# Numerics

**URL:** https://discourse.julialang.org/c/domain/numerics/20.md?page=36

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**Page:** 37

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## [DiffEqSensitivity Parameter ranges](https://discourse.julialang.org/t/diffeqsensitivity-parameter-ranges/22435)

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**Author:** [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Replies:** 4\
**Last updated:** [March 28, 2019, 9:23pm UTC](https://discourse.julialang.org/t/diffeqsensitivity-parameter-ranges/22435 "2019-03-28T21:23:17Z")

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Hi, I’ve been working with DifferentialEquations Package - I am ready to run some global sensitivity analysis (GSA) I noticed that the way to input the ranges of evaluation goes something like this Let’s say my param…

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## [Looking for documentation related to sparse matrix factorization](https://discourse.julialang.org/t/looking-for-documentation-related-to-sparse-matrix-factorization/21976)

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**Author:** [@siddMahen](https://discourse.julialang.org/u/siddMahen)\
**Replies:** 4\
**Last updated:** [March 22, 2019, 9:15pm UTC](https://discourse.julialang.org/t/looking-for-documentation-related-to-sparse-matrix-factorization/21976 "2019-03-22T21:15:16Z")

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This is surely a dumb question, but I can’t seem to find documentation describing LU factorization for sparse matrices. Could anyone direct me to the docs? Thanks

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## [Insufficient orthogonality of eigenvectors](https://discourse.julialang.org/t/insufficient-orthogonality-of-eigenvectors/22193)

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**Author:** [@ivanslapnicar](https://discourse.julialang.org/u/ivanslapnicar)\
**Replies:** 1\
**Last updated:** [March 22, 2019, 1:12pm UTC](https://discourse.julialang.org/t/insufficient-orthogonality-of-eigenvectors/22193 "2019-03-22T13:12:28Z")

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In eigen.jl function eigen() calls eigen!() which appears to call LAPACK.geevx!() for all types of matrices (symmetric and non-symmetric). For symmetric matrices this results in insufficiently orthogonal eigenvectors …

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## [Error while using DifferentialEquations.jl stiff methods](https://discourse.julialang.org/t/error-while-using-differentialequations-jl-stiff-methods/22004)

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**Author:** [@Andre\_Mello](https://discourse.julialang.org/u/Andre_Mello)\
**Replies:** 3\
**Last updated:** [March 19, 2019, 4:42pm UTC](https://discourse.julialang.org/t/error-while-using-differentialequations-jl-stiff-methods/22004 "2019-03-19T16:42:41Z")

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Hi all, The DifferentialEquations’ suggested integration methods when trying to solve this stiff problem all yield the same error. The native Julia ones, that is. Sundial’s CVODE\_BDF as well as lsoda are able to solve t…

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## [Accumulating error in for loop generated by tensor macro vs sum](https://discourse.julialang.org/t/accumulating-error-in-for-loop-generated-by-tensor-macro-vs-sum/21647)

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**Author:** [@grahamas](https://discourse.julialang.org/u/grahamas)\
**Replies:** 1\
**Last updated:** [March 8, 2019, 11:52pm UTC](https://discourse.julialang.org/t/accumulating-error-in-for-loop-generated-by-tensor-macro-vs-sum/21647 "2019-03-08T23:52:08Z")

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Could anyone give me a pointer on a numerical inaccuracy that’s causing my simulation to explode? Here’s a toy example of the operation I’m running, though in practice it accumulates as b += S(C), where S is a nonlinear…

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## [Trouble with boundary conditions in DiffEqOperators.jl](https://discourse.julialang.org/t/trouble-with-boundary-conditions-in-diffeqoperators-jl/21488)

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**Author:** [@danielc](https://discourse.julialang.org/u/danielc)\
**Replies:** 9\
**Last updated:** [March 6, 2019, 12:12am UTC](https://discourse.julialang.org/t/trouble-with-boundary-conditions-in-diffeqoperators-jl/21488 "2019-03-06T00:12:14Z")

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Hello, I’m trying to learn how to use the DiffEqOperators.jl module. It’s quite new. Chris Rackauckas gave a talk at JuliaCon 2018. To get started, I tried to choose a very simple problem: Compute the second derivati…

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## [State of reverse mode AD tools](https://discourse.julialang.org/t/state-of-reverse-mode-ad-tools/21467)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 8\
**Last updated:** [March 5, 2019, 10:51am UTC](https://discourse.julialang.org/t/state-of-reverse-mode-ad-tools/21467 "2019-03-05T10:51:09Z")

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(Opening a new topic instead of resurrecting some older ones.) I am wondering about the current state of libraries for reverse mode AD, specifically for differentiating \\mathbb{R}^n \\to \\mathbb{R} functions that accep…

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## [Unexpected? result of multiplication with adjoint()](https://discourse.julialang.org/t/unexpected-result-of-multiplication-with-adjoint/21447)

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**Author:** [@ivanslapnicar](https://discourse.julialang.org/u/ivanslapnicar)\
**Replies:** 1\
**Last updated:** [March 4, 2019, 12:20pm UTC](https://discourse.julialang.org/t/unexpected-result-of-multiplication-with-adjoint/21447 "2019-03-04T12:20:25Z")

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On Julia Version 1.0.2 the output of the following code using LinearAlgebra unblock(A) = mapreduce(identity, hcat, \[mapreduce(identity, vcat, A\[:,i\]) for i = 1:size(A,2)\]) x=Vector{Any}(undef,2) x\[1\]=\[1+2im 1-im;-3 4+3i…

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## [Out-of-core MUMPS.jl Implementation](https://discourse.julialang.org/t/out-of-core-mumps-jl-implementation/21372)

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**Author:** [@Uche](https://discourse.julialang.org/u/Uche)\
**Replies:** 1\
**Last updated:** [March 2, 2019, 6:27pm UTC](https://discourse.julialang.org/t/out-of-core-mumps-jl-implementation/21372 "2019-03-02T18:27:48Z")

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So how does the out-of-core MUMPS.jl work? Is there any specific thing a user should do to use this option? Thanks. Uche.

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## [Understanding BigInt](https://discourse.julialang.org/t/understanding-bigint/21337)

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**Author:** [@johnh](https://discourse.julialang.org/u/johnh)\
**Replies:** 3\
**Last updated:** [March 1, 2019, 11:46am UTC](https://discourse.julialang.org/t/understanding-bigint/21337 "2019-03-01T11:46:49Z")

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Playing aroudn with types yesterday I found typemax(BigInt) does not exist. Which makes perfect sense. the Julia documentation on Arbitrary Precision Arithmetic refers to the Gnu GMP. Would this be the best place to rea…

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## [Rounding to a multiple of float](https://discourse.julialang.org/t/rounding-to-a-multiple-of-float/21295)

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**Author:** [@cedeerwe](https://discourse.julialang.org/u/cedeerwe)\
**Replies:** 25\
**Last updated:** [February 28, 2019, 9:52pm UTC](https://discourse.julialang.org/t/rounding-to-a-multiple-of-float/21295 "2019-02-28T21:52:22Z")

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I am trying to solve a simple problem - rounding a number to a nearest multiple of a given float. As an example, I would like roundmult(3811.47123123, 0.01) = 3811.47. However, the simplest implementation of roundmult(va…

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## [Smallest Eigenvalue of a Moler Matrix \[Again\]](https://discourse.julialang.org/t/smallest-eigenvalue-of-a-moler-matrix-again/21112)

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**Author:** [@Hans\_W\_Borchers](https://discourse.julialang.org/u/Hans_W_Borchers)\
**Replies:** 6\
**Last updated:** [February 26, 2019, 12:43pm UTC](https://discourse.julialang.org/t/smallest-eigenvalue-of-a-moler-matrix-again/21112 "2019-02-26T12:43:12Z")

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I am referring to help I received from Andreas Noack 10 months ago. https://discourse.julialang.org/t/smallest-eigenvalue-of-a-moler-matrix/10510 I wanted to compute the smallest eigenvalue of Moler matrices with high …

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## [SVD of Matrix w/ updated columns](https://discourse.julialang.org/t/svd-of-matrix-w-updated-columns/21048)

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**Author:** [@DrPapa](https://discourse.julialang.org/u/DrPapa)\
**Replies:** 7\
**Last updated:** [February 22, 2019, 5:26pm UTC](https://discourse.julialang.org/t/svd-of-matrix-w-updated-columns/21048 "2019-02-22T17:26:20Z")

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I have a M\\times N matrix A where N\>\>M. I need to compute the SVD of sub-matrices using a sliding window over the columns, i.e. svd(A\[:,1:k\]), svd(A\[:,2:k+1\]), svd(A\[:,3:k+2\])… Does anybody know of an efficient way to u…

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## [Rank-revealing QR/SVD Decompositions](https://discourse.julialang.org/t/rank-revealing-qr-svd-decompositions/21155)

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**Author:** [@Hans\_W\_Borchers](https://discourse.julialang.org/u/Hans_W_Borchers)\
**Replies:** 0\
**Last updated:** [February 24, 2019, 8:27pm UTC](https://discourse.julialang.org/t/rank-revealing-qr-svd-decompositions/21155 "2019-02-24T20:27:23Z")

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Are there implementations of rank-revealing QR/SVD decompositions, resp. QR and SVD updating / downdating mechanisms in any Julia package? See for instance: \[1\] Li and Zheng, A Rank-revealing Method with Updating, Down…

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## [UpwindOperator from DiffEqOperators.jl](https://discourse.julialang.org/t/upwindoperator-from-diffeqoperators-jl/21053)

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**Author:** [@boutor2](https://discourse.julialang.org/u/boutor2)\
**Replies:** 2\
**Last updated:** [February 22, 2019, 8:38am UTC](https://discourse.julialang.org/t/upwindoperator-from-diffeqoperators-jl/21053 "2019-02-22T08:38:36Z")

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I have been playing around with DifferentialEquations.jl, mainly for solving reaction diffusion PDE’s. I now wish to add an advection term to my model. For this purpose I discovered DiffEqOperators.jl. UpwindOperator sou…

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## [New blog post on banded matrices and ordinary differential equations using BandedMatrices.jl](https://discourse.julialang.org/t/new-blog-post-on-banded-matrices-and-ordinary-differential-equations-using-bandedmatrices-jl/18564)

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**Author:** [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Replies:** 31\
**Last updated:** [February 9, 2019, 7:12am UTC](https://discourse.julialang.org/t/new-blog-post-on-banded-matrices-and-ordinary-differential-equations-using-bandedmatrices-jl/18564 "2019-02-09T07:12:55Z")

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I just posted my first blog post, on using BandedMatrices.jl to solve ordinary differential equations via finite differences / spectral methods: Banded matrices and ordinary differential equations This is first of a ser…

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## [DifferentialEquations.jl: complex-value matrix equations without in-place update](https://discourse.julialang.org/t/differentialequations-jl-complex-value-matrix-equations-without-in-place-update/20110)

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**Author:** [@Egwene\_al\_Vere](https://discourse.julialang.org/u/Egwene_al_Vere)\
**Replies:** 1\
**Last updated:** [February 7, 2019, 2:49pm UTC](https://discourse.julialang.org/t/differentialequations-jl-complex-value-matrix-equations-without-in-place-update/20110 "2019-02-07T14:49:30Z")

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To solve a stiff complex-value matrix equation, I’m using the Rosenbrock23() solver. As a minimum working example, (may not be stiff, just to illustrate the error I got) With in-place du, (function taking 4 arguments: d…

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## [What other language allows you to do Rational matrix inversion?](https://discourse.julialang.org/t/what-other-language-allows-you-to-do-rational-matrix-inversion/20340)

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**Author:** [@xiaodai](https://discourse.julialang.org/u/xiaodai)\
**Replies:** 15\
**Last updated:** [February 6, 2019, 1:20am UTC](https://discourse.julialang.org/t/what-other-language-allows-you-to-do-rational-matrix-inversion/20340 "2019-02-06T01:20:37Z")

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I was just doing some Hackerrank for fun, in particular this one. Basically, you can describe the problem as a sequence of recurrence relations, and they told you that the solution is in the form of a rational number. S…

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## [How to do Arpack.eigs(v-\>A\*v, ...)?](https://discourse.julialang.org/t/how-to-do-arpack-eigs-v-a-v/20192)

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**Author:** [@bsxfan](https://discourse.julialang.org/u/bsxfan)\
**Replies:** 4\
**Last updated:** [January 29, 2019, 1:05pm UTC](https://discourse.julialang.org/t/how-to-do-arpack-eigs-v-a-v/20192 "2019-01-29T13:05:47Z")

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I need to find a few of the principal eigenvalues and eigenvectors of a very large (symmetric, real) matrix that is implicitly defined via its matrix-vector product. I know Arpack can do this, because it only needs to do…

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## [Cholesky factorization for slightly non-Hermitian matrices](https://discourse.julialang.org/t/cholesky-factorization-for-slightly-non-hermitian-matrices/20063)

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**Author:** [@caldwellshane](https://discourse.julialang.org/u/caldwellshane)\
**Replies:** 18\
**Last updated:** [January 28, 2019, 12:30pm UTC](https://discourse.julialang.org/t/cholesky-factorization-for-slightly-non-hermitian-matrices/20063 "2019-01-28T12:30:39Z")

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I wrote a function to rotate the coordinates of a 2D MvNormal distribution, and in the course of testing it I discovered this, surprising to me, behavior of the Cholesky factorization: julia\> VERSION v"1.1.0" julia\> ro…

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## [DifferentialEquations.jl: marked point processes (or storing user data)](https://discourse.julialang.org/t/differentialequations-jl-marked-point-processes-or-storing-user-data/19453)

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**Author:** [@yha](https://discourse.julialang.org/u/yha)\
**Replies:** 6\
**Last updated:** [January 27, 2019, 4:27pm UTC](https://discourse.julialang.org/t/differentialequations-jl-marked-point-processes-or-storing-user-data/19453 "2019-01-27T16:27:19Z")

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I’m trying to simulate a simple marked point process with DifferentialEquations. As far as I can tell, this is not directly supported (the documentation does mention a mark in the context of RegularJump, but this seems t…

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## [Extend SparseMatrixCSC interface (nzrange - rowvals - nonzeros) to views of sparse matrices](https://discourse.julialang.org/t/extend-sparsematrixcsc-interface-nzrange-rowvals-nonzeros-to-views-of-sparse-matrices/19837)

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**Author:** [@klacru](https://discourse.julialang.org/u/klacru)\
**Replies:** 0\
**Last updated:** [January 20, 2019, 10:23am UTC](https://discourse.julialang.org/t/extend-sparsematrixcsc-interface-nzrange-rowvals-nonzeros-to-views-of-sparse-matrices/19837 "2019-01-20T10:23:47Z")

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I want to extend the nzrange - rowvals - nonzeros interface from SparseMatrixCSC to views of sparse matrices. That would allow to re-formulate many of the standard algorithms for SparseMatrixCSC and extend them to the vi…

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## [Integro-differential equations with DifferentialEquations.jl](https://discourse.julialang.org/t/integro-differential-equations-with-differentialequations-jl/19265)

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**Author:** [@lappet](https://discourse.julialang.org/u/lappet)\
**Replies:** 4\
**Last updated:** [January 8, 2019, 7:52am UTC](https://discourse.julialang.org/t/integro-differential-equations-with-differentialequations-jl/19265 "2019-01-08T07:52:01Z")

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The integro-differential equations I need to solve are of this form: http://mathb.in/30204. While I already have written a solver for a simple test problem (s. code below), the type of equation shown in the link above ca…

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## [Request for examples: Systems of nonlinear equations that have jacobians with special structure](https://discourse.julialang.org/t/request-for-examples-systems-of-nonlinear-equations-that-have-jacobians-with-special-structure/18936)

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**Author:** [@pkofod](https://discourse.julialang.org/u/pkofod)\
**Replies:** 1\
**Last updated:** [December 23, 2018, 8:43pm UTC](https://discourse.julialang.org/t/request-for-examples-systems-of-nonlinear-equations-that-have-jacobians-with-special-structure/18936 "2018-12-23T20:43:31Z")

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I’m changing some things in NLsolve.jl, in particular the possibility to chose the solver than solves the linear system of equations to determine the step direction. This means that if you have a package MySpecialLinsolv…

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## [How do I use MATLAB.jl and vpa?](https://discourse.julialang.org/t/how-do-i-use-matlab-jl-and-vpa/18595)

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**Author:** [@Noel\_Araujo](https://discourse.julialang.org/u/Noel_Araujo)\
**Replies:** 6\
**Last updated:** [December 12, 2018, 10:21pm UTC](https://discourse.julialang.org/t/how-do-i-use-matlab-jl-and-vpa/18595 "2018-12-12T22:21:22Z")

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Hello everyone, I am want to do something conceptually simple using MATLAB.jl package. I have a BigFloat matrix in Julia, and I want to send to Matlab to compute its inverse/determinant/eigenvalues with arbitrary-precis…

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## [\\ left division operator in editors (emacs)](https://discourse.julialang.org/t/left-division-operator-in-editors-emacs/18225)

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**Author:** [@jlapeyre](https://discourse.julialang.org/u/jlapeyre)\
**Replies:** 5\
**Last updated:** [December 4, 2018, 12:00pm UTC](https://discourse.julialang.org/t/left-division-operator-in-editors-emacs/18225 "2018-12-04T12:00:00Z")

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This operator \\ puts my emacs julia-mode in a bad state. After this symbol, it no longer understands expressions. If I want to use it, or add methods, I do eval(Meta.parse("import Base: \\\\")) const left\_division = eval…

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## [Advice on numerical integration of a very "sparse" function](https://discourse.julialang.org/t/advice-on-numerical-integration-of-a-very-sparse-function/18176)

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**Author:** [@yakir12](https://discourse.julialang.org/u/yakir12)\
**Replies:** 25\
**Last updated:** [November 30, 2018, 2:59pm UTC](https://discourse.julialang.org/t/advice-on-numerical-integration-of-a-very-sparse-function/18176 "2018-11-30T14:59:46Z")

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I have a function that when sampled evenly across its two domains looks something like this: Almost everything is zero… I need to integrate it. I tried HCubature.jl and Cuba.jl but they either returned zero or faile…

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## [Elegant way to construct a set of multi-index](https://discourse.julialang.org/t/elegant-way-to-construct-a-set-of-multi-index/18081)

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**Author:** [@OlivierHnt](https://discourse.julialang.org/u/OlivierHnt)\
**Replies:** 19\
**Last updated:** [November 29, 2018, 2:25pm UTC](https://discourse.julialang.org/t/elegant-way-to-construct-a-set-of-multi-index/18081 "2018-11-29T14:25:14Z")

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Good evening, I wish to build an array containing specific multi-index. More precisely, in the 2-D case the multi-index are given by (i, j) where 0 \<= i , j \<= N+1 such that i+j \<= N+1. The way I do it is make a (N+1)x…

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## [\`Complex{Dual}\` or \`Dual{Complex}\`](https://discourse.julialang.org/t/complex-dual-or-dual-complex/5455)

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**Author:** [@gasagna](https://discourse.julialang.org/u/gasagna)\
**Replies:** 12\
**Last updated:** [November 27, 2018, 5:57am UTC](https://discourse.julialang.org/t/complex-dual-or-dual-complex/5455 "2018-11-27T05:57:37Z")

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TLDR: I think Dual should be \<:Real and that Complex{Dual} leads to more generic code than Dual{Complex}. Hi all, I am toying with mixed complex and dual numbers. My use case is numerical integration of a nonlinear PD…

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## [IdentityMatrix.jl: efficient methods](https://discourse.julialang.org/t/identitymatrix-jl-efficient-methods/17999)

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**Author:** [@jlapeyre](https://discourse.julialang.org/u/jlapeyre)\
**Replies:** 0\
**Last updated:** [November 26, 2018, 2:55am UTC](https://discourse.julialang.org/t/identitymatrix-jl-efficient-methods/17999 "2018-11-26T02:55:17Z")

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There are a lot of possible efficiency improvements for operations involving identity matrices. This package is intended to get several improved (or specialized) methods into circulation. This is not intended to be their…

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