%pylab inline

from qutip import *

import time

reps = 1

def plot_bm_mat(bm_mat, N_vec, solvers):
    
    fig, ax = subplots(figsize=(12, 8))
    
    for idx, solver in enumerate(solvers):
        solver_name, solver_func = solver
        ax.plot(N_vec, bm_mat[:, idx], label=solver_name, linewidth=2)
        
    ax.set_yscale('log')
    ax.set_xlabel("Hilbert space size (N)", fontsize=18)
    ax.set_ylabel("Elapsed time", fontsize=18)
    ax.legend(loc=0)
    ax.axis('tight')

def benchmark_steadystate_solvers(N_vec, solvers, problem_func):

    bm_mat = zeros((len(N_vec), len(solvers)))

    for N_idx, N in enumerate(N_vec):
        H, c_ops = problem_func(N)
    
        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[N_idx, sol_idx] = (t2 - t1)/reps
        
            except:
                bm_mat[N_idx, sol_idx] = 0
            
    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

N_vec = array([2, 5, 10, 15, 20, 25, 30, 35])

bm_mat = benchmark_steadystate_solvers(N_vec, solvers, bm_problem1)

plot_bm_mat(bm_mat, 2 * N_vec, solvers)

N_vec = arange(25, 400, 25)

bm_mat = benchmark_steadystate_solvers(N_vec, large_solvers, bm_problem1)

plot_bm_mat(bm_mat, 2 * N_vec, large_solvers)

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

N_vec = array([2, 5, 10, 15, 20, 25])

bm_mat = benchmark_steadystate_solvers(N_vec, solvers, bm_problem2)

plot_bm_mat(bm_mat, N_vec, solvers)

N_vec = arange(25, 300, 25)

bm_mat = benchmark_steadystate_solvers(N_vec, large_solvers, bm_problem2)

plot_bm_mat(bm_mat, N_vec, large_solvers)

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

N_vec = array([2, 4, 6, 8, 10])

bm_mat = benchmark_steadystate_solvers(N_vec, large_solvers, bm_problem3)

plot_bm_mat(bm_mat, N_vec ** 2, large_solvers)

def bm_problem4(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

N_vec = array([2, 3, 4, 5, 6])

bm_mat = benchmark_steadystate_solvers(N_vec, large_solvers, bm_problem3)

plot_bm_mat(bm_mat, N_vec, large_solvers)

H, c_ops = bm_problem1(300)

%%prun -q -T steadystate.txt

steadystate(H, c_ops)

!head -n 20 steadystate.txt

%%prun -q -T steadystate_direct.txt

steadystate(H, c_ops, method="direct")

!head -n 20 steadystate_direct.txt

%%prun -q -T steadystate_iterative.txt

steadystate(H, c_ops, method="iterative")

!head -n 20 steadystate_iterative.txt

%%prun -q -T steadystate_iterative.txt

steadystate(H, c_ops, method="iterative-bicg")

!head -n 20 steadystate_iterative.txt

from qutip.ipynbtools import version_table

version_table()