int submatrix_determinant(const integer_matrix& matrix, const submatrix_indices& submatrix)
{
typedef boost::numeric::ublas::matrix_indirect <const integer_matrix, submatrix_indices::indirect_array_type> indirect_matrix_t;
assert (submatrix.rows.size() == submatrix.columns.size());
const indirect_matrix_t indirect_matrix(matrix, submatrix.rows, submatrix.columns);
boost::numeric::ublas::matrix <float> float_matrix(indirect_matrix);
boost::numeric::ublas::permutation_matrix <size_t> permutation_matrix(float_matrix.size1());
/// LU-factorize
int result = boost::numeric::ublas::lu_factorize(float_matrix, permutation_matrix);
if (result != 0)
return 0;
/// Calculate the determinant as a product of the diagonal entries, taking the permutation matrix into account.
float det = 1.0f;
for (size_t i = 0; i < float_matrix.size1(); ++i)
{
det *= float_matrix(i, i);
if (i != permutation_matrix(i))
det = -det;
}
return (int) det;
}
/* Initialize MAX1 maps */
void InitializeMAX1map()
{
int img, orient, x, y, here, i, trace[2];
/* calculate MAX1 maps and record the shifts */
pooledMax1map = float_matrix(numOrient, sizexSubsample*sizeySubsample);
MAX1map = float_matrix(numImage*numOrient, sizexSubsample*sizeySubsample);
trackMap = int_matrix(numImage*numOrient, sizexSubsample*sizeySubsample);
startx = floor((halfFilterSize+1)/subsample)+1+locationShiftLimit;
endx = floor((sizex-halfFilterSize)/subsample)-1-locationShiftLimit;
starty = floor((halfFilterSize+1)/subsample)+1+locationShiftLimit;
endy = floor((sizey-halfFilterSize)/subsample)-1-locationShiftLimit;
for (x=startx; x<=endx; x++)
for (y=starty; y<=endy; y++)
{
here = px(x, y, sizexSubsample, sizeySubsample);
for (orient=0; orient<numOrient; orient++)
{
pooledMax1map[orient][here] = 0.;
for (img=0; img<numImage; img++)
{
i = orient*numImage+img;
MAX1map[i][here] = LocalMaximumPooling(img, orient, x*subsample, y*subsample, trace);
trackMap[i][here] = trace[0];
pooledMax1map[orient][here] += MAX1map[i][here];
}
}
}
}
/* Initialize MAX1 maps */
void Initialize()
{
int img, orient, x, y, here, i, trace[2];
pooledMax1map = float_matrix(numOrient, sizexSubsample*sizeySubsample);
startx = floor(((double)halfFilterSize+1)/subsample)+1+locationShiftLimit;
endx = floor((double)(sizex-halfFilterSize)/subsample)-1-locationShiftLimit;
starty = floor((double)(halfFilterSize+1)/subsample)+1+locationShiftLimit;
endy = floor((double)(sizey-halfFilterSize)/subsample)-1-locationShiftLimit;
for (x=startx; x<=endx; x++)
for (y=starty; y<=endy; y++)
{
here = px(x, y, sizexSubsample, sizeySubsample);
for (orient=0; orient<numOrient; orient++)
{
pooledMax1map[orient][here] = 0.;
for (img=0; img<numImage; img++)
pooledMax1map[orient][here] += MAX1map[orient*numImage+img][here];
}
}
}
/* compute sigmoid transformation */
void LocalNormalize()
{
int x, y, here, orient, leftx, rightx, upy, lowy, k, startx[8], endx[8], starty[8], endy[8], copyx[8], copyy[8], fx, fy;
float maxAverage, averageDivide;
/* compute the sum over all the orientations at each pixel */
SUM1mapAll = float_matrix(sizex, sizey);
for (x=0; x<sizex; x++)
for (y=0; y<sizey; y++)
{
SUM1mapAll[x][y] = 0.;
here = px(x+1, y+1, sizex, sizey);
for (orient=0; orient<numOrient; orient++)
{
SUM1mapAll[x][y] += SUM1map[orient][here];
}
}
/* compute the integral map */
integralMap = float_matrix(sizex, sizey);
integralMap[0][0] = SUM1mapAll[0][0];
for (x=1; x<sizex; x++)
integralMap[x][0] = integralMap[x-1][0]+SUM1mapAll[x][0];
for (y=1; y<sizey; y++)
integralMap[0][y] = integralMap[0][y-1]+SUM1mapAll[0][y];
for (x=1; x<sizex; x++)
for (y=1; y<sizey; y++)
integralMap[x][y] = integralMap[x][y-1]+integralMap[x-1][y]-integralMap[x-1][y-1]+SUM1mapAll[x][y];
/* compute the local average around each pixel */
averageMap = float_matrix(sizex, sizey);
leftx = halfFilterSize+localHalfx; rightx = sizex-halfFilterSize-localHalfx;
upy = halfFilterSize+localHalfy; lowy = sizey-halfFilterSize-localHalfy;
maxAverage = NEGMAX;
if ((leftx<rightx)&&(upy<lowy))
{
for (x=leftx; x<rightx; x++)
for (y=upy; y<lowy; y++)
{
averageMap[x][y] = (integralMap[x+localHalfx][y+localHalfy]
- integralMap[x-localHalfx-1][y+localHalfy] - integralMap[x+localHalfx][y-localHalfy-1]
+ integralMap[x-localHalfx-1][y-localHalfy-1])/(2.*localHalfx+1.)/(2.*localHalfy+1.)/numOrient;
if (maxAverage < averageMap[x][y])
maxAverage = averageMap[x][y];
}
/* take care of the boundaries */
k = 0;
/* four corners */
startx[k] = 0; endx[k] = leftx; starty[k] = 0; endy[k] = upy; copyx[k] = leftx; copyy[k] = upy; k++;
startx[k] = 0; endx[k] = leftx; starty[k] = lowy; endy[k] = sizey; copyx[k] = leftx; copyy[k] = lowy-1; k++;
startx[k] = rightx; endx[k] = sizex; starty[k] = 0; endy[k] = upy; copyx[k] = rightx-1; copyy[k] = upy; k++;
startx[k] = rightx; endx[k] = sizex; starty[k] = lowy; endy[k] = sizey; copyx[k] = rightx-1; copyy[k] = lowy-1; k++;
/* four sides */
startx[k] = 0; endx[k] = leftx; starty[k] = upy; endy[k] = lowy; copyx[k] = leftx; copyy[k] = -1; k++;
startx[k] = rightx; endx[k] = sizex; starty[k] = upy; endy[k] = lowy; copyx[k] = rightx-1; copyy[k] = -1; k++;
startx[k] = leftx; endx[k] = rightx; starty[k] = 0; endy[k] = upy; copyx[k] = -1; copyy[k] = upy; k++;
startx[k] = leftx; endx[k] = rightx; starty[k] = lowy; endy[k] = sizey; copyx[k] = -1; copyy[k] = lowy-1; k++;
/* propagate the average to the boundaries */
for (k=0; k<8; k++)
for (x=startx[k]; x<endx[k]; x++)
for (y=starty[k]; y<endy[k]; y++)
{
if (copyx[k]<0)
fx = x;
else
fx = copyx[k];
if (copyy[k]<0)
fy = y;
else
fy = copyy[k];
averageMap[x][y] = averageMap[fx][fy];
}
/* normalize the responses by local averages */
for (x=0; x<sizex; x++)
for (y=0; y<sizey; y++)
{
here = px(x+1, y+1, sizex, sizey);
averageDivide = MAX(averageMap[x][y], maxAverage*thresholdFactor);
for (orient=0; orient<numOrient; orient++)
SUM1map[orient][here] /= averageDivide;
}
}
/* free intermediate matrices */
free_matrix(SUM1mapAll, sizex, sizey);
free_matrix(integralMap, sizex, sizey);
free_matrix(averageMap, sizex, sizey);
}
int closest_vector(IntMatrix &b, const IntVect &int_target, IntVect &sol_coord, int method, int flags)
{
// d = lattice dimension (note that it might decrease during preprocessing)
int d = b.get_rows();
// n = dimension of the space
int n = b.get_cols();
FPLLL_CHECK(d > 0 && n > 0, "closestVector: empty matrix");
FPLLL_CHECK(d <= n, "closestVector: number of vectors > size of the vectors");
// Sets the floating-point precision
// Error bounds on GSO are valid if prec >= minprec
double rho;
int min_prec = gso_min_prec(rho, d, LLL_DEF_DELTA, LLL_DEF_ETA);
int prec = max(53, min_prec + 10);
int old_prec = Float::set_prec(prec);
// Allocates space for vectors and matrices in constructors
IntMatrix empty_mat;
MatGSO<Integer, Float> gso(b, empty_mat, empty_mat, GSO_INT_GRAM);
FloatVect target_coord;
Float max_dist;
Integer itmp1;
// Computes the Gram-Schmidt orthogonalization in floating-point
gso.update_gso();
gen_zero_vect(sol_coord, d);
/* Applies Babai's algorithm. Because we use fp, it might be necessary to
do it several times (if ||target|| >> ||b_i||) */
FloatMatrix float_matrix(d, n);
FloatVect target(n), babai_sol;
IntVect int_new_target = int_target;
for (int i = 0; i < d; i++)
for (int j = 0; j < n; j++)
float_matrix(i, j).set_z(b(i, j));
for (int loop_idx = 0;; loop_idx++)
{
if (loop_idx >= 0x100 && ((loop_idx & (loop_idx - 1)) == 0))
FPLLL_INFO("warning: possible infinite loop in Babai's algorithm");
for (int i = 0; i < n; i++)
{
target[i].set_z(int_new_target[i]);
}
babai(float_matrix, gso.get_mu_matrix(), gso.get_r_matrix(), target, babai_sol);
int idx;
for (idx = 0; idx < d && babai_sol[idx] >= -1 && babai_sol[idx] <= 1; idx++)
{
}
if (idx == d)
break;
for (int i = 0; i < d; i++)
{
itmp1.set_f(babai_sol[i]);
sol_coord[i].add(sol_coord[i], itmp1);
for (int j = 0; j < n; j++)
int_new_target[j].submul(itmp1, b(i, j));
}
}
// FPLLL_TRACE("BabaiSol=" << sol_coord);
get_gscoords(float_matrix, gso.get_mu_matrix(), gso.get_r_matrix(), target, target_coord);
/* Computes a very large bound to make the algorithm work
until the first solution is found */
max_dist = 0.0;
for (int i = 1; i < d; i++)
{
// get_r_exp(i, i) = r(i, i) because gso is initialized without GSO_ROW_EXPO
max_dist.add(max_dist, gso.get_r_exp(i, i));
}
vector<int> max_indices;
if (method & CVPM_PROVED)
{
// For Exact CVP, we need to reset enum below depth with maximal r_i
max_indices = vector<int>(d);
int cur, max_index, previous_max_index;
previous_max_index = max_index = d-1;
Float max_val;
while (max_index > 0)
{
max_val = gso.get_r_exp(max_index, max_index);
for (cur = previous_max_index - 1 ; cur >= 0 ; --cur)
{
if (max_val <= gso.get_r_exp(cur, cur))
{
max_val = gso.get_r_exp(cur, cur);
max_index = cur;
}
}
for (cur = max_index ; cur < previous_max_index ; ++cur)
max_indices[cur] = max_index;
max_indices[previous_max_index] = previous_max_index;
previous_max_index = max_index;
--max_index;
}
}
FPLLL_TRACE("max_indices " << max_indices);
FastEvaluator<Float> evaluator(n, gso.get_mu_matrix(), gso.get_r_matrix(), EVALMODE_CV);
// Main loop of the enumeration
Enumeration<Float> enumobj(gso, evaluator, max_indices);
enumobj.enumerate(0, d, max_dist, 0, target_coord);
int result = RED_ENUM_FAILURE;
if (!evaluator.sol_coord.empty())
{
FPLLL_TRACE("evaluator.sol_coord=" << evaluator.sol_coord);
if (flags & CVP_VERBOSE)
FPLLL_INFO("max_dist=" << max_dist);
for (int i = 0; i < d; i++)
{
itmp1.set_f(evaluator.sol_coord[i]);
sol_coord[i].add(sol_coord[i], itmp1);
}
result = RED_SUCCESS;
}
Float::set_prec(old_prec);
return result;
}