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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;
+ }
+
+
+
+//! @}