Sameer, I have submitted the issue on https://github.com/ceres-solver/ceres-solver/issues.
Oleg On Sun, Jun 28, 2020 at 3:59 PM Sameer Agarwal <[email protected]> wrote: > 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 >>> >>> >>> >>>
