1 | ///////////////////////////////////////////////////////////////////////////////// |
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2 | //// |
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3 | //// Verification routines for the jacobians employed in the expert & simple drivers |
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4 | //// for sparse bundle adjustment based on the Levenberg - Marquardt minimization algorithm |
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5 | //// Copyright (C) 2005 Manolis Lourakis (lourakis@ics.forth.gr) |
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6 | //// Institute of Computer Science, Foundation for Research & Technology - Hellas |
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7 | //// Heraklion, Crete, Greece. |
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8 | //// |
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9 | //// This program is free software; you can redistribute it and/or modify |
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10 | //// it under the terms of the GNU General Public License as published by |
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11 | //// the Free Software Foundation; either version 2 of the License, or |
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12 | //// (at your option) any later version. |
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13 | //// |
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14 | //// This program is distributed in the hope that it will be useful, |
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15 | //// but WITHOUT ANY WARRANTY; without even the implied warranty of |
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16 | //// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 | //// GNU General Public License for more details. |
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18 | //// |
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19 | /////////////////////////////////////////////////////////////////////////////////// |
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20 | |
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21 | #include <stdio.h> |
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22 | #include <stdlib.h> |
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23 | #include <math.h> |
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24 | #include <float.h> |
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25 | |
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26 | #include "sba.h" |
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27 | |
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28 | #define emalloc(sz) emalloc_(__FILE__, __LINE__, sz) |
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29 | |
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30 | #define FABS(x) (((x)>=0)? (x) : -(x)) |
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31 | |
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32 | |
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33 | /* inline */ |
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34 | #ifdef _MSC_VER |
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35 | #define inline __inline //MSVC |
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36 | #elif !defined(__GNUC__) |
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37 | #define inline //other than MSVC, GCC: define empty |
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38 | #endif |
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39 | |
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40 | /* auxiliary memory allocation routine with error checking */ |
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41 | inline static void *emalloc_(char *file, int line, size_t sz) |
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42 | { |
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43 | void *ptr; |
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44 | |
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45 | ptr=(void *)malloc(sz); |
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46 | if(ptr==NULL){ |
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47 | fprintf(stderr, "memory allocation request for %u bytes failed in file %s, line %d, exiting", sz, file, line); |
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48 | exit(1); |
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49 | } |
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50 | |
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51 | return ptr; |
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52 | } |
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53 | |
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54 | /* |
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55 | * Check the jacobian of a projection function in nvars variables |
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56 | * evaluated at a point p, for consistency with the function itself. |
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57 | * Expert version |
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58 | * |
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59 | * Based on fortran77 subroutine CHKDER by |
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60 | * Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More |
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61 | * Argonne National Laboratory. MINPACK project. March 1980. |
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62 | * |
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63 | * |
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64 | * func points to a function from R^{nvars} --> R^{nobs}: Given a p in R^{nvars} |
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65 | * it yields hx in R^{nobs} |
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66 | * jacf points to a function implementing the jacobian of func, whose consistency with |
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67 | * func is to be tested. Given a p in R^{nvars}, jacf computes into the nvis*(Asz+Bsz) |
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68 | * matrix jac the jacobian of func at p. Note the jacobian is sparse, consisting of |
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69 | * all A_ij, B_ij and that row i of jac corresponds to the gradient of the i-th |
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70 | * component of func, evaluated at p. |
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71 | * p is an input array of length nvars containing the point of evaluation. |
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72 | * idxij, rcidxs, rcsubs, mcon, cnp, pnp, mnp are as usual. Note that if cnp=0 or |
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73 | * pnp=0 a jacobian corresponding resp. to motion or camera parameters |
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74 | * only is assumed. |
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75 | * func_adata, jac_adata point to possible additional data and are passed |
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76 | * uninterpreted to func, jacf respectively. |
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77 | * err is an array of length nobs. On output, err contains measures |
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78 | * of correctness of the respective gradients. if there is |
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79 | * no severe loss of significance, then if err[i] is 1.0 the |
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80 | * i-th gradient is correct, while if err[i] is 0.0 the i-th |
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81 | * gradient is incorrect. For values of err between 0.0 and 1.0, |
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82 | * the categorization is less certain. In general, a value of |
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83 | * err[i] greater than 0.5 indicates that the i-th gradient is |
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84 | * probably correct, while a value of err[i] less than 0.5 |
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85 | * indicates that the i-th gradient is probably incorrect. |
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86 | * |
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87 | * CAUTION: THIS FUNCTION IS NOT 100% FOOLPROOF. The |
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88 | * following excerpt comes from CHKDER's documentation: |
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89 | * |
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90 | * "The function does not perform reliably if cancellation or |
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91 | * rounding errors cause a severe loss of significance in the |
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92 | * evaluation of a function. therefore, none of the components |
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93 | * of p should be unusually small (in particular, zero) or any |
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94 | * other value which may cause loss of significance." |
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95 | */ |
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96 | |
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97 | void sba_motstr_chkjac_x( |
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98 | void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), |
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99 | void (*jacf)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), |
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100 | double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, int mcon, int cnp, int pnp, int mnp, void *func_adata, void *jac_adata) |
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101 | { |
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102 | const double factor=100.0, one=1.0, zero=0.0; |
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103 | double *fvec, *fjac, *pp, *fvecp, *buf, *err; |
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104 | |
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105 | int nvars, nobs, m, n, Asz, Bsz, nnz; |
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106 | register int i, j, ii, jj; |
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107 | double eps, epsf, temp, epsmch, epslog; |
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108 | register double *ptr1, *ptr2, *pab; |
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109 | double *pa, *pb; |
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110 | int fvec_sz, pp_sz, fvecp_sz, numerr=0; |
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111 | |
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112 | nobs=idxij->nnz*mnp; |
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113 | n=idxij->nr; m=idxij->nc; |
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114 | nvars=m*cnp + n*pnp; |
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115 | epsmch=DBL_EPSILON; |
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116 | eps=sqrt(epsmch); |
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117 | |
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118 | Asz=mnp*cnp; Bsz=mnp*pnp; |
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119 | fjac=(double *)emalloc(idxij->nnz*(Asz+Bsz)*sizeof(double)); |
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120 | |
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121 | fvec_sz=fvecp_sz=nobs; |
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122 | pp_sz=nvars; |
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123 | buf=(double *)emalloc((fvec_sz + pp_sz + fvecp_sz)*sizeof(double)); |
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124 | fvec=buf; |
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125 | pp=fvec+fvec_sz; |
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126 | fvecp=pp+pp_sz; |
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127 | |
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128 | err=(double *)emalloc(nobs*sizeof(double)); |
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129 | |
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130 | /* compute fvec=func(p) */ |
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131 | (*func)(p, idxij, rcidxs, rcsubs, fvec, func_adata); |
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132 | |
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133 | /* compute the jacobian at p */ |
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134 | (*jacf)(p, idxij, rcidxs, rcsubs, fjac, jac_adata); |
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135 | |
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136 | /* compute pp */ |
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137 | for(j=0; j<nvars; ++j){ |
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138 | temp=eps*FABS(p[j]); |
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139 | if(temp==zero) temp=eps; |
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140 | pp[j]=p[j]+temp; |
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141 | } |
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142 | |
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143 | /* compute fvecp=func(pp) */ |
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144 | (*func)(pp, idxij, rcidxs, rcsubs, fvecp, func_adata); |
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145 | |
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146 | epsf=factor*epsmch; |
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147 | epslog=log10(eps); |
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148 | |
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149 | for(i=0; i<nobs; ++i) |
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150 | err[i]=zero; |
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151 | |
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152 | pa=p; |
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153 | pb=p + m*cnp; |
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154 | for(i=0; i<n; ++i){ |
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155 | nnz=sba_crsm_row_elmidxs(idxij, i, rcidxs, rcsubs); /* find nonzero A_ij, B_ij, j=0...m-1, actual column numbers in rcsubs */ |
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156 | for(j=0; j<nnz; ++j){ |
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157 | if(rcsubs[j]<mcon) continue; // A_ij, B_ij are zero |
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158 | |
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159 | ptr2=err + idxij->val[rcidxs[j]]*mnp; // set ptr2 to point into err |
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160 | |
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161 | if(cnp){ |
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162 | ptr1=fjac + idxij->val[rcidxs[j]]*Asz; // set ptr1 to point to A_ij |
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163 | pab=pa + rcsubs[j]*cnp; |
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164 | for(jj=0; jj<cnp; ++jj){ |
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165 | temp=FABS(pab[jj]); |
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166 | if(temp==zero) temp=one; |
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167 | |
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168 | for(ii=0; ii<mnp; ++ii) |
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169 | ptr2[ii]+=temp*ptr1[ii*cnp+jj]; |
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170 | } |
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171 | } |
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172 | |
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173 | if(pnp){ |
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174 | ptr1=fjac + idxij->nnz*Asz + idxij->val[rcidxs[j]]*Bsz; // set ptr1 to point to B_ij |
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175 | pab=pb + i*pnp; |
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176 | for(jj=0; jj<pnp; ++jj){ |
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177 | temp=FABS(pab[jj]); |
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178 | if(temp==zero) temp=one; |
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179 | |
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180 | for(ii=0; ii<mnp; ++ii) |
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181 | ptr2[ii]+=temp*ptr1[ii*pnp+jj]; |
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182 | } |
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183 | } |
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184 | } |
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185 | } |
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186 | |
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187 | for(i=0; i<nobs; ++i){ |
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188 | temp=one; |
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189 | if(fvec[i]!=zero && fvecp[i]!=zero && FABS(fvecp[i]-fvec[i])>=epsf*FABS(fvec[i])) |
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190 | temp=eps*FABS((fvecp[i]-fvec[i])/eps - err[i])/(FABS(fvec[i])+FABS(fvecp[i])); |
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191 | err[i]=one; |
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192 | if(temp>epsmch && temp<eps) |
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193 | err[i]=(log10(temp) - epslog)/epslog; |
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194 | if(temp>=eps) err[i]=zero; |
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195 | } |
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196 | |
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197 | free(fjac); |
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198 | free(buf); |
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199 | |
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200 | for(i=0; i<n; ++i){ |
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201 | nnz=sba_crsm_row_elmidxs(idxij, i, rcidxs, rcsubs); /* find nonzero err_ij, j=0...m-1 */ |
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202 | for(j=0; j<nnz; ++j){ |
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203 | if(rcsubs[j]<mcon) continue; // corresponding gradients are taken to be zero |
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204 | |
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205 | ptr1=err + idxij->val[rcidxs[j]]*mnp; // set ptr1 to point into err |
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206 | for(ii=0; ii<mnp; ++ii) |
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207 | if(ptr1[ii]<=0.5){ |
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208 | fprintf(stderr, "Gradient %d (corresponding to element %d of the projection of point %d on camera %d) is %s (err=%g)\n", |
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209 | idxij->val[rcidxs[j]]*mnp+ii, ii, i, rcsubs[j], (ptr1[ii]==0.0)? "wrong" : "probably wrong", ptr1[ii]); |
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210 | ++numerr; |
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211 | } |
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212 | } |
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213 | } |
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214 | if(numerr) fprintf(stderr, "Found %d suspicious gradients out of %d\n\n", numerr, nobs); |
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215 | |
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216 | free(err); |
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217 | |
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218 | return; |
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219 | } |
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220 | |
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221 | void sba_mot_chkjac_x( |
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222 | void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), |
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223 | void (*jacf)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), |
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224 | double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, int mcon, int cnp, int mnp, void *func_adata, void *jac_adata) |
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225 | { |
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226 | sba_motstr_chkjac_x(func, jacf, p, idxij, rcidxs, rcsubs, mcon, cnp, 0, mnp, func_adata, jac_adata); |
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227 | } |
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228 | |
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229 | void sba_str_chkjac_x( |
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230 | void (*func)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *hx, void *adata), |
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231 | void (*jacf)(double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, double *jac, void *adata), |
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232 | double *p, struct sba_crsm *idxij, int *rcidxs, int *rcsubs, int pnp, int mnp, void *func_adata, void *jac_adata) |
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233 | { |
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234 | sba_motstr_chkjac_x(func, jacf, p, idxij, rcidxs, rcsubs, 0, 0, pnp, mnp, func_adata, jac_adata); |
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235 | } |
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236 | |
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237 | #if 0 |
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238 | /* Routines for directly checking the jacobians supplied to the simple drivers. |
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239 | * They shouldn't be necessary since these jacobians can be verified indirectly |
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240 | * through the expert sba_XXX_chkjac_x() routines. |
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241 | */ |
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242 | |
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243 | /*****************************************************************************************/ |
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244 | // Sample code for using sba_motstr_chkjac(): |
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245 | |
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246 | for(i=0; i<n; ++i) |
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247 | for(j=mcon; j<m; ++j){ |
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248 | if(!vmask[i*m+j]) continue; // point i does not appear in image j |
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249 | |
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250 | sba_motstr_chkjac(proj, projac, p+j*cnp, p+m*cnp+i*pnp, j, i, cnp, pnp, mnp, adata, adata); |
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251 | } |
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252 | |
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253 | |
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254 | /*****************************************************************************************/ |
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255 | |
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256 | |
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257 | /* union used for passing pointers to the user-supplied functions for the motstr/mot/str simple drivers */ |
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258 | union proj_projac{ |
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259 | struct{ |
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260 | void (*proj)(int j, int i, double *aj, double *bi, double *xij, void *adata); |
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261 | void (*projac)(int j, int i, double *aj, double *bi, double *Aij, double *Bij, void *adata); |
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262 | } motstr; |
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263 | |
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264 | struct{ |
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265 | void (*proj)(int j, int i, double *aj, double *xij, void *adata); |
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266 | void (*projac)(int j, int i, double *aj, double *Aij, void *adata); |
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267 | } mot; |
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268 | |
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269 | struct{ |
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270 | void (*proj)(int j, int i, double *bi, double *xij, void *adata); |
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271 | void (*projac)(int j, int i, double *bi, double *Bij, void *adata); |
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272 | } str; |
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273 | }; |
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274 | |
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275 | |
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276 | /* |
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277 | * Check the jacobian of a projection function in cnp+pnp variables |
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278 | * evaluated at a point p, for consistency with the function itself. |
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279 | * Simple version of the above, NOT to be called directly |
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280 | * |
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281 | * Based on fortran77 subroutine CHKDER by |
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282 | * Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More |
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283 | * Argonne National Laboratory. MINPACK project. March 1980. |
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284 | * |
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285 | * |
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286 | * proj points to a function from R^{cnp+pnp} --> R^{mnp}: Given a p=(aj, bi) in R^{cnp+pnp} |
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287 | * it yields hx in R^{mnp} |
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288 | * projac points to a function implementing the jacobian of func, whose consistency with proj |
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289 | * is to be tested. Given a p in R^{cnp+pnp}, jacf computes into the matrix jac=[Aij | Bij] |
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290 | * jacobian of proj at p. Note that row i of jac corresponds to the gradient of the i-th |
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291 | * component of proj, evaluated at p. |
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292 | * aj, bi are input arrays of lengths cnp, pnp containing the parameters for the point of |
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293 | * evaluation, i.e. j-th camera and i-th point |
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294 | * jj, ii specify the point (ii) whose projection jacobian in image (jj) is being checked |
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295 | * cnp, pnp, mnp are as usual. Note that if cnp=0 or |
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296 | * pnp=0 a jacobian corresponding resp. to motion or camera parameters |
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297 | * only is assumed. |
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298 | * func_adata, jac_adata point to possible additional data and are passed |
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299 | * uninterpreted to func, jacf respectively. |
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300 | * err is an array of length mnp. On output, err contains measures |
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301 | * of correctness of the respective gradients. if there is |
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302 | * no severe loss of significance, then if err[i] is 1.0 the |
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303 | * i-th gradient is correct, while if err[i] is 0.0 the i-th |
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304 | * gradient is incorrect. For values of err between 0.0 and 1.0, |
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305 | * the categorization is less certain. In general, a value of |
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306 | * err[i] greater than 0.5 indicates that the i-th gradient is |
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307 | * probably correct, while a value of err[i] less than 0.5 |
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308 | * indicates that the i-th gradient is probably incorrect. |
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309 | * |
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310 | * CAUTION: THIS FUNCTION IS NOT 100% FOOLPROOF. The |
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311 | * following excerpt comes from CHKDER's documentation: |
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312 | * |
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313 | * "The function does not perform reliably if cancellation or |
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314 | * rounding errors cause a severe loss of significance in the |
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315 | * evaluation of a function. therefore, none of the components |
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316 | * of p should be unusually small (in particular, zero) or any |
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317 | * other value which may cause loss of significance." |
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318 | */ |
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319 | |
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320 | static void sba_chkjac( |
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321 | union proj_projac *funcs, double *aj, double *bi, int jj, int ii, int cnp, int pnp, int mnp, void *func_adata, void *jac_adata) |
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322 | { |
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323 | const double factor=100.0, one=1.0, zero=0.0; |
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324 | double *fvec, *fjac, *Aij, *Bij, *ajp, *bip, *fvecp, *buf, *err; |
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325 | |
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326 | int Asz, Bsz; |
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327 | register int i, j; |
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328 | double eps, epsf, temp, epsmch, epslog; |
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329 | int fvec_sz, ajp_sz, bip_sz, fvecp_sz, err_sz, numerr=0; |
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330 | |
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331 | epsmch=DBL_EPSILON; |
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332 | eps=sqrt(epsmch); |
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333 | |
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334 | Asz=mnp*cnp; Bsz=mnp*pnp; |
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335 | fjac=(double *)emalloc((Asz+Bsz)*sizeof(double)); |
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336 | Aij=fjac; |
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337 | Bij=Aij+Asz; |
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338 | |
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339 | fvec_sz=fvecp_sz=mnp; |
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340 | ajp_sz=cnp; bip_sz=pnp; |
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341 | err_sz=mnp; |
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342 | buf=(double *)emalloc((fvec_sz + ajp_sz + bip_sz + fvecp_sz + err_sz)*sizeof(double)); |
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343 | fvec=buf; |
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344 | ajp=fvec+fvec_sz; |
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345 | bip=ajp+ajp_sz; |
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346 | fvecp=bip+bip_sz; |
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347 | err=fvecp+fvecp_sz; |
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348 | |
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349 | /* compute fvec=proj(p), p=(aj, bi) & the jacobian at p */ |
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350 | if(cnp && pnp){ |
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351 | (*(funcs->motstr.proj))(jj, ii, aj, bi, fvec, func_adata); |
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352 | (*(funcs->motstr.projac))(jj, ii, aj, bi, Aij, Bij, jac_adata); |
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353 | } |
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354 | else if(cnp){ |
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355 | (*(funcs->mot.proj))(jj, ii, aj, fvec, func_adata); |
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356 | (*(funcs->mot.projac))(jj, ii, aj, Aij, jac_adata); |
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357 | } |
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358 | else{ |
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359 | (*(funcs->str.proj))(jj, ii, bi, fvec, func_adata); |
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360 | (*(funcs->str.projac))(jj, ii, bi, Bij, jac_adata); |
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361 | } |
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362 | |
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363 | /* compute pp, pp=(ajp, bip) */ |
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364 | for(j=0; j<cnp; ++j){ |
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365 | temp=eps*FABS(aj[j]); |
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366 | if(temp==zero) temp=eps; |
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367 | ajp[j]=aj[j]+temp; |
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368 | } |
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369 | for(j=0; j<pnp; ++j){ |
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370 | temp=eps*FABS(bi[j]); |
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371 | if(temp==zero) temp=eps; |
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372 | bip[j]=bi[j]+temp; |
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373 | } |
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374 | |
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375 | /* compute fvecp=proj(pp) */ |
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376 | if(cnp && pnp) |
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377 | (*(funcs->motstr.proj))(jj, ii, ajp, bip, fvecp, func_adata); |
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378 | else if(cnp) |
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379 | (*(funcs->mot.proj))(jj, ii, ajp, fvecp, func_adata); |
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380 | else |
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381 | (*(funcs->str.proj))(jj, ii, bip, fvecp, func_adata); |
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382 | |
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383 | epsf=factor*epsmch; |
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384 | epslog=log10(eps); |
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385 | |
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386 | for(i=0; i<mnp; ++i) |
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387 | err[i]=zero; |
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388 | |
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389 | for(j=0; j<cnp; ++j){ |
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390 | temp=FABS(aj[j]); |
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391 | if(temp==zero) temp=one; |
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392 | |
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393 | for(i=0; i<mnp; ++i) |
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394 | err[i]+=temp*Aij[i*cnp+j]; |
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395 | } |
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396 | for(j=0; j<pnp; ++j){ |
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397 | temp=FABS(bi[j]); |
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398 | if(temp==zero) temp=one; |
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399 | |
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400 | for(i=0; i<mnp; ++i) |
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401 | err[i]+=temp*Bij[i*pnp+j]; |
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402 | } |
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403 | |
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404 | for(i=0; i<mnp; ++i){ |
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405 | temp=one; |
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406 | if(fvec[i]!=zero && fvecp[i]!=zero && FABS(fvecp[i]-fvec[i])>=epsf*FABS(fvec[i])) |
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407 | temp=eps*FABS((fvecp[i]-fvec[i])/eps - err[i])/(FABS(fvec[i])+FABS(fvecp[i])); |
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408 | err[i]=one; |
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409 | if(temp>epsmch && temp<eps) |
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410 | err[i]=(log10(temp) - epslog)/epslog; |
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411 | if(temp>=eps) err[i]=zero; |
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412 | } |
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413 | |
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414 | for(i=0; i<mnp; ++i) |
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415 | if(err[i]<=0.5){ |
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416 | fprintf(stderr, "Gradient %d (corresponding to element %d of the projection of point %d on camera %d) is %s (err=%g)\n", |
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417 | i, i, ii, jj, (err[i]==0.0)? "wrong" : "probably wrong", err[i]); |
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418 | ++numerr; |
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419 | } |
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420 | if(numerr) fprintf(stderr, "Found %d suspicious gradients out of %d\n\n", numerr, mnp); |
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421 | |
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422 | free(fjac); |
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423 | free(buf); |
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424 | |
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425 | return; |
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426 | } |
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427 | |
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428 | void sba_motstr_chkjac( |
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429 | void (*proj)(int jj, int ii, double *aj, double *bi, double *xij, void *adata), |
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430 | void (*projac)(int jj, int ii, double *aj, double *bi, double *Aij, double *Bij, void *adata), |
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431 | double *aj, double *bi, int jj, int ii, int cnp, int pnp, int mnp, void *func_adata, void *jac_adata) |
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432 | { |
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433 | union proj_projac funcs; |
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434 | |
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435 | funcs.motstr.proj=proj; |
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436 | funcs.motstr.projac=projac; |
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437 | |
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438 | sba_chkjac(&funcs, aj, bi, jj, ii, cnp, pnp, mnp, func_adata, jac_adata); |
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439 | } |
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440 | |
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441 | void sba_mot_chkjac( |
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442 | void (*proj)(int jj, int ii, double *aj, double *xij, void *adata), |
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443 | void (*projac)(int jj, int ii, double *aj, double *Aij, void *adata), |
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444 | double *aj, double *bi, int jj, int ii, int cnp, int pnp, int mnp, void *func_adata, void *jac_adata) |
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445 | { |
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446 | union proj_projac funcs; |
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447 | |
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448 | funcs.mot.proj=proj; |
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449 | funcs.mot.projac=projac; |
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450 | |
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451 | sba_chkjac(&funcs, aj, NULL, jj, ii, cnp, 0, mnp, func_adata, jac_adata); |
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452 | } |
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453 | |
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454 | void sba_str_chkjac( |
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455 | void (*proj)(int jj, int ii, double *bi, double *xij, void *adata), |
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456 | void (*projac)(int jj, int ii, double *bi, double *Bij, void *adata), |
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457 | double *aj, double *bi, int jj, int ii, int cnp, int pnp, int mnp, void *func_adata, void *jac_adata) |
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458 | { |
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459 | union proj_projac funcs; |
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460 | |
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461 | funcs.str.proj=proj; |
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462 | funcs.str.projac=projac; |
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463 | |
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464 | sba_chkjac(&funcs, NULL, bi, jj, ii, 0, pnp, mnp, func_adata, jac_adata); |
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465 | } |
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466 | #endif /* 0 */ |
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