<jupyter_start><jupyter_text>Data Processing Unit<jupyter_code>xlin_supernova = np.load("assets/two-freq-real-ize-xlin-1000000-1.0-1e-10.npy")
prob0_supernova = np.load("assets/two-freq-real-ize-prob0-1000000-1.0-1e-10.npy")
prob1_supernova = np.load("assets/two-freq-real-ize-prob1-1000000-1.0-1e-10.npy")

xlin_supernova_1_8 = np.load("assets/two-freq-real-ize-xlin-1000000-1.0-1e-08.npy")
prob0_supernova_1_8 = np.load("assets/two-freq-real-ize-prob0-1000000-1.0-1e-08.npy")
prob1_supernova_1_8 = np.load("assets/two-freq-real-ize-prob1-1000000-1.0-1e-08.npy")

xlin_supernova_1_9 = np.load("assets/two-freq-real-ize-xlin-1000000-1.0-1e-09.npy")
prob0_supernova_1_9 = np.load("assets/two-freq-real-ize-prob0-1000000-1.0-1e-09.npy")
prob1_supernova_1_9 = np.load("assets/two-freq-real-ize-prob1-1000000-1.0-1e-09.npy")

xlin_supernova2 = np.load("assets/two-freq-real-ize-xlin-1000000-10.0-1e-09.npy")
prob0_supernova2 = np.load("assets/two-freq-real-ize-prob0-1000000-10.0-1e-09.npy")
prob1_supernova2 = np.load("assets/two-freq-real-ize-prob1-1000000-10.0-1e-09.npy")

xlin_supernova_10_10 = np.load("assets/two-freq-real-ize-xlin-1000000-10.0-1e-10.npy")
prob0_supernova_10_10 = np.load("assets/two-freq-real-ize-prob0-1000000-10.0-1e-10.npy")
prob1_supernova_10_10 = np.load("assets/two-freq-real-ize-prob1-1000000-10.0-1e-10.npy")


xlin_supernova3 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-08.npy")
prob0_supernova3 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-08.npy")
prob1_supernova3 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-08.npy")

xlin_supernova_100_9 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-09.npy")
prob0_supernova_100_9 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-09.npy")
prob1_supernova_100_9 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-09.npy")

xlin_supernova_100_10 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-10.npy")
prob0_supernova_100_10 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-10.npy")
prob1_supernova_100_10 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-10.npy")

xlin_supernova4 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-12.npy")
prob0_supernova4 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-12.npy")
prob1_supernova4 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-12.npy")

xlin_supernova5 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-14.npy")
prob0_supernova5 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-14.npy")
prob1_supernova5 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-14.npy")

xlin_supernova6 = np.load("assets/two-freq-real-ize-xlin-1000000-10.0-1e-13.npy")
prob0_supernova6 = np.load("assets/two-freq-real-ize-prob0-1000000-10.0-1e-13.npy")
prob1_supernova6 = np.load("assets/two-freq-real-ize-prob1-1000000-10.0-1e-13.npy")

xlin_supernova7 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-05.npy")
prob0_supernova7 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-05.npy")
prob1_supernova7 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-05.npy")

xlin_supernova8 = np.load("assets/two-freq-real-ize-xlin-1000000-10.0-1e-08.npy")
prob0_supernova8 = np.load("assets/two-freq-real-ize-prob0-1000000-10.0-1e-08.npy")
prob1_supernova8 = np.load("assets/two-freq-real-ize-prob1-1000000-10.0-1e-08.npy")


xlin_supernova_100_18 = np.load("assets/two-freq-real-ize-xlin-1000000-100.0-1e-18.npy")
prob0_supernova_100_18 = np.load("assets/two-freq-real-ize-prob0-1000000-100.0-1e-18.npy")
prob1_supernova_100_18 = np.load("assets/two-freq-real-ize-prob1-1000000-100.0-1e-18.npy")




stepsize_figure = 1.0
rtol_figure = 1e-10

stepsize_figure_1_8 = 1.0
rtol_figure_1_8 = 1e-8

stepsize_figure_1_9 = 1.0
rtol_figure_1_9 = 1e-9


stepsize_figure2 = 10.0
rtol_figure2 = 1e-9

stepsize_figure_10_10 = 10.0
rtol_figure_10_10 = 1e-10

stepsize_figure6 = 10.0
rtol_figure6 = 1e-13

stepsize_figure3 = 100.0
rtol_figure3 = 1e-8

stepsize_figure_100_9 = 100.0
rtol_figure_100_9 = 1e-9

stepsize_figure_100_10 = 100.0
rtol_figure_100_10 = 1e-10

stepsize_figure4 = 100.0
rtol_figure4 = 1e-12

stepsize_figure5 = 100.0
rtol_figure5 = 1e-14

stepsize_figure_100_18 = 100.0
rtol_figure_100_18 = 1e-18

stepsize_figure7 = 100.0
rtol_figure7 = 1e-5

stepsize_figure8 = 10.0
rtol_figure8 = 1e-8


# plt.figure(figsize=(18,13))

# plt.plot(xlin_supernova, prob0_supernova,'-')
# plt.title("Probability $P_{1\\to1}$ (step="+str(stepsize_figure) + ", rtol =" + str(rtol_figure) +")",fontsize=20)
# plt.xlabel("$\hat x$",fontsize=20)
# plt.ylabel("Probability",fontsize=20)
# plt.show()


# plt.figure(figsize=(18,13))

# plt.plot(xlin_supernova, prob1_supernova,'-')
# plt.title("Probability $P_{1\\to2}$ (step="+str(stepsize_figure)+")",fontsize=20)
# plt.xlabel("$\hat x$",fontsize=20)
# plt.ylabel("Probability",fontsize=20)
# plt.show()

# plt.figure(figsize=(18,13))

# plt.plot(xlin_supernova, prob1_supernova+prob0_supernova,'r-')
# plt.title("Total Probability (step="+str(stepsize_figure)+")",fontsize=20)
# plt.xlabel("$\hat x$",fontsize=20)
# plt.ylabel("Probability",fontsize=20)
# plt.show()



plt.figure(figsize=(18,13))

plt.plot(xlin_supernova_1_8, prob1_supernova_1_8 + prob0_supernova_1_8,'r-', label="step size = "+str(stepsize_figure_1_8) + ", rtol = " + str(rtol_figure_1_8) )
plt.plot(xlin_supernova_1_9, prob1_supernova_1_9 + prob0_supernova_1_9,'r--', label="step size = "+str(stepsize_figure_1_9) + ", rtol = " + str(rtol_figure_1_9) )
plt.plot(xlin_supernova, prob1_supernova+prob0_supernova,'r-.', label="step size = "+str(stepsize_figure) + ", rtol = " + str(rtol_figure) )
plt.plot(xlin_supernova8, prob1_supernova8+prob0_supernova8,'b-', label="step size = "+str(stepsize_figure8) + ", rtol = " + str(rtol_figure8))
plt.plot(xlin_supernova2, prob1_supernova2+prob0_supernova2,'b--', label="step size = "+str(stepsize_figure2) + ", rtol = " + str(rtol_figure2) )
plt.plot(xlin_supernova_10_10, prob1_supernova_10_10 + prob0_supernova_10_10,'b-.', label="step size = "+str(stepsize_figure_10_10) + ", rtol = " + str(rtol_figure_10_10) )
plt.plot(xlin_supernova6, prob1_supernova6+prob0_supernova6,'b:', label="step size = "+str(stepsize_figure6) + ", rtol = " + str(rtol_figure6) )
plt.plot(xlin_supernova3, prob1_supernova3+prob0_supernova3,'m-',label="step size = "+str(stepsize_figure3) + ", rtol = " + str(rtol_figure3) )
plt.plot(xlin_supernova_100_9, prob1_supernova_100_9 + prob0_supernova_100_9,'m--',label="step size = "+str(stepsize_figure_100_9) + ", rtol = " + str(rtol_figure_100_9) )
plt.plot(xlin_supernova_100_10, prob1_supernova_100_10 + prob0_supernova_100_10,'m-.',label="step size = "+str(stepsize_figure_100_10) + ", rtol = " + str(rtol_figure_100_10) )
plt.plot(xlin_supernova4, prob1_supernova4+prob0_supernova4,'m:',label="step size = "+str(stepsize_figure4) + ", rtol = " + str(rtol_figure4) )
plt.plot(xlin_supernova5, prob1_supernova5+prob0_supernova5,'k-', label="step size = "+str(stepsize_figure5) + ", rtol = " + str(rtol_figure5))
plt.plot(xlin_supernova_100_18, prob1_supernova_100_18 + prob0_supernova_100_18,'k--', label="step size = "+str(stepsize_figure_100_18) + ", rtol = " + str(rtol_figure_100_18))
#plt.plot(xlin_supernova7, prob1_supernova7+prob0_supernova7,'m:', label="step size = "+str(stepsize_figure7) + ", rtol = " + str(rtol_figure7))

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()


plt.figure(figsize=(18,13))
plt.plot(xlin_supernova_1_8, prob1_supernova_1_8 + prob0_supernova_1_8,'r-', label="step size = "+str(stepsize_figure_1_8) + ", rtol = " + str(rtol_figure_1_8) )
plt.plot(xlin_supernova_1_9, prob1_supernova_1_9 + prob0_supernova_1_9,'r--', label="step size = "+str(stepsize_figure_1_9) + ", rtol = " + str(rtol_figure_1_9) )
plt.plot(xlin_supernova, prob1_supernova+prob0_supernova,'r-.', label="step size = "+str(stepsize_figure) + ", rtol = " + str(rtol_figure) )

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()

plt.figure(figsize=(18,13))
plt.plot(xlin_supernova8, prob1_supernova8+prob0_supernova8,'b-', label="step size = "+str(stepsize_figure8) + ", rtol = " + str(rtol_figure8))
plt.plot(xlin_supernova2, prob1_supernova2+prob0_supernova2,'b--', label="step size = "+str(stepsize_figure2) + ", rtol = " + str(rtol_figure2) )
plt.plot(xlin_supernova_10_10, prob1_supernova_10_10 + prob0_supernova_10_10,'b-.', label="step size = "+str(stepsize_figure_10_10) + ", rtol = " + str(rtol_figure_10_10) )
plt.plot(xlin_supernova6, prob1_supernova6+prob0_supernova6,'b:', label="step size = "+str(stepsize_figure6) + ", rtol = " + str(rtol_figure6) )

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()

plt.figure(figsize=(18,13))
plt.plot(xlin_supernova3, prob1_supernova3+prob0_supernova3,'m-',label="step size = "+str(stepsize_figure3) + ", rtol = " + str(rtol_figure3) )
plt.plot(xlin_supernova_100_9, prob1_supernova_100_9 + prob0_supernova_100_9,'m--',label="step size = "+str(stepsize_figure_100_9) + ", rtol = " + str(rtol_figure_100_9) )
plt.plot(xlin_supernova_100_10, prob1_supernova_100_10 + prob0_supernova_100_10,'m-.',label="step size = "+str(stepsize_figure_100_10) + ", rtol = " + str(rtol_figure_100_10) )
plt.plot(xlin_supernova4, prob1_supernova4+prob0_supernova4,'m:',label="step size = "+str(stepsize_figure4) + ", rtol = " + str(rtol_figure4) )
plt.plot(xlin_supernova5, prob1_supernova5+prob0_supernova5,'k-', label="step size = "+str(stepsize_figure5) + ", rtol = " + str(rtol_figure5))
plt.plot(xlin_supernova_100_18, prob1_supernova_100_18 + prob0_supernova_100_18,'k--', label="step size = "+str(stepsize_figure_100_18) + ", rtol = " + str(rtol_figure_100_18))
#plt.plot(xlin_supernova7, prob1_supernova7+prob0_supernova7,'k-.', label="step size = "+str(stepsize_figure7) + ", rtol = " + str(rtol_figure7))

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()



plt.figure(figsize=(18,13))
plt.plot(xlin_supernova, prob1_supernova+prob0_supernova,'r-.', label="step size = "+str(stepsize_figure) + ", rtol = " + str(rtol_figure) )
plt.plot(xlin_supernova_10_10, prob1_supernova_10_10 + prob0_supernova_10_10,'b-.', label="step size = "+str(stepsize_figure_10_10) + ", rtol = " + str(rtol_figure_10_10) )
plt.plot(xlin_supernova_100_10, prob1_supernova_100_10 + prob0_supernova_100_10,'m-.',label="step size = "+str(stepsize_figure_100_10) + ", rtol = " + str(rtol_figure_100_10) )
#plt.plot(xlin_supernova7, prob1_supernova7+prob0_supernova7,'m:', label="step size = "+str(stepsize_figure7) + ", rtol = " + str(rtol_figure7))

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()


plt.figure(figsize=(18,13))
plt.plot(xlin_supernova_1_8, prob1_supernova_1_8 + prob0_supernova_1_8,'r-', label="step size = "+str(stepsize_figure_1_8) + ", rtol = " + str(rtol_figure_1_8) )
plt.plot(xlin_supernova8, prob1_supernova8+prob0_supernova8,'b-', label="step size = "+str(stepsize_figure8) + ", rtol = " + str(rtol_figure8))
plt.plot(xlin_supernova3, prob1_supernova3+prob0_supernova3,'m-',label="step size = "+str(stepsize_figure3) + ", rtol = " + str(rtol_figure3) )

plt.title("Total Probability",fontsize=20)
plt.xlabel("$\hat x$",fontsize=20)
plt.ylabel("Probability",fontsize=20)
plt.legend(loc="upper left")
plt.show()<jupyter_output><empty_output><jupyter_text>Examples of odeint<jupyter_code>def pend(y, t, b, c):
    theta, omega = y
    dydt = [omega, -b*omega - c*np.sin(theta)]
    return dydt

b = 0.25
c = 5.0

y0 = [np.pi - 0.1, 0.0]

t = np.linspace(0, 10, 101)

sol = odeint(pend, y0, t, args=(b, c),full_output=1)


plt.plot(t, sol[0][:, 0], 'b', label='theta(t)')
plt.plot(t, sol[0][:, 1], 'g', label='omega(t)')
plt.legend(loc='best')
plt.xlabel('t')
plt.grid()
plt.show()
sol[1]<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.1814618211514904, 'fraction_numerical': 0.11359738668844427, 'mean_word_length': 6.394927536231884, 'pattern_counts': {'":': 0, '<': 9, '<?xml version=': 0, '>': 9, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '2', 'dir': 'jupyter-structured-clean-dedup', 'id': '375464', 'license': 'MIT', 'n_tokens_mistral': 6264, 'n_tokens_neox': 5570, 'n_words': 527, 'path': 'ipynb/matter/real-ize-schrodinger-eq-and-solve.ipynb', 'repo_name': 'NeuPhysics/codebase-lite', 'size': '12245'}