Copyright (C) 2013, Paul D. Nation & Robert J. Johansson
%pylab inline
Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline]. For more information, type 'help(pylab)'.
from qutip import *
import time
reps = 1
from IPython.display import HTML
def show_bm_mat(bm_mat, solvers):
m = bm_mat[bm_mat > 0].min()
html = "<table>"
html += "<tr><td><b>Solver</b></td><td><b>Elapsed time</b></td><td><b>Ratio</b></td></tr>"
for idx, (desc, func) in enumerate(solvers):
if bm_mat[idx] == m:
html += "<tr><td><b>%s</b></td><td><b>%.8f</b></td><td><b>%.2f</b></td></tr>" % \
(desc, bm_mat[idx], bm_mat[idx]/m)
else:
html += "<tr><td>%s</td><td>%.8f</td><td>%.2f</td></tr>" % \
(desc, bm_mat[idx], bm_mat[idx]/m)
html += "</table>"
return HTML(html)
def benchmark_steadystate_solvers(args, solvers, problem_func):
bm_mat = zeros(len(solvers))
H, c_ops = problem_func(args)
for sol_idx, solver in enumerate(solvers):
solver_name, solver_func = solver
try:
t1 = time.time()
for r in range(reps):
rhoss = solver_func(H, c_ops)
t2 = time.time()
bm_mat[sol_idx] = (t2 - t1)/reps
except:
bm_mat[sol_idx] = nan
return bm_mat
solvers = [["power use_umfpack=True",
lambda H, c_ops: steadystate(H, c_ops, method='power', use_umfpack=True)],
["power use_umfpack=False",
lambda H, c_ops: steadystate(H, c_ops, method='power', use_umfpack=False)],
["direct sparse use_umfpack=True",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=True, sparse=True)],
["direct sparse use_umfpack=False",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=False, sparse=True)],
["iterative use_precond=True",
lambda H, c_ops: steadystate(H, c_ops, method='iterative', use_precond=True)],
["iterative use_precond=False",
lambda H, c_ops: steadystate(H, c_ops, method='iterative', use_precond=False)],
["iterative-bicg use_precond=True",
lambda H, c_ops: steadystate(H, c_ops, method='iterative-bicg', use_precond=True)],
["iterative-bicg use_precond=False",
lambda H, c_ops: steadystate(H, c_ops, method='iterative-bicg', use_precond=False)],
["direct dense use_umfpack=True",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=True, sparse=False)],
["direct dense use_umfpack=False",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=False, sparse=False)],
["svd_dense",
lambda H, c_ops: steadystate(H, c_ops, method='svd')],
["lu",
lambda H, c_ops: steadystate(H, c_ops, method='lu')],
]
large_solvers = [
["power use_umfpack=True",
lambda H, c_ops: steadystate(H, c_ops, method='power', use_umfpack=True)],
["power use_umfpack=False",
lambda H, c_ops: steadystate(H, c_ops, method='power', use_umfpack=False)],
["direct sparse use_umfpack=True",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=True, sparse=True)],
["direct sparse use_umfpack=False",
lambda H, c_ops: steadystate(H, c_ops, use_umfpack=False, sparse=True)],
["iterative use_precond=True",
lambda H, c_ops: steadystate(H, c_ops, method='iterative', use_precond=True)],
["iterative-bicg use_precond=True",
lambda H, c_ops: steadystate(H, c_ops, method='iterative-bicg', use_precond=True)],
]
def bm_problem1(N):
a = tensor(destroy(N), identity(2))
b = tensor(identity(N), destroy(2))
H = a.dag() * a + b.dag() * b + 0.25 * (a + a.dag()) * (b + b.dag())
c_ops = [sqrt(0.1) * a, sqrt(0.075) * a.dag(), sqrt(0.1) * b]
return H, c_ops
bm_mat = benchmark_steadystate_solvers(10, solvers, bm_problem1)
show_bm_mat(bm_mat, solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.02930117 | 1.86 |
power use_umfpack=False | 0.02769184 | 1.76 |
direct sparse use_umfpack=True | 0.01657772 | 1.05 |
direct sparse use_umfpack=False | 0.01577711 | 1.00 |
iterative use_precond=True | 0.01887131 | 1.20 |
iterative use_precond=False | 0.42715192 | 27.07 |
iterative-bicg use_precond=True | 0.01824522 | 1.16 |
iterative-bicg use_precond=False | 0.05967665 | 3.78 |
direct dense use_umfpack=True | 0.03680706 | 2.33 |
direct dense use_umfpack=False | 0.03597355 | 2.28 |
svd_dense | 0.43549585 | 27.60 |
lu | 0.01581359 | 1.00 |
bm_mat = benchmark_steadystate_solvers(50, large_solvers, bm_problem1)
show_bm_mat(bm_mat, large_solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.30860066 | 2.16 |
power use_umfpack=False | 0.30906749 | 2.16 |
direct sparse use_umfpack=True | 0.26223445 | 1.83 |
direct sparse use_umfpack=False | 0.30435157 | 2.13 |
iterative use_precond=True | 0.14319158 | 1.00 |
iterative-bicg use_precond=True | 0.14433670 | 1.01 |
def bm_problem2(N):
a = destroy(N)
H = a.dag() * a
nth = N / 4
gamma = 0.05
c_ops = [sqrt(gamma * (nth + 1)) * a, sqrt(gamma * nth) * a.dag()]
return H, c_ops
bm_mat = benchmark_steadystate_solvers(50, solvers, bm_problem2)
show_bm_mat(bm_mat, solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.03091383 | 2.33 |
power use_umfpack=False | 0.02793431 | 2.11 |
direct sparse use_umfpack=True | 0.01574659 | 1.19 |
direct sparse use_umfpack=False | 0.01326680 | 1.00 |
iterative use_precond=True | 0.01814747 | 1.37 |
iterative use_precond=False | 0.08728552 | 6.58 |
iterative-bicg use_precond=True | 0.01731229 | 1.30 |
iterative-bicg use_precond=False | 0.03140640 | 2.37 |
direct dense use_umfpack=True | 3.13456941 | 236.27 |
direct dense use_umfpack=False | 3.13574004 | 236.36 |
svd_dense | 71.83850408 | 5414.91 |
lu | 0.01391077 | 1.05 |
def bm_problem3(N):
a = tensor(destroy(N), identity(N))
b = tensor(identity(N), destroy(N))
H = a.dag() * a + 0.25 * b.dag() * b + 0.05 * a.dag() * a * (b + b.dag()) + 0.1 * (a + a.dag())
c_ops = [sqrt(0.05) * a, sqrt(0.015) * a.dag(), sqrt(0.1) * b, sqrt(0.075) * b.dag()]
return H, c_ops
bm_mat = benchmark_steadystate_solvers(10, large_solvers, bm_problem3)
show_bm_mat(bm_mat, large_solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 5.09422636 | 7.99 |
power use_umfpack=False | 35.79435349 | 56.16 |
direct sparse use_umfpack=True | 5.80584502 | 9.11 |
direct sparse use_umfpack=False | 30.20628524 | 47.40 |
iterative use_precond=True | 0.71662021 | 1.12 |
iterative-bicg use_precond=True | 0.63732290 | 1.00 |
def bm_problem4(args=None):
sz = sigmaz()
sx = sigmax()
H = sz
c_ops = [sqrt(0.05) * sx]
return H, c_ops
bm_mat = benchmark_steadystate_solvers(None, solvers, bm_problem4)
show_bm_mat(bm_mat, solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.01852179 | 3.05 |
power use_umfpack=False | 0.01754975 | 2.89 |
direct sparse use_umfpack=True | 0.00707531 | 1.17 |
direct sparse use_umfpack=False | 0.00687790 | 1.13 |
iterative use_precond=True | 0.00709677 | 1.17 |
iterative use_precond=False | 0.00711107 | 1.17 |
iterative-bicg use_precond=True | 0.01673436 | 2.76 |
iterative-bicg use_precond=False | 0.00678062 | 1.12 |
direct dense use_umfpack=True | 0.00611544 | 1.01 |
direct dense use_umfpack=False | 0.00606394 | 1.00 |
svd_dense | 0.00769496 | 1.27 |
lu | 0.00651836 | 1.07 |
def bm_problem5(N=1):
H = 0
for m in range(N):
H += tensor([sigmaz() if n == m else identity(2) for n in range(N)])
for m in range(N-1):
H += tensor([sigmax() if n in [m,m+1] else identity(2) for n in range(N)])
c_ops = [sqrt(0.05) * tensor([sigmam() if n == m else identity(2) for n in range(N)])
for m in range(N)]
return H, c_ops
bm_mat = benchmark_steadystate_solvers(2, solvers, bm_problem5)
show_bm_mat(bm_mat, solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.02150130 | 2.35 |
power use_umfpack=False | 0.02094078 | 2.28 |
direct sparse use_umfpack=True | 0.01023006 | 1.12 |
direct sparse use_umfpack=False | 0.00997591 | 1.09 |
iterative use_precond=True | 0.01020479 | 1.11 |
iterative use_precond=False | 0.01033449 | 1.13 |
iterative-bicg use_precond=True | 0.00971484 | 1.06 |
iterative-bicg use_precond=False | 0.01010346 | 1.10 |
direct dense use_umfpack=True | 0.00918984 | 1.00 |
direct dense use_umfpack=False | 0.00916553 | 1.00 |
svd_dense | 0.01097131 | 1.20 |
lu | 0.00957203 | 1.04 |
bm_mat = benchmark_steadystate_solvers(4, solvers, bm_problem5)
show_bm_mat(bm_mat, solvers)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 0.03119278 | 1.59 |
power use_umfpack=False | 0.03097486 | 1.58 |
direct sparse use_umfpack=True | 0.01957011 | 1.00 |
direct sparse use_umfpack=False | 0.01961446 | 1.00 |
iterative use_precond=True | 0.02565002 | 1.31 |
iterative use_precond=False | 0.27903152 | 14.26 |
iterative-bicg use_precond=True | 0.02416730 | 1.23 |
iterative-bicg use_precond=False | 0.06678843 | 3.41 |
direct dense use_umfpack=True | 0.02458715 | 1.26 |
direct dense use_umfpack=False | 0.02418828 | 1.24 |
svd_dense | 0.16517234 | 8.44 |
lu | 0.01960063 | 1.00 |
bm_mat = benchmark_steadystate_solvers(6, large_solvers, bm_problem5)
show_bm_mat(bm_mat, large_solvers)
/usr/local/lib/python3.3/dist-packages/qutip/steadystate.py:314: UserWarning: Preconditioning failed. Continuing without. UserWarning)
Solver | Elapsed time | Ratio |
power use_umfpack=True | 1.09917188 | 1.08 |
power use_umfpack=False | 9.79997540 | 9.60 |
direct sparse use_umfpack=True | 1.02135420 | 1.00 |
direct sparse use_umfpack=False | 9.18890977 | 9.00 |
iterative use_precond=True | 13.48026681 | 13.20 |
iterative-bicg use_precond=True | 2.67135262 | 2.62 |
from qutip.ipynbtools import version_table
version_table()
Software | Version |
---|---|
OS | posix [linux] |
IPython | 1.0.dev |
Numpy | 1.8.0.dev-c5694c5 |
QuTiP | 2.3.0.dev-169f358 |
Cython | 0.19.1 |
SciPy | 0.13.0.dev-38faf7c |
Python | 3.3.1 (default, Apr 17 2013, 22:30:32) [GCC 4.7.3] |
matplotlib | 1.4.x |
Fri Jul 19 14:08:27 2013 JST |