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40 lines
1.3 KiB
40 lines
1.3 KiB
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef IGL_ORTH_H
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#define IGL_ORTH_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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namespace igl
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{
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/// Orthogonalization of a matrix. ORTH(A,Q) produces Q as an orthonormal
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/// basis for the range of A. That is, Q'*Q = I, the columns of Q span the
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/// same space as the columns of A, and the number of columns of Q is the rank
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/// of A.
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///
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///
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/// The algorithm uses singular value decomposition, SVD, instead of
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/// orthogonal factorization, QR. This doubles the computation time, but
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/// provides more reliable and consistent rank determination. Closely follows
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/// MATLAB implementation in orth.m
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///
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/// @param[in] A m by n matrix
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/// @param[out] Q m by n matrix with orthonormal columns spanning same column
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/// space as A
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///
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/// \warning Implementation listed as "Broken"
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IGL_INLINE void orth(const Eigen::MatrixXd &A, Eigen::MatrixXd &Q);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "orth.cpp"
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#endif
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#endif
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