Extending Eigen::EigenBase with operator() - c++

Question

I would like to use MatrixXd class for meshes with offsets (0.5, 0) and (0, 0.5). In mathematical formulas, velocity is calculated between cells i,i+1, and this is written as vel(i+0.5,j). I would like to introduce syntax like this one:
#include <Eigen/Dense>
int main() {
Eigen::MatrixXd m = Eigen::MatrixXd::Zero(5,5);
// Want to use similar syntax:
// m(0, 1.5) = 1.0;
// and
// m(3.5, 1) = 2.0;
// Instead of:
m(0, 2) = 1.0;
m(4, 1) = 2.0;
}
Using EIGEN_MATRIXBASE_PLUGIN like this one:
inline Scalar& operator()(int r, int c) {
return Base::operator()(r, c);
}
inline Scalar& operator()(double r, int c) {
return Base::operator()(int(r + 0.5), c);
}
inline Scalar& operator()(int r, double c) {
return Base::operator()(r, int(c + 0.5));
}
However, this approach:
Works only for only X-axis or only Y-axis offset, not both at the same time.
Works only for specific offset hardcoded into plugin.
Breaks some internal Eigen convections, which can be demostrated by trying to compile BiCG example with IncompleteLUT preconditioner:
int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
/* ... fill A and b ... */
BiCGSTAB<SparseMatrix<double>,IncompleteLUT<double>> solver;
solver.compute(A);
x = solver.solve(b);
Causes following errors:
term does not evaluate to a function taking 1 arguments
'Eigen::SparseMatrix<double,1,int>::insertBackByOuterInnerUnordered': function does not take 1 arguments
Adding operator()(double offset_col, double offset_row) to adress second issue like this:
double r_offset = -0.5, c_offset = -0.5;
inline void set_r_offset(double val) { r_offset = val; }
inline void set_c_offset(double val) { c_offset = val; }
inline double get_r_offset() { return r_offset; }
inline double get_c_offset() { return c_offset; }
inline Scalar& operator()(double r, double c) {
// double r_offset = -0.5, c_offset = -0.5;
return Base::operator()(int(r - r_offset), int(c - c_offset));
}
This causes illegal free:
==6035== Invalid free() / delete / delete[] / realloc()
==6035== at 0x4C30D3B: free (in /usr/lib/valgrind/vgpreload_memcheck-amd64-linux.so)
==6035== by 0x4E4224A: aligned_free (Memory.h:177)
==6035== by 0x4E4224A: conditional_aligned_free<true> (Memory.h:230)
==6035== by 0x4E4224A: conditional_aligned_delete_auto<double, true> (Memory.h:416)
==6035== by 0x4E4224A: resize (DenseStorage.h:406)
==6035== by 0x4E4224A: resize (PlainObjectBase.h:293)
==6035== by 0x4E4224A: resize_if_allowed<Eigen::Matrix<double, -1, -1>, Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> >, double, double> (AssignEvaluator.h:720)
==6035== by 0x4E4224A: call_dense_assignment_loop<Eigen::Matrix<double, -1, -1>, Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> >, Eigen::internal::assign_op<double, double> > (AssignEvaluator.h:734)
==6035== by 0x4E4224A: run (AssignEvaluator.h:879)
==6035== by 0x4E4224A: call_assignment_no_alias<Eigen::Matrix<double, -1, -1>, Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> >, Eigen::internal::assign_op<double, double> > (AssignEvaluator.h:836)
==6035== by 0x4E4224A: call_assignment<Eigen::Matrix<double, -1, -1>, Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> >, Eigen::internal::assign_op<double, double> > (AssignEvaluator.h:804)
==6035== by 0x4E4224A: call_assignment<Eigen::Matrix<double, -1, -1>, Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> > > (AssignEvaluator.h:782)
==6035== by 0x4E4224A: _set<Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> > > (PlainObjectBase.h:710)
==6035== by 0x4E4224A: operator=<Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<double>, Eigen::Matrix<double, -1, -1> > > (Matrix.h:225)
==6035== by 0x11044C: main (Runner.cpp:16)
==6035== Address 0x2e642f73726573 is not stack'd, malloc'd or (recently) free'd
If offsets are not introduced as class members, but are local variables in operator(), no errors are detected by valgrind.
Is it possible to implement new MatrixXd::operator()(double, double) with settable offsets?
EDIT:
Operator() is defined in a parent class DenseCoeffsBase:
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
{
eigen_assert(row >= 0 && row < rows()
&& col >= 0 && col < cols());
return coeff(row, col);
}

Answer 1

Perhaps, I see one problem with your operator which returns reference to temporary object of Scalar:
inline Scalar& operator()(double r, double c) {
// double r_offset = -0.5, c_offset = -0.5;
return Base::operator()(int(r - r_offset), int(c - c_offset));
}
So you should return Scalar by copy.
Could you share code of Base::operator()(int(r - r_offset), int(c - c_offset));?