bfgs_funcs.cpp

/*************************************************************
  Generalized-ICP Copyright (c) 2009 Aleksandr Segal.
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  or promote products derived from this software
  without specific prior written permission.

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*************************************************************/

#include "optimize.h"

namespace dgc {
  namespace gicp {
    // GICP cost function
    double GICPOptimizer::f(const gsl_vector *x, void *params) {
      GICPOptData *opt_data = (GICPOptData *)params;
      double pt1[3];
      double pt2[3]; 
      double res[3]; // residual
      double temp[3];
      gsl_vector_view gsl_pt1 = gsl_vector_view_array(pt1, 3);
      gsl_vector_view gsl_pt2 = gsl_vector_view_array(pt2, 3);
      gsl_vector_view gsl_res = gsl_vector_view_array(res, 3);
      gsl_vector_view gsl_temp = gsl_vector_view_array(temp, 3);
      gsl_matrix_view gsl_M;
      dgc_transform_t t;

      // initialize the temp variable; if it happens to be NaN at start, bad things will happen in blas routines below
      temp[0] = 0;
      temp[1] = 0;
      temp[2] = 0;
      

      // take the base transformation
      dgc_transform_copy(t, opt_data->base_t); 
      // apply the current state
      apply_state(t, x);
            
      double f = 0;
      double temp_double = 0;
      int N = opt_data->p1->Size();
      for(int i = 0; i < N; i++) {
	int j = opt_data->nn_indecies[i];	
	if(j != -1) {
	  // get point 1
	  pt1[0] = (*opt_data->p1)[i].x;
	  pt1[1] = (*opt_data->p1)[i].y;
	  pt1[2] = (*opt_data->p1)[i].z;
	  
	  // get point 2
	  pt2[0] = (*opt_data->p2)[j].x;
	  pt2[1] = (*opt_data->p2)[j].y;
	  pt2[2] = (*opt_data->p2)[j].z;
	  
	  //get M-matrix
	  gsl_M = gsl_matrix_view_array(&opt_data->M[i][0][0], 3, 3);
	  
	  
	  //transform point 1
	  dgc_transform_point(&pt1[0], &pt1[1], &pt1[2], t);
	  res[0] = pt1[0] - pt2[0];
	  res[1] = pt1[1] - pt2[1];
	  res[2] = pt1[2] - pt2[2];

	  //cout << "res: (" << res[0] << ", " <<res[1] <<", " << res[2] << ")" << endl;
	  
	  // temp := M*res
	  gsl_blas_dsymv(CblasLower, 1., &gsl_M.matrix, &gsl_res.vector, 0., &gsl_temp.vector);
	  // temp_double := res'*temp = temp'*M*temp
	  gsl_blas_ddot(&gsl_res.vector, &gsl_temp.vector, &temp_double);
	  // increment total error
	  
	  f += temp_double/(double)opt_data->num_matches;	  
	  //cout << "temp: " << temp_double << endl;
	  //cout << "f: " << f << "\t (" << opt_data->num_matches << ")" << endl;
	  //print_gsl_matrix(&gsl_M.matrix, "M");
	}
      }
      
      return f;
    }
    void GICPOptimizer::df(const gsl_vector *x, void *params, gsl_vector *g) {
      GICPOptData *opt_data = (GICPOptData *)params;
      double pt1[3];
      double pt2[3]; 
      double res[3]; // residual
      double temp[3]; // temp local vector
      double temp_mat[9]; // temp matrix used for accumulating the rotation gradient
      gsl_vector_view gsl_pt1 = gsl_vector_view_array(pt1, 3);
      gsl_vector_view gsl_pt2 = gsl_vector_view_array(pt2, 3);
      gsl_vector_view gsl_res = gsl_vector_view_array(res, 3);
      gsl_vector_view gsl_temp = gsl_vector_view_array(temp, 3);
      gsl_vector_view gsl_gradient_t = gsl_vector_subvector(g, 0, 3); // translation comp. of gradient
      gsl_matrix_view gsl_temp_mat_r = gsl_matrix_view_array(temp_mat, 3, 3);
      gsl_matrix_view gsl_M;
      dgc_transform_t t;
      double temp_double;
      
      // take the base transformation
      dgc_transform_copy(t, opt_data->base_t); 
      // apply the current state
      apply_state(t, x);
      
      // zero all accumulator variables
      gsl_vector_set_zero(g);
      gsl_vector_set_zero(&gsl_temp.vector);
      gsl_matrix_set_zero(&gsl_temp_mat_r.matrix);
            
      for(int i = 0; i < opt_data->p1->Size(); i++) {
	int j = opt_data->nn_indecies[i];	
	if(j != -1) {
	  // get point 1
	  pt1[0] = (*opt_data->p1)[i].x;
	  pt1[1] = (*opt_data->p1)[i].y;
	  pt1[2] = (*opt_data->p1)[i].z;
	  
	  // get point 2
	  pt2[0] = (*opt_data->p2)[j].x;
	  pt2[1] = (*opt_data->p2)[j].y;
	  pt2[2] = (*opt_data->p2)[j].z;
	  
	  //get M-matrix
	  gsl_M = gsl_matrix_view_array(&opt_data->M[i][0][0], 3, 3);	  

	  //transform point 1
	  dgc_transform_point(&pt1[0], &pt1[1], &pt1[2], t);
	  res[0] = pt1[0] - pt2[0];
	  res[1] = pt1[1] - pt2[1];
	  res[2] = pt1[2] - pt2[2];
	  
	  // temp := M*res
	  gsl_blas_dsymv(CblasLower, 1., &gsl_M.matrix, &gsl_res.vector, 0., &gsl_temp.vector);
	  // temp_double := res'*temp = temp'*M*res
	  gsl_blas_ddot(&gsl_res.vector, &gsl_temp.vector, &temp_double);

	  // increment total translation gradient:
	  // gsl_gradient_t += 2*M*res/num_matches
	  gsl_blas_dsymv(CblasLower, 2./(double)opt_data->num_matches, &gsl_M.matrix, &gsl_res.vector, 1., &gsl_gradient_t.vector);	  
	  
	  if(opt_data->solve_rotation) {
	    // compute rotation gradient here
	    // get back the original untransformed point to compute the rotation gradient
	    pt1[0] = (*opt_data->p1)[i].x;
	    pt1[1] = (*opt_data->p1)[i].y;
	    pt1[2] = (*opt_data->p1)[i].z;
	    dgc_transform_point(&pt1[0], &pt1[1], &pt1[2], opt_data->base_t);
	    gsl_blas_dger(2./(double)opt_data->num_matches, &gsl_pt1.vector, &gsl_temp.vector, &gsl_temp_mat_r.matrix);
	  }
	}
      }
      // the above loop sets up the gradient with respect to the translation, and the matrix derivative w.r.t. the rotation matrix
      // this code sets up the matrix derivatives dR/dPhi, dR/dPsi, dR/dTheta. i.e. the derivatives of the whole rotation matrix with respect to the euler angles
      // note that this code assumes the XYZ order of euler angles, with the Z rotation corresponding to bearing. This means the Z angle is negative of what it would be
      // in the regular XYZ euler-angle convention.
      
      // now use the d/dR matrix to compute the derivative with respect to euler angles and put it directly into g[3], g[4], g[5];
      if(opt_data->solve_rotation) {
	compute_dr(x, &gsl_temp_mat_r.matrix, g);
      }
    }
    
    void GICPOptimizer::fdf(const gsl_vector *x, void *params, double * f, gsl_vector *g) {
      GICPOptData *opt_data = (GICPOptData *)params;
      double pt1[3];
      double pt2[3]; 
      double res[3]; // residual
      double temp[3]; // temp local vector
      double temp_mat[9]; // temp matrix used for accumulating the rotation gradient
      gsl_vector_view gsl_pt1 = gsl_vector_view_array(pt1, 3);
      gsl_vector_view gsl_pt2 = gsl_vector_view_array(pt2, 3);
      gsl_vector_view gsl_res = gsl_vector_view_array(res, 3);
      gsl_vector_view gsl_temp = gsl_vector_view_array(temp, 3);
      gsl_vector_view gsl_gradient_t = gsl_vector_subvector(g, 0, 3); // translation comp. of gradient
      gsl_vector_view gsl_gradient_r = gsl_vector_subvector(g, 3, 3); // rotation comp. of gradient
      gsl_matrix_view gsl_temp_mat_r = gsl_matrix_view_array(temp_mat, 3, 3);
      gsl_matrix_view gsl_M;
      dgc_transform_t t;
      double temp_double;

      // take the base transformation
      dgc_transform_copy(t, opt_data->base_t); 
      // apply the current state      
      apply_state(t, x);
            
      // zero all accumulator variables
      *f = 0;
      gsl_vector_set_zero(g);
      gsl_vector_set_zero(&gsl_temp.vector);
      gsl_matrix_set_zero(&gsl_temp_mat_r.matrix);
      
      for(int i = 0; i < opt_data->p1->Size(); i++) {
	int j = opt_data->nn_indecies[i];	
	if(j != -1) {
	  // get point 1
	  pt1[0] = (*opt_data->p1)[i].x;
	  pt1[1] = (*opt_data->p1)[i].y;
	  pt1[2] = (*opt_data->p1)[i].z;
	  
	  // get point 2
	  pt2[0] = (*opt_data->p2)[j].x;
	  pt2[1] = (*opt_data->p2)[j].y;
	  pt2[2] = (*opt_data->p2)[j].z;
	  
	  //cout << "accessing " << i << " of " << opt_data->p1->Size() << ", " << opt_data->p2->Size() << endl;
	  //get M-matrix
	  gsl_M = gsl_matrix_view_array(&opt_data->M[i][0][0], 3, 3);	  
	  
	  //transform point 1
	  dgc_transform_point(&pt1[0], &pt1[1], &pt1[2], t);
	  res[0] = pt1[0] - pt2[0];
	  res[1] = pt1[1] - pt2[1];
	  res[2] = pt1[2] - pt2[2];
	  
	  // compute the transformed residual
	  // temp := M*res
	  //print_gsl_matrix(&gsl_M.matrix, "gsl_m");
	  gsl_blas_dsymv(CblasLower, 1., &gsl_M.matrix, &gsl_res.vector, 0., &gsl_temp.vector);
	  
	  // compute M-norm of the residual
	  // temp_double := res'*temp = temp'*M*res
	  gsl_blas_ddot(&gsl_res.vector, &gsl_temp.vector, &temp_double);
	  
	  // accumulate total error: f += res'*M*res
	  *f += temp_double/(double)opt_data->num_matches;
	  
	  // accumulate translation gradient:
	  // gsl_gradient_t += 2*M*res
	  gsl_blas_dsymv(CblasLower, 2./(double)opt_data->num_matches, &gsl_M.matrix, &gsl_res.vector, 1., &gsl_gradient_t.vector);	  
	  
	  if(opt_data->solve_rotation) {
	    // accumulate the rotation gradient matrix
	    // get back the original untransformed point to compute the rotation gradient
	    pt1[0] = (*opt_data->p1)[i].x;
	    pt1[1] = (*opt_data->p1)[i].y;
	    pt1[2] = (*opt_data->p1)[i].z;
	    dgc_transform_point(&pt1[0], &pt1[1], &pt1[2], opt_data->base_t);
	    // gsl_temp_mat_r += 2*(gsl_temp).(gsl_pt1)' [ = (2*M*residual).(gsl_pt1)' ]	  
	    gsl_blas_dger(2./(double)opt_data->num_matches, &gsl_pt1.vector, &gsl_temp.vector, &gsl_temp_mat_r.matrix); 
	  }
	}
      }      
      // the above loop sets up the gradient with respect to the translation, and the matrix derivative w.r.t. the rotation matrix
      // this code sets up the matrix derivatives dR/dPhi, dR/dPsi, dR/dTheta. i.e. the derivatives of the whole rotation matrix with respect to the euler angles
      // note that this code assumes the XYZ order of euler angles, with the Z rotation corresponding to bearing. This means the Z angle is negative of what it would be
      // in the regular XYZ euler-angle convention.
      if(opt_data->solve_rotation) {
	// now use the d/dR matrix to compute the derivative with respect to euler angles and put it directly into g[3], g[4], g[5];
	compute_dr(x, &gsl_temp_mat_r.matrix, g);
      }
    }
  }
}