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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_interp2
//! @{
template<typename eT>
inline
void
interp2_helper_nearest(const Mat<eT>& XG, const Mat<eT>& ZG, const Mat<eT>& XI, Mat<eT>& ZI, const eT extrap_val, const uword mode)
{
arma_extra_debug_sigprint();
const eT XG_min = XG.min();
const eT XG_max = XG.max();
// mode = 0: interpolate across rows (eg. expand in vertical direction)
// mode = 1: interpolate across columns (eg. expand in horizontal direction)
if(mode == 0) { ZI.set_size(XI.n_elem, ZG.n_cols); }
if(mode == 1) { ZI.set_size(ZG.n_rows, XI.n_elem); }
const eT* XG_mem = XG.memptr();
const eT* XI_mem = XI.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))
{
if(mode == 0) { ZI.row(i).fill(extrap_val); }
if(mode == 1) { ZI.col(i).fill(extrap_val); }
}
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
}
}
if(mode == 0) { ZI.row(i) = ZG.row(best_j); }
if(mode == 1) { ZI.col(i) = ZG.col(best_j); }
}
}
}
template<typename eT>
inline
void
interp2_helper_linear(const Mat<eT>& XG, const Mat<eT>& ZG, const Mat<eT>& XI, Mat<eT>& ZI, const eT extrap_val, const uword mode)
{
arma_extra_debug_sigprint();
const eT XG_min = XG.min();
const eT XG_max = XG.max();
// mode = 0: interpolate across rows (eg. expand in vertical direction)
// mode = 1: interpolate across columns (eg. expand in horizontal direction)
if(mode == 0) { ZI.set_size(XI.n_elem, ZG.n_cols); }
if(mode == 1) { ZI.set_size(ZG.n_rows, XI.n_elem); }
const eT* XG_mem = XG.memptr();
const eT* XI_mem = XI.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))
{
if(mode == 0) { ZI.row(i).fill(extrap_val); }
if(mode == 1) { ZI.col(i).fill(extrap_val); }
}
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);
if(mode == 0) { ZI.row(i) = (eT(1) - weight)*ZG.row(a_best_j) + (weight)*ZG.row(b_best_j); }
if(mode == 1) { ZI.col(i) = (eT(1) - weight)*ZG.col(a_best_j) + (weight)*ZG.col(b_best_j); }
}
}
}
template<typename T1, typename T2, typename T3, typename T4, typename T5>
inline
typename
enable_if2< is_real<typename T1::elem_type>::value, void >::result
interp2
(
const Base<typename T1::elem_type, T1>& X,
const Base<typename T1::elem_type, T2>& Y,
const Base<typename T1::elem_type, T3>& Z,
const Base<typename T1::elem_type, T4>& XI,
const Base<typename T1::elem_type, T5>& YI,
Mat<typename T1::elem_type>& ZI,
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;
const char sig = (method != nullptr) ? method[0] : char(0);
arma_debug_check( ((sig != 'n') && (sig != 'l')), "interp2(): unsupported interpolation type" );
const quasi_unwrap<T1> UXG( X.get_ref() );
const quasi_unwrap<T2> UYG( Y.get_ref() );
const quasi_unwrap<T3> UZG( Z.get_ref() );
const quasi_unwrap<T4> UXI( XI.get_ref() );
const quasi_unwrap<T5> UYI( YI.get_ref() );
arma_debug_check( (UXG.M.is_vec() == false), "interp2(): X must resolve to a vector" );
arma_debug_check( (UYG.M.is_vec() == false), "interp2(): Y must resolve to a vector" );
arma_debug_check( (UXI.M.is_vec() == false), "interp2(): XI must resolve to a vector" );
arma_debug_check( (UYI.M.is_vec() == false), "interp2(): YI must resolve to a vector" );
arma_debug_check( (UXG.M.n_elem < 2), "interp2(): X must have at least two unique elements" );
arma_debug_check( (UYG.M.n_elem < 2), "interp2(): Y must have at least two unique elements" );
arma_debug_check( (UXG.M.n_elem != UZG.M.n_cols), "interp2(): number of elements in X must equal the number of columns in Z" );
arma_debug_check( (UYG.M.n_elem != UZG.M.n_rows), "interp2(): number of elements in Y must equal the number of rows in Z" );
arma_debug_check( (UXG.M.is_sorted("strictascend") == false), "interp2(): X must be monotonically increasing" );
arma_debug_check( (UYG.M.is_sorted("strictascend") == false), "interp2(): Y must be monotonically increasing" );
arma_debug_check( (UXI.M.is_sorted("strictascend") == false), "interp2(): XI must be monotonically increasing" );
arma_debug_check( (UYI.M.is_sorted("strictascend") == false), "interp2(): YI must be monotonically increasing" );
Mat<eT> tmp;
if( UXG.is_alias(ZI) || UXI.is_alias(ZI) )
{
Mat<eT> out;
if(sig == 'n')
{
interp2_helper_nearest(UYG.M, UZG.M, UYI.M, tmp, extrap_val, 0);
interp2_helper_nearest(UXG.M, tmp, UXI.M, out, extrap_val, 1);
}
else
if(sig == 'l')
{
interp2_helper_linear(UYG.M, UZG.M, UYI.M, tmp, extrap_val, 0);
interp2_helper_linear(UXG.M, tmp, UXI.M, out, extrap_val, 1);
}
ZI.steal_mem(out);
}
else
{
if(sig == 'n')
{
interp2_helper_nearest(UYG.M, UZG.M, UYI.M, tmp, extrap_val, 0);
interp2_helper_nearest(UXG.M, tmp, UXI.M, ZI, extrap_val, 1);
}
else
if(sig == 'l')
{
interp2_helper_linear(UYG.M, UZG.M, UYI.M, tmp, extrap_val, 0);
interp2_helper_linear(UXG.M, tmp, UXI.M, ZI, extrap_val, 1);
}
}
}
//! @}
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