def initanh(bounds,nk,popsize,angle_in):
min_b, max_b = cp.asarray(bounds).T
diff = np.fabs(min_b - max_b)
A=(cp.ones((popsize,1,4)))*cp.array(angle_in)
B=min_b+cp.random.rand(popsize,1,4)*diff
ends=cp.concatenate((A,B),axis=1)
rank=cp.arange(nk)
travel=ends[:,1]-ends[:,0]
u=cp.random.rand(popsize,1,4)*(nk-1)
sigma=(1+cp.random.rand(popsize,4)*(nk/6-1)).reshape(popsize,1,4)
print("rank")
print(rank.shape)
print("u")
print(u.shape)
print("sigma")
print(sigma.shape)
print(nk)
print((rank.reshape(1,nk,1)-u.reshape(popsize,1,4)).shape)
print(travel.reshape(popsize,1,4).shape)
A=cp.tanh(rank.reshape(1,nk,1)-u.reshape(popsize,1,4))/sigma
print(A.shape)
pop=(travel.reshape(popsize,1,4)*0.5*(1+cp.tanh((rank.reshape(1,nk,1)-u.reshape(popsize,1,4))/sigma).reshape(popsize,nk,4)))
pop+=ends[:,0].reshape(popsize,1,4)
#A=(6*cp.abs(travel)*cp.random.rand(popsize,4)-3*cp.abs(travel)).reshape(popsize,1,4)
#pop=0.5*(1+cp.tanh((1,nk,1)-u.reshape(popsize,1,4))/(2*sigma))**2
pop=pop.clip(min_b,max_b)
return pop
def backward(self, dh_next, dc_next):
Wx, Wh, b = self.params
x, h_prev, c_prev, i, f, g, o, c_next = self.cache
dt = dh_next * o
dch = dt * (1 - cp.tanh(c_next)**2)
dc = dch + dc_next
dc_prev = dc * f
df = dc * c_prev
dg = dc * i
di = dc * g
do = dh_next * cp.tanh(c_next)
di *= i * (1 - i)
df *= f * (1 - f)
do *= o * (1 - o)
dg *= (1 - g**2)
dA = cp.hstack((df, dg, di, do))
dx = cp.dot(dA, Wx.T)
dWx = cp.dot(x.T, dA)
dh_prev = cp.dot(dA, Wh.T)
dWh = cp.dot(h_prev.T, dA)
db = dA.sum(axis=0)
self.grads[0][...] = dWx
self.grads[1][...] = dWh
self.grads[2][...] = db
return dx, dh_prev, dc_prev
def lra_e(self, x, target, beta, gamma, print_flag=False):
h1 = cp.dot(x, self.W_f1)
z1 = cp.tanh(h1)
h2 = cp.dot(z1, self.W_f2)
z2 = cp.tanh(h2)
h3 = cp.dot(z2, self.W_f3)
output = softmax(h3)
e3 = -target / output
if print_flag:
print(e3)
y2 = cp.tanh(h2 - beta * cp.dot(e3, self.B3))
e2 = -2 * (y2 - z2)
y1 = cp.tanh(h1 - beta * cp.dot(e2, self.B2))
e1 = -2 * (y1 - z1)
"""
delta_Wf3 = cp.dot(z2.T, e3*h3*(1-h3))
delta_Wf2 = cp.dot(z1.T, e2*tanh_grad(h2))
delta_Wf1 = cp.dot(x.T, e1*tanh_grad(h1))
"""
delta_Wf3 = cp.dot(z2.T, e3)
delta_Wf2 = cp.dot(z1.T, e2)
delta_Wf1 = cp.dot(x.T, e1)
delta_B3 = -gamma * delta_Wf3.T
delta_B2 = -gamma * delta_Wf2.T
# print(delta_Wf3.shape)
# print(delta_Wf3)
alpha = 0.05
self.W_f1 -= alpha * delta_Wf1
self.W_f2 -= alpha * delta_Wf2
self.W_f3 -= alpha * delta_Wf3
self.B3 -= alpha * delta_B3
self.B2 -= alpha * delta_B2
def predict(self, x):
h1 = cp.dot(x, self.W_f1)
h1 = cp.tanh(h1)
h2 = cp.dot(h1, self.W_f2)
h2 = cp.tanh(h2)
h3 = cp.dot(h2, self.W_f3)
output = softmax(h3)
return output
def sigmoid_kernel(X, Y, gamma=None, coef0=1):
if gamma is None:
gamma = 1.0 / X.shape[1]
K = cp.dot(X, Y.T)
K *= gamma
K += coef0
cp.tanh(K, K)
return K
def calc_gru_z(W_z_x, U_z_h):
# z = cp.tanh((W_z_x + U_z_h) * half) * half + half
z = W_z_x
z += U_z_h
z *= 0.5
cp.tanh(z, z)
z *= 0.5
z += 0.5
return z
def calc_gru_r(W_r_x, U_r_h):
# r = cp.tanh((W_r_x + U_r_h) * half) * half + half
r = W_r_x
r += U_r_h
r *= 0.5
cp.tanh(r, r)
r *= 0.5
r += 0.5
return r
def gradient(self, x, target, epoch):
reg = 0.01
h1 = cp.dot(x, self.W_f1) + self.b1
h1_ = cp.tanh(h1)
h2 = cp.dot(h1_, self.W_f2) + self.b2
h2_ = cp.tanh(h2)
h3 = cp.dot(h2_, self.W_f3) + self.b3
h3_ = cp.tanh(h3)
h4 = cp.dot(h3_, self.W_f4) + self.b4
h4_ = cp.tanh(h4)
h5 = cp.dot(h4_, self.W_f5) + self.b5
output = softmax(h5)
delta5 = (output - target) / batch_size
self.delta_Wf5 = cp.dot(h4_.T, delta5) + reg * self.W_f5
self.delta_b5 = cp.dot(cp.ones(batch_size), delta5) + reg * self.b5
delta4 = tanh_grad(h4) * cp.dot(delta5, self.W_f5.T)
self.delta_Wf4 = cp.dot(h3_.T, delta4) + reg * self.W_f4
self.delta_b4 = cp.dot(cp.ones(batch_size), delta4) + reg * self.b4
delta3 = tanh_grad(h3) * cp.dot(delta4, self.W_f4.T)
self.delta_Wf3 = cp.dot(h2_.T, delta3) + reg * self.W_f3
self.delta_b3 = cp.dot(cp.ones(batch_size), delta3) + reg * self.b3
delta2 = tanh_grad(h2) * cp.dot(delta3, self.W_f3.T)
self.delta_Wf2 = cp.dot(h1_.T, delta2) + reg * self.W_f2
self.delta_b2 = cp.dot(cp.ones(batch_size), delta2) + reg * self.b2
delta1 = tanh_grad(h1) * cp.dot(delta2, self.W_f2.T)
self.delta_Wf1 = cp.dot(x.T, delta1) + reg * self.W_f1
self.delta_b1 = cp.dot(cp.ones(batch_size), delta1) + reg * self.b1
# print(delta_Wf1)
# eta = self.learning_rate(epoch)
eta = 0.02
# eta, self.h_W1 = self.rms_prop(self.delta_Wf1, self.h_W1)
self.W_f1 -= eta * self.delta_Wf1
# eta, self.h_W2 = self.rms_prop(self.delta_Wf2, self.h_W2)
self.W_f2 -= eta * self.delta_Wf2
# eta, self.h_W3 = self.rms_prop(self.delta_Wf3, self.h_W3)
self.W_f3 -= eta * self.delta_Wf3
# eta, self.h_W4 = self.rms_prop(self.delta_Wf4, self.h_W4)
self.W_f4 -= eta * self.delta_Wf4
# eta, self.h_W5 = self.rms_prop(self.delta_Wf5, self.h_W5)
self.W_f5 -= eta * self.delta_Wf5
# eta, self.h_b1 = self.rms_prop(self.delta_b1, self.h_b1)
self.b1 -= eta * self.delta_b1
# eta, self.h_b2 = self.rms_prop(self.delta_b2, self.h_b2)
self.b2 -= eta * self.delta_b2
# eta, self.h_b3 = self.rms_prop(self.delta_b3, self.h_b3)
self.b3 -= eta * self.delta_b3
# eta, self.h_b4 = self.rms_prop(self.delta_b4, self.h_b4)
self.b4 -= eta * self.delta_b4
# eta, self.h_b5 = self.rms_prop(self.delta_b5, self.h_b5)
self.b5 -= eta * self.delta_b5
def forward(self, x, y_prev, c_prev):
u = np.matmul(x, self.w) + np.matmul(y_prev, self.v) + self.b.reshape(4, 1, -1)
a0 = sigmoid(u[0])
a1 = sigmoid(u[1])
a2 = np.tanh(u[2])
a3 = sigmoid(u[3])
self.gates = np.stack((a0, a1, a2, a3))
self.c = a0 * c_prev + a1 * a2
self.y = a3 * np.tanh(self.c)
def get_phase(num_of_vort, pos, x_pts, y_pts, grid_x, grid_y, grid_len_x,
grid_len_y, component):
""" Gets phase distribution of N dipoles."""
# Phase initialisation
theta_tot = cp.empty((x_pts, y_pts))
# Scale pts:
x_tilde = 2 * cp.pi * ((grid_x - grid_x.min()) / grid_len_x)
y_tilde = 2 * cp.pi * ((grid_y - grid_y.min()) / grid_len_y)
if component == '2':
switch = True
else:
switch = False
for i in range(num_of_vort // 2):
theta_k = cp.zeros((x_pts, y_pts))
if i % 24 == 0 and i > 0:
switch ^= True
if switch:
x_p, y_p = next(pos)
x_m, y_m = next(pos)
else:
x_m, y_m = next(pos)
x_p, y_p = next(pos)
# Scaling vortex positions:
x_m_tilde = 2 * cp.pi * ((x_m - grid_x.min()) / grid_len_x)
y_m_tilde = 2 * cp.pi * ((y_m - grid_y.min()) / grid_len_y)
x_p_tilde = 2 * cp.pi * ((x_p - grid_x.min()) / grid_len_x)
y_p_tilde = 2 * cp.pi * ((y_p - grid_y.min()) / grid_len_y)
# Aux variables
Y_minus = y_tilde - y_m_tilde
X_minus = x_tilde - x_m_tilde
Y_plus = y_tilde - y_p_tilde
X_plus = x_tilde - x_p_tilde
heav_xp = cp.asarray(np.heaviside(cp.asnumpy(X_plus), 1.))
heav_xm = cp.asarray(np.heaviside(cp.asnumpy(X_minus), 1.))
for nn in cp.arange(-5, 6):
theta_k += cp.arctan(cp.tanh((Y_minus + 2 * cp.pi * nn) / 2) * cp.tan((X_minus - cp.pi) / 2)) \
- cp.arctan(cp.tanh((Y_plus + 2 * cp.pi * nn) / 2) * cp.tan((X_plus - cp.pi) / 2)) \
+ cp.pi * (heav_xp - heav_xm)
theta_k -= y_tilde * (x_p_tilde - x_m_tilde) / (2 * cp.pi)
theta_tot += theta_k
return theta_tot
def time_fusion_lstm_grad_grad(c_prev, a, i, f, o, c, gc, gh, ggc_prev,
gga, ggi, ggf, ggo, gc_prev, ga, gi, gf, go,
gc_next, ggc, ggh):
def _cupy_sigmoid(x):
half = x.dtype.type(0.5)
return cupy.tanh(x * half) * half + half
def _grad_grad_sigmoid(x):
return x * (1 - x) * (1 - 2 * x)
def _grad_sigmoid(x):
return x * (1 - x)
def _grad_tanh(x):
return 1 - x * x
def _grad_grad_tanh(x, gx):
return -2 * x * gx
sig_o = _cupy_sigmoid(o)
gsig_o = _grad_sigmoid(sig_o)
ggsig_o = _grad_grad_sigmoid(sig_o)
sig_i = _cupy_sigmoid(i)
gsig_i = _grad_sigmoid(sig_i)
ggsig_i = _grad_grad_sigmoid(sig_i)
sig_f = _cupy_sigmoid(f)
gsig_f = _grad_sigmoid(sig_f)
ggsig_f = _grad_grad_sigmoid(sig_f)
tanh_a = cupy.tanh(a)
gtanh_a = _grad_tanh(tanh_a)
ggtanh_a = _grad_grad_tanh(tanh_a, gtanh_a)
tanh_c = cupy.tanh(c)
gtanh_c = _grad_tanh(tanh_c)
ggtanh_c = _grad_grad_tanh(tanh_c, gtanh_c)
gc_bar = gh * sig_o * gtanh_c + gc
gc_prev[:] = ggf * gc_bar * gsig_f
ga[:] = (gga * sig_i * ggtanh_a + ggi * gtanh_a * gsig_i) * gc_bar
gi[:] = (gga * gtanh_a * gsig_i + ggi * tanh_a * ggsig_i) * gc_bar
gf[:] = (ggc_prev * (gh * sig_o * gtanh_c + gc) * gsig_f +
ggf * gc_bar * c_prev * ggsig_f)
ggc[:] = (ggc_prev * sig_f + gga * sig_i * gtanh_a +
ggi * tanh_a * gsig_i + ggf * c_prev * gsig_f)
dgc_do = gh * gsig_o * gtanh_c
go[:] = ggc * dgc_do + ggo * gh * tanh_c * ggsig_o
dgc_dc = gh * sig_o * ggtanh_c
gc_next[:] = ggc * dgc_dc + ggo * gh * gtanh_c * gsig_o
ggh[:] = ggc * sig_o * gtanh_c + ggo * tanh_c * gsig_o
return gc_prev, ga, gi, gf, go, gc_next, ggc, ggh
def predict(self, x):
h1 = cp.dot(x, self.W_f1) + self.b1
h1 = cp.tanh(h1)
h2 = cp.dot(h1, self.W_f2) + self.b2
h2 = cp.tanh(h2)
h3 = cp.dot(h2, self.W_f3) + self.b3
h3 = cp.tanh(h3)
h4 = cp.dot(h3, self.W_f4) + self.b4
h4 = cp.tanh(h4)
h5 = cp.dot(h4, self.W_f5) + self.b5
output = softmax(h5)
return output
def get_phase(num_of_vort, pos, grid_x, grid_y):
"""
num_of_vort: number of vortices to imprint
pos: iterable of positions to imprint the vortices
grid_x: X-meshgrid
grid_y: Y-meshgrid
"""
# Constructing necessary grid parameters:
x_pts, y_pts = len(grid_x[:, 0]), len(grid_y[0, :])
dx, dy = grid_x[0, 1] - grid_x[0, 0], grid_y[1, 0] - grid_y[0, 0]
grid_len_x, grid_len_y = x_pts * dx, y_pts * dy
# Phase initialisation
theta_tot = cp.empty((x_pts, y_pts))
# Scale pts:
x_tilde = 2 * cp.pi * ((grid_x - grid_x.min()) / grid_len_x)
y_tilde = 2 * cp.pi * ((grid_y - grid_y.min()) / grid_len_y)
for _ in range(num_of_vort // 2):
theta_k = cp.zeros((x_pts, y_pts))
x_m, y_m = next(pos)
x_p, y_p = next(pos)
# Scaling vortex positions:
x_m_tilde = 2 * cp.pi * ((x_m - grid_x.min()) / grid_len_x)
y_m_tilde = 2 * cp.pi * ((y_m - grid_y.min()) / grid_len_y)
x_p_tilde = 2 * cp.pi * ((x_p - grid_x.min()) / grid_len_x)
y_p_tilde = 2 * cp.pi * ((y_p - grid_y.min()) / grid_len_y)
# Aux variables
Y_minus = y_tilde - y_m_tilde
X_minus = x_tilde - x_m_tilde
Y_plus = y_tilde - y_p_tilde
X_plus = x_tilde - x_p_tilde
heav_xp = cp.asarray(np.heaviside(cp.asnumpy(X_plus), 1.))
heav_xm = cp.asarray(np.heaviside(cp.asnumpy(X_minus), 1.))
for nn in cp.arange(-5, 6):
theta_k += cp.arctan(cp.tanh((Y_minus + 2 * cp.pi * nn) / 2) * cp.tan((X_minus - cp.pi) / 2)) \
- cp.arctan(cp.tanh((Y_plus + 2 * cp.pi * nn) / 2) * cp.tan((X_plus - cp.pi) / 2)) \
+ cp.pi * (heav_xp - heav_xm)
theta_k -= y_tilde * (x_p_tilde - x_m_tilde) / (2 * cp.pi)
theta_tot += theta_k
return theta_tot
def go_cupy():
import cupy as cp
a = cp.arange(100).reshape(10, 10)
trace = 0.0
for i in range(a.shape[0]):
trace += cp.tanh(a[i, i])
return a + trace
def test_elementwise_trinary(self):
desc_a = cutensor.create_tensor_descriptor(self.a, ct.OP_SQRT)
desc_b = cutensor.create_tensor_descriptor(self.b, ct.OP_TANH)
desc_c = cutensor.create_tensor_descriptor(self.c, ct.OP_COS)
d = cutensor.elementwise_trinary(self.alpha,
self.a,
desc_a,
self.mode_a,
self.beta,
self.b,
desc_b,
self.mode_b,
self.gamma,
self.c,
desc_c,
self.mode_c,
op_AB=ct.OP_ADD,
op_ABC=ct.OP_MUL)
testing.assert_allclose((self.alpha * cupy.sqrt(self.a_transposed) +
self.beta * cupy.tanh(self.b_transposed)) *
self.gamma * cupy.cos(self.c),
d,
rtol=1e-6,
atol=1e-6)
def tanh_ac(z):
if (cupy_ready and (z.size > 400000) and (z.size <= gpu_array_max_size)):
z_gpu = cp.asarray(z)
r_gpu = cp.tanh(z_gpu)
return cp.asnumpy(r_gpu)
else:
return np.tanh(z)
def tanh(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.tanh <numpy.tanh>`.
See its docstring for more information.
"""
if x.dtype not in _floating_dtypes:
raise TypeError("Only floating-point dtypes are allowed in tanh")
return Array._new(np.tanh(x._array))
def free_esn(self, wash, simulation_time):
x = self.x
r = self.r
states_T = cp.zeros((self.N, simulation_time))
for i in range(simulation_time):
x = (1.0 - wash) * x + wash * cp.tanh(cp.matmul(self.M, x))
states_T[:, i] = x[:, 0]
self.x = x
return states_T
def gradient(self, x, target):
h1 = cp.dot(x, self.W_f1) + self.b1
h1_ = cp.tanh(h1)
h2 = cp.dot(h1_, self.W_f2) + self.b2
h2_ = cp.tanh(h2)
h3 = cp.dot(h2_, self.W_f3) + self.b3
h3_ = cp.tanh(h3)
h4 = cp.dot(h3_, self.W_f4) + self.b4
# h4_ = cp.tanh(h4)
# h5 = cp.dot(h4_, self.W_f5) + self.b5
output = softmax(h4)
delta4 = (output - target) / batch_size
# delta_Wf5 = cp.dot(h4_.T, delta5)
# delta_b5 = cp.dot(cp.ones(batch_size), delta5)
# delta4 = tanh_grad(h4) * cp.dot(delta5, self.B5)
delta_Wf4 = cp.dot(h3_.T, delta4)
delta_b4 = cp.dot(cp.ones(batch_size), delta4)
delta3 = tanh_grad(h3) * cp.dot(delta4, self.W_f4.T)
delta_Wf3 = cp.dot(h2_.T, delta3)
delta_b3 = cp.dot(cp.ones(batch_size), delta3)
delta2 = tanh_grad(h2) * cp.dot(delta3, self.W_f3.T)
delta_Wf2 = cp.dot(h1_.T, delta2)
delta_b2 = cp.dot(cp.ones(batch_size), delta2)
delta1 = tanh_grad(h1) * cp.dot(delta2, self.W_f2.T)
delta_Wf1 = cp.dot(x.T, delta1)
delta_b1 = cp.dot(cp.ones(batch_size), delta1)
# print(delta_Wf1)
alpha1 = 0.02
self.W_f1 -= alpha1 * delta_Wf1
self.W_f2 -= alpha1 * delta_Wf2
self.W_f3 -= alpha1 * delta_Wf3
self.W_f4 -= alpha1 * delta_Wf4
# self.W_f5 -= alpha1 * delta_Wf5
self.b1 -= alpha1 * delta_b1
self.b2 -= alpha1 * delta_b2
self.b3 -= alpha1 * delta_b3
self.b4 -= alpha1 * delta_b4
def update_reservoir(self, u, n, Y):
# u is input at specific time
# u has shape (N_u (3 for L63))
# See page 16 eqtn 18 of Lukosevicius PracticalESN for feedback info.
x_n_tilde = cp.tanh(
cp.matmul(self.W, self.x[n]) +
cp.array(sp.matmul(self.W_in, sp.hstack((sp.array([1]), u)))) +
cp.array(sp.matmul(self.W_fb, Y)))
self.x[n+1] = cp.multiply((1-cp.array(self.alpha_matrix)), cp.array(self.x[n])) \
+ cp.multiply(cp.array(self.alpha_matrix), x_n_tilde)
def free_run(self, dt, simulation_time):
x = self.x
r = self.r
tspan = cp.array(cp.arange(0, simulation_time, dt))
states_T = cp.zeros((self.N, len(tspan)))
for i, t in enumerate(tspan):
x = (1.0 - dt) * x + cp.dot(self.M, r * dt)
r = cp.tanh(x) #(N,1)
states_T[:, i] = x[:, 0]
return states_T
def gradient(self, x, target, epoch):
h1 = cp.dot(x, self.W_f1) + self.b1
h1_ = cp.tanh(h1)
h2 = cp.dot(h1_, self.W_f2) + self.b2
h2_ = cp.tanh(h2)
h3 = cp.dot(h2_, self.W_f3) + self.b3
h3_ = cp.tanh(h3)
h4 = cp.dot(h3_, self.W_f4) + self.b4
h4_ = cp.tanh(h4)
h5 = cp.dot(h4_, self.W_f5) + self.b5
output = softmax(h5)
delta5 = (output - target) / batch_size
self.delta_Wf5 = cp.dot(h4_.T, delta5)
self.delta_b5 = cp.dot(cp.ones(batch_size), delta5)
delta4 = tanh_grad(h4) * cp.dot(delta5, self.W_f5.T)
self.delta_Wf4 = cp.dot(h3_.T, delta4)
self.delta_b4 = cp.dot(cp.ones(batch_size), delta4)
delta3 = tanh_grad(h3) * cp.dot(delta4, self.W_f4.T)
self.delta_Wf3 = cp.dot(h2_.T, delta3)
self.delta_b3 = cp.dot(cp.ones(batch_size), delta3)
delta2 = tanh_grad(h2) * cp.dot(delta3, self.W_f3.T)
self.delta_Wf2 = cp.dot(h1_.T, delta2)
self.delta_b2 = cp.dot(cp.ones(batch_size), delta2)
delta1 = tanh_grad(h1) * cp.dot(delta2, self.W_f2.T)
self.delta_Wf1 = cp.dot(x.T, delta1)
self.delta_b1 = cp.dot(cp.ones(batch_size), delta1)
eta = 0.02
self.W_f1 -= eta * self.delta_Wf1
self.W_f2 -= eta * self.delta_Wf2
self.W_f3 -= eta * self.delta_Wf3
self.W_f4 -= eta * self.delta_Wf4
self.W_f5 -= eta * self.delta_Wf5
self.b1 -= eta * self.delta_b1
self.b2 -= eta * self.delta_b2
self.b3 -= eta * self.delta_b3
self.b4 -= eta * self.delta_b4
self.b5 -= eta * self.delta_b5
def tanh(inp) -> 'Tensor':
_check_tensors(inp)
engine = _get_engine(inp)
output_array = engine.tanh(inp.data)
return _create_tensor(
inp,
data=output_array,
func=wrapped_partial(tanh_backward, inp=inp, out=output_array)
)
def gradient(self, x, target, alpha):
h1 = cp.dot(x, self.W_f1)
h1_ = cp.tanh(h1)
h2 = cp.dot(h1_, self.W_f2)
h2_ = cp.tanh(h2)
h3 = cp.dot(h2_, self.W_f3)
output = softmax(h3)
delta3 = (output - target) / batch_size
delta_Wf3 = cp.dot(h2_.T, delta3)
delta2 = tanh_grad(h2) * cp.dot(delta3, self.W_f3.T)
delta_Wf2 = cp.dot(h1_.T, delta2)
delta1 = tanh_grad(h1) * cp.dot(delta2, self.W_f2.T)
delta_Wf1 = cp.dot(x.T, delta1)
self.W_f1 -= alpha * delta_Wf1
self.W_f2 -= alpha * delta_Wf2
self.W_f3 -= alpha * delta_Wf3
def tanh(X):
"""Compute the hyperbolic tan function inplace.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
The transformed data.
"""
return np.tanh(X, out=X)
def tanh_derivative(self, x):
#convert to 2d array of shape (features, 1)
x=cp.expand_dims(x, axis=1)
#compute matrix multiplication for data with hidden layer matrix into hidden_output
wtx=cp.matmul(self.h_matrix, x)
#compute link function on hidden_outputs
wtx=self.tanh_link(wtx)
return cp.ones(wtx.shape)-cp.square(cp.tanh(wtx))
def sample(memory, seed_ix, n):
"""
sample a sequence of integers from the model
h is memory state, seed_ix is seed letter for first time step
"""
h, c = memory
x = cp.zeros((vocab_size, 1))
#seed_ix = cp.asnumpy(seed_ix)
x[seed_ix] = 1
ixes = []
for t in range(n):
wes = Wex @ x
z = cp.vstack((h, wes))
f = sigmoid(Wf @ z + bf)
ins = sigmoid(Wi @ z + bi)
c_ = cp.tanh(Wc @ z + bc)
cs = cp.multiply(f, c) + cp.multiply(ins, c_)
o = sigmoid(Wo @ z + bo)
h = cp.multiply(o, cp.tanh(cs))
y = Why @ h + by
p = softmax(y)
# forward pass again, but we do not have to store the activations now
#loss, activations, memory = forward(inputs, targets, (hprev, nprev))
p = cp.exp(y) / cp.sum(cp.exp(y))
#p = cp.asnumpy(p)
ix = cp.random.choice(a=range(vocab_size), size=1, p=p.ravel()).item()
index = ix
x = cp.zeros((vocab_size, 1))
x[index] = 1
ixes.append(index)
return ixes
def forward(self, x, h_prev, c_prev):
Wx, Wh, b = self.params
N, H = h_prev.shape
A = cp.dot(x, Wx) + cp.dot(h_prev, Wh) + b
# slice
f = A[:, :H]
g = A[:, H:2 * H]
i = A[:, 2 * H:3 * H]
o = A[:, 3 * H:]
f = sigmoid(f)
g = cp.tanh(g)
i = sigmoid(i)
o = sigmoid(o)
c_next = f * c_prev + g * i
h_next = o * cp.tanh(c_next)
self.cache = (x, h_prev, c_prev, i, f, g, o, c_next)
return h_next, c_next
def get_phase(num_of_vort, pos, x_pts, y_pts, grid_x, grid_y, grid_len_x,
grid_len_y):
# Phase initialisation
theta_tot = cp.empty((x_pts, y_pts))
# Scale pts:
x_tilde = 2 * cp.pi * ((grid_x - grid_x.min()) / grid_len_x)
y_tilde = 2 * cp.pi * ((grid_y - grid_y.min()) / grid_len_y)
for _ in range(num_of_vort // 2):
theta_k = cp.zeros((x_pts, y_pts))
x_m, y_m = next(pos)
x_p, y_p = next(pos)
# Scaling vortex positions:
x_m_tilde = 2 * cp.pi * ((x_m - grid_x.min()) / grid_len_x)
y_m_tilde = 2 * cp.pi * ((y_m - grid_y.min()) / grid_len_y)
x_p_tilde = 2 * cp.pi * ((x_p - grid_x.min()) / grid_len_x)
y_p_tilde = 2 * cp.pi * ((y_p - grid_y.min()) / grid_len_y)
# Aux variables
Y_minus = y_tilde - y_m_tilde
X_minus = x_tilde - x_m_tilde
Y_plus = y_tilde - y_p_tilde
X_plus = x_tilde - x_p_tilde
heav_xp = cp.asarray(np.heaviside(cp.asnumpy(X_plus), 1.))
heav_xm = cp.asarray(np.heaviside(cp.asnumpy(X_minus), 1.))
for nn in cp.arange(-5, 6):
theta_k += cp.arctan(cp.tanh((Y_minus + 2 * cp.pi * nn) / 2) * cp.tan((X_minus - cp.pi) / 2)) \
- cp.arctan(cp.tanh((Y_plus + 2 * cp.pi * nn) / 2) * cp.tan((X_plus - cp.pi) / 2)) \
+ cp.pi * (heav_xp - heav_xm)
theta_k -= y_tilde * (x_p_tilde - x_m_tilde) / (2 * cp.pi)
theta_tot += theta_k
return theta_tot
def forward():
for i in range(l):
a = cache['a' + str(i)]
w = parameters['w' + str(i + 1)]
b = parameters['b' + str(i + 1)]
z = cp.dot(w, a) + b
if i != l - 1:
a = cp.tanh(z)
else:
a = softmax(z)
cache['a' + str(i + 1)] = a
cache['z' + str(i + 1)] = z
return a