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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 fn_norm
//! @{
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
norm
(
const T1& X,
const uword k = uword(2),
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
const Proxy<T1> P(X);
if(P.get_n_elem() == 0) { return T(0); }
const bool is_vec = (T1::is_xvec) || (T1::is_row) || (T1::is_col) || (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
if(is_vec)
{
if(k == uword(1)) { return op_norm::vec_norm_1(P); }
if(k == uword(2)) { return op_norm::vec_norm_2(P); }
arma_debug_check( (k == 0), "norm(): unsupported vector norm type" );
return op_norm::vec_norm_k(P, int(k));
}
else
{
const quasi_unwrap<typename Proxy<T1>::stored_type> U(P.Q);
if(k == uword(1)) { return op_norm::mat_norm_1(U.M); }
if(k == uword(2)) { return op_norm::mat_norm_2(U.M); }
arma_stop_logic_error("norm(): unsupported matrix norm type");
}
return T(0);
}
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
norm
(
const T1& X,
const char* method,
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
const Proxy<T1> P(X);
if(P.get_n_elem() == 0) { return T(0); }
const char sig = (method != nullptr) ? method[0] : char(0);
const bool is_vec = (T1::is_xvec) || (T1::is_row) || (T1::is_col) || (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
if(is_vec)
{
if( (sig == 'i') || (sig == 'I') || (sig == '+') ) { return op_norm::vec_norm_max(P); }
if( (sig == '-') ) { return op_norm::vec_norm_min(P); }
if( (sig == 'f') || (sig == 'F') ) { return op_norm::vec_norm_2(P); }
arma_stop_logic_error("norm(): unsupported vector norm type");
}
else
{
if( (sig == 'i') || (sig == 'I') || (sig == '+') ) // inf norm
{
const quasi_unwrap<typename Proxy<T1>::stored_type> U(P.Q);
return op_norm::mat_norm_inf(U.M);
}
else
if( (sig == 'f') || (sig == 'F') )
{
return op_norm::vec_norm_2(P);
}
arma_stop_logic_error("norm(): unsupported matrix norm type");
}
return T(0);
}
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_type<T1>::value, double >::result
norm
(
const T1& X,
const uword k = uword(2),
const typename arma_integral_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
if(resolves_to_colvector<T1>::value) { return norm(conv_to< Col<double> >::from(X), k); }
if(resolves_to_rowvector<T1>::value) { return norm(conv_to< Row<double> >::from(X), k); }
return norm(conv_to< Mat<double> >::from(X), k);
}
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_type<T1>::value, double >::result
norm
(
const T1& X,
const char* method,
const typename arma_integral_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
if(resolves_to_colvector<T1>::value) { return norm(conv_to< Col<double> >::from(X), method); }
if(resolves_to_rowvector<T1>::value) { return norm(conv_to< Row<double> >::from(X), method); }
return norm(conv_to< Mat<double> >::from(X), method);
}
//
// norms for sparse matrices
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
norm
(
const T1& expr,
const uword k = uword(2),
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
if(is_SpSubview_col<T1>::value)
{
const SpSubview_col<eT>& sv = reinterpret_cast< const SpSubview_col<eT>& >(expr);
if(sv.n_rows == sv.m.n_rows)
{
const SpMat<eT>& m = sv.m;
const uword col = sv.aux_col1;
const eT* mem = &(m.values[ m.col_ptrs[col] ]);
return spop_norm::vec_norm_k(mem, sv.n_nonzero, k);
}
}
const unwrap_spmat<T1> U(expr);
const SpMat<eT>& X = U.M;
if(X.n_nonzero == 0) { return T(0); }
const bool is_vec = (T1::is_xvec) || (T1::is_row) || (T1::is_col) || (X.n_rows == 1) || (X.n_cols == 1);
if(is_vec)
{
return spop_norm::vec_norm_k(X.values, X.n_nonzero, k);
}
else
{
if(k == uword(1)) { return spop_norm::mat_norm_1(X); }
if(k == uword(2)) { return spop_norm::mat_norm_2(X); }
arma_stop_logic_error("norm(): unsupported or unimplemented norm type for sparse matrices");
}
return T(0);
}
template<typename T1>
arma_warn_unused
inline
typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
norm
(
const T1& expr,
const char* method,
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
const unwrap_spmat<T1> U(expr);
const SpMat<eT>& X = U.M;
if(X.n_nonzero == 0) { return T(0); }
// create a fake dense vector to allow reuse of code for dense vectors
Col<eT> fake_vector( access::rwp(X.values), X.n_nonzero, false );
const Proxy< Col<eT> > P_fake_vector(fake_vector);
const char sig = (method != nullptr) ? method[0] : char(0);
const bool is_vec = (T1::is_xvec) || (T1::is_row) || (T1::is_col) || (X.n_rows == 1) || (X.n_cols == 1);
if(is_vec)
{
if( (sig == 'i') || (sig == 'I') || (sig == '+') ) // max norm
{
return op_norm::vec_norm_max(P_fake_vector);
}
else
if(sig == '-') // min norm
{
const T val = op_norm::vec_norm_min(P_fake_vector);
return (X.n_nonzero < X.n_elem) ? T((std::min)(T(0), val)) : T(val);
}
else
if( (sig == 'f') || (sig == 'F') )
{
return op_norm::vec_norm_2(P_fake_vector);
}
arma_stop_logic_error("norm(): unsupported vector norm type");
}
else
{
if( (sig == 'i') || (sig == 'I') || (sig == '+') ) // inf norm
{
return spop_norm::mat_norm_inf(X);
}
else
if( (sig == 'f') || (sig == 'F') )
{
return op_norm::vec_norm_2(P_fake_vector);
}
arma_stop_logic_error("norm(): unsupported matrix norm type");
}
return T(0);
}
//
// approximate norms
template<typename T1>
arma_warn_unused
inline
typename T1::pod_type
norm2est
(
const Base<typename T1::elem_type, T1>& X,
const typename T1::pod_type tolerance = 0,
const uword max_iter = 100,
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
return op_norm2est::norm2est(X.get_ref(), tolerance, max_iter);
}
template<typename T1>
arma_warn_unused
inline
typename T1::pod_type
norm2est
(
const SpBase<typename T1::elem_type, T1>& X,
const typename T1::pod_type tolerance = 0,
const uword max_iter = 100,
const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
return op_norm2est::norm2est(X.get_ref(), tolerance, max_iter);
}
//! @}
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