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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_norm2est
//! @{
template<typename eT>
inline
norm2est_randu_filler<eT>::norm2est_randu_filler()
{
arma_extra_debug_sigprint();
typedef typename std::mt19937_64::result_type local_seed_type;
local_engine.seed(local_seed_type(123));
typedef typename std::uniform_real_distribution<eT>::param_type local_param_type;
local_u_distr.param(local_param_type(-1.0, +1.0));
}
template<typename eT>
inline
void
norm2est_randu_filler<eT>::fill(eT* mem, const uword N)
{
arma_extra_debug_sigprint();
for(uword i=0; i<N; ++i) { mem[i] = eT( local_u_distr(local_engine) ); }
}
//
template<typename T>
inline
norm2est_randu_filler< std::complex<T> >::norm2est_randu_filler()
{
arma_extra_debug_sigprint();
typedef typename std::mt19937_64::result_type local_seed_type;
local_engine.seed(local_seed_type(123));
typedef typename std::uniform_real_distribution<T>::param_type local_param_type;
local_u_distr.param(local_param_type(-1.0, +1.0));
}
template<typename T>
inline
void
norm2est_randu_filler< std::complex<T> >::fill(std::complex<T>* mem, const uword N)
{
arma_extra_debug_sigprint();
for(uword i=0; i<N; ++i)
{
std::complex<T>& mem_i = mem[i];
mem_i.real( T(local_u_distr(local_engine)) );
mem_i.imag( T(local_u_distr(local_engine)) );
}
}
//
//
//
template<typename T1>
inline
typename T1::pod_type
op_norm2est::norm2est
(
const Base<typename T1::elem_type, T1>& X,
const typename T1::pod_type tolerance,
const uword max_iter
)
{
arma_extra_debug_sigprint();
typedef typename T1::pod_type T;
typedef typename T1::elem_type eT;
arma_debug_check( (tolerance < T(0)), "norm2est(): parameter 'tolerance' must be > 0" );
arma_debug_check( (max_iter == uword(0)), "norm2est(): parameter 'max_iter' must be > 0" );
const T tol = (tolerance == T(0)) ? T(1e-6) : T(tolerance);
const quasi_unwrap<T1> U(X.get_ref());
const Mat<eT>& A = U.M;
if(A.n_elem == 0) { return T(0); }
if(A.internal_has_nonfinite()) { arma_debug_warn_level(1, "norm2est(): given matrix has non-finite elements"); }
if((A.n_rows == 1) || (A.n_cols == 1)) { return op_norm::vec_norm_2( Proxy< Mat<eT> >(A) ); }
norm2est_randu_filler<eT> randu_filler;
Col<eT> x(A.n_rows, fill::none);
Col<eT> y(A.n_cols, fill::none);
randu_filler.fill(y.memptr(), y.n_elem);
T est_old = 0;
T est_cur = 0;
for(uword i=0; i<max_iter; ++i)
{
arma_extra_debug_print(arma_str::format("norm2est(): iteration: %u") % i);
x = A * y;
T x_norm = op_norm::vec_norm_2( Proxy< Col<eT> >(x) );
if(x_norm == T(0) || (arma_isfinite(x_norm) == false) || (x.internal_has_nonfinite()))
{
randu_filler.fill(x.memptr(), x.n_elem);
x_norm = op_norm::vec_norm_2( Proxy< Col<eT> >(x) );
}
if(x_norm != T(0)) { x /= x_norm; }
y = A.t() * x;
est_old = est_cur;
est_cur = op_norm::vec_norm_2( Proxy< Col<eT> >(y) );
arma_extra_debug_print(arma_str::format("norm2est(): est_old: %e") % est_old);
arma_extra_debug_print(arma_str::format("norm2est(): est_cur: %e") % est_cur);
if(arma_isfinite(est_cur) == false) { return est_old; }
if( ((std::abs)(est_cur - est_old)) <= (tol * (std::max)(est_cur,est_old)) ) { break; }
}
return est_cur;
}
//
//
//
template<typename T1>
inline
typename T1::pod_type
op_norm2est::norm2est
(
const SpBase<typename T1::elem_type, T1>& X,
const typename T1::pod_type tolerance,
const uword max_iter
)
{
arma_extra_debug_sigprint();
typedef typename T1::pod_type T;
typedef typename T1::elem_type eT;
arma_debug_check( (tolerance < T(0)), "norm2est(): parameter 'tolerance' must be > 0" );
arma_debug_check( (max_iter == uword(0)), "norm2est(): parameter 'max_iter' must be > 0" );
const T tol = (tolerance == T(0)) ? T(1e-6) : T(tolerance);
const unwrap_spmat<T1> U(X.get_ref());
const SpMat<eT>& A = U.M;
if(A.n_nonzero == 0) { return T(0); }
if(A.internal_has_nonfinite()) { arma_debug_warn_level(1, "norm2est(): given matrix has non-finite elements"); }
if((A.n_rows == 1) || (A.n_cols == 1)) { return spop_norm::vec_norm_k(A.values, A.n_nonzero, 2); }
norm2est_randu_filler<eT> randu_filler;
Mat<eT> x(A.n_rows, 1, fill::none);
Mat<eT> y(A.n_cols, 1, fill::none);
randu_filler.fill(y.memptr(), y.n_elem);
T est_old = 0;
T est_cur = 0;
for(uword i=0; i<max_iter; ++i)
{
arma_extra_debug_print(arma_str::format("norm2est(): iteration: %u") % i);
x = A * y;
T x_norm = op_norm::vec_norm_2( Proxy< Mat<eT> >(x) );
if(x_norm == T(0) || (arma_isfinite(x_norm) == false) || (x.internal_has_nonfinite()))
{
randu_filler.fill(x.memptr(), x.n_elem);
x_norm = op_norm::vec_norm_2( Proxy< Mat<eT> >(x) );
}
if(x_norm != T(0)) { x /= x_norm; }
y = A.t() * x;
est_old = est_cur;
est_cur = op_norm::vec_norm_2( Proxy< Mat<eT> >(y) );
arma_extra_debug_print(arma_str::format("norm2est(): est_old: %e") % est_old);
arma_extra_debug_print(arma_str::format("norm2est(): est_cur: %e") % est_cur);
if(arma_isfinite(est_cur) == false) { return est_old; }
if( ((std::abs)(est_cur - est_old)) <= (tol * (std::max)(est_cur,est_old)) ) { break; }
}
return est_cur;
}
//! @}
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