free(rqf);
free(rr);
free(lb);
free(rlb);
free(lg);
free(rlg);
free(lgN);
free(ub);
free(rub);
free(ug);
free(rug);
free(ugN);
free(rx);
free(ru);
free(rpi);
free(rlam);
free(rt);
free(rwork);
#endif
// new high level interface
free(lb0);
free(ub0);
free(lb1);
free(ub1);
free(lbN);
free(ubN);
free(lg0);
free(ug0);
free(lg1);
free(ug1);
free(work1);
for(ii=0; ii<N; ii++)
{
free(hx[ii]);
free(hu[ii]);
free(hpi1[ii]);
free(hlam1[ii]);
free(ht1[ii]);
}
free(hx[N]);
free(hlam1[N]);
free(ht1[N]);
return 0;
}