Why A1 and A2 have different precision and A1 != A2, though mathematically, they should have the same results. I’m wondering is there anything special about matrix slicing that would affect the precision? or the results are caused by something esle? Example(Julia 0.6.4): A = randn(Float64, 200, 10…

[image] Caesar_KG: mathematically, they should have the same results [image] PSA: floating-point arithmetic Offtopic Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 …

I think you’re just hitting rounding errors (as already said above). You may find it interesting to try the same thing using DoubleFloats (see below). Note that if you use ≈ instead of == in your example it also “works” but that doesn’t answer your question I guess. julia> using DoubleFloats julia> …

Rounding issues, as others have said. Use this to calculate the relative norm (“error”): julia> norm(A1-A2) / max(norm(A1), norm(A2)) 2.0277114478533147e-15 Seems small enough. And here’s what you can use instead of ==: julia> isapprox(A1, A2; rtol = 1e-10) true julia> isapprox(A1, A2; rtol = 1e…

I’ve read the previous post already. But I still don’t understand. Aren’t the numbers in the first two column of matrix A used for calculation the same in both cases? If they are same, the results should be the same following the floating point arithmetic rules. BTW, thanks for the tip regarding co…

Thanks for the tip on DoubleFloats. Really helps!

I think the reason is to be found behind ordering of operations. Julia may re-order operations to get optimal performance and if you sum floating point numbers in different orders you may get different results. Small experiment below: using Random using LinearAlgebra Random.seed!(125) A = hcat(on…

Thanks for the help, man! That may explain the issue. It’s related to the Julia implementation of floating point arithmetic. I tried it on python and A1==A2 is true. import numpy as np import numpy.random as nprd In [27]: A = np.c_[np.ones((200, 1)), nprd.randn(200, 100)] In [28]: B = nprd.rand…

[image] Caesar_KG: That may explain the issue. It’s related to the Julia implementation of floating point arithmetic. I tried it on python and A1==A2 is true. that’s misleading (or you got lucky). I just had a shot and without surprise >>> A1 - A2 array([[-1.77635684e-15], [-5.329070…

OK. That’s weird. Mine is: In [27]: A = np.c_[np.ones((200, 1)), nprd.randn(200, 100)] In [28]: B = nprd.randn(200, 1) In [29]: ApB = np.dot(A.T, B) In [30]: idx = [1, 2] In [31]: A1 = ApB[idx] In [32]: A2 = np.dot(A[:, idx].T, B) In [33]: A1 == A2 Out[33]: array([[ True], [ True]]) …

Have you tried several times? I set the seed to 1515 (at least doing that here gives me a standard epsilon machine error) anyway. Another thing to note is that your Python might use MKL as a BLAS backend (mine does) where your Julia would use OpenBLAS, slight differences would then be expected. PS…

Matrix multiplication precision issue

General Usage

Tamas_Papp January 28, 2019, 8:13am 2

Also, please quote code

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Matrix multiplication precision issue

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