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Question: procedure becomes slower and slower with every call

Question:procedure becomes slower and slower with every call

quantum 154 Maple
complex
November 14 2007
0
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[8]); # # 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 # norm [see Toth, quant-ph/0709.0948]. # local rho, temp; temp := Matrix(d^N, d^N, RandomTools[Generate](distribution(Normal(0, 1)), makeproc=true), datatype=complex[8]); temp := LinearAlgebra[Add](temp, Matrix(d^N, d^N, RandomTools[Generate](distribution(Normal(0, 1)), makeproc=true), datatype=complex[8]), 1,I); rho := LinearAlgebra[HermitianTranspose](temp).temp; return(rho/LinearAlgebra[Trace](rho)); end proc: Obviously, I use only native Maple commands and do not request any caching/remember tables action. So what can I do to i) speed things up ii) keep the execution time (roughly) constant? Thanks in advance for any thoughts!
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