diff options
Diffstat (limited to 'redist/sba/sba_levmar.c')
| -rw-r--r-- | redist/sba/sba_levmar.c | 2715 |
1 files changed, 2715 insertions, 0 deletions
diff --git a/redist/sba/sba_levmar.c b/redist/sba/sba_levmar.c new file mode 100644 index 0000000..2f85f2a --- /dev/null +++ b/redist/sba/sba_levmar.c @@ -0,0 +1,2715 @@ +///////////////////////////////////////////////////////////////////////////////// +//// +//// 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 <float.h> +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.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 %zu 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; +} |