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 >>>>> >>>>> 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 >>>>>>>> >>>>>>>>
