Why do you say that? You could be solving for multiple right-hand sides. Is b know to have 1 column at compile time?
On Tue, Jun 2, 2020 at 1:31 AM Oleg Shirokobrod <[email protected]> wrote: > Hi Rasmus, > > I have just tested COD decomposition in Eigen library. It arises the same > problem. This is defect of Eigen decomposition module type reduction of > result of solve method. If > template <typename T> Matrix<T, Dynamic, Dynamic> A; and ArraXd b;, than > x = A.solve(b) should be of type <typename T> Matrix<T, Dynamic, 1.>. > > I like the idea to use COD as an alternative to QR or SVD and I added this > option to my code. > > > On Tue, Jun 2, 2020 at 10:36 AM Oleg Shirokobrod < > [email protected]> wrote: > >> Rasmus, I wiil have a look at COD. Brad, I did not try CppAD.I am >> working in given framework: ceres nonlinear least squares solver + ceres >> autodiff + Eigen decomposition modules SVD or QR. The problem is not just >> on autodiff side. The problem is that Eigen decomposition modul does not >> work properly with autodiff type variable. >> >> Thank you everybody for advice. >> >> On Mon, Jun 1, 2020 at 8:41 PM Rasmus Munk Larsen <[email protected]> >> wrote: >> >>> >>> >>> On Mon, Jun 1, 2020 at 10:33 AM Patrik Huber <[email protected]> >>> wrote: >>> >>>> Hi Rasmus, >>>> >>>> This is slightly off-topic to this thread here, but it would be great >>>> if you added your COD to the list/table of decompositions in Eigen: >>>> https://eigen.tuxfamily.org/dox/group__TopicLinearAlgebraDecompositions.html >>>> >>>> First, it would make it easier for people to find, and second, it would >>>> also help a lot to see on that page how the algorithm compares to the >>>> others, to be able to choose it appropriately. >>>> >>> >>> Good point. Will do. >>> >>> >>>> >>>> >>>> Unrelated: @All/Maintainers: It seems like lots (all) of the images on >>>> the documentation website are broken? At least for me. E.g.: >>>> >>>> [image: image.png] >>>> >>>> >>>> Best wishes, >>>> Patrik >>>> >>>> On Mon, 1 Jun 2020 at 17:59, Rasmus Munk Larsen <[email protected]> >>>> wrote: >>>> >>>>> Hi Oleg and Sameer, >>>>> >>>>> A faster option than SVD, but more robust than QR (since it also >>>>> handles the under-determined case) is the complete orthogonal >>>>> decomposition >>>>> that I implemented in Eigen a few years ago. >>>>> >>>>> >>>>> https://eigen.tuxfamily.org/dox/classEigen_1_1CompleteOrthogonalDecomposition.html >>>>> >>>>> (Looks like the docstring is broken - oops!) >>>>> >>>>> It appears to also be available in the 3.3 branch: >>>>> https://gitlab.com/libeigen/eigen/-/blob/3.3/Eigen/src/QR/CompleteOrthogonalDecomposition.h >>>>> >>>>> Rasmus >>>>> >>>>> On Mon, Jun 1, 2020 at 6:57 AM Sameer Agarwal < >>>>> [email protected]> wrote: >>>>> >>>>>> Oleg, >>>>>> Two ideas: >>>>>> >>>>>> 1. You may have an easier time using QR factorization instead of SVD >>>>>> to solve your least squares problem. >>>>>> 2. But you can do better, instead of trying to solve linear least >>>>>> squares problem involving a matrix of Jets, you are better off, solving >>>>>> the >>>>>> linear least squares problem on the scalars, and then using the implicit >>>>>> function theorem >>>>>> <https://en.wikipedia.org/wiki/Implicit_function_theorem> to compute >>>>>> the derivative w.r.t the parameters and then applying the chain rule. >>>>>> >>>>>> i.e., start with min |A x = b| >>>>>> >>>>>> the solution satisfies the equation >>>>>> >>>>>> A'A x - A'b = 0. >>>>>> >>>>>> solve this equation to get the optimal value of x, and then compute >>>>>> the jacobian of this equation w.r.t A, b and x. and apply the implicit >>>>>> theorem. >>>>>> >>>>>> Sameer >>>>>> >>>>>> >>>>>> On Mon, Jun 1, 2020 at 4:46 AM Oleg Shirokobrod < >>>>>> [email protected]> wrote: >>>>>> >>>>>>> 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 >>>>>>> >>>>>>>
