## 154 Reputation

17 years, 317 days

## create procedure with many arguments pro...

Maple
Hello Maple experts, lets assume I want to minimize some complicated objective function (procedure) objective(x1,x2,...,xn) with many problem variables. In order to use Maple's Optimization package, I have to specify all the arguments of my objective function in the form ``` objective := proc(x1,x2,...,xn) ...some complicated computation... end proc: ``` However, this has to be written manually and for many variables, say 100 or 150, this is not very elegant. Isn't there a more elegant way of creating a procedure that is suitable for the Optimization package or the Global Optimization Toolbox?

Maple
Hello Maple experts, during my studies, I have developed a number of Maple procedures that deal with quantum information/quantum computation. This means I use excessively the Matrix data structure and the LinearAlgebra package. Given the fact that I'm not the most talented programmer in general and also that I had no experience with Maple before, I have now a Maple package that is sometimes really slow. Especially when working numerically, I'm often jealous about the performance I could have achieved with Matlab. This is although I already try to use Digits=14 (which should, in principle, enable hardware floating point operations). However, procedures involving Matrix objects are mostly not supported by evalhf (and cannot be compiled, right?). In order to improve that I want to do a profiling. One way of doing that is using

## procedure becomes slower and slower with...

Maple
Hi Maple experts, I have a seemingly simple procedure that is supposed to create random matrices. What surprises me is the fact that it takes more CPU time evertime I call it (even in a fresh session). The procedure is as follows: ``` Feynman_random_rho := proc(N::posint, d::posint:=2)::'Matrix'(complex); # # returns a random N-qudit density matrix where the optional second argument, d, # specifies the dimension of each subsystem. By default, d=2 is assumed so that # an N-qubit density matrix is generated. # The density matrices are uniformly distributed according to the Hilbert-Schmidt ```

## local optimization with Optimization pac...

Maple
Hello Maple community!

As a part of a more complex (global) optimization problem I have a simple trigonometric parametrization of a classical probability distribution, i.e. just a list of positive number that sum up to 1. For test purposes, I take now one arbitrary element, p, of that probability list and use it as a target function for an optimization. Of course, one expects that one will find suitable parameter sets for minimizing/maximizing p. So here is my simple target function for the case of N=10 probabilities (requiring N-1=9 parameters):

objective := proc(x1, x2, x3, x4, x5, x6, x7, x8, x9)

## Efficient parametrization of unitary mat...

Maple
Hello Maple community, although I'm using Maple (now version 11) for quite a while now, I still have problems in designing and writing efficient procedures. Within the context of quantum information theory, I want to write a procedure that parametrizes unitary matrices of arbitrary dimension NxN (in order to perform an optimization over this space). For the beginning, I just want to create random unitary matrices of a given dimension. For this, I implemented the formulas for the "Generalized Euler angle parametrization" (math-ph/0205016). This involves first the creation of N^2-1 matrices that serve as generators for SU(N) and, in a second step, several matrix exponentials and matrix products. These two steps I put in two procedures ("hermitian_basis" and "parametrize_unitary_Euler") (see the linked worksheet).
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