arma_hot
inline
void
spglue_plus::apply_noalias(SpMat<eT>& out, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
{
arma_extra_debug_sigprint();
arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "addition");
if( (pa.get_n_nonzero() != 0) && (pb.get_n_nonzero() != 0) )
{
out.set_size(pa.get_n_rows(), pa.get_n_cols());
// Resize memory to correct size.
out.mem_resize(n_unique(pa, pb, op_n_unique_add()));
// Now iterate across both matrices.
typename SpProxy<T1>::const_iterator_type x_it = pa.begin();
typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
typename SpProxy<T1>::const_iterator_type x_end = pa.end();
typename SpProxy<T2>::const_iterator_type y_end = pb.end();
uword cur_val = 0;
while( (x_it != x_end) || (y_it != y_end) )
{
if(x_it == y_it)
{
const eT val = (*x_it) + (*y_it);
if (val != eT(0))
{
access::rw(out.values[cur_val]) = val;
access::rw(out.row_indices[cur_val]) = x_it.row();
++access::rw(out.col_ptrs[x_it.col() + 1]);
++cur_val;
}
++x_it;
++y_it;
}
else
{
const uword x_it_row = x_it.row();
const uword x_it_col = x_it.col();
const uword y_it_row = y_it.row();
const uword y_it_col = y_it.col();
if((x_it_col < y_it_col) || ((x_it_col == y_it_col) && (x_it_row < y_it_row))) // if y is closer to the end
{
access::rw(out.values[cur_val]) = (*x_it);
access::rw(out.row_indices[cur_val]) = x_it_row;
++access::rw(out.col_ptrs[x_it_col + 1]);
++cur_val;
++x_it;
}
else
{
access::rw(out.values[cur_val]) = (*y_it);
access::rw(out.row_indices[cur_val]) = y_it_row;
++access::rw(out.col_ptrs[y_it_col + 1]);
++cur_val;
++y_it;
}
}
}
const uword out_n_cols = out.n_cols;
uword* col_ptrs = access::rwp(out.col_ptrs);
// Fix column pointers to be cumulative.
for(uword c = 1; c <= out_n_cols; ++c)
{
col_ptrs[c] += col_ptrs[c - 1];
}
}
else
{
if(pa.get_n_nonzero() == 0)
{
out = pb.Q;
return;
}
if(pb.get_n_nonzero() == 0)
{
out = pa.Q;
return;
}
}
}
arma_hot
inline
void
spglue_minus::apply_noalias(SpMat<eT>& result, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
{
arma_extra_debug_sigprint();
arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "subtraction");
result.set_size(pa.get_n_rows(), pa.get_n_cols());
// Resize memory to correct size.
result.mem_resize(n_unique(pa, pb, op_n_unique_sub()));
// Now iterate across both matrices.
typename SpProxy<T1>::const_iterator_type x_it = pa.begin();
typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
uword cur_val = 0;
while((x_it.pos() < pa.get_n_nonzero()) || (y_it.pos() < pb.get_n_nonzero()))
{
if(x_it == y_it)
{
const typename T1::elem_type val = (*x_it) - (*y_it);
if (val != 0)
{
access::rw(result.values[cur_val]) = val;
access::rw(result.row_indices[cur_val]) = x_it.row();
++access::rw(result.col_ptrs[x_it.col() + 1]);
++cur_val;
}
++x_it;
++y_it;
}
else
{
if((x_it.col() < y_it.col()) || ((x_it.col() == y_it.col()) && (x_it.row() < y_it.row()))) // if y is closer to the end
{
access::rw(result.values[cur_val]) = (*x_it);
access::rw(result.row_indices[cur_val]) = x_it.row();
++access::rw(result.col_ptrs[x_it.col() + 1]);
++cur_val;
++x_it;
}
else
{
access::rw(result.values[cur_val]) = -(*y_it);
access::rw(result.row_indices[cur_val]) = y_it.row();
++access::rw(result.col_ptrs[y_it.col() + 1]);
++cur_val;
++y_it;
}
}
}
// Fix column pointers to be cumulative.
for(uword c = 1; c <= result.n_cols; ++c)
{
access::rw(result.col_ptrs[c]) += result.col_ptrs[c - 1];
}
}
arma_hot
inline
void
spglue_minus::apply_noalias(SpMat<eT>& out, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
{
arma_extra_debug_sigprint();
arma_debug_assert_same_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "subtraction");
if(pa.get_n_nonzero() == 0) { out = pb.Q; out *= eT(-1); return; }
if(pb.get_n_nonzero() == 0) { out = pa.Q; return; }
const uword max_n_nonzero = spglue_elem_helper::max_n_nonzero_plus(pa, pb);
// Resize memory to upper bound
out.reserve(pa.get_n_rows(), pa.get_n_cols(), max_n_nonzero);
// Now iterate across both matrices.
typename SpProxy<T1>::const_iterator_type x_it = pa.begin();
typename SpProxy<T1>::const_iterator_type x_end = pa.end();
typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
typename SpProxy<T2>::const_iterator_type y_end = pb.end();
uword count = 0;
while( (x_it != x_end) || (y_it != y_end) )
{
eT out_val;
const uword x_it_row = x_it.row();
const uword x_it_col = x_it.col();
const uword y_it_row = y_it.row();
const uword y_it_col = y_it.col();
bool use_y_loc = false;
if(x_it == y_it)
{
out_val = (*x_it) - (*y_it);
++x_it;
++y_it;
}
else
{
if((x_it_col < y_it_col) || ((x_it_col == y_it_col) && (x_it_row < y_it_row))) // if y is closer to the end
{
out_val = (*x_it);
++x_it;
}
else
{
out_val = -(*y_it); // take the negative
++y_it;
use_y_loc = true;
}
}
if(out_val != eT(0))
{
access::rw(out.values[count]) = out_val;
const uword out_row = (use_y_loc == false) ? x_it_row : y_it_row;
const uword out_col = (use_y_loc == false) ? x_it_col : y_it_col;
access::rw(out.row_indices[count]) = out_row;
access::rw(out.col_ptrs[out_col + 1])++;
++count;
}
}
const uword out_n_cols = out.n_cols;
uword* col_ptrs = access::rwp(out.col_ptrs);
// Fix column pointers to be cumulative.
for(uword c = 1; c <= out_n_cols; ++c)
{
col_ptrs[c] += col_ptrs[c - 1];
}
if(count < max_n_nonzero)
{
if(count <= (max_n_nonzero/2))
{
out.mem_resize(count);
}
else
{
// quick resize without reallocating memory and copying data
access::rw( out.n_nonzero) = count;
access::rw( out.values[count]) = eT(0);
access::rw(out.row_indices[count]) = uword(0);
}
}
}
arma_hot
inline
void
spglue_times::apply_noalias(SpMat<eT>& c, const SpProxy<T1>& pa, const SpProxy<T2>& pb)
{
arma_extra_debug_sigprint();
const uword x_n_rows = pa.get_n_rows();
const uword x_n_cols = pa.get_n_cols();
const uword y_n_rows = pb.get_n_rows();
const uword y_n_cols = pb.get_n_cols();
arma_debug_assert_mul_size(x_n_rows, x_n_cols, y_n_rows, y_n_cols, "matrix multiplication");
// First we must determine the structure of the new matrix (column pointers).
// This follows the algorithm described in 'Sparse Matrix Multiplication
// Package (SMMP)' (R.E. Bank and C.C. Douglas, 2001). Their description of
// "SYMBMM" does not include anything about memory allocation. In addition it
// does not consider that there may be elements which space may be allocated
// for but which evaluate to zero anyway. So we have to modify the algorithm
// to work that way. For the "SYMBMM" implementation we will not determine
// the row indices but instead just the column pointers.
//SpMat<typename T1::elem_type> c(x_n_rows, y_n_cols); // Initializes col_ptrs to 0.
c.zeros(x_n_rows, y_n_cols);
//if( (pa.get_n_elem() == 0) || (pb.get_n_elem() == 0) )
if( (pa.get_n_nonzero() == 0) || (pb.get_n_nonzero() == 0) )
{
return;
}
// Auxiliary storage which denotes when items have been found.
podarray<uword> index(x_n_rows);
index.fill(x_n_rows); // Fill with invalid links.
typename SpProxy<T2>::const_iterator_type y_it = pb.begin();
typename SpProxy<T2>::const_iterator_type y_end = pb.end();
// SYMBMM: calculate column pointers for resultant matrix to obtain a good
// upper bound on the number of nonzero elements.
uword cur_col_length = 0;
uword last_ind = x_n_rows + 1;
do
{
const uword y_it_row = y_it.row();
// Look through the column that this point (*y_it) could affect.
typename SpProxy<T1>::const_iterator_type x_it = pa.begin_col(y_it_row);
while(x_it.col() == y_it_row)
{
// A point at x(i, j) and y(j, k) implies a point at c(i, k).
if(index[x_it.row()] == x_n_rows)
{
index[x_it.row()] = last_ind;
last_ind = x_it.row();
++cur_col_length;
}
++x_it;
}
const uword old_col = y_it.col();
++y_it;
// See if column incremented.
if(old_col != y_it.col())
{
// Set column pointer (this is not a cumulative count; that is done later).
access::rw(c.col_ptrs[old_col + 1]) = cur_col_length;
cur_col_length = 0;
// Return index markers to zero. Use last_ind for traversal.
while(last_ind != x_n_rows + 1)
{
const uword tmp = index[last_ind];
index[last_ind] = x_n_rows;
last_ind = tmp;
}
}
}
while(y_it != y_end);
// Accumulate column pointers.
for(uword i = 0; i < c.n_cols; ++i)
{
access::rw(c.col_ptrs[i + 1]) += c.col_ptrs[i];
}
// Now that we know a decent bound on the number of nonzero elements, allocate
// the memory and fill it.
c.mem_resize(c.col_ptrs[c.n_cols]);
// Now the implementation of the NUMBMM algorithm.
uword cur_pos = 0; // Current position in c matrix.
podarray<eT> sums(x_n_rows); // Partial sums.
sums.zeros();
// setting the size of 'sorted_indices' to x_n_rows is a better-than-nothing guess;
// the correct minimum size is determined later
podarray<uword> sorted_indices(x_n_rows);
// last_ind is already set to x_n_rows, and cur_col_length is already set to 0.
// We will loop through all columns as necessary.
uword cur_col = 0;
while(cur_col < c.n_cols)
{
// Skip to next column with elements in it.
while((cur_col < c.n_cols) && (c.col_ptrs[cur_col] == c.col_ptrs[cur_col + 1]))
{
// Update current column pointer to actual number of nonzero elements up
// to this point.
access::rw(c.col_ptrs[cur_col]) = cur_pos;
++cur_col;
}
if(cur_col == c.n_cols)
{
break;
}
// Update current column pointer.
access::rw(c.col_ptrs[cur_col]) = cur_pos;
// Check all elements in this column.
typename SpProxy<T2>::const_iterator_type y_col_it = pb.begin_col(cur_col);
while(y_col_it.col() == cur_col)
{
// Check all elements in the column of the other matrix corresponding to
// the row of this column.
typename SpProxy<T1>::const_iterator_type x_col_it = pa.begin_col(y_col_it.row());
const eT y_value = (*y_col_it);
while(x_col_it.col() == y_col_it.row())
{
// A point at x(i, j) and y(j, k) implies a point at c(i, k).
// Add to partial sum.
const eT x_value = (*x_col_it);
sums[x_col_it.row()] += (x_value * y_value);
// Add point if it hasn't already been marked.
if(index[x_col_it.row()] == x_n_rows)
{
index[x_col_it.row()] = last_ind;
last_ind = x_col_it.row();
}
++x_col_it;
}
++y_col_it;
}
// Now sort the indices that were used in this column.
//podarray<uword> sorted_indices(c.col_ptrs[cur_col + 1] - c.col_ptrs[cur_col]);
sorted_indices.set_min_size(c.col_ptrs[cur_col + 1] - c.col_ptrs[cur_col]);
// .set_min_size() can only enlarge the array to the specified size,
// hence if we request a smaller size than already allocated,
// no new memory allocation is done
uword cur_index = 0;
while(last_ind != x_n_rows + 1)
{
const uword tmp = last_ind;
// Check that it wasn't a "fake" nonzero element.
if(sums[tmp] != eT(0))
{
// Assign to next open position.
sorted_indices[cur_index] = tmp;
++cur_index;
}
last_ind = index[tmp];
index[tmp] = x_n_rows;
}
// Now sort the indices.
if (cur_index != 0)
{
op_sort::direct_sort_ascending(sorted_indices.memptr(), cur_index);
for(uword k = 0; k < cur_index; ++k)
{
const uword row = sorted_indices[k];
access::rw(c.row_indices[cur_pos]) = row;
access::rw(c.values[cur_pos]) = sums[row];
sums[row] = eT(0);
++cur_pos;
}
}
// Move to next column.
++cur_col;
}
// Update last column pointer and resize to actual memory size.
access::rw(c.col_ptrs[c.n_cols]) = cur_pos;
c.mem_resize(cur_pos);
}