VS
DiffEq.jl will help you with integration in time (t-variable), but you should read about Runge-Kutta methods and their stability properties to succeed.
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2020 March 26
АО
Yeah. Another thing to consider, DiffEq is designed to solve Cauchy problems and your task is boundary one. My knowledge is rusty, but I guess first approach is to do something like Fourier expansion and reduce the problem to the system of ODE. Of course, you should carefully calculate initial conditions and there could be problems if solution is non differentiable (has cusps).
A
Третьего дня таки позапускал примеры и почитал доки PUMAS https://docs.pumas.ai/dev/index.html Ничего кроме фармакокинетики там нету, и примеров расчетов с генерацией отчета по типу http://pkpd.kmu.edu.tw/bear/ тоже не завезли. Описание вообще не соответствует содержимому :(
VS
Yeah. Another thing to consider, DiffEq is designed to solve Cauchy problems and your task is boundary one. My knowledge is rusty, but I guess first approach is to do something like Fourier expansion and reduce the problem to the system of ODE. Of course, you should carefully calculate initial conditions and there could be problems if solution is non differentiable (has cusps).
The Fourier expansion/transform is not the best choice here, because the system is non-linear. I suggest grid-point discretization of the laplace operator to get the system of ode.
АО
Why nonlinearity is a problem? I thought you can multiply two Fourier sum and extract coefficients in a usual manner. Of course it’s not an easy task to do by hand, but it can be automated.
VS
Why nonlinearity is a problem? I thought you can multiply two Fourier sum and extract coefficients in a usual manner. Of course it’s not an easy task to do by hand, but it can be automated.
1) it is not an easy task, that is the main problem😊. It is feasible for quadratic nonlinearity and much harder for, say, log(x)/x
2) it seems to need N^2 operations for easy implementation of quadratic non-linearity
2) it seems to need N^2 operations for easy implementation of quadratic non-linearity
АО
But there is no log(x)/x in these equations
АО
And matrix would be calculated only once, I suppose most of the time will be spent in solving ODE anyway.
VS
In atmospheric modelling community it is(actually was) usual to obtain grid-point values using inversed fft, then calculate non-linear terms and then use fft to go back in fourier space.
VS
Is f(u) an arbitrary function?
АО
Ah, yes you are right, there was nothing said about f(u). So this task can be arbitrarily complex.
АО
Well, yes, this is definitely not about programming language, op should put some time into researching a problem itself.
VS
And matrix would be calculated only once, I suppose most of the time will be spent in solving ODE anyway.
It depends on how many fourier coefficients you use (N^2 for Fourier row non-linear transform vs N operations to multiply vector by sparse matrix)
VS
Well, yes, this is definitely not about programming language, op should put some time into researching a problem itself.
Excuse me for off-topic. That is right time for me to stop😊
2020 March 27
V
Третьего дня таки позапускал примеры и почитал доки PUMAS https://docs.pumas.ai/dev/index.html Ничего кроме фармакокинетики там нету, и примеров расчетов с генерацией отчета по типу http://pkpd.kmu.edu.tw/bear/ тоже не завезли. Описание вообще не соответствует содержимому :(
Очень странный пакет с учётом того что он ещё ограничен для коммерческого применения, как я понял. Не очень понятно как там все это работать должно, есть пакет Bioequivalence.jl который как бы спутником идёт - описания нормального тоже нет. Расчета выборки нет, движка симуляцией вроде как тоже нет.
2020 March 29
V
А можно ли в Джулии как-то умножить друг на друга матрицы функций?
KT
Там алгоритм перемножения матриц не зависит же от того, элементы какого кольца используются. Просто наверное надо доопределить + и * для Function
V
Точно! Наверно не стоит надеяться что после этого inv() заработает?
2020 March 30
И
А кто знает, можно ли заставить Flux более эффективно работать на CPU (он использует по факту только 1 ядро) ?
Или он плохо умеет работать на CPU ?
Или он плохо умеет работать на CPU ?
RS
JULIA_NUM_THREADS env variable
но не более числа доступных ядер