# Numerics

**URL:** https://discourse.julialang.org/c/domain/numerics/20.md?page=42

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**Page:** 43

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## [Heterogeneous blocked matrices](https://discourse.julialang.org/t/heterogeneous-blocked-matrices/2130)

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**Author:** [@dmbates](https://discourse.julialang.org/u/dmbates)\
**Replies:** 3\
**Last updated:** [February 16, 2017, 5:15pm UTC](https://discourse.julialang.org/t/heterogeneous-blocked-matrices/2130 "2017-02-16T17:15:49Z")

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I am struggling to come up with a sufficiently specific method signature to handle the Cholesky decomposition of heterogeneous blocked matrices, by which I mean that I have a square matrix of AbstractMatrix{Float64}, say…

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## [Zero pivot error in LDLt factorization for large matrices](https://discourse.julialang.org/t/zero-pivot-error-in-ldlt-factorization-for-large-matrices/1966)

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**Author:** [@joernc](https://discourse.julialang.org/u/joernc)\
**Replies:** 3\
**Last updated:** [February 8, 2017, 3:51am UTC](https://discourse.julialang.org/t/zero-pivot-error-in-ldlt-factorization-for-large-matrices/1966 "2017-02-08T03:51:35Z")

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I encountered a problem with the LDLt factorization in the finite-difference solution of a 2D Poisson equation: u\_xx + u\_yy = -1 on 0 \< x \< 1 and 0 \< y \< 1 with u = 0 Dirichlet boundary conditions. The factorization work…

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## [eigvals!(A) vs eigvals!(A, B)?](https://discourse.julialang.org/t/eigvals-a-vs-eigvals-a-b/1734)

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**Author:** [@e3c6](https://discourse.julialang.org/u/e3c6)\
**Replies:** 1\
**Last updated:** [January 27, 2017, 11:41pm UTC](https://discourse.julialang.org/t/eigvals-a-vs-eigvals-a-b/1734 "2017-01-27T23:41:16Z")

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What is the difference between eigvals!(A) and eigvals!(A,B)? I understand that eigvals!(A) will replace A with a “scaled” version, where rows and columns are more equal in norm and the matrix becomes closer to upper tr…

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## [Unified Interface for Linear Solving](https://discourse.julialang.org/t/unified-interface-for-linear-solving/699)

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**Author:** [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Replies:** 34\
**Last updated:** [January 25, 2017, 3:04am UTC](https://discourse.julialang.org/t/unified-interface-for-linear-solving/699 "2017-01-25T03:04:50Z")

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Building off of the rootfinding topic, I would like to propose some common interface for linear solving in Julia for the same reasons: allowing packages which use linear solvers to easy “swap out methods”. While \\ is nic…

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## [Is there an iterative solver that is able to operate on block-matrices (non-concatenated)](https://discourse.julialang.org/t/is-there-an-iterative-solver-that-is-able-to-operate-on-block-matrices-non-concatenated/1516)

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**Author:** [@rleegates](https://discourse.julialang.org/u/rleegates)\
**Replies:** 6\
**Last updated:** [January 18, 2017, 8:58am UTC](https://discourse.julialang.org/t/is-there-an-iterative-solver-that-is-able-to-operate-on-block-matrices-non-concatenated/1516 "2017-01-18T08:58:59Z")

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Dear users, I haven’t been able to find an implementation of an iterative solver (invertible matrix, no further specialization) general enough to work on matrices of matrices, i.e. A = \[B C D…; E F G…; H I J…; …\], b = \[…

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## [How to compute the smallest integer number strictly greater than a given number?](https://discourse.julialang.org/t/how-to-compute-the-smallest-integer-number-strictly-greater-than-a-given-number/1304)

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**Author:** [@chobbes](https://discourse.julialang.org/u/chobbes)\
**Replies:** 3\
**Last updated:** [January 14, 2017, 2:48am UTC](https://discourse.julialang.org/t/how-to-compute-the-smallest-integer-number-strictly-greater-than-a-given-number/1304 "2017-01-14T02:48:30Z")

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Is there a Julia function that returns the smallest integer number strictly greater than a given number? For example, if I give 0.5, it returns me 1.0. If I give 1.0, it returns 2.0? ceil() can do the former example for …

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## [ANN: QNaNs.jl (easier quiet NaNs)](https://discourse.julialang.org/t/ann-qnans-jl-easier-quiet-nans/1387)

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**Author:** [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)\
**Replies:** 2\
**Last updated:** [January 10, 2017, 12:50pm UTC](https://discourse.julialang.org/t/ann-qnans-jl-easier-quiet-nans/1387 "2017-01-10T12:50:37Z")

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QNaNs.jl Simplifies the use of quiet NaNs to propagate information from within numerical computations. ####Quick Look \> Pkg.add("QNaNs") \> using QNaNs \> a\_qnan = qnan(36) NaN \> payload = qnan( a\_qnan ) 36 \> typeof(a\_…

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## [ForwardDiff chunk size: for what kinds of problems does it make a large difference?](https://discourse.julialang.org/t/forwarddiff-chunk-size-for-what-kinds-of-problems-does-it-make-a-large-difference/1234)

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**Author:** [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Replies:** 3\
**Last updated:** [January 2, 2017, 2:48am UTC](https://discourse.julialang.org/t/forwarddiff-chunk-size-for-what-kinds-of-problems-does-it-make-a-large-difference/1234 "2017-01-02T02:48:55Z")

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How much have you guys noticed the chunk size mattering for ForwardDiff.jl timings? I don’t see anything more than like 2% of a timing difference in the functions I am testing on (I am testing it through NLsolve as well)…

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## [QR factorization with custom dot product](https://discourse.julialang.org/t/qr-factorization-with-custom-dot-product/1208)

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**Author:** [@mzaffalon](https://discourse.julialang.org/u/mzaffalon)\
**Replies:** 5\
**Last updated:** [December 30, 2016, 9:42pm UTC](https://discourse.julialang.org/t/qr-factorization-with-custom-dot-product/1208 "2016-12-30T21:42:09Z")

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Is there a way of passing a custom dot product to the QR factorization routine? In my application, the column vectors are the coefficients of a basis of continuous functions and the dot product is the integral over a vol…

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## [Implementing Low rank update of block-LDLᵀ decomposition in Julia](https://discourse.julialang.org/t/implementing-low-rank-update-of-block-ldl-decomposition-in-julia/1207)

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**Author:** [@pushpendre\_rastogi](https://discourse.julialang.org/u/pushpendre_rastogi)\
**Replies:** 0\
**Last updated:** [December 29, 2016, 7:31pm UTC](https://discourse.julialang.org/t/implementing-low-rank-update-of-block-ldl-decomposition-in-julia/1207 "2016-12-29T19:31:20Z")

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Hi, I was wondering if any one has implemented stable algorithms for efficiently updating the block-LDLᵀ decomposition of symmetric indefinite matrices in Julia? I know that the dsytf2\* functions in LAPACK compute the d…

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## [Cannot build Rational{Poly}](https://discourse.julialang.org/t/cannot-build-rational-poly/1119)

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**Author:** [@MA\_Laforge](https://discourse.julialang.org/u/MA_Laforge)\
**Replies:** 5\
**Last updated:** [December 24, 2016, 7:16pm UTC](https://discourse.julialang.org/t/cannot-build-rational-poly/1119 "2016-12-24T19:16:17Z")

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Hi, I tried creating a polynomial ratio: using Polynomials julia\> a=Rational{Poly}(Poly(\[1,2\]),Poly(\[3\])) , but got the following error: ERROR: TypeError: Rational: in T, expected T\<:Integer, got Type{Polynomials.Po…

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## [Block-triangular-form permutation?](https://discourse.julialang.org/t/block-triangular-form-permutation/818)

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**Author:** [@stustd](https://discourse.julialang.org/u/stustd)\
**Replies:** 2\
**Last updated:** [December 14, 2016, 10:02am UTC](https://discourse.julialang.org/t/block-triangular-form-permutation/818 "2016-12-14T10:02:30Z")

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Is there a function that permutes a sparse matrix (or its incidence graph) into block triangular form (BTF)?

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## [Column reordering of Cholesky using Givens rotations](https://discourse.julialang.org/t/column-reordering-of-cholesky-using-givens-rotations/323)

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**Author:** [@dmbates](https://discourse.julialang.org/u/dmbates)\
**Replies:** 3\
**Last updated:** [December 13, 2016, 10:00pm UTC](https://discourse.julialang.org/t/column-reordering-of-cholesky-using-givens-rotations/323 "2016-12-13T22:00:10Z")

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Linpack, the predecessor of LAPACK, provided update/downdate functions for Cholesky decompositions (dchud, dchdd) as well as a function, dchex, to restore a Cholesky factor to triangular form after a left or right circul…

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## [Announcement: ApproxFun v0.4.1, with documentation](https://discourse.julialang.org/t/announcement-approxfun-v0-4-1-with-documentation/769)

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**Author:** [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Replies:** 0\
**Last updated:** [December 6, 2016, 8:50pm UTC](https://discourse.julialang.org/t/announcement-approxfun-v0-4-1-with-documentation/769 "2016-12-06T20:50:32Z")

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I’ve tagged a new release of ApproxFun, a package for approximating functions and solving linear equations, such as ODEs, PDEs and integral equations. I have (finally!) added documentation. Any suggestions for improvem…

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## [PyPlot conflict with Intel MKL?](https://discourse.julialang.org/t/pyplot-conflict-with-intel-mkl/720)

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**Author:** [@stustd](https://discourse.julialang.org/u/stustd)\
**Replies:** 1\
**Last updated:** [December 4, 2016, 11:42am UTC](https://discourse.julialang.org/t/pyplot-conflict-with-intel-mkl/720 "2016-12-04T11:42:08Z")

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I’ve been invariably unsuccessful in trying to make PyPlot work with any Python 3.5 version that compiles Numpy against the (multicore) Intel MKL library (I have tried it with two versions: Intelpython35 from Intel Corp,…

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## [Convergence of hcubature](https://discourse.julialang.org/t/convergence-of-hcubature/660)

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**Author:** [@mzaffalon](https://discourse.julialang.org/u/mzaffalon)\
**Replies:** 10\
**Last updated:** [December 2, 2016, 1:38pm UTC](https://discourse.julialang.org/t/convergence-of-hcubature/660 "2016-12-02T13:38:43Z")

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I am trying to integrate a Lorentzian offset by a smooth function which is defined on a 3D polar domain. Here is the code: using Cubature lorentzian\_re(freq, ampl, freq0, fwhm) = ampl ./ (1 + ((freq - freq0) / fwhm).^2…

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## [Pros/Cons of ApproxFun](https://discourse.julialang.org/t/pros-cons-of-approxfun/396)

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**Author:** [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Replies:** 17\
**Last updated:** [November 20, 2016, 2:59am UTC](https://discourse.julialang.org/t/pros-cons-of-approxfun/396 "2016-11-20T02:59:42Z")

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I am not too familiar with the ApproxFun “style” of numerical analysis. From what I gather relies on doing Chebyshev or Fourier approximations which sound really nice since they can have spectral convergence. However, th…

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