inline
Row<eT>::Row()
: Mat<eT>(arma_vec_indicator(), 2)
{
arma_extra_debug_sigprint();
}
inline
GlueCube<T1,T2,glue_type>::~GlueCube()
{
arma_extra_debug_sigprint();
}
inline
bool
eig_gen
(
Col< std::complex<eT> >& eigval,
Mat< std::complex<eT> >& eigvec,
const Base<eT, T1>& X,
const char side = 'r',
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
//std::cout << "real" << std::endl;
arma_debug_check( ( ((void*)(&eigval)) == ((void*)(&eigvec)) ), "eig_gen(): eigval is an alias of eigvec" );
Mat<eT> dummy_eigvec;
Mat<eT> tmp_eigvec;
bool status;
switch(side)
{
case 'r':
status = auxlib::eig_gen(eigval, dummy_eigvec, tmp_eigvec, X, side);
break;
case 'l':
status = auxlib::eig_gen(eigval, tmp_eigvec, dummy_eigvec, X, side);
break;
default:
arma_stop("eig_gen(): parameter 'side' is invalid");
status = false;
}
if(status == false)
{
eigval.reset();
eigvec.reset();
arma_bad("eig_gen(): failed to converge", false);
}
else
{
const uword n = eigval.n_elem;
if(n > 0)
{
eigvec.set_size(n,n);
for(uword j=0; j<n; ++j)
{
if( (j < n-1) && (eigval[j] == std::conj(eigval[j+1])) )
{
// eigvec.col(j) = Mat< std::complex<eT> >( tmp_eigvec.col(j), tmp_eigvec.col(j+1) );
// eigvec.col(j+1) = Mat< std::complex<eT> >( tmp_eigvec.col(j), -tmp_eigvec.col(j+1) );
for(uword i=0; i<n; ++i)
{
eigvec.at(i,j) = std::complex<eT>( tmp_eigvec.at(i,j), tmp_eigvec.at(i,j+1) );
eigvec.at(i,j+1) = std::complex<eT>( tmp_eigvec.at(i,j), -tmp_eigvec.at(i,j+1) );
}
++j;
}
else
{
// eigvec.col(i) = tmp_eigvec.col(i);
for(uword i=0; i<n; ++i)
{
eigvec.at(i,j) = std::complex<eT>(tmp_eigvec.at(i,j), eT(0));
}
}
}
}
}
return status;
}
inline
subview_cube_each1<eT>::~subview_cube_each1()
{
arma_extra_debug_sigprint();
}
inline
void
running_stat_vec_aux::update_stats(running_stat_vec< std::complex<T> >& x, const Mat< std::complex<T> >& sample)
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
const T N = x.counter.value();
if(N > T(0))
{
arma_debug_assert_same_size(x.r_mean, sample, "running_stat_vec(): dimensionality mismatch");
const u32 n_elem = sample.n_elem;
const eT* sample_mem = sample.memptr();
eT* r_mean_mem = x.r_mean.memptr();
T* r_var_mem = x.r_var.memptr();
eT* min_val_mem = x.min_val.memptr();
eT* max_val_mem = x.max_val.memptr();
T* min_val_norm_mem = x.min_val_norm.memptr();
T* max_val_norm_mem = x.max_val_norm.memptr();
const T N_plus_1 = x.counter.value_plus_1();
const T N_minus_1 = x.counter.value_minus_1();
if(x.calc_cov == true)
{
Mat<eT>& tmp1 = x.tmp1;
Mat<eT>& tmp2 = x.tmp2;
tmp1 = sample - x.r_mean;
if(sample.n_cols == 1)
{
tmp2 = conj(tmp1)*trans(tmp1);
}
else
{
tmp2 = trans(conj(tmp1))*tmp1;
}
x.r_cov *= (N_minus_1/N);
x.r_cov += tmp2 / N_plus_1;
}
for(u32 i=0; i<n_elem; ++i)
{
const eT& val = sample_mem[i];
const T val_norm = std::norm(val);
if(val_norm < min_val_norm_mem[i])
{
min_val_norm_mem[i] = val_norm;
min_val_mem[i] = val;
}
if(val_norm > max_val_norm_mem[i])
{
max_val_norm_mem[i] = val_norm;
max_val_mem[i] = val;
}
const eT& r_mean_val = r_mean_mem[i];
r_var_mem[i] = N_minus_1/N * r_var_mem[i] + std::norm(val - r_mean_val)/N_plus_1;
r_mean_mem[i] = r_mean_val + (val - r_mean_val)/N_plus_1;
}
}
else
{
arma_debug_check( (sample.is_vec() == false), "running_stat_vec(): given sample is not a vector");
x.r_mean.set_size(sample.n_rows, sample.n_cols);
x.r_var.zeros(sample.n_rows, sample.n_cols);
if(x.calc_cov == true)
{
x.r_cov.zeros(sample.n_elem, sample.n_elem);
}
x.min_val.set_size(sample.n_rows, sample.n_cols);
x.max_val.set_size(sample.n_rows, sample.n_cols);
x.min_val_norm.set_size(sample.n_rows, sample.n_cols);
x.max_val_norm.set_size(sample.n_rows, sample.n_cols);
const u32 n_elem = sample.n_elem;
const eT* sample_mem = sample.memptr();
eT* r_mean_mem = x.r_mean.memptr();
eT* min_val_mem = x.min_val.memptr();
eT* max_val_mem = x.max_val.memptr();
T* min_val_norm_mem = x.min_val_norm.memptr();
T* max_val_norm_mem = x.max_val_norm.memptr();
for(u32 i=0; i<n_elem; ++i)
{
const eT& val = sample_mem[i];
const T val_norm = std::norm(val);
r_mean_mem[i] = val;
min_val_mem[i] = val;
max_val_mem[i] = val;
min_val_norm_mem[i] = val_norm;
max_val_norm_mem[i] = val_norm;
}
}
x.counter++;
}
inline
std::streamsize
arma_ostream::modify_stream(std::ostream& o, typename SpMat<eT>::const_iterator begin, const uword n_elem, const typename arma_not_cx<eT>::result* junk)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
o.unsetf(ios::showbase);
o.unsetf(ios::uppercase);
o.unsetf(ios::showpos);
o.fill(' ');
std::streamsize cell_width;
bool use_layout_B = false;
bool use_layout_C = false;
for(typename SpMat<eT>::const_iterator it = begin; it.pos() < n_elem; ++it)
{
const eT val = *it;
if(
val >= eT(+100) ||
( (is_signed<eT>::value == true) && (val <= eT(-100)) ) ||
( (is_non_integral<eT>::value == true) && (val > eT(0)) && (val <= eT(+1e-4)) ) ||
( (is_non_integral<eT>::value == true) && (is_signed<eT>::value == true) && (val < eT(0)) && (val >= eT(-1e-4)) )
)
{
use_layout_C = true;
break;
}
if(
(val >= eT(+10)) || ( (is_signed<eT>::value == true) && (val <= eT(-10)) )
)
{
use_layout_B = true;
}
}
if(use_layout_C == true)
{
o.setf(ios::scientific);
o.setf(ios::right);
o.unsetf(ios::fixed);
o.precision(4);
cell_width = 13;
}
else
if(use_layout_B == true)
{
o.unsetf(ios::scientific);
o.setf(ios::right);
o.setf(ios::fixed);
o.precision(4);
cell_width = 10;
}
else
{
o.unsetf(ios::scientific);
o.setf(ios::right);
o.setf(ios::fixed);
o.precision(4);
cell_width = 9;
}
return cell_width;
}
inline
void
arma_ostream::print(std::ostream& o, const SpMat<eT>& m, const bool modify)
{
arma_extra_debug_sigprint();
const arma_ostream_state stream_state(o);
o.unsetf(ios::showbase);
o.unsetf(ios::uppercase);
o.unsetf(ios::showpos);
o.unsetf(ios::scientific);
o.setf(ios::right);
o.setf(ios::fixed);
o.precision(2);
const uword m_n_nonzero = m.n_nonzero;
o << "[matrix size: " << m.n_rows << 'x' << m.n_cols << "; n_nonzero: " << m_n_nonzero
<< "; density: " << ((m.n_elem > 0) ? (double(m_n_nonzero) / double(m.n_elem) * double(100)) : double(0))
<< "%]\n\n";
if(modify == false) { stream_state.restore(o); }
if(m_n_nonzero > 0)
{
const std::streamsize cell_width = modify ? modify_stream<eT>(o, m.begin(), m_n_nonzero) : o.width();
typename SpMat<eT>::const_iterator begin = m.begin();
while(begin != m.end())
{
const uword row = begin.row();
// TODO: change the maximum number of spaces before and after each location to be dependent on n_rows and n_cols
if(row < 10) { o << " "; }
else if(row < 100) { o << " "; }
else if(row < 1000) { o << " "; }
else if(row < 10000) { o << " "; }
else if(row < 100000) { o << ' '; }
const uword col = begin.col();
o << '(' << row << ", " << col << ") ";
if(col < 10) { o << " "; }
else if(col < 100) { o << " "; }
else if(col < 1000) { o << " "; }
else if(col < 10000) { o << " "; }
else if(col < 100000) { o << ' '; }
if(cell_width > 0) { o.width(cell_width); }
arma_ostream::print_elem(o, eT(*begin), modify);
o << '\n';
++begin;
}
o << '\n';
}
o.flush();
stream_state.restore(o);
}
inline
void
spop_var::apply_noalias
(
SpMat<typename T1::pod_type>& out,
const SpProxy<T1>& p,
const uword norm_type,
const uword dim
)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type in_eT;
//typedef typename T1::pod_type out_eT;
const uword p_n_rows = p.get_n_rows();
const uword p_n_cols = p.get_n_cols();
// TODO: this is slow; rewrite based on the approach used by sparse mean()
if(dim == 0) // find variance in each column
{
arma_extra_debug_print("spop_var::apply_noalias(): dim = 0");
out.set_size((p_n_rows > 0) ? 1 : 0, p_n_cols);
if( (p_n_rows == 0) || (p.get_n_nonzero() == 0) ) { return; }
for(uword col = 0; col < p_n_cols; ++col)
{
if(SpProxy<T1>::must_use_iterator)
{
// We must use an iterator; we can't access memory directly.
typename SpProxy<T1>::const_iterator_type it = p.begin_col(col);
typename SpProxy<T1>::const_iterator_type end = p.begin_col(col + 1);
const uword n_zero = p_n_rows - (end.pos() - it.pos());
// in_eT is used just to get the specialization right (complex / noncomplex)
out.at(0, col) = spop_var::iterator_var(it, end, n_zero, norm_type, in_eT(0));
}
else
{
// We can use direct memory access to calculate the variance.
out.at(0, col) = spop_var::direct_var
(
&p.get_values()[p.get_col_ptrs()[col]],
p.get_col_ptrs()[col + 1] - p.get_col_ptrs()[col],
p_n_rows,
norm_type
);
}
}
}
else
if(dim == 1) // find variance in each row
{
arma_extra_debug_print("spop_var::apply_noalias(): dim = 1");
out.set_size(p_n_rows, (p_n_cols > 0) ? 1 : 0);
if( (p_n_cols == 0) || (p.get_n_nonzero() == 0) ) { return; }
for(uword row = 0; row < p_n_rows; ++row)
{
// We have to use an iterator here regardless of whether or not we can
// directly access memory.
typename SpProxy<T1>::const_row_iterator_type it = p.begin_row(row);
typename SpProxy<T1>::const_row_iterator_type end = p.end_row(row);
const uword n_zero = p_n_cols - (end.pos() - it.pos());
out.at(row, 0) = spop_var::iterator_var(it, end, n_zero, norm_type, in_eT(0));
}
}
}
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.zeros(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
{
const eT val = (*x_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;
}
else
{
const eT val = (*y_it);
if(val != eT(0))
{
access::rw(out.values[cur_val]) = val;
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;
}
}
}
inline
typename arma_cx_only<typename T1::elem_type>::result
op_max::max_with_index(const Proxy<T1>& P, uword& index_of_max_val)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename get_pod_type<eT>::result T;
const uword n_elem = P.get_n_elem();
if(n_elem == 0)
{
arma_debug_check(true, "max(): object has no elements");
return Datum<eT>::nan;
}
T best_val = priv::most_neg<T>();
if(Proxy<T1>::prefer_at_accessor == false)
{
typedef typename Proxy<T1>::ea_type ea_type;
ea_type A = P.get_ea();
uword best_index = 0;
for(uword i=0; i<n_elem; ++i)
{
const T tmp = std::abs(A[i]);
if(tmp > best_val) { best_val = tmp; best_index = i; }
}
index_of_max_val = best_index;
return( A[best_index] );
}
else
{
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
uword best_row = 0;
uword best_col = 0;
uword best_index = 0;
if(n_rows == 1)
{
for(uword col=0; col < n_cols; ++col)
{
const T tmp = std::abs(P.at(0,col));
if(tmp > best_val) { best_val = tmp; best_col = col; }
}
best_index = best_col;
}
else
if(n_cols == 1)
{
for(uword row=0; row < n_rows; ++row)
{
const T tmp = std::abs(P.at(row,0));
if(tmp > best_val) { best_val = tmp; best_row = row; }
}
best_index = best_row;
}
else
{
uword count = 0;
for(uword col=0; col < n_cols; ++col)
for(uword row=0; row < n_rows; ++row)
{
const T tmp = std::abs(P.at(row,col));
if(tmp > best_val)
{
best_val = tmp;
best_row = row;
best_col = col;
best_index = count;
}
++count;
}
}
index_of_max_val = best_index;
return P.at(best_row, best_col);
}
}
inline
eT
spop_var::direct_var
(
const eT* const X,
const uword length,
const uword N,
const uword norm_type
)
{
arma_extra_debug_sigprint();
if(length >= 2 && N >= 2)
{
const eT acc1 = spop_mean::direct_mean(X, length, N);
eT acc2 = eT(0);
eT acc3 = eT(0);
uword i, j;
for(i = 0, j = 1; j < length; i += 2, j += 2)
{
const eT Xi = X[i];
const eT Xj = X[j];
const eT tmpi = acc1 - Xi;
const eT tmpj = acc1 - Xj;
acc2 += tmpi * tmpi + tmpj * tmpj;
acc3 += tmpi + tmpj;
}
if(i < length)
{
const eT Xi = X[i];
const eT tmpi = acc1 - Xi;
acc2 += tmpi * tmpi;
acc3 += tmpi;
}
// Now add in all zero elements.
acc2 += (N - length) * (acc1 * acc1);
acc3 += (N - length) * acc1;
const eT norm_val = (norm_type == 0) ? eT(N - 1) : eT(N);
const eT var_val = (acc2 - (acc3 * acc3) / eT(N)) / norm_val;
return var_val;
}
else if(length == 1 && N > 1) // if N == 1, then variance is zero.
{
const eT mean = X[0] / eT(N);
const eT val = mean - X[0];
const eT acc2 = (val * val) + (N - length) * (mean * mean);
const eT acc3 = val + (N - length) * mean;
const eT norm_val = (norm_type == 0) ? eT(N - 1) : eT(N);
const eT var_val = (acc2 - (acc3 * acc3) / eT(N)) / norm_val;
return var_val;
}
else
{
return eT(0);
}
}
inline
std::complex<T>
op_max::max(const subview< std::complex<T> >& X)
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
if(X.n_elem == 0)
{
arma_debug_check(true, "max(): object has no elements");
return Datum<eT>::nan;
}
const Mat<eT>& A = X.m;
const uword X_n_rows = X.n_rows;
const uword X_n_cols = X.n_cols;
const uword start_row = X.aux_row1;
const uword start_col = X.aux_col1;
const uword end_row_p1 = start_row + X_n_rows;
const uword end_col_p1 = start_col + X_n_cols;
T max_val = priv::most_neg<T>();
uword best_row = 0;
uword best_col = 0;
if(X_n_rows == 1)
{
best_col = 0;
for(uword col=start_col; col < end_col_p1; ++col)
{
const T tmp_val = std::abs( A.at(start_row, col) );
if(tmp_val > max_val)
{
max_val = tmp_val;
best_col = col;
}
}
best_row = start_row;
}
else
{
for(uword col=start_col; col < end_col_p1; ++col)
for(uword row=start_row; row < end_row_p1; ++row)
{
const T tmp_val = std::abs( A.at(row, col) );
if(tmp_val > max_val)
{
max_val = tmp_val;
best_row = row;
best_col = col;
}
}
}
return A.at(best_row, best_col);
}
inline
mtGlue<out_eT,T1,T2,glue_type>::~mtGlue()
{
arma_extra_debug_sigprint();
}
inline
Row<eT>::Row(const uword in_n_elem)
: Mat<eT>(arma_vec_indicator(), 1, in_n_elem, 2)
{
arma_extra_debug_sigprint();
}
inline
void
glue_join::apply_noalias(Mat<eT>& out, const Mat<eT>& A, const Mat<eT>& B, const uword join_type)
{
arma_extra_debug_sigprint();
const uword A_n_rows = A.n_rows;
const uword A_n_cols = A.n_cols;
const uword B_n_rows = B.n_rows;
const uword B_n_cols = B.n_cols;
if(join_type == 0)
{
arma_debug_check
(
( (A_n_cols != B_n_cols) && ( (A_n_rows > 0) || (A_n_cols > 0) ) && ( (B_n_rows > 0) || (B_n_cols > 0) ) ),
"join_cols() / join_vert(): number of columns must be the same"
);
}
else
{
arma_debug_check
(
( (A_n_rows != B.n_rows) && ( (A_n_rows > 0) || (A_n_cols > 0) ) && ( (B_n_rows > 0) || (B_n_cols > 0) ) ),
"join_rows() / join_horiz(): number of rows must be the same"
);
}
if(join_type == 0) // join columns (i.e. result matrix has more rows)
{
out.set_size( A_n_rows + B_n_rows, (std::max)(A_n_cols, B_n_cols) );
if( out.n_elem > 0 )
{
if(A.is_empty() == false)
{
out.submat(0, 0, A_n_rows-1, out.n_cols-1) = A;
}
if(B.is_empty() == false)
{
out.submat(A_n_rows, 0, out.n_rows-1, out.n_cols-1) = B;
}
}
}
else // join rows (i.e. result matrix has more columns)
{
out.set_size( (std::max)(A_n_rows, B_n_rows), A_n_cols + B_n_cols );
if( out.n_elem > 0 )
{
if(A.is_empty() == false)
{
out.submat(0, 0, out.n_rows-1, A.n_cols-1) = A;
}
if(B.is_empty() == false)
{
out.submat(0, A_n_cols, out.n_rows-1, out.n_cols-1) = B;
}
}
}
}
inline
static
void
apply_blas_type( Mat<eT>& C, const TA& A, const TB& B, const eT alpha = eT(1), const eT beta = eT(0) )
{
arma_extra_debug_sigprint();
if( (A.n_rows <= 4) && (A.n_rows == A.n_cols) && (A.n_rows == B.n_rows) && (B.n_rows == B.n_cols) && (is_cx<eT>::no) )
{
if(do_trans_B == false)
{
gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, B, alpha, beta);
}
else
{
Mat<eT> BB(B.n_rows, B.n_rows);
op_strans::apply_mat_noalias_tinysq(BB, B);
gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
}
}
else
{
#if defined(ARMA_USE_ATLAS)
{
arma_extra_debug_print("atlas::cblas_gemm()");
atlas::cblas_gemm<eT>
(
atlas::CblasColMajor,
(do_trans_A) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
(do_trans_B) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
C.n_rows,
C.n_cols,
(do_trans_A) ? A.n_rows : A.n_cols,
(use_alpha) ? alpha : eT(1),
A.mem,
(do_trans_A) ? A.n_rows : C.n_rows,
B.mem,
(do_trans_B) ? C.n_cols : ( (do_trans_A) ? A.n_rows : A.n_cols ),
(use_beta) ? beta : eT(0),
C.memptr(),
C.n_rows
);
}
#elif defined(ARMA_USE_BLAS)
{
arma_extra_debug_print("blas::gemm()");
const char trans_A = (do_trans_A) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
const char trans_B = (do_trans_B) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
const blas_int m = C.n_rows;
const blas_int n = C.n_cols;
const blas_int k = (do_trans_A) ? A.n_rows : A.n_cols;
const eT local_alpha = (use_alpha) ? alpha : eT(1);
const blas_int lda = (do_trans_A) ? k : m;
const blas_int ldb = (do_trans_B) ? n : k;
const eT local_beta = (use_beta) ? beta : eT(0);
arma_extra_debug_print( arma_boost::format("blas::gemm(): trans_A = %c") % trans_A );
arma_extra_debug_print( arma_boost::format("blas::gemm(): trans_B = %c") % trans_B );
blas::gemm<eT>
(
&trans_A,
&trans_B,
&m,
&n,
&k,
&local_alpha,
A.mem,
&lda,
B.mem,
&ldb,
&local_beta,
C.memptr(),
&m
);
}
#else
{
gemm_emul<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C,A,B,alpha,beta);
}
#endif
}
}
inline
void
op_diagmat::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_diagmat>& X)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const unwrap<T1> tmp(X.m);
const Mat<eT>& A = tmp.M;
if(A.is_vec() == true)
{
// generate a diagonal matrix out of a vector
const u32 N = A.n_elem;
const eT* A_mem = A.memptr();
if(&out != &A)
{
// no aliasing
out.zeros(N,N);
for(u32 i=0; i<N; ++i)
{
out.at(i,i) = A_mem[i];
}
}
else
{
// aliasing
const podarray<eT> tmp(A_mem, N);
const eT* tmp_mem = tmp.memptr();
out.zeros(N,N);
for(u32 i=0; i<N; ++i)
{
out.at(i,i) = tmp_mem[i];
}
}
}
else
{
// generate a diagonal matrix out of a matrix
arma_debug_check( (A.is_square() == false), "diagmat(): given matrix is not square" );
const u32 N = A.n_rows;
out.set_size(N,N);
for(u32 col=0; col<N; ++col)
{
for(u32 row=0; row<col; ++row) { out.at(row,col) = eT(0); }
out.at(col,col) = A.at(col,col);
for(u32 row=col+1; row<N; ++row) { out.at(row,col) = eT(0); }
}
}
}
arma_hot
inline
static
void
apply
(
Mat<eT>& C,
const TA& A,
const TB& B,
const eT alpha = eT(1),
const eT beta = eT(0)
)
{
arma_extra_debug_sigprint();
const uword A_n_rows = A.n_rows;
const uword A_n_cols = A.n_cols;
const uword B_n_rows = B.n_rows;
const uword B_n_cols = B.n_cols;
if( (do_trans_A == false) && (do_trans_B == false) )
{
arma_aligned podarray<eT> tmp(A_n_cols);
eT* A_rowdata = tmp.memptr();
for(uword row_A=0; row_A < A_n_rows; ++row_A)
{
tmp.copy_row(A, row_A);
for(uword col_B=0; col_B < B_n_cols; ++col_B)
{
const eT acc = op_dot::direct_dot_arma(B_n_rows, A_rowdata, B.colptr(col_B));
if( (use_alpha == false) && (use_beta == false) ) { C.at(row_A,col_B) = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { C.at(row_A,col_B) = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { C.at(row_A,col_B) = acc + beta*C.at(row_A,col_B); }
else if( (use_alpha == true ) && (use_beta == true ) ) { C.at(row_A,col_B) = alpha*acc + beta*C.at(row_A,col_B); }
}
}
}
else
if( (do_trans_A == true) && (do_trans_B == false) )
{
for(uword col_A=0; col_A < A_n_cols; ++col_A)
{
// col_A is interpreted as row_A when storing the results in matrix C
const eT* A_coldata = A.colptr(col_A);
for(uword col_B=0; col_B < B_n_cols; ++col_B)
{
const eT acc = op_dot::direct_dot_arma(B_n_rows, A_coldata, B.colptr(col_B));
if( (use_alpha == false) && (use_beta == false) ) { C.at(col_A,col_B) = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { C.at(col_A,col_B) = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { C.at(col_A,col_B) = acc + beta*C.at(col_A,col_B); }
else if( (use_alpha == true ) && (use_beta == true ) ) { C.at(col_A,col_B) = alpha*acc + beta*C.at(col_A,col_B); }
}
}
}
else
if( (do_trans_A == false) && (do_trans_B == true) )
{
Mat<eT> BB;
op_strans::apply_mat_noalias(BB, B);
gemm_emul_large<false, false, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
}
else
if( (do_trans_A == true) && (do_trans_B == true) )
{
// mat B_tmp = trans(B);
// dgemm_arma<true, false, use_alpha, use_beta>::apply(C, A, B_tmp, alpha, beta);
// By using the trans(A)*trans(B) = trans(B*A) equivalency,
// transpose operations are not needed
arma_aligned podarray<eT> tmp(B.n_cols);
eT* B_rowdata = tmp.memptr();
for(uword row_B=0; row_B < B_n_rows; ++row_B)
{
tmp.copy_row(B, row_B);
for(uword col_A=0; col_A < A_n_cols; ++col_A)
{
const eT acc = op_dot::direct_dot_arma(A_n_rows, B_rowdata, A.colptr(col_A));
if( (use_alpha == false) && (use_beta == false) ) { C.at(col_A,row_B) = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { C.at(col_A,row_B) = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { C.at(col_A,row_B) = acc + beta*C.at(col_A,row_B); }
else if( (use_alpha == true ) && (use_beta == true ) ) { C.at(col_A,row_B) = alpha*acc + beta*C.at(col_A,row_B); }
}
}
}
}
inline
void
arma_ostream::print_dense(std::ostream& o, const SpMat<eT>& m, const bool modify)
{
arma_extra_debug_sigprint();
const arma_ostream_state stream_state(o);
const uword m_n_rows = m.n_rows;
const uword m_n_cols = m.n_cols;
if(m.n_nonzero > 0)
{
const std::streamsize cell_width = modify ? modify_stream<eT>(o, m.begin(), m.n_nonzero) : o.width();
typename SpMat<eT>::const_iterator begin = m.begin();
if(m_n_cols > 0)
{
if(cell_width > 0)
{
// An efficient row_iterator would make this simpler and faster
for(uword row=0; row < m_n_rows; ++row)
{
for(uword col=0; col < m_n_cols; ++col)
{
// the cell width appears to be reset after each element is printed,
// hence we need to restore it
o.width(cell_width);
eT val = eT(0);
for(typename SpMat<eT>::const_iterator it = begin; it.pos() < m.n_nonzero; ++it)
{
if(it.row() == row && it.col() == col)
{
val = *it;
break;
}
}
arma_ostream::print_elem(o,eT(val), modify);
}
o << '\n';
}
}
else
{
// An efficient row_iterator would make this simpler and faster
for(uword row=0; row < m_n_rows; ++row)
{
for(uword col=0; col < m_n_cols; ++col)
{
eT val = eT(0);
for(typename SpMat<eT>::const_iterator it = begin; it.pos() < m.n_nonzero; ++it)
{
if(it.row() == row && it.col() == col)
{
val = *it;
break;
}
}
arma_ostream::print_elem(o,eT(val), modify);
o << ' ';
}
o << '\n';
}
}
}
}
else
{
if(m.n_elem == 0)
{
o << "[matrix size: " << m_n_rows << 'x' << m_n_cols << "]\n";
}
else
{
eT tmp[1];
tmp[0] = eT(0);
const std::streamsize cell_width = modify ? arma_ostream::modify_stream(o, &tmp[0], 1) : o.width();
for(uword row=0; row < m_n_rows; ++row)
{
for(uword col=0; col < m_n_cols; ++col)
{
o.width(cell_width);
arma_ostream::print_elem_zero<eT>(o, modify);
o << ' ';
}
o << '\n';
}
}
}
o.flush();
stream_state.restore(o);
}
inline explicit Proxy(const eOp<T1, eop_type>& A)
: Q(A)
{
arma_extra_debug_sigprint();
}
inline
subview_cube_each2<eT,TB>::~subview_cube_each2()
{
arma_extra_debug_sigprint();
}
inline explicit Proxy(const eGlue<T1, T2, eglue_type>& A)
: Q(A)
{
arma_extra_debug_sigprint();
}
inline
subview_cube_each1<eT>::subview_cube_each1(const Cube<eT>& in_p)
: subview_cube_each_common<eT>::subview_cube_each_common(in_p)
{
arma_extra_debug_sigprint();
}
inline explicit Proxy(const mtOp<out_eT, T1, op_type>& A)
: Q(A)
{
arma_extra_debug_sigprint();
}
inline
void
op_pinv::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv>& in)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename get_pod_type<eT>::result T;
const bool use_divide_and_conquer = (in.aux_uword_a == 1);
T tol = access::tmp_real(in.aux);
arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
const Proxy<T1> P(in.m);
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if( (n_rows*n_cols) == 0 )
{
out.set_size(n_cols,n_rows);
return;
}
// economical SVD decomposition
Mat<eT> U;
Col< T> s;
Mat<eT> V;
bool status = false;
if(use_divide_and_conquer)
{
status = (n_cols > n_rows) ? auxlib::svd_dc_econ(U, s, V, trans(P.Q)) : auxlib::svd_dc_econ(U, s, V, P.Q);
}
else
{
status = (n_cols > n_rows) ? auxlib::svd_econ(U, s, V, trans(P.Q), 'b') : auxlib::svd_econ(U, s, V, P.Q, 'b');
}
if(status == false)
{
out.reset();
arma_bad("pinv(): svd failed");
return;
}
const uword s_n_elem = s.n_elem;
const T* s_mem = s.memptr();
// set tolerance to default if it hasn't been specified as an argument
if( (tol == T(0)) && (s_n_elem > 0) )
{
tol = (std::max)(n_rows, n_cols) * eop_aux::direct_eps( op_max::direct_max(s_mem, s_n_elem) );
}
// count non zero valued elements in s
uword count = 0;
for(uword i = 0; i < s_n_elem; ++i)
{
if(s_mem[i] > tol) { ++count; }
}
if(count > 0)
{
Col<T> s2(count);
T* s2_mem = s2.memptr();
uword count2 = 0;
for(uword i=0; i < s_n_elem; ++i)
{
const T val = s_mem[i];
if(val > tol) { s2_mem[count2] = T(1) / val; ++count2; }
}
if(n_rows >= n_cols)
{
out = ( (V.n_cols > count) ? V.cols(0,count-1) : V ) * diagmat(s2) * trans( (U.n_cols > count) ? U.cols(0,count-1) : U );
}
else
{
out = ( (U.n_cols > count) ? U.cols(0,count-1) : U ) * diagmat(s2) * trans( (V.n_cols > count) ? V.cols(0,count-1) : V );
}
}
else
{
out.zeros(n_cols, n_rows);
}
}
inline explicit Proxy(const mtGlue<out_eT, T1, T2, glue_type>& A)
: Q(A)
{
arma_extra_debug_sigprint();
}
inline
bool
op_logmat_cx::apply_common(Mat< std::complex<T> >& out, Mat< std::complex<T> >& S, const uword n_iters)
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
Mat<eT> U;
const bool schur_ok = auxlib::schur(U,S);
if(schur_ok == false) { arma_extra_debug_print("logmat(): schur decomposition failed"); return false; }
//double theta[] = { 1.10e-5, 1.82e-3, 1.62e-2, 5.39e-2, 1.14e-1, 1.87e-1, 2.64e-1 };
double theta[] = { 0.0, 0.0, 1.6206284795015624e-2, 5.3873532631381171e-2, 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };
// theta[0] and theta[1] not really used
const uword N = S.n_rows;
uword p = 0;
uword m = 6;
uword iter = 0;
while(iter < n_iters)
{
const T tau = norm( (S - eye< Mat<eT> >(N,N)), 1 );
if(tau <= theta[6])
{
p++;
uword j1 = 0;
uword j2 = 0;
for(uword i=2; i<=6; ++i) { if( tau <= theta[i]) { j1 = i; break; } }
for(uword i=2; i<=6; ++i) { if((tau/2.0) <= theta[i]) { j2 = i; break; } }
// sanity check, for development purposes only
arma_debug_check( (j2 > j1), "internal error: op_logmat::apply_direct(): j2 > j1" );
if( ((j1 - j2) <= 1) || (p == 2) ) { m = j1; break; }
}
const bool sqrtmat_ok = op_sqrtmat_cx::apply_direct(S,S);
if(sqrtmat_ok == false) { arma_extra_debug_print("logmat(): sqrtmat() failed"); return false; }
iter++;
}
if(iter >= n_iters) { arma_debug_warn("logmat(): reached max iterations without full convergence"); }
S.diag() -= eT(1);
if(m >= 1)
{
const bool helper_ok = op_logmat_cx::helper(S,m);
if(helper_ok == false) { return false; }
}
out = U * S * U.t();
out *= eT(eop_aux::pow(double(2), double(iter)));
return true;
}
inline explicit Proxy(const Col<eT>& A)
: Q(A)
{
arma_extra_debug_sigprint();
}
inline
typename arma_not_cx<typename T1::elem_type>::result
op_min::min(const Base<typename T1::elem_type,T1>& X)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const Proxy<T1> P(X.get_ref());
const uword n_elem = P.get_n_elem();
arma_debug_check( (n_elem == 0), "min(): given object has no elements" );
eT min_val = priv::most_pos<eT>();
if(Proxy<T1>::prefer_at_accessor == false)
{
typedef typename Proxy<T1>::ea_type ea_type;
ea_type A = P.get_ea();
uword i,j;
for(i=0, j=1; j<n_elem; i+=2, j+=2)
{
const eT tmp_i = A[i];
const eT tmp_j = A[j];
if(tmp_i < min_val) { min_val = tmp_i; }
if(tmp_j < min_val) { min_val = tmp_j; }
}
if(i < n_elem)
{
const eT tmp_i = A[i];
if(tmp_i < min_val) { min_val = tmp_i; }
}
}
else
{
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if(n_rows == 1)
{
uword i,j;
for(i=0, j=1; j < n_cols; i+=2, j+=2)
{
const eT tmp_i = P.at(0,i);
const eT tmp_j = P.at(0,j);
if(tmp_i < min_val) { min_val = tmp_i; }
if(tmp_j < min_val) { min_val = tmp_j; }
}
if(i < n_cols)
{
const eT tmp_i = P.at(0,i);
if(tmp_i < min_val) { min_val = tmp_i; }
}
}
else
{
for(uword col=0; col < n_cols; ++col)
{
uword i,j;
for(i=0, j=1; j < n_rows; i+=2, j+=2)
{
const eT tmp_i = P.at(i,col);
const eT tmp_j = P.at(j,col);
if(tmp_i < min_val) { min_val = tmp_i; }
if(tmp_j < min_val) { min_val = tmp_j; }
}
if(i < n_rows)
{
const eT tmp_i = P.at(i,col);
if(tmp_i < min_val) { min_val = tmp_i; }
}
}
}
}
return min_val;
}
inline
void
op_princomp::direct_princomp
(
Mat< std::complex<T> >& coeff_out,
Mat< std::complex<T> >& score_out,
const Mat< std::complex<T> >& in
)
{
arma_extra_debug_sigprint();
typedef std::complex<T> eT;
const u32 n_rows = in.n_rows;
const u32 n_cols = in.n_cols;
if(n_rows > 1) // more than one sample
{
// subtract the mean - use score_out as temporary matrix
score_out = in - repmat(mean(in), n_rows, 1);
// singular value decomposition
Mat<eT> U;
Col< T> s;
const bool svd_ok = svd(U,s,coeff_out,score_out);
if(svd_ok == false)
{
arma_print("princomp(): singular value decomposition failed");
coeff_out.reset();
score_out.reset();
return;
}
// U.reset();
// normalize the eigenvalues
s /= std::sqrt(n_rows - 1);
// project the samples to the principals
score_out *= coeff_out;
if(n_rows <= n_cols) // number of samples is less than their dimensionality
{
score_out.cols(n_rows-1,n_cols-1).zeros();
}
}
else // single sample - row
{
if(n_rows == 1)
{
coeff_out = eye< Mat<eT> >(n_cols, n_cols);
score_out.copy_size(in);
score_out.zeros();
}
else
{
coeff_out.reset();
score_out.reset();
}
}
}