int LEVMAR_BC_DER(
void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in R^n */
void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata), /* function to evaluate the Jacobian \part x / \part p */
LM_REAL *p, /* I/O: initial parameter estimates. On output has the estimated solution */
LM_REAL *x, /* I: measurement vector. NULL implies a zero vector */
int m, /* I: parameter vector dimension (i.e. #unknowns) */
int n, /* I: measurement vector dimension */
LM_REAL *lb, /* I: vector of lower bounds. If NULL, no lower bounds apply */
LM_REAL *ub, /* I: vector of upper bounds. If NULL, no upper bounds apply */
LM_REAL *dscl, /* I: diagonal scaling constants. NULL implies no scaling */
int itmax, /* I: maximum number of iterations */
LM_REAL opts[4], /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3]. Respectively the scale factor for initial \mu,
* stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2. Set to NULL for defaults to be used.
* Note that ||J^T e||_inf is computed on free (not equal to lb[i] or ub[i]) variables only.
*/
LM_REAL info[LM_INFO_SZ],
/* O: information regarding the minimization. Set to NULL if don't care
* info[0]= ||e||_2 at initial p.
* info[1-4]=[ ||e||_2, ||J^T e||_inf, ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
* info[5]= # iterations,
* info[6]=reason for terminating: 1 - stopped by small gradient J^T e
* 2 - stopped by small Dp
* 3 - stopped by itmax
* 4 - singular matrix. Restart from current p with increased mu
* 5 - no further error reduction is possible. Restart with increased mu
* 6 - stopped by small ||e||_2
* 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
* info[7]= # function evaluations
* info[8]= # Jacobian evaluations
* info[9]= # linear systems solved, i.e. # attempts for reducing error
*/
LM_REAL *work, /* working memory at least LM_BC_DER_WORKSZ() reals large, allocated if NULL */
LM_REAL *covar, /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
void *adata) /* pointer to possibly additional data, passed uninterpreted to func & jacf.
* Set to NULL if not needed
*/
{
register int i, j, k, l;
int worksz, freework=0, issolved;
/* temp work arrays */
LM_REAL *e, /* nx1 */
*hx, /* \hat{x}_i, nx1 */
*jacTe, /* J^T e_i mx1 */
*jac, /* nxm */
*jacTjac, /* mxm */
*Dp, /* mx1 */
*diag_jacTjac, /* diagonal of J^T J, mx1 */
*pDp, /* p + Dp, mx1 */
*sp_pDp=NULL; /* dscl*p or dscl*pDp, mx1 */
register LM_REAL mu, /* damping constant */
tmp; /* mainly used in matrix & vector multiplications */
LM_REAL p_eL2, jacTe_inf, pDp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+Dp)||_2 */
LM_REAL p_L2, Dp_L2=LM_REAL_MAX, dF, dL;
LM_REAL tau, eps1, eps2, eps2_sq, eps3;
LM_REAL init_p_eL2;
int nu=2, nu2, stop=0, nfev, njev=0, nlss=0;
const int nm=n*m;
/* variables for constrained LM */
struct FUNC_STATE fstate;
LM_REAL alpha=LM_CNST(1e-4), beta=LM_CNST(0.9), gamma=LM_CNST(0.99995), rho=LM_CNST(1e-8);
LM_REAL t, t0, jacTeDp;
LM_REAL tmin=LM_CNST(1e-12), tming=LM_CNST(1e-18); /* minimum step length for LS and PG steps */
const LM_REAL tini=LM_CNST(1.0); /* initial step length for LS and PG steps */
int nLMsteps=0, nLSsteps=0, nPGsteps=0, gprevtaken=0;
int numactive;
int (*linsolver)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m)=NULL;
mu=jacTe_inf=t=0.0; /* -Wall */
if(n<m){
fprintf(stderr, LCAT(LEVMAR_BC_DER, "(): cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n"), n, m);
return LM_ERROR;
}
if(!jacf){
fprintf(stderr, RCAT("No function specified for computing the Jacobian in ", LEVMAR_BC_DER)
RCAT("().\nIf no such function is available, use ", LEVMAR_BC_DIF) RCAT("() rather than ", LEVMAR_BC_DER) "()\n");
return LM_ERROR;
}
if(!LEVMAR_BOX_CHECK(lb, ub, m)){
fprintf(stderr, LCAT(LEVMAR_BC_DER, "(): at least one lower bound exceeds the upper one\n"));
return LM_ERROR;
}
if(dscl){ /* check that scaling consts are valid */
for(i=m; i-->0; )
if(dscl[i]<=0.0){
fprintf(stderr, LCAT(LEVMAR_BC_DER, "(): scaling constants should be positive (scale %d: %g <= 0)\n"), i, dscl[i]);
return LM_ERROR;
}
sp_pDp=(LM_REAL *)malloc(m*sizeof(LM_REAL));
if(!sp_pDp){
fprintf(stderr, LCAT(LEVMAR_BC_DER, "(): memory allocation request failed\n"));
return LM_ERROR;
}
}
if(opts){
tau=opts[0];
eps1=opts[1];
eps2=opts[2];
eps2_sq=opts[2]*opts[2];
eps3=opts[3];
}
else{ // use default values
tau=LM_CNST(LM_INIT_MU);
eps1=LM_CNST(LM_STOP_THRESH);
eps2=LM_CNST(LM_STOP_THRESH);
eps2_sq=LM_CNST(LM_STOP_THRESH)*LM_CNST(LM_STOP_THRESH);
eps3=LM_CNST(LM_STOP_THRESH);
}
if(!work){
worksz=LM_BC_DER_WORKSZ(m, n); //2*n+4*m + n*m + m*m;
work=(LM_REAL *)malloc(worksz*sizeof(LM_REAL)); /* allocate a big chunk in one step */
if(!work){
fprintf(stderr, LCAT(LEVMAR_BC_DER, "(): memory allocation request failed\n"));
return LM_ERROR;
}
freework=1;
}
/* set up work arrays */
e=work;
hx=e + n;
jacTe=hx + n;
jac=jacTe + m;
jacTjac=jac + nm;
Dp=jacTjac + m*m;
diag_jacTjac=Dp + m;
pDp=diag_jacTjac + m;
fstate.n=n;
fstate.hx=hx;
fstate.x=x;
fstate.lb=lb;
fstate.ub=ub;
fstate.adata=adata;
fstate.nfev=&nfev;
/* see if starting point is within the feasible set */
for(i=0; i<m; ++i)
pDp[i]=p[i];
BOXPROJECT(p, lb, ub, m); /* project to feasible set */
for(i=0; i<m; ++i)
if(pDp[i]!=p[i])
fprintf(stderr, RCAT("Warning: component %d of starting point not feasible in ", LEVMAR_BC_DER) "()! [%g projected to %g]\n",
i, pDp[i], p[i]);
/* compute e=x - f(p) and its L2 norm */
(*func)(p, hx, m, n, adata); nfev=1;
/* ### e=x-hx, p_eL2=||e|| */
#if 1
p_eL2=LEVMAR_L2NRMXMY(e, x, hx, n);
#else
for(i=0, p_eL2=0.0; i<n; ++i){
e[i]=tmp=x[i]-hx[i];
p_eL2+=tmp*tmp;
}
#endif
init_p_eL2=p_eL2;
if(!LM_FINITE(p_eL2)) stop=7;
if(dscl){
/* scale starting point and constraints */
for(i=m; i-->0; ) p[i]/=dscl[i];
BOXSCALE(lb, ub, dscl, m, 1);
}
for(k=0; k<itmax && !stop; ++k){
/* Note that p and e have been updated at a previous iteration */
if(p_eL2<=eps3){ /* error is small */
stop=6;
break;
}
/* Compute the Jacobian J at p, J^T J, J^T e, ||J^T e||_inf and ||p||^2.
* Since J^T J is symmetric, its computation can be sped up by computing
* only its upper triangular part and copying it to the lower part
*/
if(!dscl){
(*jacf)(p, jac, m, n, adata); ++njev;
}
else{
for(i=m; i-->0; ) sp_pDp[i]=p[i]*dscl[i];
(*jacf)(sp_pDp, jac, m, n, adata); ++njev;
/* compute jac*D */
for(i=n; i-->0; ){
register LM_REAL *jacim;
jacim=jac+i*m;
for(j=m; j-->0; )
jacim[j]*=dscl[j]; // jac[i*m+j]*=dscl[j];
}
}
/* J^T J, J^T e */
if(nm<__BLOCKSZ__SQ){ // this is a small problem
/* J^T*J_ij = \sum_l J^T_il * J_lj = \sum_l J_li * J_lj.
* Thus, the product J^T J can be computed using an outer loop for
* l that adds J_li*J_lj to each element ij of the result. Note that
* with this scheme, the accesses to J and JtJ are always along rows,
* therefore induces less cache misses compared to the straightforward
* algorithm for computing the product (i.e., l loop is innermost one).
* A similar scheme applies to the computation of J^T e.
* However, for large minimization problems (i.e., involving a large number
* of unknowns and measurements) for which J/J^T J rows are too large to
* fit in the L1 cache, even this scheme incures many cache misses. In
* such cases, a cache-efficient blocking scheme is preferable.
*
* Thanks to John Nitao of Lawrence Livermore Lab for pointing out this
* performance problem.
*
* Note that the non-blocking algorithm is faster on small
* problems since in this case it avoids the overheads of blocking.
*/
register LM_REAL alpha, *jaclm, *jacTjacim;
/* looping downwards saves a few computations */
for(i=m*m; i-->0; )
jacTjac[i]=0.0;
for(i=m; i-->0; )
jacTe[i]=0.0;
for(l=n; l-->0; ){
jaclm=jac+l*m;
for(i=m; i-->0; ){
jacTjacim=jacTjac+i*m;
alpha=jaclm[i]; //jac[l*m+i];
for(j=i+1; j-->0; ) /* j<=i computes lower triangular part only */
jacTjacim[j]+=jaclm[j]*alpha; //jacTjac[i*m+j]+=jac[l*m+j]*alpha
/* J^T e */
jacTe[i]+=alpha*e[l];
}
}
for(i=m; i-->0; ) /* copy to upper part */
for(j=i+1; j<m; ++j)
jacTjac[i*m+j]=jacTjac[j*m+i];
}
else{ // this is a large problem
/* Cache efficient computation of J^T J based on blocking
*/
LEVMAR_TRANS_MAT_MAT_MULT(jac, jacTjac, n, m);
/* cache efficient computation of J^T e */
for(i=0; i<m; ++i)
jacTe[i]=0.0;
for(i=0; i<n; ++i){
register LM_REAL *jacrow;
for(l=0, jacrow=jac+i*m, tmp=e[i]; l<m; ++l)
jacTe[l]+=jacrow[l]*tmp;
}
}
/* Compute ||J^T e||_inf and ||p||^2. Note that ||J^T e||_inf
* is computed for free (i.e. inactive) variables only.
* At a local minimum, if p[i]==ub[i] then g[i]>0;
* if p[i]==lb[i] g[i]<0; otherwise g[i]=0
*/
for(i=j=numactive=0, p_L2=jacTe_inf=0.0; i<m; ++i){
if(ub && p[i]==ub[i]){ ++numactive; if(jacTe[i]>0.0) ++j; }
else if(lb && p[i]==lb[i]){ ++numactive; if(jacTe[i]<0.0) ++j; }
else if(jacTe_inf < (tmp=FABS(jacTe[i]))) jacTe_inf=tmp;
diag_jacTjac[i]=jacTjac[i*m+i]; /* save diagonal entries so that augmentation can be later canceled */
p_L2+=p[i]*p[i];
}
//p_L2=sqrt(p_L2);
#if 0
if(!(k%100)){
printf("Current estimate: ");
for(i=0; i<m; ++i)
printf("%.9g ", p[i]);
printf("-- errors %.9g %0.9g, #active %d [%d]\n", jacTe_inf, p_eL2, numactive, j);
}
#endif
/* check for convergence */
if(j==numactive && (jacTe_inf <= eps1)){
Dp_L2=0.0; /* no increment for p in this case */
stop=1;
break;
}
/* compute initial damping factor */
if(k==0){
if(!lb && !ub){ /* no bounds */
for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
if(diag_jacTjac[i]>tmp) tmp=diag_jacTjac[i]; /* find max diagonal element */
mu=tau*tmp;
}
else
mu=LM_CNST(0.5)*tau*p_eL2; /* use Kanzow's starting mu */
}
/* determine increment using a combination of adaptive damping, line search and projected gradient search */
while(1){
/* augment normal equations */
for(i=0; i<m; ++i)
jacTjac[i*m+i]+=mu;
/* solve augmented equations */
#ifdef HAVE_LAPACK
/* 7 alternatives are available: LU, Cholesky + Cholesky with PLASMA, LDLt, 2 variants of QR decomposition and SVD.
* For matrices with dimensions of at least a few hundreds, the PLASMA implementation of Cholesky is the fastest.
* From the serial solvers, Cholesky is the fastest but might occasionally be inapplicable due to numerical round-off;
* QR is slower but more robust; SVD is the slowest but most robust; LU is quite robust but
* slower than LDLt; LDLt offers a good tradeoff between robustness and speed
*/
issolved=AX_EQ_B_BK(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_BK;
//issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
//issolved=AX_EQ_B_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_CHOL;
#ifdef HAVE_PLASMA
//issolved=AX_EQ_B_PLASMA_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_PLASMA_CHOL;
#endif
//issolved=AX_EQ_B_QR(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_QR;
//issolved=AX_EQ_B_QRLS(jacTjac, jacTe, Dp, m, m); ++nlss; linsolver=(int (*)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m))AX_EQ_B_QRLS;
//issolved=AX_EQ_B_SVD(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_SVD;
#else
/* use the LU included with levmar */
issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
#endif /* HAVE_LAPACK */
if(issolved){
for(i=0; i<m; ++i)
pDp[i]=p[i] + Dp[i];
/* compute p's new estimate and ||Dp||^2 */
BOXPROJECT(pDp, lb, ub, m); /* project to feasible set */
for(i=0, Dp_L2=0.0; i<m; ++i){
Dp[i]=tmp=pDp[i]-p[i];
Dp_L2+=tmp*tmp;
}
//Dp_L2=sqrt(Dp_L2);
if(Dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */
stop=2;
break;
}
if(Dp_L2>=(p_L2+eps2)/(LM_CNST(EPSILON)*LM_CNST(EPSILON))){ /* almost singular */
stop=4;
break;
}
if(!dscl){
(*func)(pDp, hx, m, n, adata); ++nfev; /* evaluate function at p + Dp */
}
else{
for(i=m; i-->0; ) sp_pDp[i]=pDp[i]*dscl[i];
(*func)(sp_pDp, hx, m, n, adata); ++nfev; /* evaluate function at p + Dp */
}
/* ### hx=x-hx, pDp_eL2=||hx|| */
#if 1
pDp_eL2=LEVMAR_L2NRMXMY(hx, x, hx, n);
#else
for(i=0, pDp_eL2=0.0; i<n; ++i){ /* compute ||e(pDp)||_2 */
hx[i]=tmp=x[i]-hx[i];
pDp_eL2+=tmp*tmp;
}
#endif
/* the following test ensures that the computation of pDp_eL2 has not overflowed.
* Such an overflow does no harm here, thus it is not signalled as an error
*/
if(!LM_FINITE(pDp_eL2) && !LM_FINITE(VECNORM(hx, n))){
stop=7;
break;
}
if(pDp_eL2<=gamma*p_eL2){
for(i=0, dL=0.0; i<m; ++i)
dL+=Dp[i]*(mu*Dp[i]+jacTe[i]);
#if 1
if(dL>0.0){
dF=p_eL2-pDp_eL2;
tmp=(LM_CNST(2.0)*dF/dL-LM_CNST(1.0));
tmp=LM_CNST(1.0)-tmp*tmp*tmp;
mu=mu*( (tmp>=LM_CNST(ONE_THIRD))? tmp : LM_CNST(ONE_THIRD) );
}
else{
tmp=LM_CNST(0.1)*pDp_eL2; /* pDp_eL2 is the new p_eL2 */
mu=(mu>=tmp)? tmp : mu;
}
#else
tmp=LM_CNST(0.1)*pDp_eL2; /* pDp_eL2 is the new p_eL2 */
mu=(mu>=tmp)? tmp : mu;
#endif
nu=2;
for(i=0 ; i<m; ++i) /* update p's estimate */
p[i]=pDp[i];
for(i=0; i<n; ++i) /* update e and ||e||_2 */
e[i]=hx[i];
p_eL2=pDp_eL2;
++nLMsteps;
gprevtaken=0;
break;
}
/* note that if the LM step is not taken, code falls through to the LM line search below */
}
else{
/* the augmented linear system could not be solved, increase mu */
mu*=nu;
nu2=nu<<1; // 2*nu;
if(nu2<=nu){ /* nu has wrapped around (overflown). Thanks to Frank Jordan for spotting this case */
stop=5;
break;
}
nu=nu2;
for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
jacTjac[i*m+i]=diag_jacTjac[i];
continue; /* solve again with increased nu */
}
/* if this point is reached, the LM step did not reduce the error;
* see if it is a descent direction
*/
/* negate jacTe (i.e. g) & compute g^T * Dp */
for(i=0, jacTeDp=0.0; i<m; ++i){
jacTe[i]=-jacTe[i];
jacTeDp+=jacTe[i]*Dp[i];
}
if(jacTeDp<=-rho*pow(Dp_L2, LM_CNST(_POW_)/LM_CNST(2.0))){
/* Dp is a descent direction; do a line search along it */
#if 1
/* use Schnabel's backtracking line search; it requires fewer "func" evaluations */
{
int mxtake, iretcd;
LM_REAL stepmx, steptl=LM_CNST(1e3)*(LM_REAL)sqrt(LM_REAL_EPSILON);
tmp=(LM_REAL)sqrt(p_L2); stepmx=LM_CNST(1e3)*( (tmp>=LM_CNST(1.0))? tmp : LM_CNST(1.0) );
LNSRCH(m, p, p_eL2, jacTe, Dp, alpha, pDp, &pDp_eL2, func, &fstate,
&mxtake, &iretcd, stepmx, steptl, dscl); /* NOTE: LNSRCH() updates hx */
if(iretcd!=0 || !LM_FINITE(pDp_eL2)) goto gradproj; /* rather inelegant but effective way to handle LNSRCH() failures... */
}
#else
/* use the simpler (but slower!) line search described by Kanzow et al */
for(t=tini; t>tmin; t*=beta){
for(i=0; i<m; ++i)
pDp[i]=p[i] + t*Dp[i];
BOXPROJECT(pDp, lb, ub, m); /* project to feasible set */
if(!dscl){
(*func)(pDp, hx, m, n, adata); ++nfev; /* evaluate function at p + t*Dp */
}
else{
for(i=m; i-->0; ) sp_pDp[i]=pDp[i]*dscl[i];
(*func)(sp_pDp, hx, m, n, adata); ++nfev; /* evaluate function at p + t*Dp */
}
/* compute ||e(pDp)||_2 */
/* ### hx=x-hx, pDp_eL2=||hx|| */
#if 1
pDp_eL2=LEVMAR_L2NRMXMY(hx, x, hx, n);
#else
for(i=0, pDp_eL2=0.0; i<n; ++i){
hx[i]=tmp=x[i]-hx[i];
pDp_eL2+=tmp*tmp;
}
#endif /* ||e(pDp)||_2 */
if(!LM_FINITE(pDp_eL2)) goto gradproj; /* treat as line search failure */
//if(LM_CNST(0.5)*pDp_eL2<=LM_CNST(0.5)*p_eL2 + t*alpha*jacTeDp) break;
if(pDp_eL2<=p_eL2 + LM_CNST(2.0)*t*alpha*jacTeDp) break;
}
#endif /* line search alternatives */
++nLSsteps;
gprevtaken=0;
/* NOTE: new estimate for p is in pDp, associated error in hx and its norm in pDp_eL2.
* These values are used below to update their corresponding variables
*/
}
else{
/* Note that this point can also be reached via a goto when LNSRCH() fails. */
gradproj:
/* jacTe has been negated above. Being a descent direction, it is next used
* to make a projected gradient step
*/
/* compute ||g|| */
for(i=0, tmp=0.0; i<m; ++i)
tmp+=jacTe[i]*jacTe[i];
tmp=(LM_REAL)sqrt(tmp);
tmp=LM_CNST(100.0)/(LM_CNST(1.0)+tmp);
t0=(tmp<=tini)? tmp : tini; /* guard against poor scaling & large steps; see (3.50) in C.T. Kelley's book */
/* if the previous step was along the gradient descent, try to use the t employed in that step */
for(t=(gprevtaken)? t : t0; t>tming; t*=beta){
for(i=0; i<m; ++i)
pDp[i]=p[i] - t*jacTe[i];
BOXPROJECT(pDp, lb, ub, m); /* project to feasible set */
for(i=0, Dp_L2=0.0; i<m; ++i){
Dp[i]=tmp=pDp[i]-p[i];
Dp_L2+=tmp*tmp;
}
if(!dscl){
(*func)(pDp, hx, m, n, adata); ++nfev; /* evaluate function at p - t*g */
}
else{
for(i=m; i-->0; ) sp_pDp[i]=pDp[i]*dscl[i];
(*func)(sp_pDp, hx, m, n, adata); ++nfev; /* evaluate function at p - t*g */
}
/* compute ||e(pDp)||_2 */
/* ### hx=x-hx, pDp_eL2=||hx|| */
#if 1
pDp_eL2=LEVMAR_L2NRMXMY(hx, x, hx, n);
#else
for(i=0, pDp_eL2=0.0; i<n; ++i){
hx[i]=tmp=x[i]-hx[i];
pDp_eL2+=tmp*tmp;
}
#endif
/* the following test ensures that the computation of pDp_eL2 has not overflowed.
* Such an overflow does no harm here, thus it is not signalled as an error
*/
if(!LM_FINITE(pDp_eL2) && !LM_FINITE(VECNORM(hx, n))){
stop=7;
goto breaknested;
}
/* compute ||g^T * Dp||. Note that if pDp has not been altered by projection
* (i.e. BOXPROJECT), jacTeDp=-t*||g||^2
*/
for(i=0, jacTeDp=0.0; i<m; ++i)
jacTeDp+=jacTe[i]*Dp[i];
if(gprevtaken && pDp_eL2<=p_eL2 + LM_CNST(2.0)*LM_CNST(0.99999)*jacTeDp){ /* starting t too small */
t=t0;
gprevtaken=0;
continue;
}
//if(LM_CNST(0.5)*pDp_eL2<=LM_CNST(0.5)*p_eL2 + alpha*jacTeDp) terminatePGLS;
if(pDp_eL2<=p_eL2 + LM_CNST(2.0)*alpha*jacTeDp) goto terminatePGLS;
//if(pDp_eL2<=p_eL2 - LM_CNST(2.0)*alpha/t*Dp_L2) goto terminatePGLS; // sufficient decrease condition proposed by Kelley in (5.13)
}
/* if this point is reached then the gradient line search has failed */
gprevtaken=0;
break;
terminatePGLS:
++nPGsteps;
gprevtaken=1;
/* NOTE: new estimate for p is in pDp, associated error in hx and its norm in pDp_eL2 */
}
/* update using computed values */
for(i=0, Dp_L2=0.0; i<m; ++i){
tmp=pDp[i]-p[i];
Dp_L2+=tmp*tmp;
}
//Dp_L2=sqrt(Dp_L2);
if(Dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */
stop=2;
break;
}
for(i=0 ; i<m; ++i) /* update p's estimate */
p[i]=pDp[i];
for(i=0; i<n; ++i) /* update e and ||e||_2 */
e[i]=hx[i];
p_eL2=pDp_eL2;
break;
} /* inner loop */
}
breaknested: /* NOTE: this point is also reached via an explicit goto! */
if(k>=itmax) stop=3;
for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
jacTjac[i*m+i]=diag_jacTjac[i];
if(info){
info[0]=init_p_eL2;
info[1]=p_eL2;
info[2]=jacTe_inf;
info[3]=Dp_L2;
for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
if(tmp<jacTjac[i*m+i]) tmp=jacTjac[i*m+i];
info[4]=mu/tmp;
info[5]=(LM_REAL)k;
info[6]=(LM_REAL)stop;
info[7]=(LM_REAL)nfev;
info[8]=(LM_REAL)njev;
info[9]=(LM_REAL)nlss;
}
/* covariance matrix */
if(covar){
LEVMAR_COVAR(jacTjac, covar, p_eL2, m, n);
if(dscl){ /* correct for the scaling */
for(i=m; i-->0; )
for(j=m; j-->0; )
covar[i*m+j]*=(dscl[i]*dscl[j]);
}
}
if(freework) free(work);
#ifdef LINSOLVERS_RETAIN_MEMORY
if(linsolver) (*linsolver)(NULL, NULL, NULL, 0);
#endif
#if 0
printf("%d LM steps, %d line search, %d projected gradient\n", nLMsteps, nLSsteps, nPGsteps);
#endif
if(dscl){
/* scale final point and constraints */
for(i=0; i<m; ++i) p[i]*=dscl[i];
BOXSCALE(lb, ub, dscl, m, 0);
free(sp_pDp);
}
return (stop!=4 && stop!=7)? k : LM_ERROR;
}
Numeric LMSubspaceOptimizer::optimize( const VariablePtrVec & vars,
const FactorPtrVec & factors, NumericVec & xval,
Numeric & deltaFval, const bool printdbg ) {
// // box-constrained minimization
// extern int dlevmar_bc_der(
// void (*func)(double *p, double *hx, int m, int n, void *adata),
// void (*jacf)(double *p, double *j, int m, int n, void *adata),
// double *p, double *x, int m, int n, double *lb, double *ub, double *dscl,
// int itmax, double *opts, double *info, double *work, double *covar,
// void *adata);
//#define USE_LEVMAR
#ifdef USE_LEVMAR
const Clock::time_point starttime = Clock::now();
// initstate.assign( xval.begin(), xval.end() );
LMSSOpt::AuxData aux( vars, factors, f, pgtemp );
const int m = vars.size();
const int n = std::max( factors.size(), (size_t) m );
initeval.resize( n );
finaleval.resize( n );
// double lb[ m ];
// double ub[ m ];
//
// for ( size_t i = 0; i < vars.size(); ++i ) {
// NumericInterval dom = vars[i]->getDomain().interval();
// lb[i] = ( dom.lower() <= -DBL_MAX ? DBL_MAX : dom.lower() );
// ub[i] = ( dom.upper() >= DBL_MAX ? DBL_MAX : dom.upper() );
// }
double * dscl = NULL;
double opts[ LM_OPTS_SZ ];
// double * opts = NULL;
double info[ LM_INFO_SZ ];
double * work = new double[ LM_BC_DER_WORKSZ( m, n ) ];
double * covar = NULL;
if ( printdbg ) {
std::cout << "LM SS opt m=" << m << ", n=" << n << " (" << vars.size()
<< " vars, " << factors.size() << " factors)" << std::endl;
}
// LMSSOpt::evalFunc( xval.data(), initeval.data(), m, n, &aux );
// const Numeric ival = NumericVecOps::dot( initeval, initeval ) / 2.0;
Numeric ferr = 0.0;
const Numeric ival = f.evalFactors( factors, ferr );
opts[0] = 1e-3; // initial \mu scale factor
opts[1] = 1e-15; // stopping thresh. for ||J^T e||_inf
opts[2] = 1e-15; // stopping thresh. for ||Dp||_2
opts[3] = ftol; // stopping thresh. for ||e||_2
// int niters = dlevmar_bc_der(
// &LMSSOpt::evalFunc,
// &LMSSOpt::evalJacf,
// xval.data(), NULL, xval.size(), n, lb, ub,
// NULL, maxiters, opts, info, work, covar, &aux );
int niters = dlevmar_der(
&LMSSOpt::evalFunc,
&LMSSOpt::evalJacf,
xval.data(), NULL, xval.size(), n,
maxiters, opts, info, work, covar, &aux );
// sanitize values to be within the domain of this variable (note that they
// are sanitized in quickAssign(), so just copy them out after)
LMSSOpt::quickAssignVals( aux, m, xval.data() );
for ( size_t i = 0; i < vars.size(); ++i ) {
xval[i] = vars[i]->eval();
}
// LMSSOpt::evalFunc( xval.data(), finaleval.data(), m, n, &aux );
// const Numeric fval = NumericVecOps::dot( finaleval, finaleval ) / 2.0;
Numeric fval = f.evalFactors( factors, ferr );
// Numeric asdf = 0;
// for ( size_t i = 0; i < factors.size(); ++i ) {
// asdf += factors[i]->evalNoCache();
// std::cout << i << ": f " << factors[i]->getID() << " diff " <<
// ( finaleval[i]*finaleval[i]/2.0 - factors[i]->eval() ) << " ("
// << factors[i]->eval() << ")" << std::endl;
// }
// std::cout << "asdf: " << asdf << std::endl;
//
// std::cout << "f.eval " << f.eval() << std::endl;
// Numeric ferr = 0.0;
// std::cout << "f fact eval " << f.evalFactors( factors, ferr ) << std::endl;
//
// std::cout << "xval: " << xval << std::endl;
// double err[n];
// dlevmar_chkjac( &LMSSOpt::evalFunc, &LMSSOpt::evalJacf, xval.data(), m, n,
// &aux, err );
//
// for ( size_t i = 0; i < m; ++i ) {
// if ( err[i] < 0.5 ) {
// std::cout << i << ": var " << vars[i]->getID() << " has jac err "
// << err[i] << std::endl;
// }
// }
delete work;
deltaFval = ( fval - ival);
const Duration dur = ( Clock::now() - starttime );
if ( printdbg ) {
std::cout << "LM SS opt returned " << fval << " (init " << ival
<< ", diff " << deltaFval << ") after " << niters <<
" iterations in " << dur.count() << " seconds" << std::endl;
std::cout << "LM SS opt info -- termination: " << info[6] <<
", #fevals: " << info[7] << ", #jevals: " << info[8] <<
", #linsolves" << info[9] << std::endl;
}
// if ( deltaFval > 0 ) {
// fval = ival;
// xval.assign( initstate.begin(), initstate.end() );
// deltaFval = 0;
// std::cout << "LM SS made no progress -- returning initial state" << std::endl;
// }
return fval;
#else // USE_LEVMAR
std::cout << "ERROR: Cannot use LM subspace optimizer without levmar.h." <<
" Rebuild with -DUSE_LEVMAR and link to liblevmar." << std::endl;
std::exit( -1 );
return 0;
#endif // USE_LEVMAR
}