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Diffstat (limited to 'libmoped/libs/sba-1.6/sba_levmar.c')
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diff --git a/libmoped/libs/sba-1.6/sba_levmar.c b/libmoped/libs/sba-1.6/sba_levmar.c new file mode 100644 index 0000000..aa6b2e9 --- /dev/null +++ b/libmoped/libs/sba-1.6/sba_levmar.c @@ -0,0 +1,2528 @@ +///////////////////////////////////////////////////////////////////////////////// +//// +//// Expert drivers for sparse bundle adjustment based on the +//// Levenberg - Marquardt minimization algorithm +//// Copyright (C) 2004-2009 Manolis Lourakis (lourakis at ics forth gr) +//// Institute of Computer Science, Foundation for Research & Technology - Hellas +//// Heraklion, Crete, Greece. +//// +//// This program is free software; you can redistribute it and/or modify +//// it under the terms of the GNU General Public License as published by +//// the Free Software Foundation; either version 2 of the License, or +//// (at your option) any later version. +//// +//// This program is distributed in the hope that it will be useful, +//// but WITHOUT ANY WARRANTY; without even the implied warranty of +//// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +//// GNU General Public License for more details. +//// +/////////////////////////////////////////////////////////////////////////////////// + +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include <float.h> + +#include "compiler.h" +#include "sba.h" +#include "sba_chkjac.h" + + +#define SBA_EPSILON 1E-12 +#define SBA_EPSILON_SQ ( (SBA_EPSILON)*(SBA_EPSILON) ) + +#define SBA_ONE_THIRD 0.3333333334 /* 1.0/3.0 */ + + +#define emalloc(sz) emalloc_(__FILE__, __LINE__, sz) + +#define FABS(x) (((x)>=0)? (x) : -(x)) + +#define ROW_MAJOR 0 +#define COLUMN_MAJOR 1 +#define MAT_STORAGE COLUMN_MAJOR + + +/* contains information necessary for computing a finite difference approximation to a jacobian, + * e.g. function to differentiate, problem dimensions and pointers to working memory buffers + */ +struct fdj_data_x_ { + void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata); /* function to differentiate */ + int cnp, pnp, mnp; /* parameter numbers */ + int *func_rcidxs, + *func_rcsubs; /* working memory for func invocations. + * Notice that this has to be different + * than the working memory used for + * evaluating the jacobian! + */ + double *hx, *hxx; /* memory to save results in */ + void *adata; +}; + +/* auxiliary memory allocation routine with error checking */ +inline static void *emalloc_(char *file, int line, size_t sz) +{ +void *ptr; + + ptr=(void *)malloc(sz); + if(ptr==NULL){ + fprintf(stderr, "SBA: memory allocation request for %u bytes failed in file %s, line %d, exiting", sz, file, line); + exit(1); + } + + return ptr; +} + +/* auxiliary routine for clearing an array of doubles */ +inline static void _dblzero(register double *arr, register int count) +{ + while(--count>=0) + *arr++=0.0; +} + +/* auxiliary routine for computing the mean reprojection error; used for debugging */ +static double sba_mean_repr_error(int n, int mnp, double *x, double *hx, struct sba_crsm *idxij, int *rcidxs, int *rcsubs) +{ +register int i, j; +int nnz, nprojs; +double *ptr1, *ptr2; +double err; + + for(i=nprojs=0, err=0.0; i<n; ++i){ + nnz=sba_crsm_row_elmidxs(idxij, i, rcidxs, rcsubs); /* find nonzero x_ij, j=0...m-1 */ + nprojs+=nnz; + for(j=0; j<nnz; ++j){ /* point i projecting on camera rcsubs[j] */ + ptr1=x + idxij->val[rcidxs[j]]*mnp; + ptr2=hx + idxij->val[rcidxs[j]]*mnp; + + err+=sqrt((ptr1[0]-ptr2[0])*(ptr1[0]-ptr2[0]) + (ptr1[1]-ptr2[1])*(ptr1[1]-ptr2[1])); + } + } + + return err/((double)(nprojs)); +} + +/* print the solution in p using sba's text format. If cnp/pnp==0 only points/cameras are printed */ +static void sba_print_sol(int n, int m, double *p, int cnp, int pnp, double *x, int mnp, struct sba_crsm *idxij, int *rcidxs, int *rcsubs) +{ +register int i, j, ii; +int nnz; +double *ptr; + + if(cnp){ + /* print camera parameters */ + for(j=0; j<m; ++j){ + ptr=p+cnp*j; + for(ii=0; ii<cnp; ++ii) + printf("%g ", ptr[ii]); + printf("\n"); + } + } + + if(pnp){ + /* 3D & 2D point parameters */ + printf("\n\n\n# X Y Z nframes frame0 x0 y0 frame1 x1 y1 ...\n"); + for(i=0; i<n; ++i){ + ptr=p+cnp*m+i*pnp; + for(ii=0; ii<pnp; ++ii) // print 3D coordinates + printf("%g ", ptr[ii]); + + nnz=sba_crsm_row_elmidxs(idxij, i, rcidxs, rcsubs); /* find nonzero x_ij, j=0...m-1 */ + printf("%d ", nnz); + + for(j=0; j<nnz; ++j){ /* point i projecting on camera rcsubs[j] */ + ptr=x + idxij->val[rcidxs[j]]*mnp; + + printf("%d ", rcsubs[j]); + for(ii=0; ii<mnp; ++ii) // print 2D coordinates + printf("%g ", ptr[ii]); + } + printf("\n"); + } + } +} + +/* Compute e=x-y for two n-vectors x and y and return the squared L2 norm of e. + * e can coincide with either x or y. + * Uses loop unrolling and blocking to reduce bookkeeping overhead & pipeline + * stalls and increase instruction-level parallelism; see http://www.abarnett.demon.co.uk/tutorial.html + */ +static double nrmL2xmy(double *const e, const double *const x, const double *const y, const int n) +{ +const int blocksize=8, bpwr=3; /* 8=2^3 */ +register int i; +int j1, j2, j3, j4, j5, j6, j7; +int blockn; +register double sum0=0.0, sum1=0.0, sum2=0.0, sum3=0.0; + + /* n may not be divisible by blocksize, + * go as near as we can first, then tidy up. + */ + blockn = (n>>bpwr)<<bpwr; /* (n / blocksize) * blocksize; */ + + /* unroll the loop in blocks of `blocksize'; looping downwards gains some more speed */ + for(i=blockn-1; i>0; i-=blocksize){ + e[i ]=x[i ]-y[i ]; sum0+=e[i ]*e[i ]; + j1=i-1; e[j1]=x[j1]-y[j1]; sum1+=e[j1]*e[j1]; + j2=i-2; e[j2]=x[j2]-y[j2]; sum2+=e[j2]*e[j2]; + j3=i-3; e[j3]=x[j3]-y[j3]; sum3+=e[j3]*e[j3]; + j4=i-4; e[j4]=x[j4]-y[j4]; sum0+=e[j4]*e[j4]; + j5=i-5; e[j5]=x[j5]-y[j5]; sum1+=e[j5]*e[j5]; + j6=i-6; e[j6]=x[j6]-y[j6]; sum2+=e[j6]*e[j6]; + j7=i-7; e[j7]=x[j7]-y[j7]; sum3+=e[j7]*e[j7]; + } + + /* + * There may be some left to do. + * This could be done as a simple for() loop, + * but a switch is faster (and more interesting) + */ + + i=blockn; + if(i<n){ + /* Jump into the case at the place that will allow + * us to finish off the appropriate number of items. + */ + switch(n - i){ + case 7 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 6 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 5 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 4 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 3 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 2 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + case 1 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i; + } + } + + return sum0+sum1+sum2+sum3; +} + +/* Compute e=W*(x-y) for two n-vectors x and y and return the squared L2 norm of e. + * This norm equals the squared C norm of x-y with C=W^T*W, W being block diagonal + * matrix with nvis mnp*mnp blocks: e^T*e=(x-y)^T*W^T*W*(x-y)=||x-y||_C. + * Note that n=nvis*mnp; e can coincide with either x or y. + * + * Similarly to nrmL2xmy() above, uses loop unrolling and blocking + */ +static double nrmCxmy(double *const e, const double *const x, const double *const y, + const double *const W, const int mnp, const int nvis) +{ +const int n=nvis*mnp; +const int blocksize=8, bpwr=3; /* 8=2^3 */ +register int i, ii, k; +int j1, j2, j3, j4, j5, j6, j7; +int blockn, mnpsq; +register double norm, sum; +register const double *Wptr, *auxptr; +register double *eptr; + + /* n may not be divisible by blocksize, + * go as near as we can first, then tidy up. + */ + blockn = (n>>bpwr)<<bpwr; /* (n / blocksize) * blocksize; */ + + /* unroll the loop in blocks of `blocksize'; looping downwards gains some more speed */ + for(i=blockn-1; i>0; i-=blocksize){ + e[i ]=x[i ]-y[i ]; + j1=i-1; e[j1]=x[j1]-y[j1]; + j2=i-2; e[j2]=x[j2]-y[j2]; + j3=i-3; e[j3]=x[j3]-y[j3]; + j4=i-4; e[j4]=x[j4]-y[j4]; + j5=i-5; e[j5]=x[j5]-y[j5]; + j6=i-6; e[j6]=x[j6]-y[j6]; + j7=i-7; e[j7]=x[j7]-y[j7]; + } + + /* + * There may be some left to do. + * This could be done as a simple for() loop, + * but a switch is faster (and more interesting) + */ + + i=blockn; + if(i<n){ + /* Jump into the case at the place that will allow + * us to finish off the appropriate number of items. + */ + switch(n - i){ + case 7 : e[i]=x[i]-y[i]; ++i; + case 6 : e[i]=x[i]-y[i]; ++i; + case 5 : e[i]=x[i]-y[i]; ++i; + case 4 : e[i]=x[i]-y[i]; ++i; + case 3 : e[i]=x[i]-y[i]; ++i; + case 2 : e[i]=x[i]-y[i]; ++i; + case 1 : e[i]=x[i]-y[i]; ++i; + } + } + + /* compute w_x_ij e_ij in e and its L2 norm. + * Since w_x_ij is upper triangular, the products can be safely saved + * directly in e_ij, without the need for intermediate storage + */ + mnpsq=mnp*mnp; + /* Wptr, eptr point to w_x_ij, e_ij below */ + for(i=0, Wptr=W, eptr=e, norm=0.0; i<nvis; ++i, Wptr+=mnpsq, eptr+=mnp){ + for(ii=0, auxptr=Wptr; ii<mnp; ++ii, auxptr+=mnp){ /* auxptr=Wptr+ii*mnp */ + for(k=ii, sum=0.0; k<mnp; ++k) // k>=ii since w_x_ij is upper triangular + sum+=auxptr[k]*eptr[k]; //Wptr[ii*mnp+k]*eptr[k]; + eptr[ii]=sum; + norm+=sum*sum; + } + } + + return norm; +} + +/* search for & print image projection components that are infinite; useful for identifying errors */ +static void sba_print_inf(double *hx, int nimgs, int mnp, struct sba_crsm *idxij, int *rcidxs, int *rcsubs) +{ +register int i, j, k; +int nnz; +double *phxij; + + for(j=0; j<nimgs; ++j){ + nnz=sba_crsm_col_elmidxs(idxij, j, rcidxs, rcsubs); /* find nonzero hx_ij, i=0...n-1 */ + for(i=0; i<nnz; ++i){ + phxij=hx + idxij->val[rcidxs[i]]*mnp; + for(k=0; k<mnp; ++k) + if(!SBA_FINITE(phxij[k])) + printf("SBA: component %d of the estimated projection of point %d on camera %d is invalid!\n", k, rcsubs[i], j); + } + } +} + +/* Given a parameter vector p made up of the 3D coordinates of n points and the parameters of m cameras, compute in + * jac the jacobian of the predicted measurements, i.e. the jacobian of the projections of 3D points in the m images. + * The jacobian is approximated with the aid of finite differences and is returned in the order + * (A_11, B_11, ..., A_1m, B_1m, ..., A_n1, B_n1, ..., A_nm, B_nm), + * where A_ij=dx_ij/da_j and B_ij=dx_ij/db_i (see HZ). + * Notice that depending on idxij, some of the A_ij, B_ij might be missing + * + * Problem-specific information is assumed to be stored in a structure pointed to by "dat". + * + * NOTE: The jacobian (for n=4, m=3) in matrix form has the following structure: + * A_11 0 0 B_11 0 0 0 + * 0 A_12 0 B_12 0 0 0 + * 0 0 A_13 B_13 0 0 0 + * A_21 0 0 0 B_21 0 0 + * 0 A_22 0 0 B_22 0 0 + * 0 0 A_23 0 B_23 0 0 + * A_31 0 0 0 0 B_31 0 + * 0 A_32 0 0 0 B_32 0 + * 0 0 A_33 0 0 B_33 0 + * A_41 0 0 0 0 0 B_41 + * 0 A_42 0 0 0 0 B_42 + * 0 0 A_43 0 0 0 B_43 + * To reduce the total number of objective function evaluations, this structure can be + * exploited as follows: A certain d is added to the j-th parameters of all cameras and + * the objective function is evaluated at the resulting point. This evaluation suffices + * to compute the corresponding columns of *all* A_ij through finite differences. A similar + * strategy allows the computation of the B_ij. Overall, only cnp+pnp+1 objective function + * evaluations are needed to compute the jacobian, much fewer compared to the m*cnp+n*pnp+1 + * that would be required by the naive strategy of computing one column of the jacobian + * per function evaluation. See Nocedal-Wright, ch. 7, pp. 169. Although this approach is + * much faster compared to the naive strategy, it is not preferable to analytic jacobians, + * since the latter are considerably faster to compute and result in fewer LM iterations. + */ +static void sba_fdjac_x( + double *p, /* I: current parameter estimate, (m*cnp+n*pnp)x1 */ + struct sba_crsm *idxij, /* I: sparse matrix containing the location of x_ij in hx */ + int *rcidxs, /* work array for the indexes of nonzero elements of a single sparse matrix row/column */ + int *rcsubs, /* work array for the subscripts of nonzero elements in a single sparse matrix row/column */ + double *jac, /* O: array for storing the approximated jacobian */ + void *dat) /* I: points to a "fdj_data_x_" structure */ +{ + register int i, j, ii, jj; + double *pa, *pb, *pqr, *ppt; + register double *pAB, *phx, *phxx; + int n, m, nm, nnz, Asz, Bsz, ABsz, idx; + + double *tmpd; + register double d; + + struct fdj_data_x_ *fdjd; + void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata); + double *hx, *hxx; + int cnp, pnp, mnp; + void *adata; + + + /* retrieve problem-specific information passed in *dat */ + fdjd=(struct fdj_data_x_ *)dat; + func=fdjd->func; + cnp=fdjd->cnp; pnp=fdjd->pnp; mnp=fdjd->mnp; + hx=fdjd->hx; + hxx=fdjd->hxx; + adata=fdjd->adata; + + n=idxij->nr; m=idxij->nc; + pa=p; pb=p+m*cnp; + Asz=mnp*cnp; Bsz=mnp*pnp; ABsz=Asz+Bsz; + + nm=(n>=m)? n : m; // max(n, m); + tmpd=(double *)emalloc(nm*sizeof(double)); + + (*func)(p, idxij, fdjd->func_rcidxs, fdjd->func_rcsubs, hx, adata); // evaluate supplied function on current solution + + if(cnp){ // is motion varying? + /* compute A_ij */ + for(jj=0; jj<cnp; ++jj){ + for(j=0; j<m; ++j){ + pqr=pa+j*cnp; // j-th camera parameters + /* determine d=max(SBA_DELTA_SCALE*|pqr[jj]|, SBA_MIN_DELTA), see HZ */ + d=(double)(SBA_DELTA_SCALE)*pqr[jj]; // force evaluation + d=FABS(d); + if(d<SBA_MIN_DELTA) d=SBA_MIN_DELTA; + + tmpd[j]=d; + pqr[jj]+=d; + } + + (*func)(p, idxij, fdjd->func_rcidxs, fdjd->func_rcsubs, hxx, adata); + + for(j=0; j<m; ++j){ + pqr=pa+j*cnp; // j-th camera parameters + pqr[jj]-=tmpd[j]; /* restore */ + d=1.0/tmpd[j]; /* invert so that divisions can be carried out faster as multiplications */ + + nnz=sba_crsm_col_elmidxs(idxij, j, rcidxs, rcsubs); /* find nonzero A_ij, i=0...n-1 */ + for(i=0; i<nnz; ++i){ + idx=idxij->val[rcidxs[i]]; + phx=hx + idx*mnp; // set phx to point to hx_ij + phxx=hxx + idx*mnp; // set phxx to point to hxx_ij + pAB=jac + idx*ABsz; // set pAB to point to A_ij + + for(ii=0; ii<mnp; ++ii) + pAB[ii*cnp+jj]=(phxx[ii]-phx[ii])*d; + } + } + } + } + + if(pnp){ // is structure varying? + /* compute B_ij */ + for(jj=0; jj<pnp; ++jj){ + for(i=0; i<n; ++i){ + ppt=pb+i*pnp; // i-th point parameters + /* determine d=max(SBA_DELTA_SCALE*|ppt[jj]|, SBA_MIN_DELTA), see HZ */ + d=(double)(SBA_DELTA_SCALE)*ppt[jj]; // force evaluation + d=FABS(d); + if(d<SBA_MIN_DELTA) d=SBA_MIN_DELTA; + + tmpd[i]=d; + ppt[jj]+=d; + } + + (*func)(p, idxij, fdjd->func_rcidxs, fdjd->func_rcsubs, hxx, adata); + + for(i=0; i<n; ++i){ + ppt=pb+i*pnp; // i-th point parameters + ppt[jj]-=tmpd[i]; /* restore */ + d=1.0/tmpd[i]; /* invert so that divisions can be carried out faster as multiplications */ + + nnz=sba_crsm_row_elmidxs(idxij, i, rcidxs, rcsubs); /* find nonzero B_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + idx=idxij->val[rcidxs[j]]; + phx=hx + idx*mnp; // set phx to point to hx_ij + phxx=hxx + idx*mnp; // set phxx to point to hxx_ij + pAB=jac + idx*ABsz + Asz; // set pAB to point to B_ij + + for(ii=0; ii<mnp; ++ii) + pAB[ii*pnp+jj]=(phxx[ii]-phx[ii])*d; + } + } + } + } + + free(tmpd); +} + +typedef int (*PLS)(double *A, double *B, double *x, int m, int iscolmaj); + +/* Bundle adjustment on camera and structure parameters + * using the sparse Levenberg-Marquardt as described in HZ p. 568 + * + * Returns the number of iterations (>=0) if successfull, SBA_ERROR if failed + */ + +int sba_motstr_levmar_x( + const int n, /* number of points */ + const int ncon,/* number of points (starting from the 1st) whose parameters should not be modified. + * All B_ij (see below) with i<ncon are assumed to be zero + */ + const int m, /* number of images */ + const int mcon,/* number of images (starting from the 1st) whose parameters should not be modified. + * All A_ij (see below) with j<mcon are assumed to be zero + */ + char *vmask, /* visibility mask: vmask[i, j]=1 if point i visible in image j, 0 otherwise. nxm */ + double *p, /* initial parameter vector p0: (a1, ..., am, b1, ..., bn). + * aj are the image j parameters, bi are the i-th point parameters, + * size m*cnp + n*pnp + */ + const int cnp,/* number of parameters for ONE camera; e.g. 6 for Euclidean cameras */ + const int pnp,/* number of parameters for ONE point; e.g. 3 for Euclidean points */ + double *x, /* measurements vector: (x_11^T, .. x_1m^T, ..., x_n1^T, .. x_nm^T)^T where + * x_ij is the projection of the i-th point on the j-th image. + * NOTE: some of the x_ij might be missing, if point i is not visible in image j; + * see vmask[i, j], max. size n*m*mnp + */ + double *covx, /* measurements covariance matrices: (Sigma_x_11, .. Sigma_x_1m, ..., Sigma_x_n1, .. Sigma_x_nm), + * where Sigma_x_ij is the mnp x mnp covariance of x_ij stored row-by-row. Set to NULL if no + * covariance estimates are available (identity matrices are implicitly used in this case). + * NOTE: a certain Sigma_x_ij is missing if the corresponding x_ij is also missing; + * see vmask[i, j], max. size n*m*mnp*mnp + */ + const int mnp,/* number of parameters for EACH measurement; usually 2 */ + void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), + /* functional relation describing measurements. Given a parameter vector p, + * computes a prediction of the measurements \hat{x}. p is (m*cnp + n*pnp)x1, + * \hat{x} is (n*m*mnp)x1, maximum + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + */ + void (*fjac)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), + /* function to evaluate the sparse jacobian dX/dp. + * The Jacobian is returned in jac as + * (dx_11/da_1, ..., dx_1m/da_m, ..., dx_n1/da_1, ..., dx_nm/da_m, + * dx_11/db_1, ..., dx_1m/db_1, ..., dx_n1/db_n, ..., dx_nm/db_n), or (using HZ's notation), + * jac=(A_11, B_11, ..., A_1m, B_1m, ..., A_n1, B_n1, ..., A_nm, B_nm) + * Notice that depending on idxij, some of the A_ij and B_ij might be missing. + * Note also that A_ij and B_ij are mnp x cnp and mnp x pnp matrices resp. and they + * should be stored in jac in row-major order. + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + * + * If NULL, the jacobian is approximated by repetitive func calls and finite + * differences. This is computationally inefficient and thus NOT recommended. + */ + void *adata, /* pointer to possibly additional data, passed uninterpreted to func, fjac */ + + const int itmax, /* I: maximum number of iterations. itmax==0 signals jacobian verification followed by immediate return */ + const int verbose, /* I: verbosity */ + const double opts[SBA_OPTSSZ], + /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \epsilon4]. Respectively the scale factor for initial \mu, + * stopping thresholds for ||J^T e||_inf, ||dp||_2, ||e||_2 and (||e||_2-||e_new||_2)/||e||_2 + */ + double info[SBA_INFOSZ] + /* 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 - stopped by small relative reduction in ||e||_2 + * 5 - stopped by small ||e||_2 + * 6 - too many attempts to increase damping. Restart with increased mu + * 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]= # number of linear systems solved, i.e. number of attempts for reducing error + */ +) +{ +register int i, j, ii, jj, k, l; +int nvis, nnz, retval; + +/* The following are work arrays that are dynamically allocated by sba_motstr_levmar_x() */ +double *jac; /* work array for storing the jacobian, max. size n*m*(mnp*cnp + mnp*pnp) */ +double *U; /* work array for storing the U_j in the order U_1, ..., U_m, size m*cnp*cnp */ +double *V; /* work array for storing the *strictly upper triangles* of V_i in the order V_1, ..., V_n, size n*pnp*pnp. + * V also stores the lower triangles of (V*_i)^-1 in the order (V*_1)^-1, ..., (V*_n)^-1. + * Note that diagonal elements of V_1 are saved in diagUV + */ + +double *e; /* work array for storing the e_ij in the order e_11, ..., e_1m, ..., e_n1, ..., e_nm, + max. size n*m*mnp */ +double *eab; /* work array for storing the ea_j & eb_i in the order ea_1, .. ea_m eb_1, .. eb_n size m*cnp + n*pnp */ + +double *E; /* work array for storing the e_j in the order e_1, .. e_m, size m*cnp */ + +/* Notice that the blocks W_ij, Y_ij are zero iff A_ij (equivalently B_ij) is zero. This means + * that the matrix consisting of blocks W_ij is itself sparse, similarly to the + * block matrix made up of the A_ij and B_ij (i.e. jac) + */ +double *W; /* work array for storing the W_ij in the order W_11, ..., W_1m, ..., W_n1, ..., W_nm, + max. size n*m*cnp*pnp */ +double *Yj; /* work array for storing the Y_ij for a *fixed* j in the order Y_1j, Y_nj, + max. size n*cnp*pnp */ +double *YWt; /* work array for storing \sum_i Y_ij W_ik^T, size cnp*cnp */ +double *S; /* work array for storing the block array S_jk, size m*m*cnp*cnp */ +double *dp; /* work array for storing the parameter vector updates da_1, ..., da_m, db_1, ..., db_n, size m*cnp + n*pnp */ +double *Wtda; /* work array for storing \sum_j W_ij^T da_j, size pnp */ +double *wght= /* work array for storing the weights computed from the covariance inverses, max. size n*m*mnp*mnp */ + NULL; + +/* Of the above arrays, jac, e, W, Yj, wght are sparse and + * U, V, eab, E, S, dp are dense. Sparse arrays (except Yj) are indexed + * through idxij (see below), that is with the same mechanism as the input + * measurements vector x + */ + +double *pa, *pb, *ea, *eb, *dpa, *dpb; /* pointers into p, jac, eab and dp respectively */ + +/* submatrices sizes */ +int Asz, Bsz, ABsz, Usz, Vsz, + Wsz, Ysz, esz, easz, ebsz, + YWtsz, Wtdasz, Sblsz, covsz; + +int Sdim; /* S matrix actual dimension */ + +register double *ptr1, *ptr2, *ptr3, *ptr4, sum; +struct sba_crsm idxij; /* sparse matrix containing the location of x_ij in x. This is also + * the location of A_ij, B_ij in jac, etc. + * This matrix can be thought as a map from a sparse set of pairs (i, j) to a continuous + * index k and it is used to efficiently lookup the memory locations where the non-zero + * blocks of a sparse matrix/vector are stored + */ +int maxCvis, /* max. of projections of a single point across cameras, <=m */ + maxPvis, /* max. of projections in a single camera across points, <=n */ + maxCPvis, /* max. of the above */ + *rcidxs, /* work array for the indexes corresponding to the nonzero elements of a single row or + column in a sparse matrix, size max(n, m) */ + *rcsubs; /* work array for the subscripts of nonzero elements in a single row or column of a + sparse matrix, size max(n, m) */ + +/* The following variables are needed by the LM algorithm */ +register int itno; /* iteration counter */ +int issolved; +/* temporary work arrays that are dynamically allocated */ +double *hx, /* \hat{x}_i, max. size m*n*mnp */ + *diagUV, /* diagonals of U_j, V_i, size m*cnp + n*pnp */ + *pdp; /* p + dp, size m*cnp + n*pnp */ + +double *diagU, *diagV; /* pointers into diagUV */ + +register double mu, /* damping constant */ + tmp; /* mainly used in matrix & vector multiplications */ +double p_eL2, eab_inf, pdp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+dp)||_2 */ +double p_L2, dp_L2=DBL_MAX, dF, dL; +double tau=FABS(opts[0]), eps1=FABS(opts[1]), eps2=FABS(opts[2]), eps2_sq=opts[2]*opts[2], + eps3_sq=opts[3]*opts[3], eps4_sq=opts[4]*opts[4]; +double init_p_eL2; +int nu=2, nu2, stop=0, nfev, njev=0, nlss=0; +int nobs, nvars; +const int mmcon=m-mcon; +PLS linsolver=NULL; +int (*matinv)(double *A, int m)=NULL; + +struct fdj_data_x_ fdj_data; +void *jac_adata; + +/* Initialization */ + mu=eab_inf=0.0; /* -Wall */ + + /* block sizes */ + Asz=mnp * cnp; Bsz=mnp * pnp; ABsz=Asz + Bsz; + Usz=cnp * cnp; Vsz=pnp * pnp; + Wsz=cnp * pnp; Ysz=cnp * pnp; + esz=mnp; + easz=cnp; ebsz=pnp; + YWtsz=cnp * cnp; + Wtdasz=pnp; + Sblsz=cnp * cnp; + Sdim=mmcon * cnp; + covsz=mnp * mnp; + + /* count total number of visible image points */ + for(i=nvis=0, jj=n*m; i<jj; ++i) + nvis+=(vmask[i]!=0); + + nobs=nvis*mnp; + nvars=m*cnp + n*pnp; + if(nobs<nvars){ + fprintf(stderr, "SBA: sba_motstr_levmar_x() cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n", nobs, nvars); + return SBA_ERROR; + } + + /* allocate & fill up the idxij structure */ + sba_crsm_alloc(&idxij, n, m, nvis); + for(i=k=0; i<n; ++i){ + idxij.rowptr[i]=k; + ii=i*m; + for(j=0; j<m; ++j) + if(vmask[ii+j]){ + idxij.val[k]=k; + idxij.colidx[k++]=j; + } + } + idxij.rowptr[n]=nvis; + + /* find the maximum number (for all cameras) of visible image projections coming from a single 3D point */ + for(i=maxCvis=0; i<n; ++i) + if((k=idxij.rowptr[i+1]-idxij.rowptr[i])>maxCvis) maxCvis=k; + + /* find the maximum number (for all points) of visible image projections in any single camera */ + for(j=maxPvis=0; j<m; ++j){ + for(i=ii=0; i<n; ++i) + if(vmask[i*m+j]) ++ii; + if(ii>maxPvis) maxPvis=ii; + } + maxCPvis=(maxCvis>=maxPvis)? maxCvis : maxPvis; + +#if 0 + /* determine the density of blocks in matrix S */ + for(j=mcon, ii=0; j<m; ++j){ + ++ii; /* block Sjj is surely nonzero */ + for(k=j+1; k<m; ++k) + if(sba_crsm_common_row(&idxij, j, k)) ii+=2; /* blocks Sjk & Skj are nonzero */ + } + printf("\nS block density: %.5g\n", ((double)ii)/(mmcon*mmcon)); fflush(stdout); +#endif + + /* allocate work arrays */ + /* W is big enough to hold both jac & W. Note also the extra Wsz, see the initialization of jac below for explanation */ + W=(double *)emalloc((nvis*((Wsz>=ABsz)? Wsz : ABsz) + Wsz)*sizeof(double)); + U=(double *)emalloc(m*Usz*sizeof(double)); + V=(double *)emalloc(n*Vsz*sizeof(double)); + e=(double *)emalloc(nobs*sizeof(double)); + eab=(double *)emalloc(nvars*sizeof(double)); + E=(double *)emalloc(m*cnp*sizeof(double)); + Yj=(double *)emalloc(maxPvis*Ysz*sizeof(double)); + YWt=(double *)emalloc(YWtsz*sizeof(double)); + S=(double *)emalloc(m*m*Sblsz*sizeof(double)); + dp=(double *)emalloc(nvars*sizeof(double)); + Wtda=(double *)emalloc(pnp*sizeof(double)); + rcidxs=(int *)emalloc(maxCPvis*sizeof(int)); + rcsubs=(int *)emalloc(maxCPvis*sizeof(int)); +#ifndef SBA_DESTROY_COVS + if(covx!=NULL) wght=(double *)emalloc(nvis*covsz*sizeof(double)); +#else + if(covx!=NULL) wght=covx; +#endif /* SBA_DESTROY_COVS */ + + + hx=(double *)emalloc(nobs*sizeof(double)); + diagUV=(double *)emalloc(nvars*sizeof(double)); + pdp=(double *)emalloc(nvars*sizeof(double)); + + /* to save resources, W and jac share the same memory: First, the jacobian + * is computed in some working memory that is then overwritten during the + * computation of W. To account for the case of W being larger than jac, + * extra memory is reserved "before" jac. + * Care must be taken, however, to ensure that storing a certain W_ij + * does not overwrite the A_ij, B_ij used to compute it. To achieve + * this is, note that if p1 and p2 respectively point to the first elements + * of a certain W_ij and A_ij, B_ij pair, we should have p2-p1>=Wsz. + * There are two cases: + * a) Wsz>=ABsz: Then p1=W+k*Wsz and p2=jac+k*ABsz=W+Wsz+nvis*(Wsz-ABsz)+k*ABsz + * for some k (0<=k<nvis), thus p2-p1=(nvis-k)*(Wsz-ABsz)+Wsz. + * The right side of the last equation is obviously > Wsz for all 0<=k<nvis + * + * b) Wsz<ABsz: Then p1=W+k*Wsz and p2=jac+k*ABsz=W+Wsz+k*ABsz and + * p2-p1=Wsz+k*(ABsz-Wsz), which is again > Wsz for all 0<=k<nvis + * + * In conclusion, if jac is initialized as below, the memory allocated to all + * W_ij is guaranteed not to overlap with that allocated to their corresponding + * A_ij, B_ij pairs + */ + jac=W + Wsz + ((Wsz>ABsz)? nvis*(Wsz-ABsz) : 0); + + /* set up auxiliary pointers */ + pa=p; pb=p+m*cnp; + ea=eab; eb=eab+m*cnp; + dpa=dp; dpb=dp+m*cnp; + + diagU=diagUV; diagV=diagUV + m*cnp; + + /* if no jacobian function is supplied, prepare to compute jacobian with finite difference */ + if(!fjac){ + fdj_data.func=func; + fdj_data.cnp=cnp; + fdj_data.pnp=pnp; + fdj_data.mnp=mnp; + fdj_data.hx=hx; + fdj_data.hxx=(double *)emalloc(nobs*sizeof(double)); + fdj_data.func_rcidxs=(int *)emalloc(2*maxCPvis*sizeof(int)); + fdj_data.func_rcsubs=fdj_data.func_rcidxs+maxCPvis; + fdj_data.adata=adata; + + fjac=sba_fdjac_x; + jac_adata=(void *)&fdj_data; + } + else{ + fdj_data.hxx=NULL; + jac_adata=adata; + } + + if(itmax==0){ /* verify jacobian */ + sba_motstr_chkjac_x(func, fjac, p, &idxij, rcidxs, rcsubs, ncon, mcon, cnp, pnp, mnp, adata, jac_adata); + retval=0; + goto freemem_and_return; + } + + /* covariances Sigma_x_ij are accommodated by computing the Cholesky decompositions of their + * inverses and using the resulting matrices w_x_ij to weigh A_ij, B_ij, and e_ij as w_x_ij A_ij, + * w_x_ij*B_ij and w_x_ij*e_ij. In this way, auxiliary variables as U_j=\sum_i A_ij^T A_ij + * actually become \sum_i (w_x_ij A_ij)^T w_x_ij A_ij= \sum_i A_ij^T w_x_ij^T w_x_ij A_ij = + * A_ij^T Sigma_x_ij^-1 A_ij + * + * ea_j, V_i, eb_i, W_ij are weighted in a similar manner + */ + if(covx!=NULL){ + for(i=0; i<n; ++i){ + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero x_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr1, ptr2 to point to cov_x_ij, w_x_ij resp. */ + ptr1=covx + (k=idxij.val[rcidxs[j]]*covsz); + ptr2=wght + k; + if(!sba_mat_cholinv(ptr1, ptr2, mnp)){ /* compute w_x_ij s.t. w_x_ij^T w_x_ij = cov_x_ij^-1 */ + fprintf(stderr, "SBA: invalid covariance matrix for x_ij (i=%d, j=%d) in sba_motstr_levmar_x()\n", i, rcsubs[j]); + retval=SBA_ERROR; + goto freemem_and_return; + } + } + } + sba_mat_cholinv(NULL, NULL, 0); /* cleanup */ + } + + /* compute the error vectors e_ij in hx */ + (*func)(p, &idxij, rcidxs, rcsubs, hx, adata); nfev=1; + /* ### compute e=x - f(p) [e=w*(x - f(p)] and its L2 norm */ + if(covx==NULL) + p_eL2=nrmL2xmy(e, x, hx, nobs); /* e=x-hx, p_eL2=||e|| */ + else + p_eL2=nrmCxmy(e, x, hx, wght, mnp, nvis); /* e=wght*(x-hx), p_eL2=||e||=||x-hx||_Sigma^-1 */ + if(verbose) printf("initial motstr-SBA error %g [%g]\n", p_eL2, p_eL2/nvis); + init_p_eL2=p_eL2; + if(!SBA_FINITE(p_eL2)) stop=7; + + for(itno=0; itno<itmax && !stop; ++itno){ + /* Note that p, e and ||e||_2 have been updated at the previous iteration */ + + /* compute derivative submatrices A_ij, B_ij */ + (*fjac)(p, &idxij, rcidxs, rcsubs, jac, jac_adata); ++njev; + + if(covx!=NULL){ + /* compute w_x_ij A_ij and w_x_ij B_ij. + * Since w_x_ij is upper triangular, the products can be safely saved + * directly in A_ij, B_ij, without the need for intermediate storage + */ + for(i=0; i<nvis; ++i){ + /* set ptr1, ptr2, ptr3 to point to w_x_ij, A_ij, B_ij, resp. */ + ptr1=wght + i*covsz; + ptr2=jac + i*ABsz; + ptr3=ptr2 + Asz; // ptr3=jac + i*ABsz + Asz; + + /* w_x_ij is mnp x mnp, A_ij is mnp x cnp, B_ij is mnp x pnp + * NOTE: Jamming the outter (i.e., ii) loops did not run faster! + */ + /* A_ij */ + for(ii=0; ii<mnp; ++ii) + for(jj=0; jj<cnp; ++jj){ + for(k=ii, sum=0.0; k<mnp; ++k) // k>=ii since w_x_ij is upper triangular + sum+=ptr1[ii*mnp+k]*ptr2[k*cnp+jj]; + ptr2[ii*cnp+jj]=sum; + } + + /* B_ij */ + for(ii=0; ii<mnp; ++ii) + for(jj=0; jj<pnp; ++jj){ + for(k=ii, sum=0.0; k<mnp; ++k) // k>=ii since w_x_ij is upper triangular + sum+=ptr1[ii*mnp+k]*ptr3[k*pnp+jj]; + ptr3[ii*pnp+jj]=sum; + } + } + } + + /* compute U_j = \sum_i A_ij^T A_ij */ // \Sigma here! + /* U_j is symmetric, therefore its computation can be sped up by + * computing only the upper part and then reusing it for the lower one. + * Recall that A_ij is mnp x cnp + */ + /* Also compute ea_j = \sum_i A_ij^T e_ij */ // \Sigma here! + /* Recall that e_ij is mnp x 1 + */ + _dblzero(U, m*Usz); /* clear all U_j */ + _dblzero(ea, m*easz); /* clear all ea_j */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=ea + j*easz; // set ptr2 to point to ea_j + + nnz=sba_crsm_col_elmidxs(&idxij, j, rcidxs, rcsubs); /* find nonzero A_ij, i=0...n-1 */ + for(i=0; i<nnz; ++i){ + /* set ptr3 to point to A_ij, actual row number in rcsubs[i] */ + ptr3=jac + idxij.val[rcidxs[i]]*ABsz; + + /* compute the UPPER TRIANGULAR PART of A_ij^T A_ij and add it to U_j */ + for(ii=0; ii<cnp; ++ii){ + for(jj=ii; jj<cnp; ++jj){ + for(k=0, sum=0.0; k<mnp; ++k) + sum+=ptr3[k*cnp+ii]*ptr3[k*cnp+jj]; + ptr1[ii*cnp+jj]+=sum; + } + + /* copy the LOWER TRIANGULAR PART of U_j from the upper one */ + for(jj=0; jj<ii; ++jj) + ptr1[ii*cnp+jj]=ptr1[jj*cnp+ii]; + } + + ptr4=e + idxij.val[rcidxs[i]]*esz; /* set ptr4 to point to e_ij */ + /* compute A_ij^T e_ij and add it to ea_j */ + for(ii=0; ii<cnp; ++ii){ + for(jj=0, sum=0.0; jj<mnp; ++jj) + sum+=ptr3[jj*cnp+ii]*ptr4[jj]; + ptr2[ii]+=sum; + } + } + } + + /* compute V_i = \sum_j B_ij^T B_ij */ // \Sigma here! + /* V_i is symmetric, therefore its computation can be sped up by + * computing only the upper part and then reusing it for the lower one. + * Recall that B_ij is mnp x pnp + */ + /* Also compute eb_i = \sum_j B_ij^T e_ij */ // \Sigma here! + /* Recall that e_ij is mnp x 1 + */ + _dblzero(V, n*Vsz); /* clear all V_i */ + _dblzero(eb, n*ebsz); /* clear all eb_i */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=eb + i*ebsz; // set ptr2 to point to eb_i + + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero B_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr3 to point to B_ij, actual column number in rcsubs[j] */ + ptr3=jac + idxij.val[rcidxs[j]]*ABsz + Asz; + + /* compute the UPPER TRIANGULAR PART of B_ij^T B_ij and add it to V_i */ + for(ii=0; ii<pnp; ++ii){ + for(jj=ii; jj<pnp; ++jj){ + for(k=0, sum=0.0; k<mnp; ++k) + sum+=ptr3[k*pnp+ii]*ptr3[k*pnp+jj]; + ptr1[ii*pnp+jj]+=sum; + } + } + + ptr4=e + idxij.val[rcidxs[j]]*esz; /* set ptr4 to point to e_ij */ + /* compute B_ij^T e_ij and add it to eb_i */ + for(ii=0; ii<pnp; ++ii){ + for(jj=0, sum=0.0; jj<mnp; ++jj) + sum+=ptr3[jj*pnp+ii]*ptr4[jj]; + ptr2[ii]+=sum; + } + } + } + + /* compute W_ij = A_ij^T B_ij */ // \Sigma here! + /* Recall that A_ij is mnp x cnp and B_ij is mnp x pnp + */ + for(i=ncon; i<n; ++i){ + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero W_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr1 to point to W_ij, actual column number in rcsubs[j] */ + ptr1=W + idxij.val[rcidxs[j]]*Wsz; + + if(rcsubs[j]<mcon){ /* A_ij is zero */ + //_dblzero(ptr1, Wsz); /* clear W_ij */ + continue; + } + + /* set ptr2 & ptr3 to point to A_ij & B_ij resp. */ + ptr2=jac + idxij.val[rcidxs[j]]*ABsz; + ptr3=ptr2 + Asz; + /* compute A_ij^T B_ij and store it in W_ij + * Recall that storage for A_ij, B_ij does not overlap with that for W_ij, + * see the comments related to the initialization of jac above + */ + /* assert(ptr2-ptr1>=Wsz); */ + for(ii=0; ii<cnp; ++ii) + for(jj=0; jj<pnp; ++jj){ + for(k=0, sum=0.0; k<mnp; ++k) + sum+=ptr2[k*cnp+ii]*ptr3[k*pnp+jj]; + ptr1[ii*pnp+jj]=sum; + } + } + } + + /* Compute ||J^T e||_inf and ||p||^2 */ + for(i=0, p_L2=eab_inf=0.0; i<nvars; ++i){ + if(eab_inf < (tmp=FABS(eab[i]))) eab_inf=tmp; + p_L2+=p[i]*p[i]; + } + //p_L2=sqrt(p_L2); + + /* save diagonal entries so that augmentation can be later canceled. + * Diagonal entries are in U_j and V_i + */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr2[i]=ptr1[i*cnp+i]; + } + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr2[j]=ptr1[j*pnp+j]; + } + +/* +if(!(itno%100)){ + printf("Current estimate: "); + for(i=0; i<nvars; ++i) + printf("%.9g ", p[i]); + printf("-- errors %.9g %0.9g\n", eab_inf, p_eL2); +} +*/ + + /* check for convergence */ + if((eab_inf <= eps1)){ + dp_L2=0.0; /* no increment for p in this case */ + stop=1; + break; + } + + /* compute initial damping factor */ + if(itno==0){ + /* find max diagonal element */ + for(i=mcon*cnp, tmp=DBL_MIN; i<m*cnp; ++i) + if(diagUV[i]>tmp) tmp=diagUV[i]; + for(i=m*cnp + ncon*pnp; i<nvars; ++i) /* tmp is not re-initialized! */ + if(diagUV[i]>tmp) tmp=diagUV[i]; + mu=tau*tmp; + } + + /* determine increment using adaptive damping */ + while(1){ + /* augment U, V */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]+=mu; + } + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]+=mu; + + /* compute V*_i^-1. + * Recall that only the upper triangle of the symmetric pnp x pnp matrix V*_i + * is stored in ptr1; its (also symmetric) inverse is saved in the lower triangle of ptr1 + */ + /* inverting V*_i with LDLT seems to result in faster overall execution compared to when using LU or Cholesky */ + //j=sba_symat_invert_LU(ptr1, pnp); matinv=sba_symat_invert_LU; + //j=sba_symat_invert_Chol(ptr1, pnp); matinv=sba_symat_invert_Chol; + j=sba_symat_invert_BK(ptr1, pnp); matinv=sba_symat_invert_BK; + if(!j){ + fprintf(stderr, "SBA: singular matrix V*_i (i=%d) in sba_motstr_levmar_x(), increasing damping\n", i); + goto moredamping; // increasing damping will eventually make V*_i diagonally dominant, thus nonsingular + //retval=SBA_ERROR; + //goto freemem_and_return; + } + } + + _dblzero(E, m*easz); /* clear all e_j */ + /* compute the mmcon x mmcon block matrix S and e_j */ + + /* Note that S is symmetric, therefore its computation can be + * sped up by computing only the upper part and then reusing + * it for the lower one. + */ + for(j=mcon; j<m; ++j){ + int mmconxUsz=mmcon*Usz; + + nnz=sba_crsm_col_elmidxs(&idxij, j, rcidxs, rcsubs); /* find nonzero Y_ij, i=0...n-1 */ + + /* get rid of all Y_ij with i<ncon that are treated as zeros. + * In this way, all rcsubs[i] below are guaranteed to be >= ncon + */ + if(ncon){ + for(i=ii=0; i<nnz; ++i){ + if(rcsubs[i]>=ncon){ + rcidxs[ii]=rcidxs[i]; + rcsubs[ii++]=rcsubs[i]; + } + } + nnz=ii; + } + + /* compute all Y_ij = W_ij (V*_i)^-1 for a *fixed* j. + * To save memory, the block matrix consisting of the Y_ij + * is not stored. Instead, only a block column of this matrix + * is computed & used at each time: For each j, all nonzero + * Y_ij are computed in Yj and then used in the calculations + * involving S_jk and e_j. + * Recall that W_ij is cnp x pnp and (V*_i) is pnp x pnp + */ + for(i=0; i<nnz; ++i){ + /* set ptr3 to point to (V*_i)^-1, actual row number in rcsubs[i] */ + ptr3=V + rcsubs[i]*Vsz; + + /* set ptr1 to point to Y_ij, actual row number in rcsubs[i] */ + ptr1=Yj + i*Ysz; + /* set ptr2 to point to W_ij resp. */ + ptr2=W + idxij.val[rcidxs[i]]*Wsz; + /* compute W_ij (V*_i)^-1 and store it in Y_ij. + * Recall that only the lower triangle of (V*_i)^-1 is stored + */ + for(ii=0; ii<cnp; ++ii){ + ptr4=ptr2+ii*pnp; + for(jj=0; jj<pnp; ++jj){ + for(k=0, sum=0.0; k<=jj; ++k) + sum+=ptr4[k]*ptr3[jj*pnp+k]; //ptr2[ii*pnp+k]*ptr3[jj*pnp+k]; + for( ; k<pnp; ++k) + sum+=ptr4[k]*ptr3[k*pnp+jj]; //ptr2[ii*pnp+k]*ptr3[k*pnp+jj]; + ptr1[ii*pnp+jj]=sum; + } + } + } + + /* compute the UPPER TRIANGULAR PART of S */ + for(k=j; k<m; ++k){ // j>=mcon + /* compute \sum_i Y_ij W_ik^T in YWt. Note that for an off-diagonal block defined by j, k + * YWt (and thus S_jk) is nonzero only if there exists a point that is visible in both the + * j-th and k-th images + */ + + /* Recall that Y_ij is cnp x pnp and W_ik is cnp x pnp */ + _dblzero(YWt, YWtsz); /* clear YWt */ + + for(i=0; i<nnz; ++i){ + register double *pYWt; + + /* find the min and max column indices of the elements in row i (actually rcsubs[i]) + * and make sure that k falls within them. This test handles W_ik's which are + * certain to be zero without bothering to call sba_crsm_elmidx() + */ + ii=idxij.colidx[idxij.rowptr[rcsubs[i]]]; + jj=idxij.colidx[idxij.rowptr[rcsubs[i]+1]-1]; + if(k<ii || k>jj) continue; /* W_ik == 0 */ + + /* set ptr2 to point to W_ik */ + l=sba_crsm_elmidxp(&idxij, rcsubs[i], k, j, rcidxs[i]); + //l=sba_crsm_elmidx(&idxij, rcsubs[i], k); + if(l==-1) continue; /* W_ik == 0 */ + + ptr2=W + idxij.val[l]*Wsz; + /* set ptr1 to point to Y_ij, actual row number in rcsubs[i] */ + ptr1=Yj + i*Ysz; + for(ii=0; ii<cnp; ++ii){ + ptr3=ptr1+ii*pnp; + pYWt=YWt+ii*cnp; + + for(jj=0; jj<cnp; ++jj){ + ptr4=ptr2+jj*pnp; + for(l=0, sum=0.0; l<pnp; ++l) + sum+=ptr3[l]*ptr4[l]; //ptr1[ii*pnp+l]*ptr2[jj*pnp+l]; + pYWt[jj]+=sum; //YWt[ii*cnp+jj]+=sum; + } + } + } + + /* since the linear system involving S is solved with lapack, + * it is preferable to store S in column major (i.e. fortran) + * order, so as to avoid unecessary transposing/copying. + */ +#if MAT_STORAGE==COLUMN_MAJOR + ptr2=S + (k-mcon)*mmconxUsz + (j-mcon)*cnp; // set ptr2 to point to the beginning of block j,k in S +#else + ptr2=S + (j-mcon)*mmconxUsz + (k-mcon)*cnp; // set ptr2 to point to the beginning of block j,k in S +#endif + + if(j!=k){ /* Kronecker */ + for(ii=0; ii<cnp; ++ii, ptr2+=Sdim) + for(jj=0; jj<cnp; ++jj) + ptr2[jj]= +#if MAT_STORAGE==COLUMN_MAJOR + -YWt[jj*cnp+ii]; +#else + -YWt[ii*cnp+jj]; +#endif + } + else{ + ptr1=U + j*Usz; // set ptr1 to point to U_j + + for(ii=0; ii<cnp; ++ii, ptr2+=Sdim) + for(jj=0; jj<cnp; ++jj) + ptr2[jj]= +#if MAT_STORAGE==COLUMN_MAJOR + ptr1[jj*cnp+ii] - YWt[jj*cnp+ii]; +#else + ptr1[ii*cnp+jj] - YWt[ii*cnp+jj]; +#endif + } + } + + /* copy the LOWER TRIANGULAR PART of S from the upper one */ + for(k=mcon; k<j; ++k){ +#if MAT_STORAGE==COLUMN_MAJOR + ptr1=S + (k-mcon)*mmconxUsz + (j-mcon)*cnp; // set ptr1 to point to the beginning of block j,k in S + ptr2=S + (j-mcon)*mmconxUsz + (k-mcon)*cnp; // set ptr2 to point to the beginning of block k,j in S +#else + ptr1=S + (j-mcon)*mmconxUsz + (k-mcon)*cnp; // set ptr1 to point to the beginning of block j,k in S + ptr2=S + (k-mcon)*mmconxUsz + (j-mcon)*cnp; // set ptr2 to point to the beginning of block k,j in S +#endif + for(ii=0; ii<cnp; ++ii, ptr1+=Sdim) + for(jj=0, ptr3=ptr2+ii; jj<cnp; ++jj, ptr3+=Sdim) + ptr1[jj]=*ptr3; + } + + /* compute e_j=ea_j - \sum_i Y_ij eb_i */ + /* Recall that Y_ij is cnp x pnp and eb_i is pnp x 1 */ + ptr1=E + j*easz; // set ptr1 to point to e_j + + for(i=0; i<nnz; ++i){ + /* set ptr2 to point to Y_ij, actual row number in rcsubs[i] */ + ptr2=Yj + i*Ysz; + + /* set ptr3 to point to eb_i */ + ptr3=eb + rcsubs[i]*ebsz; + for(ii=0; ii<cnp; ++ii){ + ptr4=ptr2+ii*pnp; + for(jj=0, sum=0.0; jj<pnp; ++jj) + sum+=ptr4[jj]*ptr3[jj]; //ptr2[ii*pnp+jj]*ptr3[jj]; + ptr1[ii]+=sum; + } + } + + ptr2=ea + j*easz; // set ptr2 to point to ea_j + for(i=0; i<easz; ++i) + ptr1[i]=ptr2[i] - ptr1[i]; + } + +#if 0 + if(verbose>1){ /* count the nonzeros in S */ + for(i=ii=0; i<Sdim*Sdim; ++i) + if(S[i]!=0.0) ++ii; + printf("\nS density: %.5g\n", ((double)ii)/(Sdim*Sdim)); fflush(stdout); + } +#endif + + /* solve the linear system S dpa = E to compute the da_j. + * + * Note that if MAT_STORAGE==1 S is modified in the following call; + * this is OK since S is recomputed for each iteration + */ + //issolved=sba_Axb_LU(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_LU; + issolved=sba_Axb_Chol(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_Chol; + //issolved=sba_Axb_BK(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_BK; + //issolved=sba_Axb_QRnoQ(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_QRnoQ; + //issolved=sba_Axb_QR(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_QR; + //issolved=sba_Axb_SVD(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, MAT_STORAGE); linsolver=sba_Axb_SVD; + //issolved=sba_Axb_CG(S, E+mcon*cnp, dpa+mcon*cnp, Sdim, (3*Sdim)/2, 1E-10, SBA_CG_JACOBI, MAT_STORAGE); linsolver=(PLS)sba_Axb_CG; + + ++nlss; + + _dblzero(dpa, mcon*cnp); /* no change for the first mcon camera params */ + + if(issolved){ + + /* compute the db_i */ + for(i=ncon; i<n; ++i){ + ptr1=dpb + i*ebsz; // set ptr1 to point to db_i + + /* compute \sum_j W_ij^T da_j */ + /* Recall that W_ij is cnp x pnp and da_j is cnp x 1 */ + _dblzero(Wtda, Wtdasz); /* clear Wtda */ + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero W_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr2 to point to W_ij, actual column number in rcsubs[j] */ + if(rcsubs[j]<mcon) continue; /* W_ij is zero */ + + ptr2=W + idxij.val[rcidxs[j]]*Wsz; + + /* set ptr3 to point to da_j */ + ptr3=dpa + rcsubs[j]*cnp; + + for(ii=0; ii<pnp; ++ii){ + ptr4=ptr2+ii; + for(jj=0, sum=0.0; jj<cnp; ++jj) + sum+=ptr4[jj*pnp]*ptr3[jj]; //ptr2[jj*pnp+ii]*ptr3[jj]; + Wtda[ii]+=sum; + } + } + + /* compute eb_i - \sum_j W_ij^T da_j = eb_i - Wtda in Wtda */ + ptr2=eb + i*ebsz; // set ptr2 to point to eb_i + for(ii=0; ii<pnp; ++ii) + Wtda[ii]=ptr2[ii] - Wtda[ii]; + + /* compute the product (V*_i)^-1 Wtda = (V*_i)^-1 (eb_i - \sum_j W_ij^T da_j). + * Recall that only the lower triangle of (V*_i)^-1 is stored + */ + ptr2=V + i*Vsz; // set ptr2 to point to (V*_i)^-1 + for(ii=0; ii<pnp; ++ii){ + for(jj=0, sum=0.0; jj<=ii; ++jj) + sum+=ptr2[ii*pnp+jj]*Wtda[jj]; + for( ; jj<pnp; ++jj) + sum+=ptr2[jj*pnp+ii]*Wtda[jj]; + ptr1[ii]=sum; + } + } + _dblzero(dpb, ncon*pnp); /* no change for the first ncon point params */ + + /* parameter vector updates are now in dpa, dpb */ + + /* compute p's new estimate and ||dp||^2 */ + for(i=0, dp_L2=0.0; i<nvars; ++i){ + pdp[i]=p[i] + (tmp=dp[i]); + dp_L2+=tmp*tmp; + } + //dp_L2=sqrt(dp_L2); + + if(dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */ + //if(dp_L2<=eps2*(p_L2 + eps2)){ /* relative change in p is small, stop */ + stop=2; + break; + } + + if(dp_L2>=(p_L2+eps2)/SBA_EPSILON_SQ){ /* almost singular */ + //if(dp_L2>=(p_L2+eps2)/SBA_EPSILON){ /* almost singular */ + fprintf(stderr, "SBA: the matrix of the augmented normal equations is almost singular in sba_motstr_levmar_x(),\n" + " minimization should be restarted from the current solution with an increased damping term\n"); + retval=SBA_ERROR; + goto freemem_and_return; + } + + (*func)(pdp, &idxij, rcidxs, rcsubs, hx, adata); ++nfev; /* evaluate function at p + dp */ + if(verbose>1) + printf("mean reprojection error %g\n", sba_mean_repr_error(n, mnp, x, hx, &idxij, rcidxs, rcsubs)); + /* ### compute ||e(pdp)||_2 */ + if(covx==NULL) + pdp_eL2=nrmL2xmy(hx, x, hx, nobs); /* hx=x-hx, pdp_eL2=||hx|| */ + else + pdp_eL2=nrmCxmy(hx, x, hx, wght, mnp, nvis); /* hx=wght*(x-hx), pdp_eL2=||hx|| */ + if(!SBA_FINITE(pdp_eL2)){ + if(verbose) /* identify the offending point projection */ + sba_print_inf(hx, m, mnp, &idxij, rcidxs, rcsubs); + + stop=7; + break; + } + + for(i=0, dL=0.0; i<nvars; ++i) + dL+=dp[i]*(mu*dp[i]+eab[i]); + + dF=p_eL2-pdp_eL2; + + if(verbose>1) + printf("\ndamping term %8g, gain ratio %8g, errors %8g / %8g = %g\n", mu, dL!=0.0? dF/dL : dF/DBL_EPSILON, p_eL2/nvis, pdp_eL2/nvis, p_eL2/pdp_eL2); + + if(dL>0.0 && dF>0.0){ /* reduction in error, increment is accepted */ + tmp=(2.0*dF/dL-1.0); + tmp=1.0-tmp*tmp*tmp; + mu=mu*( (tmp>=SBA_ONE_THIRD)? tmp : SBA_ONE_THIRD ); + nu=2; + + /* the test below is equivalent to the relative reduction of the RMS reprojection error: sqrt(p_eL2)-sqrt(pdp_eL2)<eps4*sqrt(p_eL2) */ + if(pdp_eL2-2.0*sqrt(p_eL2*pdp_eL2)<(eps4_sq-1.0)*p_eL2) stop=4; + + for(i=0; i<nvars; ++i) /* update p's estimate */ + p[i]=pdp[i]; + + for(i=0; i<nobs; ++i) /* update e and ||e||_2 */ + e[i]=hx[i]; + p_eL2=pdp_eL2; + break; + } + } /* issolved */ + +moredamping: + /* if this point is reached (also via an explicit goto!), either the linear system could + * not be solved or the error did not reduce; in any case, the increment must be rejected + */ + + mu*=nu; + nu2=nu<<1; // 2*nu; + if(nu2<=nu){ /* nu has wrapped around (overflown) */ + fprintf(stderr, "SBA: too many failed attempts to increase the damping factor in sba_motstr_levmar_x()! Singular Hessian matrix?\n"); + //exit(1); + stop=6; + break; + } + nu=nu2; + +#if 0 + /* restore U, V diagonal entries */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]=ptr2[i]; + } + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]=ptr2[j]; + } +#endif + } /* inner while loop */ + + if(p_eL2<=eps3_sq) stop=5; // error is small, force termination of outer loop + } + + if(itno>=itmax) stop=3; + + /* restore U, V diagonal entries */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]=ptr2[i]; + } + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]=ptr2[j]; + } + + if(info){ + info[0]=init_p_eL2; + info[1]=p_eL2; + info[2]=eab_inf; + info[3]=dp_L2; + for(j=mcon, tmp=DBL_MIN; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + for(i=0; i<cnp; ++i) + if(tmp<ptr1[i*cnp+i]) tmp=ptr1[i*cnp+i]; + } + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + for(j=0; j<pnp; ++j) + if(tmp<ptr1[j*pnp+j]) tmp=ptr1[j*pnp+j]; + } + info[4]=mu/tmp; + info[5]=itno; + info[6]=stop; + info[7]=nfev; + info[8]=njev; + info[9]=nlss; + } + + //sba_print_sol(n, m, p, cnp, pnp, x, mnp, &idxij, rcidxs, rcsubs); + retval=(stop!=7)? itno : SBA_ERROR; + +freemem_and_return: /* NOTE: this point is also reached via a goto! */ + + /* free whatever was allocated */ + free(W); free(U); free(V); + free(e); free(eab); + free(E); free(Yj); free(YWt); + free(S); free(dp); free(Wtda); + free(rcidxs); free(rcsubs); +#ifndef SBA_DESTROY_COVS + if(wght) free(wght); +#else + /* nothing to do */ +#endif /* SBA_DESTROY_COVS */ + + free(hx); free(diagUV); free(pdp); + if(fdj_data.hxx){ // cleanup + free(fdj_data.hxx); + free(fdj_data.func_rcidxs); + } + + sba_crsm_free(&idxij); + + /* free the memory allocated by the matrix inversion & linear solver routines */ + if(matinv) (*matinv)(NULL, 0); + if(linsolver) (*linsolver)(NULL, NULL, NULL, 0, 0); + + return retval; +} + + +/* Bundle adjustment on camera parameters only + * using the sparse Levenberg-Marquardt as described in HZ p. 568 + * + * Returns the number of iterations (>=0) if successfull, SBA_ERROR if failed + */ + +int sba_mot_levmar_x( + const int n, /* number of points */ + const int m, /* number of images */ + const int mcon,/* number of images (starting from the 1st) whose parameters should not be modified. + * All A_ij (see below) with j<mcon are assumed to be zero + */ + char *vmask, /* visibility mask: vmask[i, j]=1 if point i visible in image j, 0 otherwise. nxm */ + double *p, /* initial parameter vector p0: (a1, ..., am). + * aj are the image j parameters, size m*cnp */ + const int cnp,/* number of parameters for ONE camera; e.g. 6 for Euclidean cameras */ + double *x, /* measurements vector: (x_11^T, .. x_1m^T, ..., x_n1^T, .. x_nm^T)^T where + * x_ij is the projection of the i-th point on the j-th image. + * NOTE: some of the x_ij might be missing, if point i is not visible in image j; + * see vmask[i, j], max. size n*m*mnp + */ + double *covx, /* measurements covariance matrices: (Sigma_x_11, .. Sigma_x_1m, ..., Sigma_x_n1, .. Sigma_x_nm), + * where Sigma_x_ij is the mnp x mnp covariance of x_ij stored row-by-row. Set to NULL if no + * covariance estimates are available (identity matrices are implicitly used in this case). + * NOTE: a certain Sigma_x_ij is missing if the corresponding x_ij is also missing; + * see vmask[i, j], max. size n*m*mnp*mnp + */ + const int mnp,/* number of parameters for EACH measurement; usually 2 */ + void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), + /* functional relation describing measurements. Given a parameter vector p, + * computes a prediction of the measurements \hat{x}. p is (m*cnp)x1, + * \hat{x} is (n*m*mnp)x1, maximum + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + */ + void (*fjac)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), + /* function to evaluate the sparse jacobian dX/dp. + * The Jacobian is returned in jac as + * (dx_11/da_1, ..., dx_1m/da_m, ..., dx_n1/da_1, ..., dx_nm/da_m), or (using HZ's notation), + * jac=(A_11, ..., A_1m, ..., A_n1, ..., A_nm) + * Notice that depending on idxij, some of the A_ij might be missing. + * Note also that the A_ij are mnp x cnp matrices and they + * should be stored in jac in row-major order. + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + * + * If NULL, the jacobian is approximated by repetitive func calls and finite + * differences. This is computationally inefficient and thus NOT recommended. + */ + void *adata, /* pointer to possibly additional data, passed uninterpreted to func, fjac */ + + const int itmax, /* I: maximum number of iterations. itmax==0 signals jacobian verification followed by immediate return */ + const int verbose, /* I: verbosity */ + const double opts[SBA_OPTSSZ], + /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \epsilon4]. Respectively the scale factor for initial \mu, + * stopping thresholds for ||J^T e||_inf, ||dp||_2, ||e||_2 and (||e||_2-||e_new||_2)/||e||_2 + */ + double info[SBA_INFOSZ] + /* 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 - stopped by small relative reduction in ||e||_2 + * 5 - stopped by small ||e||_2 + * 6 - too many attempts to increase damping. Restart with increased mu + * 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]= # number of linear systems solved, i.e. number of attempts for reducing error + */ +) +{ +register int i, j, ii, jj, k; +int nvis, nnz, retval; + +/* The following are work arrays that are dynamically allocated by sba_mot_levmar_x() */ +double *jac; /* work array for storing the jacobian, max. size n*m*mnp*cnp */ +double *U; /* work array for storing the U_j in the order U_1, ..., U_m, size m*cnp*cnp */ + +double *e; /* work array for storing the e_ij in the order e_11, ..., e_1m, ..., e_n1, ..., e_nm, + max. size n*m*mnp */ +double *ea; /* work array for storing the ea_j in the order ea_1, .. ea_m, size m*cnp */ + +double *dp; /* work array for storing the parameter vector updates da_1, ..., da_m, size m*cnp */ + +double *wght= /* work array for storing the weights computed from the covariance inverses, max. size n*m*mnp*mnp */ + NULL; + +/* Of the above arrays, jac, e, wght are sparse and + * U, ea, dp are dense. Sparse arrays are indexed through + * idxij (see below), that is with the same mechanism as the input + * measurements vector x + */ + +/* submatrices sizes */ +int Asz, Usz, + esz, easz, covsz; + +register double *ptr1, *ptr2, *ptr3, *ptr4, sum; +struct sba_crsm idxij; /* sparse matrix containing the location of x_ij in x. This is also the location of A_ij + * in jac, e_ij in e, etc. + * This matrix can be thought as a map from a sparse set of pairs (i, j) to a continuous + * index k and it is used to efficiently lookup the memory locations where the non-zero + * blocks of a sparse matrix/vector are stored + */ +int maxCPvis, /* max. of projections across cameras & projections across points */ + *rcidxs, /* work array for the indexes corresponding to the nonzero elements of a single row or + column in a sparse matrix, size max(n, m) */ + *rcsubs; /* work array for the subscripts of nonzero elements in a single row or column of a + sparse matrix, size max(n, m) */ + +/* The following variables are needed by the LM algorithm */ +register int itno; /* iteration counter */ +int nsolved; +/* temporary work arrays that are dynamically allocated */ +double *hx, /* \hat{x}_i, max. size m*n*mnp */ + *diagU, /* diagonals of U_j, size m*cnp */ + *pdp; /* p + dp, size m*cnp */ + +register double mu, /* damping constant */ + tmp; /* mainly used in matrix & vector multiplications */ +double p_eL2, ea_inf, pdp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+dp)||_2 */ +double p_L2, dp_L2=DBL_MAX, dF, dL; +double tau=FABS(opts[0]), eps1=FABS(opts[1]), eps2=FABS(opts[2]), eps2_sq=opts[2]*opts[2], + eps3_sq=opts[3]*opts[3], eps4_sq=opts[4]*opts[4]; +double init_p_eL2; +int nu=2, nu2, stop=0, nfev, njev=0, nlss=0; +int nobs, nvars; +PLS linsolver=NULL; + +struct fdj_data_x_ fdj_data; +void *jac_adata; + +/* Initialization */ + mu=ea_inf=0.0; /* -Wall */ + + /* block sizes */ + Asz=mnp * cnp; Usz=cnp * cnp; + esz=mnp; easz=cnp; + covsz=mnp * mnp; + + /* count total number of visible image points */ + for(i=nvis=0, jj=n*m; i<jj; ++i) + nvis+=(vmask[i]!=0); + + nobs=nvis*mnp; + nvars=m*cnp; + if(nobs<nvars){ + fprintf(stderr, "SBA: sba_mot_levmar_x() cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n", nobs, nvars); + return SBA_ERROR; + } + + /* allocate & fill up the idxij structure */ + sba_crsm_alloc(&idxij, n, m, nvis); + for(i=k=0; i<n; ++i){ + idxij.rowptr[i]=k; + ii=i*m; + for(j=0; j<m; ++j) + if(vmask[ii+j]){ + idxij.val[k]=k; + idxij.colidx[k++]=j; + } + } + idxij.rowptr[n]=nvis; + + /* find the maximum number of visible image points in any single camera or coming from a single 3D point */ + /* cameras */ + for(i=maxCPvis=0; i<n; ++i) + if((k=idxij.rowptr[i+1]-idxij.rowptr[i])>maxCPvis) maxCPvis=k; + + /* points, note that maxCPvis is not reinitialized! */ + for(j=0; j<m; ++j){ + for(i=ii=0; i<n; ++i) + if(vmask[i*m+j]) ++ii; + if(ii>maxCPvis) maxCPvis=ii; + } + + /* allocate work arrays */ + jac=(double *)emalloc(nvis*Asz*sizeof(double)); + U=(double *)emalloc(m*Usz*sizeof(double)); + e=(double *)emalloc(nobs*sizeof(double)); + ea=(double *)emalloc(nvars*sizeof(double)); + dp=(double *)emalloc(nvars*sizeof(double)); + rcidxs=(int *)emalloc(maxCPvis*sizeof(int)); + rcsubs=(int *)emalloc(maxCPvis*sizeof(int)); +#ifndef SBA_DESTROY_COVS + if(covx!=NULL) wght=(double *)emalloc(nvis*covsz*sizeof(double)); +#else + if(covx!=NULL) wght=covx; +#endif /* SBA_DESTROY_COVS */ + + + hx=(double *)emalloc(nobs*sizeof(double)); + diagU=(double *)emalloc(nvars*sizeof(double)); + pdp=(double *)emalloc(nvars*sizeof(double)); + + /* if no jacobian function is supplied, prepare to compute jacobian with finite difference */ + if(!fjac){ + fdj_data.func=func; + fdj_data.cnp=cnp; + fdj_data.pnp=0; + fdj_data.mnp=mnp; + fdj_data.hx=hx; + fdj_data.hxx=(double *)emalloc(nobs*sizeof(double)); + fdj_data.func_rcidxs=(int *)emalloc(2*maxCPvis*sizeof(int)); + fdj_data.func_rcsubs=fdj_data.func_rcidxs+maxCPvis; + fdj_data.adata=adata; + + fjac=sba_fdjac_x; + jac_adata=(void *)&fdj_data; + } + else{ + fdj_data.hxx=NULL; + jac_adata=adata; + } + + if(itmax==0){ /* verify jacobian */ + sba_mot_chkjac_x(func, fjac, p, &idxij, rcidxs, rcsubs, mcon, cnp, mnp, adata, jac_adata); + retval=0; + goto freemem_and_return; + } + + /* covariances Sigma_x_ij are accommodated by computing the Cholesky decompositions of their + * inverses and using the resulting matrices w_x_ij to weigh A_ij and e_ij as w_x_ij A_ij + * and w_x_ij*e_ij. In this way, auxiliary variables as U_j=\sum_i A_ij^T A_ij + * actually become \sum_i (w_x_ij A_ij)^T w_x_ij A_ij= \sum_i A_ij^T w_x_ij^T w_x_ij A_ij = + * A_ij^T Sigma_x_ij^-1 A_ij + * + * ea_j are weighted in a similar manner + */ + if(covx!=NULL){ + for(i=0; i<n; ++i){ + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero x_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr1, ptr2 to point to cov_x_ij, w_x_ij resp. */ + ptr1=covx + (k=idxij.val[rcidxs[j]]*covsz); + ptr2=wght + k; + if(!sba_mat_cholinv(ptr1, ptr2, mnp)){ /* compute w_x_ij s.t. w_x_ij^T w_x_ij = cov_x_ij^-1 */ + fprintf(stderr, "SBA: invalid covariance matrix for x_ij (i=%d, j=%d) in sba_motstr_levmar_x()\n", i, rcsubs[j]); + retval=SBA_ERROR; + goto freemem_and_return; + } + } + } + sba_mat_cholinv(NULL, NULL, 0); /* cleanup */ + } + + /* compute the error vectors e_ij in hx */ + (*func)(p, &idxij, rcidxs, rcsubs, hx, adata); nfev=1; + /* ### compute e=x - f(p) [e=w*(x - f(p)] and its L2 norm */ + if(covx==NULL) + p_eL2=nrmL2xmy(e, x, hx, nobs); /* e=x-hx, p_eL2=||e|| */ + else + p_eL2=nrmCxmy(e, x, hx, wght, mnp, nvis); /* e=wght*(x-hx), p_eL2=||e||=||x-hx||_Sigma^-1 */ + if(verbose) printf("initial mot-SBA error %g [%g]\n", p_eL2, p_eL2/nvis); + init_p_eL2=p_eL2; + if(!SBA_FINITE(p_eL2)) stop=7; + + for(itno=0; itno<itmax && !stop; ++itno){ + /* Note that p, e and ||e||_2 have been updated at the previous iteration */ + + /* compute derivative submatrices A_ij */ + (*fjac)(p, &idxij, rcidxs, rcsubs, jac, jac_adata); ++njev; + + if(covx!=NULL){ + /* compute w_x_ij A_ij + * Since w_x_ij is upper triangular, the products can be safely saved + * directly in A_ij, without the need for intermediate storage + */ + for(i=0; i<nvis; ++i){ + /* set ptr1, ptr2 to point to w_x_ij, A_ij, resp. */ + ptr1=wght + i*covsz; + ptr2=jac + i*Asz; + + /* w_x_ij is mnp x mnp, A_ij is mnp x cnp */ + for(ii=0; ii<mnp; ++ii) + for(jj=0; jj<cnp; ++jj){ + for(k=ii, sum=0.0; k<mnp; ++k) // k>=ii since w_x_ij is upper triangular + sum+=ptr1[ii*mnp+k]*ptr2[k*cnp+jj]; + ptr2[ii*cnp+jj]=sum; + } + } + } + + /* compute U_j = \sum_i A_ij^T A_ij */ // \Sigma here! + /* U_j is symmetric, therefore its computation can be sped up by + * computing only the upper part and then reusing it for the lower one. + * Recall that A_ij is mnp x cnp + */ + /* Also compute ea_j = \sum_i A_ij^T e_ij */ // \Sigma here! + /* Recall that e_ij is mnp x 1 + */ + _dblzero(U, m*Usz); /* clear all U_j */ + _dblzero(ea, m*easz); /* clear all ea_j */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=ea + j*easz; // set ptr2 to point to ea_j + + nnz=sba_crsm_col_elmidxs(&idxij, j, rcidxs, rcsubs); /* find nonzero A_ij, i=0...n-1 */ + for(i=0; i<nnz; ++i){ + /* set ptr3 to point to A_ij, actual row number in rcsubs[i] */ + ptr3=jac + idxij.val[rcidxs[i]]*Asz; + + /* compute the UPPER TRIANGULAR PART of A_ij^T A_ij and add it to U_j */ + for(ii=0; ii<cnp; ++ii){ + for(jj=ii; jj<cnp; ++jj){ + for(k=0, sum=0.0; k<mnp; ++k) + sum+=ptr3[k*cnp+ii]*ptr3[k*cnp+jj]; + ptr1[ii*cnp+jj]+=sum; + } + + /* copy the LOWER TRIANGULAR PART of U_j from the upper one */ + for(jj=0; jj<ii; ++jj) + ptr1[ii*cnp+jj]=ptr1[jj*cnp+ii]; + } + + ptr4=e + idxij.val[rcidxs[i]]*esz; /* set ptr4 to point to e_ij */ + /* compute A_ij^T e_ij and add it to ea_j */ + for(ii=0; ii<cnp; ++ii){ + for(jj=0, sum=0.0; jj<mnp; ++jj) + sum+=ptr3[jj*cnp+ii]*ptr4[jj]; + ptr2[ii]+=sum; + } + } + } + + /* Compute ||J^T e||_inf and ||p||^2 */ + for(i=0, p_L2=ea_inf=0.0; i<nvars; ++i){ + if(ea_inf < (tmp=FABS(ea[i]))) ea_inf=tmp; + p_L2+=p[i]*p[i]; + } + //p_L2=sqrt(p_L2); + + /* save diagonal entries so that augmentation can be later canceled. + * Diagonal entries are in U_j + */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr2[i]=ptr1[i*cnp+i]; + } + +/* +if(!(itno%100)){ + printf("Current estimate: "); + for(i=0; i<nvars; ++i) + printf("%.9g ", p[i]); + printf("-- errors %.9g %0.9g\n", ea_inf, p_eL2); +} +*/ + + /* check for convergence */ + if((ea_inf <= eps1)){ + dp_L2=0.0; /* no increment for p in this case */ + stop=1; + break; + } + + /* compute initial damping factor */ + if(itno==0){ + for(i=mcon*cnp, tmp=DBL_MIN; i<nvars; ++i) + if(diagU[i]>tmp) tmp=diagU[i]; /* find max diagonal element */ + mu=tau*tmp; + } + + /* determine increment using adaptive damping */ + while(1){ + /* augment U */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]+=mu; + } + + /* solve the linear systems U_j da_j = ea_j to compute the da_j */ + _dblzero(dp, mcon*cnp); /* no change for the first mcon camera params */ + for(j=nsolved=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=ea + j*easz; // set ptr2 to point to ea_j + ptr3=dp + j*cnp; // set ptr3 to point to da_j + + //nsolved+=sba_Axb_LU(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_LU; + nsolved+=sba_Axb_Chol(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_Chol; + //nsolved+=sba_Axb_BK(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_BK; + //nsolved+=sba_Axb_QRnoQ(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_QRnoQ; + //nsolved+=sba_Axb_QR(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_QR; + //nsolved+=sba_Axb_SVD(ptr1, ptr2, ptr3, cnp, 0); linsolver=sba_Axb_SVD; + //nsolved+=(sba_Axb_CG(ptr1, ptr2, ptr3, cnp, (3*cnp)/2, 1E-10, SBA_CG_JACOBI, 0) > 0); linsolver=(PLS)sba_Axb_CG; + + ++nlss; + } + + if(nsolved==m){ + + /* parameter vector updates are now in dp */ + + /* compute p's new estimate and ||dp||^2 */ + for(i=0, dp_L2=0.0; i<nvars; ++i){ + pdp[i]=p[i] + (tmp=dp[i]); + dp_L2+=tmp*tmp; + } + //dp_L2=sqrt(dp_L2); + + if(dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */ + //if(dp_L2<=eps2*(p_L2 + eps2)){ /* relative change in p is small, stop */ + stop=2; + break; + } + + if(dp_L2>=(p_L2+eps2)/SBA_EPSILON_SQ){ /* almost singular */ + //if(dp_L2>=(p_L2+eps2)/SBA_EPSILON){ /* almost singular */ + fprintf(stderr, "SBA: the matrix of the augmented normal equations is almost singular in sba_mot_levmar_x(),\n" + " minimization should be restarted from the current solution with an increased damping term\n"); + retval=SBA_ERROR; + goto freemem_and_return; + } + + (*func)(pdp, &idxij, rcidxs, rcsubs, hx, adata); ++nfev; /* evaluate function at p + dp */ + if(verbose>1) + printf("mean reprojection error %g\n", sba_mean_repr_error(n, mnp, x, hx, &idxij, rcidxs, rcsubs)); + /* ### compute ||e(pdp)||_2 */ + if(covx==NULL) + pdp_eL2=nrmL2xmy(hx, x, hx, nobs); /* hx=x-hx, pdp_eL2=||hx|| */ + else + pdp_eL2=nrmCxmy(hx, x, hx, wght, mnp, nvis); /* hx=wght*(x-hx), pdp_eL2=||hx|| */ + if(!SBA_FINITE(pdp_eL2)){ + if(verbose) /* identify the offending point projection */ + sba_print_inf(hx, m, mnp, &idxij, rcidxs, rcsubs); + + stop=7; + break; + } + + for(i=0, dL=0.0; i<nvars; ++i) + dL+=dp[i]*(mu*dp[i]+ea[i]); + + dF=p_eL2-pdp_eL2; + + if(verbose>1) + printf("\ndamping term %8g, gain ratio %8g, errors %8g / %8g = %g\n", mu, dL!=0.0? dF/dL : dF/DBL_EPSILON, p_eL2/nvis, pdp_eL2/nvis, p_eL2/pdp_eL2); + + if(dL>0.0 && dF>0.0){ /* reduction in error, increment is accepted */ + tmp=(2.0*dF/dL-1.0); + tmp=1.0-tmp*tmp*tmp; + mu=mu*( (tmp>=SBA_ONE_THIRD)? tmp : SBA_ONE_THIRD ); + nu=2; + + /* the test below is equivalent to the relative reduction of the RMS reprojection error: sqrt(p_eL2)-sqrt(pdp_eL2)<eps4*sqrt(p_eL2) */ + if(pdp_eL2-2.0*sqrt(p_eL2*pdp_eL2)<(eps4_sq-1.0)*p_eL2) stop=4; + + for(i=0; i<nvars; ++i) /* update p's estimate */ + p[i]=pdp[i]; + + for(i=0; i<nobs; ++i) /* update e and ||e||_2 */ + e[i]=hx[i]; + p_eL2=pdp_eL2; + break; + } + } /* nsolved==m */ + + /* if this point is reached, either at least one linear system could not be solved or + * the error did not reduce; in any case, the increment must be rejected + */ + + mu*=nu; + nu2=nu<<1; // 2*nu; + if(nu2<=nu){ /* nu has wrapped around (overflown) */ + fprintf(stderr, "SBA: too many failed attempts to increase the damping factor in sba_mot_levmar_x()! Singular Hessian matrix?\n"); + //exit(1); + stop=6; + break; + } + nu=nu2; + +#if 0 + /* restore U diagonal entries */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]=ptr2[i]; + } +#endif + } /* inner while loop */ + + if(p_eL2<=eps3_sq) stop=5; // error is small, force termination of outer loop + } + + if(itno>=itmax) stop=3; + + /* restore U diagonal entries */ + for(j=mcon; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + ptr2=diagU + j*cnp; // set ptr2 to point to diagU_j + for(i=0; i<cnp; ++i) + ptr1[i*cnp+i]=ptr2[i]; + } + + if(info){ + info[0]=init_p_eL2; + info[1]=p_eL2; + info[2]=ea_inf; + info[3]=dp_L2; + for(j=mcon, tmp=DBL_MIN; j<m; ++j){ + ptr1=U + j*Usz; // set ptr1 to point to U_j + for(i=0; i<cnp; ++i) + if(tmp<ptr1[i*cnp+i]) tmp=ptr1[i*cnp+i]; + } + info[4]=mu/tmp; + info[5]=itno; + info[6]=stop; + info[7]=nfev; + info[8]=njev; + info[9]=nlss; + } + //sba_print_sol(n, m, p, cnp, 0, x, mnp, &idxij, rcidxs, rcsubs); + retval=(stop!=7)? itno : SBA_ERROR; + +freemem_and_return: /* NOTE: this point is also reached via a goto! */ + + /* free whatever was allocated */ + free(jac); free(U); + free(e); free(ea); + free(dp); + free(rcidxs); free(rcsubs); +#ifndef SBA_DESTROY_COVS + if(wght) free(wght); +#else + /* nothing to do */ +#endif /* SBA_DESTROY_COVS */ + + free(hx); free(diagU); free(pdp); + if(fdj_data.hxx){ // cleanup + free(fdj_data.hxx); + free(fdj_data.func_rcidxs); + } + + sba_crsm_free(&idxij); + + /* free the memory allocated by the linear solver routine */ + if(linsolver) (*linsolver)(NULL, NULL, NULL, 0, 0); + + return retval; +} + + +/* Bundle adjustment on structure parameters only + * using the sparse Levenberg-Marquardt as described in HZ p. 568 + * + * Returns the number of iterations (>=0) if successfull, SBA_ERROR if failed + */ + +int sba_str_levmar_x( + const int n, /* number of points */ + const int ncon,/* number of points (starting from the 1st) whose parameters should not be modified. + * All B_ij (see below) with i<ncon are assumed to be zero + */ + const int m, /* number of images */ + char *vmask, /* visibility mask: vmask[i, j]=1 if point i visible in image j, 0 otherwise. nxm */ + double *p, /* initial parameter vector p0: (b1, ..., bn). + * bi are the i-th point parameters, * size n*pnp */ + const int pnp,/* number of parameters for ONE point; e.g. 3 for Euclidean points */ + double *x, /* measurements vector: (x_11^T, .. x_1m^T, ..., x_n1^T, .. x_nm^T)^T where + * x_ij is the projection of the i-th point on the j-th image. + * NOTE: some of the x_ij might be missing, if point i is not visible in image j; + * see vmask[i, j], max. size n*m*mnp + */ + double *covx, /* measurements covariance matrices: (Sigma_x_11, .. Sigma_x_1m, ..., Sigma_x_n1, .. Sigma_x_nm), + * where Sigma_x_ij is the mnp x mnp covariance of x_ij stored row-by-row. Set to NULL if no + * covariance estimates are available (identity matrices are implicitly used in this case). + * NOTE: a certain Sigma_x_ij is missing if the corresponding x_ij is also missing; + * see vmask[i, j], max. size n*m*mnp*mnp + */ + const int mnp,/* number of parameters for EACH measurement; usually 2 */ + void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), + /* functional relation describing measurements. Given a parameter vector p, + * computes a prediction of the measurements \hat{x}. p is (n*pnp)x1, + * \hat{x} is (n*m*mnp)x1, maximum + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + */ + void (*fjac)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), + /* function to evaluate the sparse jacobian dX/dp. + * The Jacobian is returned in jac as + * (dx_11/db_1, ..., dx_1m/db_1, ..., dx_n1/db_n, ..., dx_nm/db_n), or (using HZ's notation), + * jac=(B_11, ..., B_1m, ..., B_n1, ..., B_nm) + * Notice that depending on idxij, some of the B_ij might be missing. + * Note also that B_ij are mnp x pnp matrices and they + * should be stored in jac in row-major order. + * rcidxs, rcsubs are max(m, n) x 1, allocated by the caller and can be used + * as working memory + * + * If NULL, the jacobian is approximated by repetitive func calls and finite + * differences. This is computationally inefficient and thus NOT recommended. + */ + void *adata, /* pointer to possibly additional data, passed uninterpreted to func, fjac */ + + const int itmax, /* I: maximum number of iterations. itmax==0 signals jacobian verification followed by immediate return */ + const int verbose, /* I: verbosity */ + const double opts[SBA_OPTSSZ], + /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \epsilon4]. Respectively the scale factor for initial \mu, + * stopping thresholds for ||J^T e||_inf, ||dp||_2, ||e||_2 and (||e||_2-||e_new||_2)/||e||_2 + */ + double info[SBA_INFOSZ] + /* 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 - stopped by small relative reduction in ||e||_2 + * 5 - stopped by small ||e||_2 + * 6 - too many attempts to increase damping. Restart with increased mu + * 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]= # number of linear systems solved, i.e. number of attempts for reducing error + */ +) +{ +register int i, j, ii, jj, k; +int nvis, nnz, retval; + +/* The following are work arrays that are dynamically allocated by sba_str_levmar_x() */ +double *jac; /* work array for storing the jacobian, max. size n*m*mnp*pnp */ +double *V; /* work array for storing the V_i in the order V_1, ..., V_n, size n*pnp*pnp */ + +double *e; /* work array for storing the e_ij in the order e_11, ..., e_1m, ..., e_n1, ..., e_nm, + max. size n*m*mnp */ +double *eb; /* work array for storing the eb_i in the order eb_1, .. eb_n size n*pnp */ + +double *dp; /* work array for storing the parameter vector updates db_1, ..., db_n, size n*pnp */ + +double *wght= /* work array for storing the weights computed from the covariance inverses, max. size n*m*mnp*mnp */ + NULL; + +/* Of the above arrays, jac, e, wght are sparse and + * V, eb, dp are dense. Sparse arrays are indexed through + * idxij (see below), that is with the same mechanism as the input + * measurements vector x + */ + +/* submatrices sizes */ +int Bsz, Vsz, + esz, ebsz, covsz; + +register double *ptr1, *ptr2, *ptr3, *ptr4, sum; +struct sba_crsm idxij; /* sparse matrix containing the location of x_ij in x. This is also the location + * of B_ij in jac, etc. + * This matrix can be thought as a map from a sparse set of pairs (i, j) to a continuous + * index k and it is used to efficiently lookup the memory locations where the non-zero + * blocks of a sparse matrix/vector are stored + */ +int maxCPvis, /* max. of projections across cameras & projections across points */ + *rcidxs, /* work array for the indexes corresponding to the nonzero elements of a single row or + column in a sparse matrix, size max(n, m) */ + *rcsubs; /* work array for the subscripts of nonzero elements in a single row or column of a + sparse matrix, size max(n, m) */ + +/* The following variables are needed by the LM algorithm */ +register int itno; /* iteration counter */ +int nsolved; +/* temporary work arrays that are dynamically allocated */ +double *hx, /* \hat{x}_i, max. size m*n*mnp */ + *diagV, /* diagonals of V_i, size n*pnp */ + *pdp; /* p + dp, size n*pnp */ + +register double mu, /* damping constant */ + tmp; /* mainly used in matrix & vector multiplications */ +double p_eL2, eb_inf, pdp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+dp)||_2 */ +double p_L2, dp_L2=DBL_MAX, dF, dL; +double tau=FABS(opts[0]), eps1=FABS(opts[1]), eps2=FABS(opts[2]), eps2_sq=opts[2]*opts[2], + eps3_sq=opts[3]*opts[3], eps4_sq=opts[4]*opts[4]; +double init_p_eL2; +int nu=2, nu2, stop=0, nfev, njev=0, nlss=0; +int nobs, nvars; +PLS linsolver=NULL; + +struct fdj_data_x_ fdj_data; +void *jac_adata; + +/* Initialization */ + mu=eb_inf=tmp=0.0; /* -Wall */ + + /* block sizes */ + Bsz=mnp * pnp; Vsz=pnp * pnp; + esz=mnp; ebsz=pnp; + covsz=mnp * mnp; + + /* count total number of visible image points */ + for(i=nvis=0, jj=n*m; i<jj; ++i) + nvis+=(vmask[i]!=0); + + nobs=nvis*mnp; + nvars=n*pnp; + if(nobs<nvars){ + fprintf(stderr, "SBA: sba_str_levmar_x() cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n", nobs, nvars); + return SBA_ERROR; + } + + /* allocate & fill up the idxij structure */ + sba_crsm_alloc(&idxij, n, m, nvis); + for(i=k=0; i<n; ++i){ + idxij.rowptr[i]=k; + ii=i*m; + for(j=0; j<m; ++j) + if(vmask[ii+j]){ + idxij.val[k]=k; + idxij.colidx[k++]=j; + } + } + idxij.rowptr[n]=nvis; + + /* find the maximum number of visible image points in any single camera or coming from a single 3D point */ + /* cameras */ + for(i=maxCPvis=0; i<n; ++i) + if((k=idxij.rowptr[i+1]-idxij.rowptr[i])>maxCPvis) maxCPvis=k; + + /* points, note that maxCPvis is not reinitialized! */ + for(j=0; j<m; ++j){ + for(i=ii=0; i<n; ++i) + if(vmask[i*m+j]) ++ii; + if(ii>maxCPvis) maxCPvis=ii; + } + + /* allocate work arrays */ + jac=(double *)emalloc(nvis*Bsz*sizeof(double)); + V=(double *)emalloc(n*Vsz*sizeof(double)); + e=(double *)emalloc(nobs*sizeof(double)); + eb=(double *)emalloc(nvars*sizeof(double)); + dp=(double *)emalloc(nvars*sizeof(double)); + rcidxs=(int *)emalloc(maxCPvis*sizeof(int)); + rcsubs=(int *)emalloc(maxCPvis*sizeof(int)); +#ifndef SBA_DESTROY_COVS + if(covx!=NULL) wght=(double *)emalloc(nvis*covsz*sizeof(double)); +#else + if(covx!=NULL) wght=covx; +#endif /* SBA_DESTROY_COVS */ + + + hx=(double *)emalloc(nobs*sizeof(double)); + diagV=(double *)emalloc(nvars*sizeof(double)); + pdp=(double *)emalloc(nvars*sizeof(double)); + + /* if no jacobian function is supplied, prepare to compute jacobian with finite difference */ + if(!fjac){ + fdj_data.func=func; + fdj_data.cnp=0; + fdj_data.pnp=pnp; + fdj_data.mnp=mnp; + fdj_data.hx=hx; + fdj_data.hxx=(double *)emalloc(nobs*sizeof(double)); + fdj_data.func_rcidxs=(int *)emalloc(2*maxCPvis*sizeof(int)); + fdj_data.func_rcsubs=fdj_data.func_rcidxs+maxCPvis; + fdj_data.adata=adata; + + fjac=sba_fdjac_x; + jac_adata=(void *)&fdj_data; + } + else{ + fdj_data.hxx=NULL; + jac_adata=adata; + } + + if(itmax==0){ /* verify jacobian */ + sba_str_chkjac_x(func, fjac, p, &idxij, rcidxs, rcsubs, ncon, pnp, mnp, adata, jac_adata); + retval=0; + goto freemem_and_return; + } + + /* covariances Sigma_x_ij are accommodated by computing the Cholesky decompositions of their + * inverses and using the resulting matrices w_x_ij to weigh B_ij and e_ij as + * w_x_ij*B_ij and w_x_ij*e_ij. In this way, auxiliary variables as V_i=\sum_j B_ij^T B_ij + * actually become \sum_j (w_x_ij B_ij)^T w_x_ij B_ij= \sum_j B_ij^T w_x_ij^T w_x_ij B_ij = + * B_ij^T Sigma_x_ij^-1 B_ij + * + * eb_i are weighted in a similar manner + */ + if(covx!=NULL){ + for(i=0; i<n; ++i){ + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero x_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr1, ptr2 to point to cov_x_ij, w_x_ij resp. */ + ptr1=covx + (k=idxij.val[rcidxs[j]]*covsz); + ptr2=wght + k; + if(!sba_mat_cholinv(ptr1, ptr2, mnp)){ /* compute w_x_ij s.t. w_x_ij^T w_x_ij = cov_x_ij^-1 */ + fprintf(stderr, "SBA: invalid covariance matrix for x_ij (i=%d, j=%d) in sba_motstr_levmar_x()\n", i, rcsubs[j]); + retval=SBA_ERROR; + goto freemem_and_return; + } + } + } + sba_mat_cholinv(NULL, NULL, 0); /* cleanup */ + } + + /* compute the error vectors e_ij in hx */ + (*func)(p, &idxij, rcidxs, rcsubs, hx, adata); nfev=1; + /* ### compute e=x - f(p) [e=w*(x - f(p)] and its L2 norm */ + if(covx==NULL) + p_eL2=nrmL2xmy(e, x, hx, nobs); /* e=x-hx, p_eL2=||e|| */ + else + p_eL2=nrmCxmy(e, x, hx, wght, mnp, nvis); /* e=wght*(x-hx), p_eL2=||e||=||x-hx||_Sigma^-1 */ + if(verbose) printf("initial str-SBA error %g [%g]\n", p_eL2, p_eL2/nvis); + init_p_eL2=p_eL2; + if(!SBA_FINITE(p_eL2)) stop=7; + + for(itno=0; itno<itmax && !stop; ++itno){ + /* Note that p, e and ||e||_2 have been updated at the previous iteration */ + + /* compute derivative submatrices B_ij */ + (*fjac)(p, &idxij, rcidxs, rcsubs, jac, jac_adata); ++njev; + + if(covx!=NULL){ + /* compute w_x_ij B_ij. + * Since w_x_ij is upper triangular, the products can be safely saved + * directly in B_ij, without the need for intermediate storage + */ + for(i=0; i<nvis; ++i){ + /* set ptr1, ptr2 to point to w_x_ij, B_ij, resp. */ + ptr1=wght + i*covsz; + ptr2=jac + i*Bsz; + + /* w_x_ij is mnp x mnp, B_ij is mnp x pnp */ + for(ii=0; ii<mnp; ++ii) + for(jj=0; jj<pnp; ++jj){ + for(k=ii, sum=0.0; k<mnp; ++k) // k>=ii since w_x_ij is upper triangular + sum+=ptr1[ii*mnp+k]*ptr2[k*pnp+jj]; + ptr2[ii*pnp+jj]=sum; + } + } + } + + /* compute V_i = \sum_j B_ij^T B_ij */ // \Sigma here! + /* V_i is symmetric, therefore its computation can be sped up by + * computing only the upper part and then reusing it for the lower one. + * Recall that B_ij is mnp x pnp + */ + /* Also compute eb_i = \sum_j B_ij^T e_ij */ // \Sigma here! + /* Recall that e_ij is mnp x 1 + */ + _dblzero(V, n*Vsz); /* clear all V_i */ + _dblzero(eb, n*ebsz); /* clear all eb_i */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=eb + i*ebsz; // set ptr2 to point to eb_i + + nnz=sba_crsm_row_elmidxs(&idxij, i, rcidxs, rcsubs); /* find nonzero B_ij, j=0...m-1 */ + for(j=0; j<nnz; ++j){ + /* set ptr3 to point to B_ij, actual column number in rcsubs[j] */ + ptr3=jac + idxij.val[rcidxs[j]]*Bsz; + + /* compute the UPPER TRIANGULAR PART of B_ij^T B_ij and add it to V_i */ + for(ii=0; ii<pnp; ++ii){ + for(jj=ii; jj<pnp; ++jj){ + for(k=0, sum=0.0; k<mnp; ++k) + sum+=ptr3[k*pnp+ii]*ptr3[k*pnp+jj]; + ptr1[ii*pnp+jj]+=sum; + } + + /* copy the LOWER TRIANGULAR PART of V_i from the upper one */ + for(jj=0; jj<ii; ++jj) + ptr1[ii*pnp+jj]=ptr1[jj*pnp+ii]; + } + + ptr4=e + idxij.val[rcidxs[j]]*esz; /* set ptr4 to point to e_ij */ + /* compute B_ij^T e_ij and add it to eb_i */ + for(ii=0; ii<pnp; ++ii){ + for(jj=0, sum=0.0; jj<mnp; ++jj) + sum+=ptr3[jj*pnp+ii]*ptr4[jj]; + ptr2[ii]+=sum; + } + } + } + + /* Compute ||J^T e||_inf and ||p||^2 */ + for(i=0, p_L2=eb_inf=0.0; i<nvars; ++i){ + if(eb_inf < (tmp=FABS(eb[i]))) eb_inf=tmp; + p_L2+=p[i]*p[i]; + } + //p_L2=sqrt(p_L2); + + /* save diagonal entries so that augmentation can be later canceled. + * Diagonal entries are in V_i + */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr2[j]=ptr1[j*pnp+j]; + } + +/* +if(!(itno%100)){ + printf("Current estimate: "); + for(i=0; i<nvars; ++i) + printf("%.9g ", p[i]); + printf("-- errors %.9g %0.9g\n", eb_inf, p_eL2); +} +*/ + + /* check for convergence */ + if((eb_inf <= eps1)){ + dp_L2=0.0; /* no increment for p in this case */ + stop=1; + break; + } + + /* compute initial damping factor */ + if(itno==0){ + for(i=ncon*pnp, tmp=DBL_MIN; i<nvars; ++i) + if(diagV[i]>tmp) tmp=diagV[i]; /* find max diagonal element */ + mu=tau*tmp; + } + + /* determine increment using adaptive damping */ + while(1){ + /* augment V */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]+=mu; + } + + /* solve the linear systems V*_i db_i = eb_i to compute the db_i */ + _dblzero(dp, ncon*pnp); /* no change for the first ncon point params */ + for(i=nsolved=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=eb + i*ebsz; // set ptr2 to point to eb_i + ptr3=dp + i*pnp; // set ptr3 to point to db_i + + //nsolved+=sba_Axb_LU(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_LU; + nsolved+=sba_Axb_Chol(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_Chol; + //nsolved+=sba_Axb_BK(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_BK; + //nsolved+=sba_Axb_QRnoQ(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_QRnoQ; + //nsolved+=sba_Axb_QR(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_QR; + //nsolved+=sba_Axb_SVD(ptr1, ptr2, ptr3, pnp, 0); linsolver=sba_Axb_SVD; + //nsolved+=(sba_Axb_CG(ptr1, ptr2, ptr3, pnp, (3*pnp)/2, 1E-10, SBA_CG_JACOBI, 0) > 0); linsolver=(PLS)sba_Axb_CG; + + ++nlss; + } + + if(nsolved==n){ + + /* parameter vector updates are now in dp */ + + /* compute p's new estimate and ||dp||^2 */ + for(i=0, dp_L2=0.0; i<nvars; ++i){ + pdp[i]=p[i] + (tmp=dp[i]); + dp_L2+=tmp*tmp; + } + //dp_L2=sqrt(dp_L2); + + if(dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */ + //if(dp_L2<=eps2*(p_L2 + eps2)){ /* relative change in p is small, stop */ + stop=2; + break; + } + + if(dp_L2>=(p_L2+eps2)/SBA_EPSILON_SQ){ /* almost singular */ + //if(dp_L2>=(p_L2+eps2)/SBA_EPSILON){ /* almost singular */ + fprintf(stderr, "SBA: the matrix of the augmented normal equations is almost singular in sba_motstr_levmar_x(),\n" + " minimization should be restarted from the current solution with an increased damping term\n"); + retval=SBA_ERROR; + goto freemem_and_return; + } + + (*func)(pdp, &idxij, rcidxs, rcsubs, hx, adata); ++nfev; /* evaluate function at p + dp */ + if(verbose>1) + printf("mean reprojection error %g\n", sba_mean_repr_error(n, mnp, x, hx, &idxij, rcidxs, rcsubs)); + /* ### compute ||e(pdp)||_2 */ + if(covx==NULL) + pdp_eL2=nrmL2xmy(hx, x, hx, nobs); /* hx=x-hx, pdp_eL2=||hx|| */ + else + pdp_eL2=nrmCxmy(hx, x, hx, wght, mnp, nvis); /* hx=wght*(x-hx), pdp_eL2=||hx|| */ + if(!SBA_FINITE(pdp_eL2)){ + if(verbose) /* identify the offending point projection */ + sba_print_inf(hx, m, mnp, &idxij, rcidxs, rcsubs); + + stop=7; + break; + } + + for(i=0, dL=0.0; i<nvars; ++i) + dL+=dp[i]*(mu*dp[i]+eb[i]); + + dF=p_eL2-pdp_eL2; + + if(verbose>1) + printf("\ndamping term %8g, gain ratio %8g, errors %8g / %8g = %g\n", mu, dL!=0.0? dF/dL : dF/DBL_EPSILON, p_eL2/nvis, pdp_eL2/nvis, p_eL2/pdp_eL2); + + if(dL>0.0 && dF>0.0){ /* reduction in error, increment is accepted */ + tmp=(2.0*dF/dL-1.0); + tmp=1.0-tmp*tmp*tmp; + mu=mu*( (tmp>=SBA_ONE_THIRD)? tmp : SBA_ONE_THIRD ); + nu=2; + + /* the test below is equivalent to the relative reduction of the RMS reprojection error: sqrt(p_eL2)-sqrt(pdp_eL2)<eps4*sqrt(p_eL2) */ + if(pdp_eL2-2.0*sqrt(p_eL2*pdp_eL2)<(eps4_sq-1.0)*p_eL2) stop=4; + + for(i=0; i<nvars; ++i) /* update p's estimate */ + p[i]=pdp[i]; + + for(i=0; i<nobs; ++i) /* update e and ||e||_2 */ + e[i]=hx[i]; + p_eL2=pdp_eL2; + break; + } + } /* nsolved==n */ + + /* if this point is reached, either at least one linear system could not be solved or + * the error did not reduce; in any case, the increment must be rejected + */ + + mu*=nu; + nu2=nu<<1; // 2*nu; + if(nu2<=nu){ /* nu has wrapped around (overflown) */ + fprintf(stderr, "SBA: too many failed attempts to increase the damping factor in sba_str_levmar_x()! Singular Hessian matrix?\n"); + //exit(1); + stop=6; + break; + } + nu=nu2; + +#if 0 + /* restore V diagonal entries */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]=ptr2[j]; + } +#endif + } /* inner while loop */ + + if(p_eL2<=eps3_sq) stop=5; // error is small, force termination of outer loop + } + + if(itno>=itmax) stop=3; + + /* restore V diagonal entries */ + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + ptr2=diagV + i*pnp; // set ptr2 to point to diagV_i + for(j=0; j<pnp; ++j) + ptr1[j*pnp+j]=ptr2[j]; + } + + if(info){ + info[0]=init_p_eL2; + info[1]=p_eL2; + info[2]=eb_inf; + info[3]=dp_L2; + for(i=ncon; i<n; ++i){ + ptr1=V + i*Vsz; // set ptr1 to point to V_i + for(j=0; j<pnp; ++j) + if(tmp<ptr1[j*pnp+j]) tmp=ptr1[j*pnp+j]; + } + info[4]=mu/tmp; + info[5]=itno; + info[6]=stop; + info[7]=nfev; + info[8]=njev; + info[9]=nlss; + } + //sba_print_sol(n, m, p, 0, pnp, x, mnp, &idxij, rcidxs, rcsubs); + retval=(stop!=7)? itno : SBA_ERROR; + +freemem_and_return: /* NOTE: this point is also reached via a goto! */ + + /* free whatever was allocated */ + free(jac); free(V); + free(e); free(eb); + free(dp); + free(rcidxs); free(rcsubs); +#ifndef SBA_DESTROY_COVS + if(wght) free(wght); +#else + /* nothing to do */ +#endif /* SBA_DESTROY_COVS */ + + free(hx); free(diagV); free(pdp); + if(fdj_data.hxx){ // cleanup + free(fdj_data.hxx); + free(fdj_data.func_rcidxs); + } + + sba_crsm_free(&idxij); + + /* free the memory allocated by the linear solver routine */ + if(linsolver) (*linsolver)(NULL, NULL, NULL, 0, 0); + + return retval; +} |