Tobias, I have looked into this and added some details to the issue. As I understand it, these matrix algorithms require instantiating std::complex<ceres::Jet<T, N>, that leads to problems in the STL.
Sameer On Thu, Jun 18, 2020 at 9:35 AM Sameer Agarwal <[email protected]> wrote: > sorry folks I have been missing in action, I will take a look as soon as I > can. > Sameer > > > On Sat, Jun 6, 2020 at 12:26 PM Wood, Tobias <[email protected]> > wrote: > >> Hello, >> >> >> >> I have opened an issue here: >> https://gitlab.com/libeigen/eigen/-/issues/1912 >> >> >> >> I remembered that I did previously discuss the .exp() issue with Sameer >> on the Ceres mailing list, I have added a link to that, however I am now >> getting a slightly different error message because it looks like the >> internals of the STL have changed. Also, I have changed my algorithm >> slightly and now only need .pow(), but this does not work with Jets either. >> I think the problem with .pow() looks easier to fix? >> >> >> >> Thanks, >> >> Toby >> >> >> >> *From: *Rasmus Munk Larsen <[email protected]> >> *Reply to: *"[email protected]" <[email protected]> >> *Date: *Thursday, 4 June 2020 at 18:46 >> *To: *eigen <[email protected]>, Sameer Agarwal < >> [email protected]> >> *Subject: *Re: [eigen] Using Eigen decompositions with ceres autodiff >> Jet data type. >> >> >> >> Hi Tobias, >> >> Please do. Sameer, since this is Ceres solver related, could I ask you to >> help out with this issue. >> >> Rasmus >> >> >> >> On Thu, Jun 4, 2020 at 3:06 AM Wood, Tobias <[email protected]> >> wrote: >> >> Hello, >> >> >> >> Apologies to bring up a tangentially related topic - Eigen's matrix >> exponential also doesn't work with Ceres Jets. There is some code inside >> the matrix exponential that checks if the scalar type is "known" to Eigen, >> I assume because there are some constants it requires. Jet<double> is not >> one of those types, so Eigen refuses to compile. When I encountered this >> problem earlier this year I worked around it by using Ceres numeric >> differentiation, but obviously if there's a chance to fix this and use >> auto-differentiation I would be very happy (big speed increase hopefully). >> Should I create an issue on the Eigen gitlab? >> >> >> >> Thanks, >> >> Toby >> >> >> >> *From: *Oleg Shirokobrod <[email protected]> >> *Reply to: *"[email protected]" <[email protected]> >> *Date: *Thursday, 4 June 2020 at 06:36 >> *To: *"[email protected]" <[email protected]> >> *Subject: *Re: [eigen] Using Eigen decompositions with ceres autodiff >> Jet data type. >> >> >> >> 1. I would like to have autodiff ability, so I cannot use double for both >> A and b. If I cast b: A.jacobiSVD().solve( b.cast<T>()) everything works >> fine, but BinOp(T,T) is more expensive than BinOp(T, double). I would like >> to keep b as a vector of doubles. >> >> 2. T=Jet is ceres solver autodiff implementation type. There is a trait >> definition for Jet binary operations for type deduction such that >> type(Jet*double) = Jet and so on. It works when I do direct multiplication >> VS^-1U^T >> * b. It works similar to complex scalar matrices and double rhs and there >> is the same problem for complex scalar cases. >> >> 3. I think that the mixed type deduction rule should give the same type >> for VS^-1U^T * b and for A.jcobianSVD().solve(b); where A = USV^T because >> both use the same algorithm. >> >> 4. Unless there are serious reasons, deduction rules should be similar to >> scalar type equations. complex<double> A; double b; x = A^-1 * b; type(x) = >> complex<double>. >> >> >> >> On Wed, Jun 3, 2020 at 11:16 PM Rasmus Munk Larsen <[email protected]> >> wrote: >> >> Try to compile your code in debug mode with the type assertions on. >> >> >> >> On Wed, Jun 3, 2020 at 1:14 PM Rasmus Munk Larsen <[email protected]> >> wrote: >> >> Are you saying that you compute the decomposition in one type and solve >> with a RHS of a different type? Why do you say that VS^-1U^T * b should be >> Matrix<T>? That makes an assumption about type coercion rules. In fact, you >> cannot generally mix types in Eigen expressions without explicit casting, >> and U.adjoint() * b should fail if the types are different. >> >> >> >> On Wed, Jun 3, 2020 at 11:33 AM Oleg Shirokobrod < >> [email protected]> wrote: >> >> Rasmuss, I do not quite understand this issue. Decomposition solve should >> propagate scalar type of a matrix but not scalar type of its argument. >> Example: >> >> template <typename T> Matrix<T> A; >> >> VectorXd b; >> >> A.jcobiSVD().solve(b) should be of type Matrix<T> but it is not. Type of >> result is Matrix<double>. If we make SVD decomposition of A = USV^T and >> express result as VS^-1U^T * b, than result will be of type Matrix<T>. >> Which is correct and differs from result of solve which uses the same >> algorithm but more complex result’s type deduction. This is the problem. >> >> >> >> On Wed 3. Jun 2020 at 20.19, Rasmus Munk Larsen <[email protected]> >> wrote: >> >> OK, I opened https://gitlab.com/libeigen/eigen/-/issues/1909 >> <https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.com%2Flibeigen%2Feigen%2F-%2Fissues%2F1909&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=4adEoOhABpJiEJlKW29VCAHkhG4EXH6ZnSeSQr8dmJ0%3D&reserved=0> >> for >> this. >> >> >> >> On Tue, Jun 2, 2020 at 11:06 PM Oleg Shirokobrod < >> [email protected]> wrote: >> >> Yes. At the time of computing only 1d observation (VectorXd) is known. >> >> >> >> On Tue, Jun 2, 2020 at 9:42 PM Rasmus Munk Larsen <[email protected]> >> wrote: >> >> OK, so b is declared as VectorXf or some other type with >> ColsAtCompileTime=1? >> >> >> >> On Tue, Jun 2, 2020 at 11:27 AM Oleg Shirokobrod < >> [email protected]> wrote: >> >> >> >> Yes, b is measured spectrum that is 1d array. I have to get x for 1d >> array at a time. I fit sum of peak models to 1d rhs. 1d array of peak model >> values is one column of matrix A. >> >> >> >> On Tue 2. Jun 2020 at 20.06, Rasmus Munk Larsen <[email protected]> >> wrote: >> >> 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 >> <https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Feigen.tuxfamily.org%2Fdox%2Fgroup__TopicLinearAlgebraDecompositions.html&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=BeutduNEeXIXTOtbc8%2BfWXS3FnlTvzEQq0yPrJ7nUOo%3D&reserved=0> >> >> >> 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.: >> >> >> >> >> >> >> >> 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 >> <https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Feigen.tuxfamily.org%2Fdox%2FclassEigen_1_1CompleteOrthogonalDecomposition.html&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=4ALzcdxWY8wDOlejWGXr9DfIUg%2FGV%2B9CnWkoozLWMSU%3D&reserved=0> >> >> (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 >> <https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.com%2Flibeigen%2Feigen%2F-%2Fblob%2F3.3%2FEigen%2Fsrc%2FQR%2FCompleteOrthogonalDecomposition.h&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=F4uktFTL%2BeQ%2BOqeURPZ%2FoOaoReqnH1hU2CobNC%2BNxHk%3D&reserved=0> >> >> 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://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FImplicit_function_theorem&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=wACe44wQ0vA%2BVFojAnCxvAnvRkgps4y2sIcl0d1wLC4%3D&reserved=0> >> 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 >> <https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Feigen.tuxfamily.org%2Fbz%2Fshow_bug.cgi%3Fid%3D1403&data=01%7C01%7Ctobias.wood%40kcl.ac.uk%7C9b7731b3d2c24c6ea7e908d808af4522%7C8370cf1416f34c16b83c724071654356%7C0&sdata=xcVjY1p2d8oscbHsEuiqRMdNPzGOGGI%2BLb%2FOqZUWrec%3D&reserved=0> >> >> 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 >> >> >> >>
