def main():
from matplotlib import pyplot as plt
# random matrix
W, WI = generate_random_matrix(), input_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W,
WI,
memory_max=MEM_MAX,
runs=1)[0]
smc = sum(mc)
print('RANDOM: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 1)
plt.ylim([0, 1])
plt.title("normal W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_permutation_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W,
WI,
memory_max=MEM_MAX,
runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 2)
plt.ylim([0, 1])
plt.title("perm W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_special_perm_matrix()
WI = input_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W,
WI,
memory_max=MEM_MAX,
runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 3)
plt.ylim([0, 1])
plt.title("special perm W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_special_perm_matrix()
WI = generate_special_input()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W,
WI,
memory_max=MEM_MAX,
runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 4)
plt.ylim([0, 1])
plt.title("special perm W, delta WI, mc=%.2f" % smc)
plt.plot(mc)
plt.show()
print('maco')
def main():
from matplotlib import pyplot as plt
# random matrix
W, WI = generate_random_matrix(), input_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W, WI, memory_max=MEM_MAX, runs=1)[0]
smc = sum(mc)
print('RANDOM: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 1)
plt.ylim([0,1])
plt.title("normal W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_permutation_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W, WI, memory_max=MEM_MAX, runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 2)
plt.ylim([0,1])
plt.title("perm W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_special_perm_matrix()
WI = input_matrix()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W, WI, memory_max=MEM_MAX, runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 3)
plt.ylim([0,1])
plt.title("special perm W, uniform WI, mc=%.2f" % smc)
plt.plot(mc)
W = generate_special_perm_matrix()
WI = generate_special_input()
le, mc = ljapunov_exponent(W, WI), memory_capacity(W, WI, memory_max=MEM_MAX, runs=1)[0]
smc = sum(mc)
print('PERMUT: le={0}, mc={1}'.format(le, smc))
plt.subplot(2, 2, 4)
plt.ylim([0,1])
plt.title("special perm W, delta WI, mc=%.2f" % smc)
plt.plot(mc)
plt.show()
print('maco')
def measure_mc(W, WI):
return sum(
memory_capacity(W,
WI,
memory_max=100,
iterations=7000,
iterations_skipped=200)[0])
def main():
A = random.normal(0, 0.1 , [n, n])
A = normalize_columns(A)
# A = array([[3/5, 0], [4/5, 1]])
#
# print(A)
# print("energy = %f" % energy(A))
# print(step(A))
# return
print(energy(A))
for it in range(20):
A = step(A)
print(energy(A))
print(A)
WI = random.uniform(-.1, .1, [n, 1])
#W = random.normal(0, 0.1, [100,100])
mc, err = memory_capacity(A, WI, memory_max=200)
print(sum(mc))
from matplotlib import pyplot as plt
plt.errorbar(range(len(mc)), mc, yerr=(err*3))
plt.ylim([0, 1])
plt.show()
def main():
ITERATIONS = 100
mc = zeros(ITERATIONS)
og = zeros(ITERATIONS)
#farby =
QS = 10
colors = [
[0, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
[0, 1, 1],
[1, 0, 1],
[0, 1, 1],
]
for qpre in range(QS):
q = qpre + 2
for it in range(ITERATIONS):
W = random.normal(0, 0.1, [q, q])
WI = random.uniform(-.1, .1, [q, 1])
mc[it] = sum(memory_capacity(W, WI, memory_max=200, runs=1, iterations_coef_measure=5000)[0][:q+2])
og[it] = matrix_orthogonality(W)
print(qpre, QS, it, ITERATIONS)
plt.scatter(og, mc, marker='+', label=q, c=(colors[qpre % len(colors)]))
plt.xlabel("orthogonality")
plt.ylabel("memory capacity")
plt.grid(True)
plt.legend()
plt.show()
def main():
A = random.normal(0, 0.1, [n, n])
A = normalize_columns(A)
# A = array([[3/5, 0], [4/5, 1]])
#
# print(A)
# print("energy = %f" % energy(A))
# print(step(A))
# return
print(energy(A))
for it in range(20):
A = step(A)
print(energy(A))
print(A)
WI = random.uniform(-.1, .1, [n, 1])
#W = random.normal(0, 0.1, [100,100])
mc, err = memory_capacity(A, WI, memory_max=200)
print(sum(mc))
from matplotlib import pyplot as plt
plt.errorbar(range(len(mc)), mc, yerr=(err * 3))
plt.ylim([0, 1])
plt.show()
def main2(): ITERATIONS = 10 q= 100 for it in range(ITERATIONS): W = random.uniform(-0.1, 0.1, [q, q]) WI = random.uniform(-.1, .1, [q, 1]) mc = sum(memory_capacity(W, WI, memory_max=200, runs=1)[0]) og = matrix_orthogonality(W) print(og)
def rv(xval, linepar): W = np.random.normal(0, xval, [q, q]) WI = np.random.uniform(-tau, tau, [q, 1]) for i, j in itertools.product(range(q), range(q)): if random.random() < linepar: W[i, j] = 0 #current_radius = np.max(np.abs(np.linalg.eig(W)[0])) #W = W * (xval / current_radius) return sum(memory_capacity(W, WI, iterations=1200, iterations_skipped=q, iterations_coef_measure=100)[0])
def rv(xval, linepar):
W = np.random.normal(0, xval, [q, q])
WI = np.random.uniform(-tau, tau, [q, 1])
for i, j in itertools.product(range(q), range(q)):
if random.random() < linepar:
W[i, j] = 0
#current_radius = np.max(np.abs(np.linalg.eig(W)[0]))
#W = W * (xval / current_radius)
return sum(
memory_capacity(W,
WI,
iterations=1200,
iterations_skipped=q,
iterations_coef_measure=100)[0])
def getmc(W, WI): return np.sum(memory_capacity(W, WI, memory_max=q, runs=1, iterations=1200, iterations_skipped=(q+1))[0])
def test_le_mc(W, WI): return ljapunov_exponent(W, WI), memory_capacity(W, WI, memory_max=MEM_MAX, runs=1)[0]
Y = zeros(len(sigmas))
Yerr = zeros(len(sigmas))
for ti, tau in enumerate(taus):
print(tau, "of", str(taus))
for i, sigma in enumerate(sigmas):
mcs = zeros(INSTANCES)
for inm in range(INSTANCES):
W = random.normal(0, sigma, [q, q])
WI = random.uniform(-tau, tau, [q, 1])
mcs[inm] = sum(
memory_capacity(W,
WI,
memory_max=q,
runs=1,
iterations=15000,
iterations_skipped=10000,
iterations_coef_measure=1000)[0])
Y[i] = average(mcs)
Yerr[i] = std(mcs) # / sqrt(INSTANCES)
print(i, "of", len(sigmas))
np.savetxt('saved/avg-t' + str(ti + posun) + '.txt', Y)
np.savetxt('saved/std-t' + str(ti + posun) + '.txt', Yerr)
plt.errorbar(sigmas, Y, yerr=Yerr, label=("$\\tau={0}$".format(tau)))
plt.grid(True)
plt.xlabel("sigma: $W = N(0, \\sigma)$")
plt.ylabel("MC, errbar: $1 \\times \\sigma$")
mcs = np.zeros(ITERATIONS)
for it in range(ITERATIONS):
W = np.random.normal(0, 1, [q, q])
WI = np.random.uniform(-tau, tau, [q, 1])
for i, j in itertools.product(range(q), range(q)):
if random.random() < sparsity:
W[i, j] = 0
current_radius = np.max(np.abs(np.linalg.eig(W)[0]))
W = W * (radius / current_radius)
mcs[it] = sum(
memory_capacity(W,
WI,
iterations=1200,
iterations_skipped=q,
iterations_coef_measure=100)[0])
Y[li][si] = np.average(mcs)
Yerr[li][si] = np.std(mcs)
def replot():
for li in range(len(sparsities)):
plt.errorbar(radiuses,
Y[li],
yerr=Yerr[li],
label="sparsity = {:1.2f}".format(sparsities[li]))
plt.grid(True)
plt.legend(loc=3)
Y[line] = zeros(len(svals))
Yerr[line] = zeros(len(svals))
#Yerr[line] = zeros(len(sigmas))
for qi, q in enumerate(res_sizes):
print(q, "of", str(res_sizes))
for i, sval in enumerate(svals):
mcs = zeros(INSTANCES)
for inm in range(INSTANCES):
W = random.normal(0, 1, [q, q])
# find the largest singular value and rescale the matrix
current_sv = linalg.svd(W, compute_uv=0)[0]
W = W * (sval / current_sv)
WI = random.uniform(-tau, tau, [q, 1])
mcs[inm] = sum(memory_capacity(W, WI, memory_max=q, runs=1, iterations=1200, iterations_skipped=itskip, iterations_coef_measure=100)[0])
Y[qi][i] = average(mcs)
Yerr[qi][i] = std(mcs)
print(i,"of", len(svals))
maxinlineX[qi] = svals[argmax(Y[qi])]
maxinlineY[qi] = max(Y[qi])
np.savetxt('saved/mcs-t'+str(qi + posun)+'.txt', Y[qi])
np.savetxt('saved/stds-t'+str(qi + posun)+'.txt', Yerr[qi])
plt.errorbar(svals, Y[qi], label=("res. size={0}".format(q)), yerr=Yerr[qi])
#plt.scatter(X[qi], Y[qi], label=("res. size={0}".format(q)), c=(colors[qi % len(colors)]))
plt.plot(maxinlineX, maxinlineY, c=(0,0,0), label="maxima")
plt.grid(True)
def test_le_mc(W, WI):
return ljapunov_exponent(W, WI), memory_capacity(W,
WI,
memory_max=MEM_MAX,
runs=1)[0]
sigmas = np.linspace(0.08, 0.11, 7)
tau = 0.01
ITERATIONS = 1000
bins = 20
hists = [None] * len(sigmas)
for i, sigma in enumerate(sigmas):
print(sigma,'of', str(sigmas))
mcs = np.zeros(ITERATIONS)
for it in range(ITERATIONS):
W = np.random.normal(0, sigma, [reservoir_size, reservoir_size])
WI = np.random.uniform(-tau, tau, [reservoir_size, 1])
mc = sum(memory_capacity(W, WI, memory_max=reservoir_size, runs=1)[0])
mcs[it] = mc
print("\r{} of {}".format(it, ITERATIONS), end="")
print()
hists[i] = mcs
def replot():
together= True
if together:
max_yticks = 2
fig = plt.figure()
fig.subplots_adjust(hspace=0.4)
bins = np.linspace(0, 60, 60)
for i, sigma in enumerate(sigmas):
taus = linspace(0.0001, 0.01, 20)
INSTANCES = 5 * 6
X, Y = meshgrid(sigmas, taus)
Z = zeros(X.shape)
i = 0
for sigma_r, tau_r in zip(X, Y):
j = 0
for sigma, tau in zip(sigma_r, tau_r):
mcs = zeros(INSTANCES)
for inm in range(INSTANCES):
W = random.normal(0, sigma, [q, q])
WI = random.uniform(-tau, tau, [q, 1])
mcs[inm] = sum(memory_capacity(W, WI, memory_max=q)[0])
Z[i, j] = average(mcs)
print(sigma, tau)
j += 1
i += 1
cmap = plt.get_cmap('PiYG')
c = plt.pcolormesh(X, Y, Z, cmap=cmap)
plt.colorbar()
plt.ylim([0, 0.010])
plt.xlim([0.08, 0.095])
plt.xlabel("sigma: $W = N(0, \\sigma)$")
plt.ylabel("tau: $W^I = U(-\\tau, \\tau)$")
plt.show()
sigmas = np.linspace(0.08, 0.11, 7)
tau = 0.01
ITERATIONS = 1000
bins = 20
hists = [None] * len(sigmas)
for i, sigma in enumerate(sigmas):
print(sigma, 'of', str(sigmas))
mcs = np.zeros(ITERATIONS)
for it in range(ITERATIONS):
W = np.random.normal(0, sigma, [reservoir_size, reservoir_size])
WI = np.random.uniform(-tau, tau, [reservoir_size, 1])
mc = sum(memory_capacity(W, WI, memory_max=reservoir_size, runs=1)[0])
mcs[it] = mc
print("\r{} of {}".format(it, ITERATIONS), end="")
print()
hists[i] = mcs
def replot():
together = True
if together:
max_yticks = 2
fig = plt.figure()
fig.subplots_adjust(hspace=0.4)
bins = np.linspace(0, 60, 60)
for i, sigma in enumerate(sigmas):
Yerr[li] = np.zeros(len(radiuses))
for si, radius in enumerate(radiuses):
print('point {} of {}'.format(si, len(radiuses)))
mcs = np.zeros(ITERATIONS)
for it in range(ITERATIONS):
W = np.random.normal(0, 1, [q, q])
WI = np.random.uniform(-tau, tau, [q, 1])
for i, j in itertools.product(range(q), range(q)):
if random.random() < sparsity:
W[i, j] = 0
current_radius = np.max(np.abs(np.linalg.eig(W)[0]))
W = W * (radius / current_radius)
mcs[it] = sum(memory_capacity(W, WI, iterations=1200, iterations_skipped=q, iterations_coef_measure=100)[0])
Y[li][si] = np.average(mcs)
Yerr[li][si] = np.std(mcs)
def replot():
for li in range(len(sparsities)):
plt.errorbar(radiuses, Y[li], yerr=Yerr[li], label="sparsity = {:1.2f}".format(sparsities[li]))
plt.grid(True)
plt.legend(loc=3)
plt.xlabel("$|\lambda|_{max}$")
plt.ylabel("MC")
try_save_fig()
plt.show()
def measure_mc(W, WI): return sum(memory_capacity(W, WI, memory_max=100, iterations=7000, iterations_skipped=200)[0])
X, Y = meshgrid(sigmas, taus)
Z = zeros(X.shape)
i = 0
for sigma_r, tau_r in zip(X,Y):
j = 0
for sigma, tau in zip(sigma_r, tau_r):
mcs = zeros(INSTANCES)
for inm in range(INSTANCES):
W = random.normal(0, sigma, [q, q])
WI = random.uniform(-tau, tau, [q, 1])
mcs[inm] = sum(memory_capacity(W, WI, memory_max=q)[0])
Z[i,j] = average(mcs)
print(sigma, tau)
j += 1
i += 1
cmap = plt.get_cmap('PiYG')
c = plt.pcolormesh(X, Y, Z, cmap=cmap)
plt.colorbar()
plt.ylim([0,0.010])
plt.xlim([0.08, 0.095])
plt.xlabel("sigma: $W = N(0, \\sigma)$")
plt.ylabel("tau: $W^I = U(-\\tau, \\tau)$")
plt.show()
