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mult2ind.m
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mult2ind.m
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% Compute the linear index corresponding to a two-dimensional multiindex.
%
%===============================================================================
%> @file mult2ind.m
%>
%> @brief Compute the linear index corresponding to a two-dimensional multiindex.
%===============================================================================
%>
%> @brief Compute the linear index corresponding to a two-dimensional multiindex.
%>
%> For a given two-dimensional multiindex @f$\mathbf{a} = [a^1, a^2]^T@f$
%> the corresponding linear index is computed, using the following ordering:
%>
%> a^T | ind
%> ---------+-------
%> [0,0] | 1
%> [1,0] | 2
%> [0,1] | 3
%> [2,0] | 4
%> [1,1] | 5
%> [0,2] | 6
%> [3,0] | 7
%> [2,1] | 8
%> [1,2] | 9
%> [0,3] | 10
%> ...
%>
%> This is useful, e.g., to find the index of a certain derivative in the
%> Taylor basis functions.
%>
%> @param a Two-dimensional multi-index as a row vector. Multiple
%> multi-indices can be given as multiple rows.
%> @f$[n \times 2]@f$
%>
%> @return The linear index. @f$[n \times 1]@f$
%>
%> This file is part of FESTUNG
%>
%> @copyright 2014-2016 Florian Frank, Balthasar Reuter, Vadym Aizinger
%>
%> @par License
%> @parblock
%> This program is free software: you can redistribute it and/or modify
%> it under the terms of the GNU General Public License as published by
%> the Free Software Foundation, either version 3 of the License, or
%> (at your option) any later version.
%>
%> This program is distributed in the hope that it will be useful,
%> but WITHOUT ANY WARRANTY; without even the implied warranty of
%> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%> GNU General Public License for more details.
%>
%> You should have received a copy of the GNU General Public License
%> along with this program. If not, see <https://www.gnu.org/licenses/>.
%> @endparblock
%
function ind = mult2ind(a)
assert(size(a, 2) == 2);
p = sum(a, 2);
N = p .* (p + 1) / 2;
ind = N + 1 + a(:, 2);
end