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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_norm
//! @{
template<typename eT>
inline
typename get_pod_type<eT>::result
spop_norm::mat_norm_1(const SpMat<eT>& X)
{
arma_extra_debug_sigprint();
// TODO: this can be sped up with a dedicated implementation
return as_scalar( max( sum(abs(X), 0), 1) );
}
template<typename eT>
inline
typename get_pod_type<eT>::result
spop_norm::mat_norm_2(const SpMat<eT>& X, const typename arma_real_only<eT>::result* junk)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
// norm = sqrt( largest eigenvalue of (A^H)*A ), where ^H is the conjugate transpose
// http://math.stackexchange.com/questions/4368/computing-the-largest-eigenvalue-of-a-very-large-sparse-matrix
typedef typename get_pod_type<eT>::result T;
const SpMat<eT>& A = X;
const SpMat<eT> B = trans(A);
const SpMat<eT> C = (A.n_rows <= A.n_cols) ? (A*B) : (B*A);
Col<T> eigval;
eigs_sym(eigval, C, 1);
return (eigval.n_elem > 0) ? T(std::sqrt(eigval[0])) : T(0);
}
template<typename eT>
inline
typename get_pod_type<eT>::result
spop_norm::mat_norm_2(const SpMat<eT>& X, const typename arma_cx_only<eT>::result* junk)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename get_pod_type<eT>::result T;
// we're calling eigs_gen(), which currently requires ARPACK
#if !defined(ARMA_USE_ARPACK)
{
arma_stop_logic_error("norm(): use of ARPACK must be enabled for norm of complex matrices");
return T(0);
}
#endif
const SpMat<eT>& A = X;
const SpMat<eT> B = trans(A);
const SpMat<eT> C = (A.n_rows <= A.n_cols) ? (A*B) : (B*A);
Col<eT> eigval;
eigs_gen(eigval, C, 1);
return (eigval.n_elem > 0) ? T(std::sqrt(std::real(eigval[0]))) : T(0);
}
template<typename eT>
inline
typename get_pod_type<eT>::result
spop_norm::mat_norm_inf(const SpMat<eT>& X)
{
arma_extra_debug_sigprint();
// TODO: this can be sped up with a dedicated implementation
return as_scalar( max( sum(abs(X), 1), 0) );
}
template<typename eT>
inline
typename get_pod_type<eT>::result
spop_norm::vec_norm_k(const eT* mem, const uword N, const uword k)
{
arma_extra_debug_sigprint();
arma_debug_check( (k == 0), "norm(): unsupported vector norm type" );
// create a fake dense vector to allow reuse of code for dense vectors
Col<eT> fake_vector( access::rwp(mem), N, false );
const Proxy< Col<eT> > P_fake_vector(fake_vector);
if(k == uword(1)) { return op_norm::vec_norm_1(P_fake_vector); }
if(k == uword(2)) { return op_norm::vec_norm_2(P_fake_vector); }
return op_norm::vec_norm_k(P_fake_vector, int(k));
}
//! @}
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