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// SPDX-License-Identifier: Apache-2.0
//
// 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_orth_null
//! @{
template<typename T1>
inline
void
op_orth::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_orth>& expr)
{
arma_extra_debug_sigprint();
typedef typename T1::pod_type T;
const T tol = access::tmp_real(expr.aux);
const bool status = op_orth::apply_direct(out, expr.m, tol);
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("orth(): svd failed");
}
}
template<typename T1>
inline
bool
op_orth::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, typename T1::pod_type tol)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
arma_debug_check((tol < T(0)), "orth(): tolerance must be >= 0");
Mat<eT> A(expr.get_ref());
Mat<eT> U;
Col< T> s;
Mat<eT> V;
const bool status = auxlib::svd_dc(U, s, V, A);
V.reset();
if(status == false) { return false; }
if(s.is_empty()) { out.reset(); return true; }
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)) { tol = (std::max)(A.n_rows, A.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)
{
out = U.head_cols(count); // out *= eT(-1);
}
else
{
out.set_size(A.n_rows, 0);
}
return true;
}
//
template<typename T1>
inline
void
op_null::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_null>& expr)
{
arma_extra_debug_sigprint();
typedef typename T1::pod_type T;
const T tol = access::tmp_real(expr.aux);
const bool status = op_null::apply_direct(out, expr.m, tol);
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("null(): svd failed");
}
}
template<typename T1>
inline
bool
op_null::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, typename T1::pod_type tol)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
arma_debug_check((tol < T(0)), "null(): tolerance must be >= 0");
Mat<eT> A(expr.get_ref());
Mat<eT> U;
Col< T> s;
Mat<eT> V;
const bool status = auxlib::svd_dc(U, s, V, A);
U.reset();
if(status == false) { return false; }
if(s.is_empty()) { out.reset(); return true; }
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)) { tol = (std::max)(A.n_rows, A.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 < A.n_cols)
{
out = V.tail_cols(A.n_cols - count);
const uword out_n_elem = out.n_elem;
eT* out_mem = out.memptr();
for(uword i=0; i<out_n_elem; ++i)
{
if(std::abs(out_mem[i]) < std::numeric_limits<T>::epsilon()) { out_mem[i] = eT(0); }
}
}
else
{
out.set_size(A.n_cols, 0);
}
return true;
}
//! @}
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