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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 fn_interp1
+//! @{
+
+
+
+template<typename eT>
+inline
+void
+interp1_helper_nearest(const Mat<eT>& XG, const Mat<eT>& YG, const Mat<eT>& XI, Mat<eT>& YI, const eT extrap_val)
+ {
+ arma_extra_debug_sigprint();
+
+ const eT XG_min = XG.min();
+ const eT XG_max = XG.max();
+
+ YI.copy_size(XI);
+
+ const eT* XG_mem = XG.memptr();
+ const eT* YG_mem = YG.memptr();
+ const eT* XI_mem = XI.memptr();
+ eT* YI_mem = YI.memptr();
+
+ const uword NG = XG.n_elem;
+ const uword NI = XI.n_elem;
+
+ uword best_j = 0;
+
+ for(uword i=0; i<NI; ++i)
+ {
+ eT best_err = Datum<eT>::inf;
+
+ const eT XI_val = XI_mem[i];
+
+ if((XI_val < XG_min) || (XI_val > XG_max))
+ {
+ YI_mem[i] = extrap_val;
+ }
+ else
+ if(arma_isnan(XI_val))
+ {
+ YI_mem[i] = Datum<eT>::nan;
+ }
+ else
+ {
+ // XG and XI are guaranteed to be sorted in ascending manner,
+ // so start searching XG from last known optimum position
+
+ for(uword j=best_j; j<NG; ++j)
+ {
+ const eT tmp = XG_mem[j] - XI_val;
+ const eT err = (tmp >= eT(0)) ? tmp : -tmp;
+
+ if(err >= best_err)
+ {
+ // error is going up, so we have found the optimum position
+ break;
+ }
+ else
+ {
+ best_err = err;
+ best_j = j; // remember the optimum position
+ }
+ }
+
+ YI_mem[i] = YG_mem[best_j];
+ }
+ }
+ }
+
+
+
+template<typename eT>
+inline
+void
+interp1_helper_linear(const Mat<eT>& XG, const Mat<eT>& YG, const Mat<eT>& XI, Mat<eT>& YI, const eT extrap_val)
+ {
+ arma_extra_debug_sigprint();
+
+ const eT XG_min = XG.min();
+ const eT XG_max = XG.max();
+
+ YI.copy_size(XI);
+
+ const eT* XG_mem = XG.memptr();
+ const eT* YG_mem = YG.memptr();
+ const eT* XI_mem = XI.memptr();
+ eT* YI_mem = YI.memptr();
+
+ const uword NG = XG.n_elem;
+ const uword NI = XI.n_elem;
+
+ uword a_best_j = 0;
+ uword b_best_j = 0;
+
+ for(uword i=0; i<NI; ++i)
+ {
+ const eT XI_val = XI_mem[i];
+
+ if((XI_val < XG_min) || (XI_val > XG_max))
+ {
+ YI_mem[i] = extrap_val;
+ }
+ else
+ if(arma_isnan(XI_val))
+ {
+ YI_mem[i] = Datum<eT>::nan;
+ }
+ else
+ {
+ // XG and XI are guaranteed to be sorted in ascending manner,
+ // so start searching XG from last known optimum position
+
+ eT a_best_err = Datum<eT>::inf;
+ eT b_best_err = Datum<eT>::inf;
+
+ for(uword j=a_best_j; j<NG; ++j)
+ {
+ const eT tmp = XG_mem[j] - XI_val;
+ const eT err = (tmp >= eT(0)) ? tmp : -tmp;
+
+ if(err >= a_best_err)
+ {
+ break;
+ }
+ else
+ {
+ a_best_err = err;
+ a_best_j = j;
+ }
+ }
+
+ if( (XG_mem[a_best_j] - XI_val) <= eT(0) )
+ {
+ // a_best_j is to the left of the interpolated position
+
+ b_best_j = ( (a_best_j+1) < NG) ? (a_best_j+1) : a_best_j;
+ }
+ else
+ {
+ // a_best_j is to the right of the interpolated position
+
+ b_best_j = (a_best_j >= 1) ? (a_best_j-1) : a_best_j;
+ }
+
+ b_best_err = std::abs( XG_mem[b_best_j] - XI_val );
+
+ if(a_best_j > b_best_j)
+ {
+ std::swap(a_best_j, b_best_j );
+ std::swap(a_best_err, b_best_err);
+ }
+
+ const eT weight = (a_best_err > eT(0)) ? (a_best_err / (a_best_err + b_best_err)) : eT(0);
+
+ YI_mem[i] = (eT(1) - weight)*YG_mem[a_best_j] + (weight)*YG_mem[b_best_j];
+ }
+ }
+ }
+
+
+
+template<typename eT>
+inline
+void
+interp1_helper(const Mat<eT>& X, const Mat<eT>& Y, const Mat<eT>& XI, Mat<eT>& YI, const uword sig, const eT extrap_val)
+ {
+ arma_extra_debug_sigprint();
+
+ arma_debug_check( ((X.is_vec() == false) || (Y.is_vec() == false) || (XI.is_vec() == false)), "interp1(): currently only vectors are supported" );
+
+ arma_debug_check( (X.n_elem != Y.n_elem), "interp1(): X and Y must have the same number of elements" );
+
+ arma_debug_check( (X.n_elem < 2), "interp1(): X must have at least two unique elements" );
+
+ // sig = 10: nearest neighbour
+ // sig = 11: nearest neighbour, assume monotonic increase in X and XI
+ //
+ // sig = 20: linear
+ // sig = 21: linear, assume monotonic increase in X and XI
+
+ if(sig == 11) { interp1_helper_nearest(X, Y, XI, YI, extrap_val); return; }
+ if(sig == 21) { interp1_helper_linear (X, Y, XI, YI, extrap_val); return; }
+
+ uvec X_indices;
+
+ try { X_indices = find_unique(X,false); } catch(...) { }
+
+ // NOTE: find_unique(X,false) provides indices of elements sorted in ascending order
+ // NOTE: find_unique(X,false) will reset X_indices if X has NaN
+
+ const uword N_subset = X_indices.n_elem;
+
+ arma_debug_check( (N_subset < 2), "interp1(): X must have at least two unique elements" );
+
+ Mat<eT> X_sanitised(N_subset, 1, arma_nozeros_indicator());
+ Mat<eT> Y_sanitised(N_subset, 1, arma_nozeros_indicator());
+
+ eT* X_sanitised_mem = X_sanitised.memptr();
+ eT* Y_sanitised_mem = Y_sanitised.memptr();
+
+ const eT* X_mem = X.memptr();
+ const eT* Y_mem = Y.memptr();
+
+ const uword* X_indices_mem = X_indices.memptr();
+
+ for(uword i=0; i<N_subset; ++i)
+ {
+ const uword j = X_indices_mem[i];
+
+ X_sanitised_mem[i] = X_mem[j];
+ Y_sanitised_mem[i] = Y_mem[j];
+ }
+
+
+ Mat<eT> XI_tmp;
+ uvec XI_indices;
+
+ const bool XI_is_sorted = XI.is_sorted(); // NOTE: .is_sorted() currently doesn't detect NaN
+
+ if(XI_is_sorted == false)
+ {
+ XI_indices = sort_index(XI); // NOTE: sort_index() will throw if XI has NaN
+
+ const uword N = XI.n_elem;
+
+ XI_tmp.copy_size(XI);
+
+ const uword* XI_indices_mem = XI_indices.memptr();
+
+ const eT* XI_mem = XI.memptr();
+ eT* XI_tmp_mem = XI_tmp.memptr();
+
+ for(uword i=0; i<N; ++i)
+ {
+ XI_tmp_mem[i] = XI_mem[ XI_indices_mem[i] ];
+ }
+ }
+
+ const Mat<eT>& XI_sorted = (XI_is_sorted) ? XI : XI_tmp;
+
+ // NOTE: XI_sorted may have NaN
+
+
+ if(sig == 10) { interp1_helper_nearest(X_sanitised, Y_sanitised, XI_sorted, YI, extrap_val); }
+ else if(sig == 20) { interp1_helper_linear (X_sanitised, Y_sanitised, XI_sorted, YI, extrap_val); }
+
+
+ if( (XI_is_sorted == false) && (YI.n_elem > 0) )
+ {
+ Mat<eT> YI_unsorted;
+
+ YI_unsorted.copy_size(YI);
+
+ const eT* YI_mem = YI.memptr();
+ eT* YI_unsorted_mem = YI_unsorted.memptr();
+
+ const uword N = XI_sorted.n_elem;
+ const uword* XI_indices_mem = XI_indices.memptr();
+
+ for(uword i=0; i<N; ++i)
+ {
+ YI_unsorted_mem[ XI_indices_mem[i] ] = YI_mem[i];
+ }
+
+ YI.steal_mem(YI_unsorted);
+ }
+ }
+
+
+
+template<typename T1, typename T2, typename T3>
+inline
+typename
+enable_if2
+ <
+ is_real<typename T1::elem_type>::value,
+ void
+ >::result
+interp1
+ (
+ const Base<typename T1::elem_type, T1>& X,
+ const Base<typename T1::elem_type, T2>& Y,
+ const Base<typename T1::elem_type, T3>& XI,
+ Mat<typename T1::elem_type>& YI,
+ const char* method = "linear",
+ const typename T1::elem_type extrap_val = Datum<typename T1::elem_type>::nan
+ )
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::elem_type eT;
+
+ uword sig = 0;
+
+ if(method != nullptr)
+ if(method[0] != char(0))
+ if(method[1] != char(0))
+ {
+ const char c1 = method[0];
+ const char c2 = method[1];
+
+ if(c1 == 'n') { sig = 10; } // nearest neighbour
+ else if(c1 == 'l') { sig = 20; } // linear
+ else
+ {
+ if( (c1 == '*') && (c2 == 'n') ) { sig = 11; } // nearest neighour, assume monotonic increase in X and XI
+ if( (c1 == '*') && (c2 == 'l') ) { sig = 21; } // linear, assume monotonic increase in X and XI
+ }
+ }
+
+ arma_debug_check( (sig == 0), "interp1(): unsupported interpolation type" );
+
+ const quasi_unwrap<T1> X_tmp( X.get_ref());
+ const quasi_unwrap<T2> Y_tmp( Y.get_ref());
+ const quasi_unwrap<T3> XI_tmp(XI.get_ref());
+
+ if( X_tmp.is_alias(YI) || Y_tmp.is_alias(YI) || XI_tmp.is_alias(YI) )
+ {
+ Mat<eT> tmp;
+
+ interp1_helper(X_tmp.M, Y_tmp.M, XI_tmp.M, tmp, sig, extrap_val);
+
+ YI.steal_mem(tmp);
+ }
+ else
+ {
+ interp1_helper(X_tmp.M, Y_tmp.M, XI_tmp.M, YI, sig, extrap_val);
+ }
+ }
+
+
+
+//! @}