106 lines
2.7 KiB
C++
106 lines
2.7 KiB
C++
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
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// Copyright 2008-2016 National ICT Australia (NICTA)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// ------------------------------------------------------------------------
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//! \addtogroup op_norm
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//! @{
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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spop_norm::mat_norm_1(const SpMat<eT>& X)
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{
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arma_extra_debug_sigprint();
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// TODO: this can be sped up with a dedicated implementation
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return as_scalar( max( sum(abs(X), 0), 1) );
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}
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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spop_norm::mat_norm_2(const SpMat<eT>& X, const typename arma_real_only<eT>::result* junk)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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// norm = sqrt( largest eigenvalue of (A^H)*A ), where ^H is the conjugate transpose
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// http://math.stackexchange.com/questions/4368/computing-the-largest-eigenvalue-of-a-very-large-sparse-matrix
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typedef typename get_pod_type<eT>::result T;
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const SpMat<eT>& A = X;
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const SpMat<eT> B = trans(A);
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const SpMat<eT> C = (A.n_rows <= A.n_cols) ? (A*B) : (B*A);
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Col<T> eigval;
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eigs_sym(eigval, C, 1);
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return (eigval.n_elem > 0) ? T(std::sqrt(eigval[0])) : T(0);
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}
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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spop_norm::mat_norm_2(const SpMat<eT>& X, const typename arma_cx_only<eT>::result* junk)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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typedef typename get_pod_type<eT>::result T;
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// we're calling eigs_gen(), which currently requires ARPACK
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#if !defined(ARMA_USE_ARPACK)
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{
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arma_stop_logic_error("norm(): use of ARPACK must be enabled for norm of complex matrices");
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return T(0);
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}
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#endif
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const SpMat<eT>& A = X;
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const SpMat<eT> B = trans(A);
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const SpMat<eT> C = (A.n_rows <= A.n_cols) ? (A*B) : (B*A);
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Col<eT> eigval;
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eigs_gen(eigval, C, 1);
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return (eigval.n_elem > 0) ? T(std::sqrt(std::real(eigval[0]))) : T(0);
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}
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template<typename eT>
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inline
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typename get_pod_type<eT>::result
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spop_norm::mat_norm_inf(const SpMat<eT>& X)
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{
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arma_extra_debug_sigprint();
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// TODO: this can be sped up with a dedicated implementation
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return as_scalar( max( sum(abs(X), 1), 0) );
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}
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//! @}
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