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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_pinv
+//! @{
+
+
+
+template<typename T1>
+inline
+void
+op_pinv_default::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv_default>& in)
+ {
+ arma_extra_debug_sigprint();
+
+ const bool status = op_pinv_default::apply_direct(out, in.m);
+
+ if(status == false)
+ {
+ out.soft_reset();
+ arma_stop_runtime_error("pinv(): svd failed");
+ }
+ }
+
+
+
+template<typename T1>
+inline
+bool
+op_pinv_default::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::pod_type T;
+
+ constexpr T tol = T(0);
+ constexpr uword method_id = uword(0);
+
+ return op_pinv::apply_direct(out, expr, tol, method_id);
+ }
+
+
+
+//
+
+
+
+template<typename T1>
+inline
+void
+op_pinv::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv>& in)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::pod_type T;
+
+ const T tol = access::tmp_real(in.aux);
+ const uword method_id = in.aux_uword_a;
+
+ const bool status = op_pinv::apply_direct(out, in.m, tol, method_id);
+
+ if(status == false)
+ {
+ out.soft_reset();
+ arma_stop_runtime_error("pinv(): svd failed");
+ }
+ }
+
+
+
+template<typename T1>
+inline
+bool
+op_pinv::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, typename T1::pod_type tol, const uword method_id)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::elem_type eT;
+ typedef typename T1::pod_type T;
+
+ arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
+
+ // method_id = 0 -> default setting
+ // method_id = 1 -> use standard algorithm
+ // method_id = 2 -> use divide and conquer algorithm
+
+ Mat<eT> A(expr.get_ref());
+
+ if(A.is_empty()) { out.set_size(A.n_cols,A.n_rows); return true; }
+
+ if(is_op_diagmat<T1>::value || A.is_diagmat())
+ {
+ arma_extra_debug_print("op_pinv: detected diagonal matrix");
+
+ return op_pinv::apply_diag(out, A, tol);
+ }
+
+ bool do_sym = false;
+
+ const bool is_sym_size_ok = (A.n_rows == A.n_cols) && (A.n_rows > (is_cx<eT>::yes ? uword(20) : uword(40)));
+
+ if( (is_sym_size_ok) && (arma_config::optimise_sym) && (auxlib::crippled_lapack(A) == false) )
+ {
+ bool is_approx_sym = false;
+ bool is_approx_sympd = false;
+
+ sym_helper::analyse_matrix(is_approx_sym, is_approx_sympd, A);
+
+ do_sym = ((is_cx<eT>::no) ? (is_approx_sym) : (is_approx_sym && is_approx_sympd));
+ }
+
+ if(do_sym)
+ {
+ arma_extra_debug_print("op_pinv: symmetric/hermitian optimisation");
+
+ return op_pinv::apply_sym(out, A, tol, method_id);
+ }
+
+ return op_pinv::apply_gen(out, A, tol, method_id);
+ }
+
+
+
+template<typename eT>
+inline
+bool
+op_pinv::apply_diag(Mat<eT>& out, const Mat<eT>& A, typename get_pod_type<eT>::result tol)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename get_pod_type<eT>::result T;
+
+ out.zeros(A.n_cols, A.n_rows);
+
+ const uword N = (std::min)(A.n_rows, A.n_cols);
+
+ podarray<T> diag_abs_vals(N);
+
+ T max_abs_Aii = T(0);
+
+ for(uword i=0; i<N; ++i)
+ {
+ const eT Aii = A.at(i,i);
+ const T abs_Aii = std::abs(Aii);
+
+ if(arma_isnan(Aii)) { return false; }
+
+ diag_abs_vals[i] = abs_Aii;
+
+ max_abs_Aii = (abs_Aii > max_abs_Aii) ? abs_Aii : max_abs_Aii;
+ }
+
+ if(tol == T(0)) { tol = (std::max)(A.n_rows, A.n_cols) * max_abs_Aii * std::numeric_limits<T>::epsilon(); }
+
+ for(uword i=0; i<N; ++i)
+ {
+ if(diag_abs_vals[i] >= tol)
+ {
+ const eT Aii = A.at(i,i);
+
+ if(Aii != eT(0)) { out.at(i,i) = eT(eT(1) / Aii); }
+ }
+ }
+
+ return true;
+ }
+
+
+
+template<typename eT>
+inline
+bool
+op_pinv::apply_sym(Mat<eT>& out, const Mat<eT>& A, typename get_pod_type<eT>::result tol, const uword method_id)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename get_pod_type<eT>::result T;
+
+ Col< T> eigval;
+ Mat<eT> eigvec;
+
+ const bool status = ((method_id == uword(0)) || (method_id == uword(2))) ? auxlib::eig_sym_dc(eigval, eigvec, A) : auxlib::eig_sym(eigval, eigvec, A);
+
+ if(status == false) { return false; }
+
+ if(eigval.n_elem == 0) { out.zeros(A.n_cols, A.n_rows); return true; }
+
+ Col<T> abs_eigval = arma::abs(eigval);
+
+ const uvec indices = sort_index(abs_eigval, "descend");
+
+ abs_eigval = abs_eigval.elem(indices);
+ eigval = eigval.elem(indices);
+ eigvec = eigvec.cols(indices);
+
+ // set tolerance to default if it hasn't been specified
+ if(tol == T(0)) { tol = (std::max)(A.n_rows, A.n_cols) * abs_eigval[0] * std::numeric_limits<T>::epsilon(); }
+
+ uword count = 0;
+
+ for(uword i=0; i < abs_eigval.n_elem; ++i) { count += (abs_eigval[i] >= tol) ? uword(1) : uword(0); }
+
+ if(count == 0) { out.zeros(A.n_cols, A.n_rows); return true; }
+
+ Col<T> eigval2(count, arma_nozeros_indicator());
+
+ uword count2 = 0;
+
+ for(uword i=0; i < eigval.n_elem; ++i)
+ {
+ const T abs_val = abs_eigval[i];
+ const T val = eigval[i];
+
+ if(abs_val >= tol) { eigval2[count2] = (val != T(0)) ? T(T(1) / val) : T(0); ++count2; }
+ }
+
+ const Mat<eT> eigvec_use(eigvec.memptr(), eigvec.n_rows, count, false);
+
+ out = (eigvec_use * diagmat(eigval2)).eval() * eigvec_use.t();
+
+ return true;
+ }
+
+
+
+
+template<typename eT>
+inline
+bool
+op_pinv::apply_gen(Mat<eT>& out, Mat<eT>& A, typename get_pod_type<eT>::result tol, const uword method_id)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename get_pod_type<eT>::result T;
+
+ const uword n_rows = A.n_rows;
+ const uword n_cols = A.n_cols;
+
+ // economical SVD decomposition
+ Mat<eT> U;
+ Col< T> s;
+ Mat<eT> V;
+
+ if(n_cols > n_rows) { A = trans(A); }
+
+ const bool status = ((method_id == uword(0)) || (method_id == uword(2))) ? auxlib::svd_dc_econ(U, s, V, A) : auxlib::svd_econ(U, s, V, A, 'b');
+
+ if(status == false) { return false; }
+
+ // set tolerance to default if it hasn't been specified
+ if( (tol == T(0)) && (s.n_elem > 0) ) { tol = (std::max)(n_rows, n_cols) * s[0] * std::numeric_limits<T>::epsilon(); }
+
+ uword count = 0;
+
+ for(uword i=0; i < s.n_elem; ++i) { count += (s[i] >= tol) ? uword(1) : uword(0); }
+
+ if(count == 0) { out.zeros(n_cols, n_rows); return true; }
+
+ Col<T> s2(count, arma_nozeros_indicator());
+
+ uword count2 = 0;
+
+ for(uword i=0; i < s.n_elem; ++i)
+ {
+ const T val = s[i];
+
+ if(val >= tol) { s2[count2] = (val > T(0)) ? T(T(1) / val) : T(0); ++count2; }
+ }
+
+ const Mat<eT> U_use(U.memptr(), U.n_rows, count, false);
+ const Mat<eT> V_use(V.memptr(), V.n_rows, count, false);
+
+ Mat<eT> tmp;
+
+ if(n_rows >= n_cols)
+ {
+ // out = ( (V.n_cols > count) ? V.cols(0,count-1) : V ) * diagmat(s2) * trans( (U.n_cols > count) ? U.cols(0,count-1) : U );
+
+ tmp = V_use * diagmat(s2);
+
+ out = tmp * trans(U_use);
+ }
+ else
+ {
+ // out = ( (U.n_cols > count) ? U.cols(0,count-1) : U ) * diagmat(s2) * trans( (V.n_cols > count) ? V.cols(0,count-1) : V );
+
+ tmp = U_use * diagmat(s2);
+
+ out = tmp * trans(V_use);
+ }
+
+ return true;
+ }
+
+
+
+//! @}
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