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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 glue_mvnrnd
//! @{
// implementation based on:
// James E. Gentle.
// Generation of Random Numbers.
// Computational Statistics, pp. 305-331, 2009.
// http://dx.doi.org/10.1007/978-0-387-98144-4_7
template<typename T1, typename T2>
inline
void
glue_mvnrnd_vec::apply(Mat<typename T1::elem_type>& out, const Glue<T1,T2,glue_mvnrnd_vec>& expr)
{
arma_extra_debug_sigprint();
const bool status = glue_mvnrnd::apply_direct(out, expr.A, expr.B, uword(1));
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("mvnrnd(): given covariance matrix is not symmetric positive semi-definite");
}
}
template<typename T1, typename T2>
inline
void
glue_mvnrnd::apply(Mat<typename T1::elem_type>& out, const Glue<T1,T2,glue_mvnrnd>& expr)
{
arma_extra_debug_sigprint();
const bool status = glue_mvnrnd::apply_direct(out, expr.A, expr.B, expr.aux_uword);
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("mvnrnd(): given covariance matrix is not symmetric positive semi-definite");
}
}
template<typename T1, typename T2>
inline
bool
glue_mvnrnd::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& M, const Base<typename T1::elem_type,T2>& C, const uword N)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const quasi_unwrap<T1> UM(M.get_ref());
const quasi_unwrap<T2> UC(C.get_ref());
arma_debug_check( (UM.M.is_colvec() == false) && (UM.M.is_empty() == false), "mvnrnd(): given mean must be a column vector" );
arma_debug_check( (UC.M.is_square() == false), "mvnrnd(): given covariance matrix must be square sized" );
arma_debug_check( (UM.M.n_rows != UC.M.n_rows), "mvnrnd(): number of rows in given mean vector and covariance matrix must match" );
if( UM.M.is_empty() || UC.M.is_empty() )
{
out.set_size(0,N);
return true;
}
if((arma_config::debug) && (auxlib::rudimentary_sym_check(UC.M) == false))
{
arma_debug_warn_level(1, "mvnrnd(): given matrix is not symmetric");
}
bool status = false;
if(UM.is_alias(out) || UC.is_alias(out))
{
Mat<eT> tmp;
status = glue_mvnrnd::apply_noalias(tmp, UM.M, UC.M, N);
out.steal_mem(tmp);
}
else
{
status = glue_mvnrnd::apply_noalias(out, UM.M, UC.M, N);
}
return status;
}
template<typename eT>
inline
bool
glue_mvnrnd::apply_noalias(Mat<eT>& out, const Mat<eT>& M, const Mat<eT>& C, const uword N)
{
arma_extra_debug_sigprint();
Mat<eT> D;
const bool chol_status = op_chol::apply_direct(D, C, 1); // '1' means "lower triangular"
if(chol_status == false)
{
// C is not symmetric positive definite, so find approximate square root of C
Col<eT> eigval; // NOTE: eT is constrained to be real (ie. float or double) in fn_mvnrnd.hpp
Mat<eT> eigvec;
const bool eig_status = eig_sym_helper(eigval, eigvec, C, 'd', "mvnrnd()");
if(eig_status == false) { return false; }
eT* eigval_mem = eigval.memptr();
const uword eigval_n_elem = eigval.n_elem;
// since we're doing an approximation, tolerate tiny negative eigenvalues
const eT tol = eT(-100) * Datum<eT>::eps * norm(C, "fro");
if(arma_isfinite(tol) == false) { return false; }
for(uword i=0; i<eigval_n_elem; ++i)
{
const eT val = eigval_mem[i];
if( (val < tol) || (arma_isfinite(val) == false) ) { return false; }
}
for(uword i=0; i<eigval_n_elem; ++i) { if(eigval_mem[i] < eT(0)) { eigval_mem[i] = eT(0); } }
Mat<eT> DD = eigvec * diagmat(sqrt(eigval));
D.steal_mem(DD);
}
out = D * randn< Mat<eT> >(M.n_rows, N);
if(N == 1)
{
out += M;
}
else
if(N > 1)
{
out.each_col() += M;
}
return true;
}
//! @}
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