Hi list, I am using Eigen 3.3.7 release with ceres solver 1.14.0 with
autodiff Jet data type and I have some problems. I need to solve linear
least square subproblem within variable projection algorithm, namely I need
to solve LLS equation
A(p)*x = b
Where matrix A(p) depends on nonlinear parameters p:
x(p) = pseudo-inverse(A(p))*b;
x(p) will be optimized in nonlinear least squares fitting, so I need
Jcobian. Rhs b is measured vector of doubles, e.g. VectorXd. In order to
use ceres's autodiff p must be of Jet type. Ceres provides corresponding
traits for binary operations
#if EIGEN_VERSION_AT_LEAST(3, 3, 0)
// Specifying the return type of binary operations between Jets and scalar
types
// allows you to perform matrix/array operations with Eigen matrices and
arrays
// such as addition, subtraction, multiplication, and division where one
Eigen
// matrix/array is of type Jet and the other is a scalar type. This improves
// performance by using the optimized scalar-to-Jet binary operations but
// is only available on Eigen versions >= 3.3
template <typename BinaryOp, typename T, int N>
struct ScalarBinaryOpTraits<ceres::Jet<T, N>, T, BinaryOp> {
typedef ceres::Jet<T, N> ReturnType;
};
template <typename BinaryOp, typename T, int N>
struct ScalarBinaryOpTraits<T, ceres::Jet<T, N>, BinaryOp> {
typedef ceres::Jet<T, N> ReturnType;
};
#endif // EIGEN_VERSION_AT_LEAST(3, 3, 0)
There two problems.
1. Small problem. In a function "RealScalar threshold() const" in SCDbase.h
I have to replace "return m_usePrescribedThreshold ? m_prescribedThreshold
: diagSize*
NumTraits<Scalar>::epsilon();" with "return m_usePrescribedThreshold ?
m_prescribedThreshold
: Scalar(diagSize)*
NumTraits<Scalar>::epsilon();"
This fix is similar Gael's fix of Bug 1403
<http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1403>
2. It is less trivial. I expect that x(p) = pseudo-inverse(A(p))*b; is
vector of Jet. And it is actually true for e.g SVD decompoazition
x(p) = VSU^T * b.
But if I use
JcobySVD<Matrix<Jet<double, 2>, Dynamic, Dynamic>> svd(A);
x(p) = svd.solve(b),
I got error message.
Here code for reproducing the error
// test_svd_jet.cpp
#include <ceres/jet.h>
using ceres::Jet;
int test_svd_jet()
{
typedef Matrix<Jet<double, 2>, Dynamic, Dynamic> Mat;
typedef Matrix<Jet<double, 2>, Dynamic, 1> Vec;
Mat A = MatrixXd::Random(3, 2).cast <Jet<double, 2>>();
VectorXd b = VectorXd::Random(3);
JacobiSVD<Mat> svd(A, ComputeThinU | ComputeThinV);
int l_rank = svd.rank();
Vec c = svd.matrixV().leftCols(l_rank)
* svd.singularValues().head(l_rank).asDiagonal().inverse()
* svd.matrixU().leftCols(l_rank).adjoint() * b; // *
Vec c1 = svd.solve(b.cast<Jet<double, 2>>()); // **
Vec c2 = svd.solve(b); // ***
return 0;
}
// End test_svd_jet.cpp
// * and // ** work fine an give the same results. // *** fails with VS
2019 error message
Eigen\src\Core\functors\AssignmentFunctors.h(24,1):
error C2679: binary '=': no operator found which takes
a right-hand operand of type 'const SrcScalar'
(or there is no acceptable conversion)
The error points to line //***. I thing that solution is of type VectorXd
instead of Vec and there is problem with assignment of double to Jet.
Derivatives are lost either. It should work similar to complex type. If A
is complex matrix and b is real vector, x must be complex. There is
something wrong with Type deduction in SVD or QR decomposition.
Do you have any idea of how to fix it.
Best regards,
Oleg Shirokobrod
