null space

Former-commit-id: ee271dd244408e908afdaa9146da69ee3d2c82f2

include/igl/null.cpp

@@ -0,0 +1,21 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "null.h"
+#include "EPS.h"
+
+template <typename DerivedA, typename DerivedN>
+IGL_INLINE void igl::null(
+  const Eigen::PlainObjectBase<DerivedA> & A,
+  Eigen::PlainObjectBase<DerivedN> & N)
+{
+  using namespace Eigen;
+  typedef typename DerivedA::Scalar Scalar;
+  JacobiSVD<MatrixXd> svd(A, ComputeFullV);
+  svd.setThreshold(A.cols() * svd.singularValues().maxCoeff() * EPS<Scalar>());
+  N = svd.matrixV().rightCols(A.cols()-svd.rank());
+}

include/igl/null.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_NULL_H
+#define IGL_NULL_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+
+namespace igl 
+{
+  // Like MATLAB's null
+  //
+  // Compute a basis for the null space for the given matrix A: the columns of
+  // the output N form a basis for the space orthogonal to that spanned by the
+  // rows of A.
+  //
+  // Inputs:
+  //   A  m by n matrix
+  // Outputs:
+  //   N  n by r matrix, where r is the row rank of A
+  template <typename DerivedA, typename DerivedN>
+  IGL_INLINE void null(
+    const Eigen::PlainObjectBase<DerivedA> & A,
+    Eigen::PlainObjectBase<DerivedN> & N);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "null.cpp"
+#endif
+
+#endif