plotting.py

import numpy as np
from shapely.geometry import LineString
import matplotlib.pyplot as plt

#finds the advantage of using comp over QD and trotter at their respective crossover and plots this
def crossover_advantage(qd_data, trot_data, comp_data, times):
    plt.plot(times,qd_data)
    plt.plot(times,trot_data)
    plt.plot(times, comp_data)

    line_1 = LineString(np.column_stack((times, qd_data)))
    line_2 = LineString(np.column_stack((times, trot_data)))
    intersection1 = line_1.intersection(line_2)
    x1,y1 = intersection1.xy
    plt.plot(*intersection1.xy, 'ro')

    x_intercept = []
    for i in range(len(times)):
        x_intercept.append(x1)
    y_intercept = np.linspace(0, 50000, len(times))
    
    line_3 = LineString(np.column_stack((times, comp_data)))
    line_4 = LineString(np.column_stack((x_intercept, y_intercept)))

    intersection2 = line_3.intersection(line_4)
    x2, y2 = intersection2.xy
    plt.plot(*intersection2.xy, 'ro')

    print(y1)
    print(y2)

    comp_adv = float(y1[0])  /  float(y2[0])
    return comp_adv

#plots the distribution of norms in the hamiltonian
def ham_spec(hamiltonian_list, q = 75, y_line=1):
    norms = []
    index = []
    zero_norms = 0
    for i in range(len(hamiltonian_list)):
        h = hamiltonian_list[i]
        spec = np.linalg.norm(h, ord=2)
        norms.append(spec)
        index.append(i)
        if spec == 0:
            zero_norms += 1
    norms.sort()
    q_tile = np.percentile(norms, q)
    q_tile_loc = norms.index(q_tile)

    print('q-tile is ' + str(q_tile) + ' and occurs at term '+ str(q_tile_loc))
    print(str(len(norms)) + ' total terms in H')

    trot_pot = len([i for i in norms if (i >= q_tile)])
    print(str(trot_pot) + ' potential terms in trotter, which is ' + str(trot_pot/ len(norms) * 100) + '% of the total terms')

    plt.rcParams['text.usetex'] = True
    plt.figure(figsize=(9,7))
    plt.semilogy(index, norms, 'bs-')
    plt.axvline(x = q_tile_loc, color = 'r', label = str(q_tile_loc) + ' Percentile')
    plt.axhline(y = y_line, color = 'r', label = str(q_tile_loc) + ' Percentile')
    plt.xlabel(r"$j$", size = 18)
    plt.ylabel(r"$\left| \left| H_j \right| \right|$", size = 18)
    plt.show()
    print("There are " + str(zero_norms) + " terms with 0 spectral norm")
    return norms