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// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------
//! \addtogroup op_pinv
//! @{
template<typename T1>
inline
void
op_pinv::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv>& in)
{
arma_extra_debug_sigprint();
typedef typename T1::pod_type T;
const T tol = access::tmp_real(in.aux);
const bool use_divide_and_conquer = (in.aux_uword_a == 1);
const bool status = op_pinv::apply_direct(out, in.m, tol, use_divide_and_conquer);
if(status == false)
{
arma_stop_runtime_error("pinv(): svd failed");
}
}
template<typename T1>
inline
bool
op_pinv::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, typename T1::pod_type tol, const bool use_divide_and_conquer)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
const Proxy<T1> P(expr.get_ref());
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 true;
}
// 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.soft_reset();
return false;
}
const uword s_n_elem = s.n_elem;
const T* s_mem = s.memptr();
// set tolerance to default if it hasn't been specified
if( (tol == T(0)) && (s_n_elem > 0) )
{
tol = (std::max)(n_rows, n_cols) * s_mem[0] * std::numeric_limits<T>::epsilon();
}
uword count = 0;
for(uword i = 0; i < s_n_elem; ++i)
{
count += (s_mem[i] >= tol) ? uword(1) : uword(0);
}
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] = (val > T(0)) ? T(T(1) / val) : T(0); ++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 );
Mat<eT> tmp;
if(count < V.n_cols)
{
tmp = V.cols(0,count-1) * diagmat(s2);
}
else
{
tmp = V * diagmat(s2);
}
if(count < U.n_cols)
{
out = tmp * trans(U.cols(0,count-1));
}
else
{
out = tmp * trans(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 );
Mat<eT> tmp;
if(count < U.n_cols)
{
tmp = U.cols(0,count-1) * diagmat(s2);
}
else
{
tmp = U * diagmat(s2);
}
if(count < V.n_cols)
{
out = tmp * trans(V.cols(0,count-1));
}
else
{
out = tmp * trans(V);
}
}
}
else
{
out.zeros(n_cols, n_rows);
}
return true;
}
//! @}
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