182 lines
4.0 KiB
C++
182 lines
4.0 KiB
C++
// 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;
|
|
}
|
|
|
|
|
|
|
|
//! @}
|