def get_next_state(self, cell, neighbours):
# get input vector from neighbours
input_vector = self.get_input_vector(cell, neighbours)
# get hidden layer
a1 = np.insert(input_vector, 0, 1)
hidden_layer = np.tanh(np.dot(self.theta1, a1))
# get output layer
a2 = np.insert(hidden_layer, 0, 1)
out_vector = np.tanh(np.dot(self.theta2, a2))
# set new internal state and chemicals of cell
new_internal_state = out_vector[:self.internal_state_vector_length]
new_chemicals = out_vector[-self.chemicals_vector_length:]
# add previous chemical concentration
new_chemicals += cell.state.chemicals
# get new color of cell
color_vector = np.append(new_internal_state, new_chemicals)
a3 = np.insert(color_vector, 0, 1)
new_color = (np.tanh(np.dot(self.theta3, a3)) + 1) / 2
# finally create new state
new_state = cell.state.create_state()
new_state.chemicals = new_chemicals
new_state.internal = new_internal_state
new_state.grayscale = int(new_color * 255)
return new_state
def sigmoid_kernel(X, Y=None, gamma=None, coef0=1):
"""
Compute the sigmoid kernel between X and Y::
K(X, Y) = tanh(gamma <X, Y> + coef0)
Parameters
----------
X : array of shape (n_samples_1, n_features)
Y : array of shape (n_samples_2, n_features)
degree : int
Returns
-------
Gram matrix: array of shape (n_samples_1, n_samples_2)
"""
X, Y = check_pairwise_arrays(X, Y)
if gamma is None:
gamma = 1.0 / X.shape[1]
K = linear_kernel(X, Y)
K *= gamma
K += coef0
np.tanh(K, K) # compute tanh in-place
return K
def calc_v(pos, t, x_table, c_attract, dc_attract, c_repel, dc_repel):
'''Calculate drift velocity as a function of c(pos,t) and dc(pos,t)'''
v = 22. # µm/s
chi = 50000. # µm^2/s
chi2 = 50000. # µm^2/s
k = 0.125 # mM
k2 = 0.125 # mM
if pos < x_table[0]:
pos = x_table[0]
c, dc = int_tables(pos, t, x_table, c_attract, dc_attract)
c2, dc2 = int_tables(pos, t, x_table, c_repel, dc_repel)
elif pos > x_table[-1]:
pos = x_table[-1]
c, dc = int_tables(pos, t, x_table, c_attract, dc_attract)
c2, dc2 = int_tables(pos, t, x_table, c_repel, dc_repel)
else:
c, dc = int_tables(pos, t, x_table, c_attract, dc_attract)
c2, dc2 = int_tables(pos, t, x_table, c_repel, dc_repel)
v1 = ((8*v)/(3*np.pi))*np.tanh(((chi*np.pi)/(8*v))*(k/np.power((k+c),2))*dc)
v2 = ((8*v)/(3*np.pi))*np.tanh(((chi2*np.pi)/(8*v))*(k2/np.power((k+c2),2))*dc2)
#print v1, v2
if np.abs(v1) > np.abs(v2):
return v1
else:
return v2
def set_activation(self, method, sig=None, d_sig=None, sig_0=None, d_sig_0=None):
"""
This method sets the activation functions.
Parameters
----------
method : str
'logistic' , 'htanget', or 'custom'
sig, d_sig, sig_0, and d_sig_0 : function objects
Optional arguments intended for use with the
'custom' method option. They should be functions.
sig_0 and d_sig_0 are the output layer activation functions.
"""
method = method.lower()
if method == 'logistic':
self.sig = lambda z: twod(1 / (1 + np.exp(-z)))
self.d_sig = lambda z: twod(np.multiply(self.sig(z), (1 - self.sig(z))))
self.sig_0 = self.sig
self.d_sig_0 = self.d_sig
elif method == 'htangent':
self.sig = lambda z: twod(np.tanh(z))
self.d_sig = lambda z: twod(1 - np.power(np.tanh(z), 2))
self.sig_0 = self.sig
self.d_sig_0 = self.d_sig
elif method == 'custom':
self.sig = sig
self.d_sig = d_sig
self.sig_0 = sig_0
self.d_sig_0 = d_sig_0
else:
raise ValueError('NNetClassify.set_activation: ' + str(method) + ' is not a valid option for method')
self.activation = method
def forward(self, inputs):
c_prev, x = inputs
a, i, f, o = _extract_gates(x)
batch = len(x)
if isinstance(x, numpy.ndarray):
self.a = numpy.tanh(a)
self.i = _sigmoid(i)
self.f = _sigmoid(f)
self.o = _sigmoid(o)
c_next = numpy.empty_like(c_prev)
c_next[:batch] = self.a * self.i + self.f * c_prev[:batch]
h = self.o * numpy.tanh(c_next[:batch])
else:
c_next = cuda.cupy.empty_like(c_prev)
h = cuda.cupy.empty_like(c_next[:batch])
cuda.elementwise(
'T c_prev, T a, T i_, T f, T o', 'T c, T h',
'''
COMMON_ROUTINE;
c = aa * ai + af * c_prev;
h = ao * tanh(c);
''',
'lstm_fwd', preamble=_preamble)(
c_prev[:batch], a, i, f, o, c_next[:batch], h)
c_next[batch:] = c_prev[batch:]
self.c = c_next[:batch]
return c_next, h
def forward(self, inputs):
c_prev1, c_prev2, x1, x2 = inputs
a1, i1, f1, o1 = _extract_gates(x1)
a2, i2, f2, o2 = _extract_gates(x2)
if isinstance(x1, numpy.ndarray):
self.a1 = numpy.tanh(a1)
self.i1 = _sigmoid(i1)
self.f1 = _sigmoid(f1)
self.a2 = numpy.tanh(a2)
self.i2 = _sigmoid(i2)
self.f2 = _sigmoid(f2)
self.o = _sigmoid(o1 + o2)
self.c = self.a1 * self.i1 + self.a2 * self.i2 + \
self.f1 * c_prev1 + self.f2 * c_prev2
h = self.o * numpy.tanh(self.c)
else:
self.c, h = cuda.elementwise(
'''T c_prev1, T a1, T i1, T f1, T o1,
T c_prev2, T a2, T i2, T f2, T o2''',
'T c, T h',
'''
COMMON_ROUTINE;
c = aa1 * ai1 + af1 * c_prev1 + aa2 * ai2 + af2 * c_prev2;
h = ao * tanh(c);
''',
'slstm_fwd', preamble=_preamble)(
c_prev1, a1, i1, f1, o1, c_prev2, a2, i2, f2, o2)
return self.c, h
def sample_modified(h, seed_str, n, alpha):
"""
A modified sampling method from sample().
h is updated until the end of the string before generating the text.
seed_str: a list of indices of input string
"""
m = len(seed_str)
ixes = []
# Simply output the string and Updating h
for i in xrange(m):
ixes.append(seed_str[i])
x = np.zeros((vocab_size, 1))
seed_ix = seed_str[i]
x[seed_ix] = 1
h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h) + bh)
# Generating the text
for t in xrange(n):
h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h) + bh)
y = np.dot(Why, h) + by
p = np.exp(alpha*y) / np.sum(np.exp(alpha*y))
ix = np.random.choice(range(vocab_size), p=p.ravel())
x = np.zeros((vocab_size, 1))
x[ix] = 1
ixes.append(ix)
return ixes
def ConvLSTM(self, param, layerid, layerinfo, E, R, C, RPP, padw):
u'''計算に使用; ConvLSTMの計算'''
si = str(layerid)
ch, h, w = layerinfo
zi = tensor.nnet.conv.conv2d(self.spad2d(E, padw, padw), param['cl_WE_'+si][0]).eval()
zi += tensor.nnet.conv.conv2d(self.spad2d(R, padw, padw), param['cl_WR_'+si][0]).eval()
zi += C*(param['cl_WC_'+si][0])
zi += param['cl_b_'+si][0]
zf = tensor.nnet.conv.conv2d(self.spad2d(E, padw, padw), param['cl_WE_'+si][1]).eval()
zf += tensor.nnet.conv.conv2d(self.spad2d(R, padw, padw), param['cl_WR_'+si][1]).eval()
zf += C*(param['cl_WC_'+si][1])
zf += param['cl_b_'+si][1]
zc = tensor.nnet.conv.conv2d(self.spad2d(E, padw, padw), param['cl_WE_'+si][2]).eval()
zc += tensor.nnet.conv.conv2d(self.spad2d(R, padw, padw), param['cl_WR_'+si][2]).eval()
zc += param['cl_b_'+si][2]
zo = tensor.nnet.conv.conv2d(self.spad2d(E, padw, padw), param['cl_WE_'+si][3]).eval()
zo += tensor.nnet.conv.conv2d(self.spad2d(R, padw, padw), param['cl_WR_'+si][3]).eval()
zo += C*(param['cl_WC_'+si][3])
zo += param['cl_b_'+si][3]
if RPP is not None:
zi += tensor.nnet.conv.conv2d(self.spad2d(RPP, padw, padw), param['cl_WRPP_'+si][0]).eval()
zf += tensor.nnet.conv.conv2d(self.spad2d(RPP, padw, padw), param['cl_WRPP_'+si][1]).eval()
zc += tensor.nnet.conv.conv2d(self.spad2d(RPP, padw, padw), param['cl_WRPP_'+si][2]).eval()
zo += tensor.nnet.conv.conv2d(self.spad2d(RPP, padw, padw), param['cl_WRPP_'+si][3]).eval()
i = self.sigmoid(zi)
f = self.sigmoid(zf)
Cnext = f*C + np.tanh(zc)
o = self.sigmoid(zo)
Rnext = o * np.tanh(Cnext)
return (Rnext, Cnext)
def check_forward(self, h_data, xs_data, ws_data, bs_data):
h = chainer.Variable(h_data)
xs = [chainer.Variable(x) for x in xs_data]
ws = [[chainer.Variable(w) for w in ws]
for ws in ws_data]
bs = [[chainer.Variable(b) for b in bs]
for bs in bs_data]
hy, ys = functions.n_step_bigru(
self.n_layers, self.dropout, h, ws, bs, xs)
xs_next = self.xs
e_hy = self.hx.copy()
for layer in range(self.n_layers):
# forward
di = 0
xf = []
layer_idx = layer * 2 + di
w = self.ws[layer_idx]
b = self.bs[layer_idx]
for ind in range(self.length):
x = xs_next[ind]
batch = x.shape[0]
h_prev = e_hy[layer_idx, :batch]
# GRU
z = sigmoid(x.dot(w[1].T) + h_prev.dot(w[4].T) + b[1] + b[4])
r = sigmoid(x.dot(w[0].T) + h_prev.dot(w[3].T) + b[0] + b[3])
h_bar = numpy.tanh(x.dot(w[2].T) +
r *
((h_prev).dot(w[5].T) + b[5]) + b[2])
e_h = (1 - z) * h_bar + z * h_prev
e_hy[layer_idx, :batch] = e_h
xf.append(e_h)
# backward
di = 1
xb = []
layer_idx = layer * 2 + di
w = self.ws[layer_idx]
b = self.bs[layer_idx]
for ind in reversed(range(self.length)):
x = xs_next[ind]
batch = x.shape[0]
h_prev = e_hy[layer_idx, :batch]
# GRU
z = sigmoid(x.dot(w[1].T) + h_prev.dot(w[4].T) + b[1] + b[4])
r = sigmoid(x.dot(w[0].T) + h_prev.dot(w[3].T) + b[0] + b[3])
h_bar = numpy.tanh(x.dot(w[2].T) +
r *
((h_prev).dot(w[5].T) + b[5]) + b[2])
e_h = (1 - z) * h_bar + z * h_prev
e_hy[layer_idx, :batch] = e_h
xb.append(e_h)
xb.reverse()
xs_next = [numpy.concatenate([hfi, hbi], axis=1) for (hfi, hbi) in
zip(xf, xb)]
for k, (ysi, xsi) in enumerate(zip(ys, xs_next)):
testing.assert_allclose(ysi.data, xsi, rtol=1e-4, atol=1e-4)
testing.assert_allclose(hy.data, e_hy, rtol=1e-4, atol=1e-4)
def LSTMtick(x, h_prev, c_prev):
t = 0
# setup the input vector
Hin = np.zeros((1,WLSTM.shape[0])) # xt, ht-1, bias
Hin[t,0] = 1
Hin[t,1:1+d] = x
Hin[t,1+d:] = h_prev
# LSTM tick forward
IFOG = np.zeros((1, d * 4))
IFOGf = np.zeros((1, d * 4))
C = np.zeros((1, d))
Hout = np.zeros((1, d))
IFOG[t] = Hin[t].dot(WLSTM)
IFOGf[t,:3*d] = 1.0/(1.0+np.exp(-IFOG[t,:3*d]))
IFOGf[t,3*d:] = np.tanh(IFOG[t, 3*d:])
# C[t] = IFOGf[t,:d] * IFOGf[t, 3*d:] + IFOGf[t,d:2*d] * c_prev
C[t] = (IFOGf[t,d:2*d] * IFOGf[t, 3*d:]) - IFOGf[t, 3*d:]+ IFOGf[t,d:2*d] * c_prev
if tanhC_version:
Hout[t] = IFOGf[t,2*d:3*d] * np.tanh(C[t])
else:
Hout[t] = IFOGf[t,2*d:3*d] * C[t]
Y = Hout.dot(Wd) + bd
return (Y, Hout, C) # return output, new hidden, new cell
def forward_prop_node(self, node, depth=-1, test=False):
cost = 0.0
if node.isLeaf:
node.c = self.W_in.dot(self.L[:, node.word]) + self.b_in
node.o = sigmoid(self.W_out.dot(self.L[:, node.word]) + self.b_out)
node.ct = np.tanh(node.c)
if not test:
node.mask = np.random.binomial(1, self.node_keep, self.mem_dim)
node.hActs1 = node.o * node.ct * node.mask
else:
node.hActs1 = node.o * node.ct * self.node_keep
else:
cost_left = self.forward_prop_node(node.left, depth - 1)
cost_right = self.forward_prop_node(node.right, depth - 2)
cost += (cost_left + cost_right)
children = np.hstack((node.left.hActs1, node.right.hActs1))
node.i = sigmoid(self.Ui.dot(children) + self.bi)
node.f_l = sigmoid(self.Uf_l.dot(children) + self.bf)
node.f_r = sigmoid(self.Uf_r.dot(children) + self.bf)
node.o = sigmoid(self.Uo.dot(children) + self.bo)
node.u = np.tanh(self.Uu.dot(children) + self.bu)
node.c = node.i * node.u + node.f_l * node.left.c + node.f_r * node.right.c
node.ct = np.tanh(node.c)
if not test:
node.mask = np.random.binomial(1, self.node_keep, self.mem_dim)
node.hActs1 = node.o * node.ct * node.mask
else:
node.hActs1 = node.o * node.ct * self.node_keep
return cost
def test_one_step(self):
h0 = tensor.matrix('h0')
c0 = tensor.matrix('c0')
x = tensor.matrix('x')
h1, c1 = self.lstm.apply(x, h0, c0, iterate=False)
next_h = theano.function(inputs=[x, h0, c0], outputs=[h1])
h0_val = 0.1 * numpy.array([[1, 1, 0], [0, 1, 1]],
dtype=theano.config.floatX)
c0_val = 0.1 * numpy.array([[1, 1, 0], [0, 1, 1]],
dtype=theano.config.floatX)
x_val = 0.1 * numpy.array([range(12), range(12, 24)],
dtype=theano.config.floatX)
W_state_val = 2 * numpy.ones((3, 12), dtype=theano.config.floatX)
W_cell_to_in = 2 * numpy.ones((3,), dtype=theano.config.floatX)
W_cell_to_out = 2 * numpy.ones((3,), dtype=theano.config.floatX)
W_cell_to_forget = 2 * numpy.ones((3,), dtype=theano.config.floatX)
# omitting biases because they are zero
activation = numpy.dot(h0_val, W_state_val) + x_val
def sigmoid(x):
return 1. / (1. + numpy.exp(-x))
i_t = sigmoid(activation[:, :3] + c0_val * W_cell_to_in)
f_t = sigmoid(activation[:, 3:6] + c0_val * W_cell_to_forget)
next_cells = f_t * c0_val + i_t * numpy.tanh(activation[:, 6:9])
o_t = sigmoid(activation[:, 9:12] +
next_cells * W_cell_to_out)
h1_val = o_t * numpy.tanh(next_cells)
assert_allclose(h1_val, next_h(x_val, h0_val, c0_val)[0],
rtol=1e-6)
def check_forward(self, c_prev1_data, c_prev2_data, x1_data, x2_data):
c_prev1 = chainer.Variable(c_prev1_data)
c_prev2 = chainer.Variable(c_prev2_data)
x1 = chainer.Variable(x1_data)
x2 = chainer.Variable(x2_data)
c, h = functions.slstm(c_prev1, c_prev2, x1, x2)
self.assertEqual(c.data.dtype, numpy.float32)
self.assertEqual(h.data.dtype, numpy.float32)
# Compute expected out
a1_in = self.x1[:, [0, 4]]
i1_in = self.x1[:, [1, 5]]
f1_in = self.x1[:, [2, 6]]
o1_in = self.x1[:, [3, 7]]
a2_in = self.x2[:, [0, 4]]
i2_in = self.x2[:, [1, 5]]
f2_in = self.x2[:, [2, 6]]
o2_in = self.x2[:, [3, 7]]
c_expect = _sigmoid(i1_in) * numpy.tanh(a1_in) + \
_sigmoid(i2_in) * numpy.tanh(a2_in) + \
_sigmoid(f1_in) * self.c_prev1 + \
_sigmoid(f2_in) * self.c_prev2
h_expect = _sigmoid(o1_in + o2_in) * numpy.tanh(c_expect)
gradient_check.assert_allclose(c_expect, c.data)
gradient_check.assert_allclose(h_expect, h.data)
def train(self, trainData):
recordNum = len(trainData)
trainData = np.hstack(([[1]]*recordNum, trainData))
self.w1 = np.random.uniform(-self.r, self.r, (self.d + 1, self.M))
self.w2 = np.random.uniform(-self.r, self.r, (self.M + 1,1))
for t in xrange(0, self.T):
# if t % 10000 == 0:
# print t
n = random.randint(0,recordNum-1)
x0 = trainData[n,0:3]
y = trainData[n, 3]
s1 = np.dot(self.w1.T, x0)
s1.shape = (self.M,1)
x = np.tanh(s1)
x1 = np.vstack(([1], x))
x1.shape = (self.M+1,1)
# print 'w2.shape=',self.w2.shape,self.w2
# print 'x1.shape=',x1.shape,x1
s2 = np.dot(self.w2.T, x1)
yPredict = np.tanh(s2)
e = y - yPredict
delta2 = -2 * (y - yPredict) * derivative_tanh(s2)
x = x1 * delta2
self.w2 = self.w2 - self.eta * x1 * delta2
# if t==0:
# print "delta2.shape=",delta2.shape
# print "w2.shape=",self.w2.shape
# print derivative_tanh(s1).shape
# print 'w2.shape=',self.w2.shape
# print 's1.shape=',s1.shape
delta1 = delta2 * self.w2[1:] * derivative_tanh(s1)
x0.shape = (3,1)
# print 'delta1.shape=',delta1.shape
self.w1 = self.w1 - self.eta * np.dot(x0, delta1.T)
def forward_compute(self):
if self.last_layer.type == CONV_TYPE:
m = np.size(self.last_layer.images, 0)
self.images = np.tanh(self.last_layer.images)
self.value = self.images.reshape(m, self.channel*self.height*self.width)
else:
self.value = np.tanh(self.last_layer.value)
def input_node(self, xt):
if self.ht_min_1 != []:
# If a previous step's activation was given, include it in the calculation
# of the current step's activation.
return np.tanh(np.dot(self.Wi, xt) + np.dot(self.W_ht_min_1, self.ht_min_1) + self.bi)
else:
return np.tanh(np.dot(self.Wi, xt) + self.bi)
def generate_nonuniform_grid_arctanh(inputFilename,slope,psi0):
#Calculates psi(psiN), where psiN is uniform and psi is nonuniform
# psi = h(psiN)
# h = Atanh(P(psiN)), where P = a2 s**psiN + a1*psiN + a0
# polynomial determined to make h(psiMin) = psiMin, h(psiMax) = psiMax
# and have the slope slope at psi0
inputs = perfectInput(inputFilename)
Npsi = inputs.Npsi
psiAHat = inputs.psiAHat #psiAHat for a would-be uniform map
psiN = inputs.psi #array of uniform grid points
psiNMin = inputs.psiMin
psiNMax = inputs.psiMax
t1 = numpy.tanh(psiNMin)
t2 = numpy.tanh(psiNMax)
k = slope
A = numpy.array([[psiNMin**3,psiNMin**2,psiNMin,1],[psiNMax**3,psiNMax**2,psiNMax,1],[psi0**3,psi0**2,psi0,1],[3*psi0**2,2*psi0,1,0]])
b = numpy.array([t1,t2,0,k])
coef=numpy.linalg.solve(A,b)
h = (lambda psiN: psiAHat*numpy.arctanh(coef[0]*psiN**3 + coef[1]*psiN**2 + coef[2]*psiN+coef[3]))
dhdpsiN = (lambda psiN: psiAHat*(3*coef[0]*psiN**2 + 2*coef[1]*psiN + coef[2])/(1+(coef[0]*psiN**3 + coef[1]*psiN**2 + coef[2]*psiN+coef[3])**2))
psi=[h(pN) for pN in psiN]
dpsidpsiN= [dhdpsiN(pN) for pN in psiN]
create_psiAHat_of_Npsi("psiAHat.h5",Npsi,dpsidpsiN,psi)
return (psi,dpsidpsiN)
def sigmoid_kernel(X, Y=None, gamma=None, coef0=1):
"""
Compute the sigmoid kernel between X and Y::
K(X, Y) = tanh(gamma <X, Y> + coef0)
Parameters
----------
X : ndarray of shape (n_samples_1, n_features)
Y : ndarray of shape (n_samples_2, n_features)
coef0 : int, default 1
Returns
-------
Gram matrix: array of shape (n_samples_1, n_samples_2)
"""
X, Y = check_pairwise_arrays(X, Y)
if gamma is None:
gamma = 1.0 / X.shape[1]
K = safe_sparse_dot(X, Y.T, dense_output=True)
K *= gamma
K += coef0
np.tanh(K, K) # compute tanh in-place
return K
def winf(x_hist):
pre_u = x_hist[0]
post_u = x_hist[-1]
# parameters
n = len(pre_u)
vec_pre = 0.5 * (np.ones(n) + np.tanh(a_pre * pre_u + b_pre))
return (wmax / 2.0) * np.outer((np.ones(n) + np.tanh(a_post * post_u + b_post)), vec_pre)
def calculate_KL(i):
x=x_test[i]
y = t_test[i]
[W1,W2,W3,W4,W5,b1,b2,b3,b4,b5,pi] = params
num_model = len(pi)
dimZ = W2.shape[0]/num_model
h_encoder = np.tanh(np.dot(W1,x) + b1[:,0])
KL = []
b=[x for x in range(0,num_model)]
j = np.random.uniform(0,1)
pi_soft = np.exp(pi)/np.sum(np.exp(pi))
i = 0
for i in range(0,num_model):
if pi_soft[i] > j :
break
else:
j -= pi_soft[i]
mu = np.dot(W2[int(i)*dimZ:(1+int(i))*dimZ],h_encoder) + b2[int(i)*dimZ:(1+int(i))*dimZ][0]
log_sigma = (0.5*(np.dot(W3[int(i)*dimZ:(1+int(i))*dimZ],h_encoder)))+ b3[i*dimZ:(1+i)*dimZ][0]
k = dimZ
eps = np.random.normal(0,1,[dimZ,1])
z = mu + np.exp(log_sigma)*eps[:,0]
qxz = np.power(2*np.pi,-dimZ/2)*np.exp(np.sum(log_sigma))*np.exp(-0.5*np.dot((z-mu)*(z-mu),np.exp(log_sigma).T))
pz=np.power(2*np.pi,-dimZ/2)*np.exp(-0.5*np.sum(np.square(z)))
pz = np.exp(-0.5*np.sum(np.square(z)))
kl = np.log((qxz+0.0000000000000001)/(pz+0.0000000000000001))
KL.append(kl)
h_decoder = np.tanh(np.dot(W4,z) + b4[:,0])
o = 1/(1+np.exp(-np.dot(W5,h_decoder) + b5[:,0]))
img = im.fromarray(o.reshape((28,28)))
#img.save('image.png')
logpxz = np.sum(x*np.log(o)+(1.0-x)*np.log(1.0-o))
return np.sum(KL)
def getImpedance(m1d,sigma,freq):
"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
:param numpy.ndarray, vector sigma: Physical property corresponding with the mesh.
:param numpy.ndarray, vector freq: Frequencies to calculate data at.
"""
# Initiate the impedances
Z1d = np.empty(len(freq) , dtype='complex')
h = m1d.hx #vectorNx[:-1]
# Start the process
for nrFr, fr in enumerate(freq):
om = 2*np.pi*fr
Zall = np.empty(len(h)+1,dtype='complex')
# Calculate the impedance for the bottom layer
Zall[0] = (mu_0*om)/np.sqrt(mu_0*eps_0*(om)**2 - 1j*mu_0*sigma[0]*om)
for nr,hi in enumerate(h):
# Calculate the wave number
# print(nr,sigma[nr])
k = np.sqrt(mu_0*eps_0*om**2 - 1j*mu_0*sigma[nr]*om)
Z = (mu_0*om)/k
Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
#pdb.set_trace()
Z1d[nrFr] = Zall[-1]
return Z1d
def ff(self, x):
data = oh.hcol(x, self.x_len)
self.x = data
i_arg = np.dot(self.w_x_i, data) + np.dot(self.w_h_i, self.hidden)
i_arg += np.dot(self.w_c_i, self.cell) + self.w_i
self.gate_i = sig(i_arg)
f_arg = np.dot(self.w_x_f, data) + np.dot(self.w_h_f, self.hidden)
f_arg += np.dot(self.w_c_f, self.cell) + self.w_f
self.gate_f = sig(f_arg)
c_arg = np.dot(self.w_x_c, data) + np.dot(self.w_h_c, self.hidden)
self.c_tan = np.tanh(c_arg + self.w_c)
self.cell = self.gate_f * self.cell + self.gate_i * self.c_tan
o_arg = np.dot(self.w_x_o, data) + np.dot(self.w_h_o, self.hidden)
o_arg += np.dot(self.w_c_o, self.cell) + self.w_o
self.gate_o = sig(o_arg)
self.hidden = self.gate_o * np.tanh(self.cell)
self.p = softmax(self.hidden)
return np.argmax(self.p)
def transtanh_(b=None):
"""
unused fortran translation of Newton-Raphson solver for
solving the transcendental equation
b=tanh(delta)/delta
"""
if (b > 1.0):
print ' Error form transtanh: Can not be gridded '
return delta
rlim=1.e-6
nmax=100000
delta=1.0
delta_old=delta
for n in range(nmax):
f=delta / (np.tanh(0.5 * delta) + 1.0 * 10 ** (- 60)) - 2.0 / b
df=(np.tanh(0.5 * delta) - delta * (1 - np.tanh(0.5 * delta) ** 2)) / (np.tanh(0.5 * delta) ** 2 + 1.0 * 10 ** (- 60))
delta=delta - 0.5 * f / df
res = np.abs((delta - delta_old)/ delta_old)
if res < rlim: return delta
if ((n == nmax) and ( res > rlim)):
print ' Convergence problem in transtanh dist. function !!! '
print ' residual ',((delta - delta_old) / delta_old)
print 'n= ', n, ' nmax=',nmax, ' delta=', delta, ' delta_old=',delta_old,' rlim=',rlim
delta_old= delta
return delta
def test_output_gate(self):
self.set_weights(self.lstm.right, 1)
X = np.ones((1, 1))
S = np.zeros((1, 1))
H = np.zeros((1, 1))
step = self.make_lstm_step(self.lstm)
input_gate = logistic(X)
state = np.tanh(1) * input_gate
output_gate = logistic(1)
out = output_gate * np.tanh(state)
lstm_out, lstm_state = step(X, H, S)
np.testing.assert_almost_equal(lstm_out, out)
np.testing.assert_almost_equal(lstm_state, state)
Wo = self.lstm.right.get_parameter_value('W_ox')
self.lstm.right.set_parameter_value('W_ox', Wo * 0)
input_gate = logistic(X)
state = np.tanh(1) * input_gate
output_gate = logistic(0)
out = output_gate * np.tanh(state)
lstm_out, lstm_state = step(X, H, S)
np.testing.assert_almost_equal(lstm_out, out)
np.testing.assert_almost_equal(lstm_state, state)
def classify(self, x):
# change to TANH!!!!!!
W1_bias = np.vstack((self.w1_hid, self.b1_hid))
x1_bias = np.append(x, [1])
y = np.tanh(np.transpose(np.dot(x1_bias, W1_bias)))
def squash_y(el):
if el > 0.999:
return 0.999
if el < 0.001:
return 0.001
return el
squash_y = np.vectorize(squash_y)
x2 = squash_y(y)
W2_bias = np.vstack((self.w2_hid, self.b2_hid))
x2_bias = np.append(x2, [1])
y = np.tanh(np.transpose(np.dot(x2_bias, W2_bias)))
x3 = squash_y(y)
W_out_bias = np.vstack((self.w_out, self.b_out))
x3_bias = np.append(x3, [1])
y = np.tanh(np.transpose(np.dot(x3_bias, W_out_bias)))
y = squash_y(y)
return (x, x2, x3, y)
def step_forward(self, x, prev_h, prev_c):
"""
x: input feature (N, D)
prev_h: hidden state from the previous timestep (N, H)
prev_c: previous cell state (N, H)
self.params[self.wx_name]: input-to-hidden weights (D, 4H)
self.params[self.wh_name]: hidden-to-hidden weights (H, 4H)
self.params[self.b_name]: biases (4H,)
next_h: next hidden state (N, H)
next_c: next cell state (N, H)
meta: variables needed for the backward pass
"""
next_h, next_c, meta = None, None, None
#############################################################################
# TODO: Implement the forward pass for a single timestep of an LSTM. #
# You may want to use the numerically stable sigmoid implementation above. #
#############################################################################
activation = x.dot(self.params[self.wx_name]) + prev_h.dot(self.params[self.wh_name]) + self.params[self.b_name]
ai, af, ao, ag = np.hsplit(activation, 4)
#a[:, :H], a[:, H:2*H], a[:, 2*H:3*H], a[:,3*H:]
i = sigmoid(ai)
f = sigmoid(af)
o = sigmoid(ao)
g = np.tanh(ag)
next_c = np.multiply(f, prev_c) + np.multiply(i, g)
next_h = np.multiply(o, np.tanh(next_c))
meta = [x, i, f, o, g, prev_c, next_c, prev_h, next_h]
##############################################################################
# END OF YOUR CODE #
##############################################################################
return next_h, next_c, meta
def fprop(self,input): if self.layer_no == 0: self.fprop_in = input else: self.fprop_in = numpy.tanh(input) self.fprop_in = numpy.append(self.fprop_in, numpy.ones(shape=(self.fprop_in.shape[0],1)), 1) return numpy.tanh(numpy.dot(self.fprop_in, self.W))
def makeTanh(self, res, a, c, x, val_min, val_max):
span = val_max - val_min
x_dist, y_dist = np.mgrid[-x:x:1j*res, 0:res]
tex = (1 + a * cos(pi*x_dist/2)) * (tanh(x_dist+c) - tanh(x_dist-c))
tex /= (np.max(tex) / span) #normalize and scale
tex += val_min #shift to start with val_min instead of 0
return tex
def sigmoid_kernel(X, Y, gamma=0, coef0=1):
"""
Compute the sigmoid kernel between X and Y.
K(X, Y) = tanh(gamma <X, Y> + coef0)
Parameters
----------
X: array of shape (n_samples_1, n_features)
Y: array of shape (n_samples_2, n_features)
degree: int
Returns
-------
Gram matrix: array of shape (n_samples_1, n_samples_2)
"""
if gamma == 0:
gamma = 1.0 / X.shape[1]
K = linear_kernel(X, Y)
K *= gamma
K += coef0
np.tanh(K, K) # compute tanh in-place
return K
def cue_conceptor(self,
pattern,
init_washout=100,
cue_length=30,
lambda_adapt_cue=0.01):
"""
Cue conceptor in following three stages:
1. Initial washout
2. Cueing
@param pattern: input pattern
@param init_washout: initial washout length
@param cue_length: cueing length
"""
x=np.zeros((self.num_neuron,1))
for n in xrange(init_washout):
u=pattern[:,n][None].T
x=np.tanh(self.W.dot(x)+self.W_in.dot(u)+self.bias)
C=np.zeros((self.num_neuron, self.num_neuron))
for n in xrange(cue_length):
u=pattern[:,n+init_washout][None].T
x=np.tanh(self.W.dot(x)+self.W_in.dot(u)+self.bias)
C+=self.adapt_conceptor(C, x, lambda_adapt_cue)
return C, x
lambda features, name=None: np.divide(features, (np.abs(features) + 1)))
sqrt = utils.copy_docstring(tf.math.sqrt, lambda x, name=None: np.sqrt(x))
square = utils.copy_docstring(tf.math.square,
lambda x, name=None: np.square(x))
squared_difference = utils.copy_docstring(
tf.math.squared_difference, lambda x, y, name=None: np.square(x - y))
subtract = utils.copy_docstring(tf.math.subtract,
lambda x, y, name=None: np.subtract(x, y))
tan = utils.copy_docstring(tf.math.tan, lambda x, name=None: np.tan(x))
tanh = utils.copy_docstring(tf.math.tanh, lambda x, name=None: np.tanh(x))
top_k = utils.copy_docstring(tf.math.top_k, _top_k)
truediv = utils.copy_docstring(tf.math.truediv,
lambda x, y, name=None: np.true_divide(x, y))
# unsorted_segment_max = utils.copy_docstring(
# tf.math.unsorted_segment_max,
# lambda data, segment_ids, num_segments, name=None: (
# np.unsorted_segment_max))
# unsorted_segment_mean = utils.copy_docstring(
# tf.math.unsorted_segment_mean,
# lambda data, segment_ids, num_segments, name=None: (
# np.unsorted_segment_mean))
def tanh(x):
return np.tanh(x)
def backProp(self,node,error=None):
dc_dsc = np.diag((1-node.hActs1**2).flatten())
dh_dc = dotW(dc_dsc, np.diag(self.o.flatten()))
# Inherited error
if node.parent == None:
error_at_h = error.astype('float32').squeeze()
error_at_c = dot(dh_dc, error_at_h)
if node.parent != None:
[in_ho, in_hi, in_hu] = error[0:3]
in_hl = error[3:3+self.paramDim]
in_hr = error[3+self.paramDim:3+2*self.paramDim]
in_cc = error[3+2*self.paramDim]
if node in node.parent.left:
idx = min(node.idx, self.paramDim-1)
error_at_h = dot(self.Uo[idx].T, in_ho) + dot(self.Ui[idx].T, in_hi) + dot(self.Uu[idx].T, in_hu)
for j in range(self.paramDim):
error_at_h += dot(self.Ul[j][idx].T, in_hl[j])
error_at_h += dot(self.Ur[j][idx].T, in_hr[j])
error_at_c = dot(np.diag(self.l[idx].flatten()), in_cc) + dot(dh_dc, error_at_h)
if node in node.parent.right:
idx = min(node.idx, self.paramDim-1)
error_at_h = dot(self.Vo[idx].T, in_ho) + dot(self.Vi[idx].T, in_hi) + dot(self.Vu[idx].T, in_hu)
for j in range(self.paramDim):
error_at_h += dot(self.Vl[j][idx].T, in_hl[j])
error_at_h += dot(self.Vr[j][idx].T, in_hr[j])
error_at_c = dot(np.diag(self.r[idx].flatten()), in_cc) + dot(dh_dc, error_at_h)
# Error passed to children
# o
do_dso = np.diag(np.multiply(self.o, 1-self.o).flatten())
dh_dso = dotW(do_dso, np.diag(np.tanh(node.hActs1).flatten()))
# i
di_dsi = np.diag(np.multiply(self.i, 1-self.i).flatten())
dc_dsi = dotW(di_dsi, np.diag(self.u.flatten()))
# u
du_dsu = np.diag((1-self.u**2).flatten())
dc_dsu = dotW(du_dsu, np.diag(self.i.flatten()))
if not node.isLeaf:
# l
dl_dsl = []
dc_dsl = []
for j in range(self.paramDim):
dc_dsl.append(np.zeros((self.middleDim, self.middleDim), dtype='float32'))
for j in range(self.paramDim):
dl_dsl.append(np.diag(np.multiply(self.l[j], 1-self.l[j]).flatten()))
for j in node.left:
idx = min(j.idx, self.paramDim-1)
dc_dsl[idx] += dotW(dl_dsl[idx], np.diag(j.hActs1.flatten()))
# r
dr_dsr = []
dc_dsr = []
for j in range(self.paramDim):
dc_dsr.append(np.zeros((self.middleDim, self.middleDim), dtype='float32'))
for j in range(self.paramDim):
dr_dsr.append(np.diag(np.multiply(self.r[j], 1-self.r[j]).flatten()))
for j in node.right:
idx = min(j.idx, self.paramDim-1)
dc_dsr[idx] += dotW(dr_dsr[idx], np.diag(j.hActs1.flatten()))
# Error out
dJ_dso = dot(dh_dso, error_at_h)
dJ_dsi = dot(dc_dsi, error_at_c)
dJ_dsu = dot(dc_dsu, error_at_c)
dJ_dsl = []
dJ_dsr = []
for j in range(self.paramDim):
dJ_dsl.append(dot(dc_dsl[j], error_at_c))
dJ_dsr.append(dot(dc_dsr[j], error_at_c))
out_cc = error_at_c
error_out = [dJ_dso, dJ_dsi, dJ_dsu]
for j in range(self.paramDim):
error_out.append(dJ_dsl[j])
for j in range(self.paramDim):
error_out.append(dJ_dsr[j])
error_out.append(out_cc)
# Parameter Gradients
if not node.isLeaf:
x = np.reshape(self.L[node.word,:], (self.wvecDim, 1))
# Bias
self.dbo += dJ_dso.flatten()
self.dbi += dJ_dsi.flatten()
self.dbu += dJ_dsu.flatten()
for j in range(self.paramDim):
self.dbf += dJ_dsl[j].flatten()
self.dbf += dJ_dsr[j].flatten()
# Us
for j in node.left:
idx = min(j.idx, self.paramDim-1)
self.dUo[idx] += dotW(dJ_dso[:,None], j.hActs2[None,:])
self.dUi[idx] += dotW(dJ_dsi[:,None], j.hActs2[None,:])
self.dUu[idx] += dotW(dJ_dsu[:,None], j.hActs2[None,:])
for k in range(self.paramDim):
self.dUl[k][idx] += dotW(dJ_dsl[k][:,None], j.hActs2[None,:])
self.dUr[k][idx] += dotW(dJ_dsr[k][:,None], j.hActs2[None,:])
# Vs
for j in node.right:
idx = min(j.idx, self.paramDim-1)
self.dVo[idx] += dotW(dJ_dso[:,None], j.hActs2[None,:])
self.dVi[idx] += dotW(dJ_dsi[:,None], j.hActs2[None,:])
self.dVu[idx] += dotW(dJ_dsu[:,None], j.hActs2[None,:])
for k in range(self.paramDim):
self.dVl[k][idx] += dotW(dJ_dsl[k][:,None], j.hActs2[None,:])
self.dVr[k][idx] += dotW(dJ_dsr[k][:,None], j.hActs2[None,:])
# Ws
self.dWo += dotW(dJ_dso[:,None], x.T)
self.dWu += dotW(dJ_dsu[:,None], x.T)
self.dWi += dotW(dJ_dsi[:,None], x.T)
for j in range(self.paramDim):
self.dWf += dotW(dJ_dsl[j][:,None], x.T)
self.dWf += dotW(dJ_dsr[j][:,None], x.T)
# L
temp = dot(self.Wo.T, dJ_dso).flatten() + dot(self.Wi.T, dJ_dsi).flatten() + dot(self.Wu.T, dJ_dsu).flatten()
for j in range(self.paramDim):
temp += dot(self.Wf.T, dJ_dsl[j]).flatten()
temp += dot(self.Wf.T, dJ_dsr[j]).flatten()
self.dL[node.word] = temp
# Recursion
for j in node.left:
self.backProp(j, error_out)
for j in node.right:
self.backProp(j, error_out)
else:
x = np.reshape(self.L[node.word,:], (self.wvecDim, 1))
dJ_dso = dot(dh_dso, error_at_h)
dJ_dsi = dot(dc_dsi, error_at_c)
dJ_dsu = dot(dc_dsu, error_at_c)
# Bias
self.dbo += dJ_dso.flatten()
self.dbi += dJ_dsi.flatten()
self.dbu += dJ_dsu.flatten()
# Ws
self.dWo += dotW(dJ_dso[:,None], x.T)
self.dWi += dotW(dJ_dsi[:,None], x.T)
self.dWu += dotW(dJ_dsu[:,None], x.T)
# L
self.dL[node.word] = dot(self.Wo.T, dJ_dso).flatten() + dot(self.Wi.T, dJ_dsi).flatten() + dot(self.Wu.T, dJ_dsu).flatten()
def forwardProp(self,node):
cost = total = 0.0
# this is exactly the same setup as forwardProp in rnn.py
x = np.reshape(self.L[node.word,:], (self.wvecDim, 1)).squeeze()
if node.isLeaf:
self.i = sigmoid(dot(self.Wi, x)+self.bi)
self.o = sigmoid(dot(self.Wo, x)+self.bo)
self.u = np.tanh(dot(self.Wu, x)+self.bu)
node.hActs1 = np.multiply(self.i, self.u)
else:
for j in node.left:
total += self.forwardProp(j)
for j in node.right:
total += self.forwardProp(j)
si = add(dot(self.Wi, x),self.bi)
for j in node.left:
idx = min(j.idx, self.paramDim-1)
si += dot(self.Ui[idx], j.hActs2)
for j in node.right:
idx = min(j.idx, self.paramDim-1)
si += dot(self.Vi[idx], j.hActs2)
self.i = sigmoid(si)
su = add(dot(self.Wu, x),self.bu)
for j in node.left:
idx = min(j.idx, self.paramDim-1)
su += dot(self.Uu[idx], j.hActs2)
for j in node.right:
idx = min(j.idx, self.paramDim-1)
su += dot(self.Vu[idx], j.hActs2)
self.u = np.tanh(su)
so = add(dot(self.Wo, x),self.bo)
for j in node.left:
idx = min(j.idx, self.paramDim-1)
so += dot(self.Uo[idx], j.hActs2)
for j in node.right:
idx = min(j.idx, self.paramDim-1)
so += dot(self.Vo[idx], j.hActs2)
self.o = sigmoid(so)
temp = add(dot(self.Wf, x),self.bf)
sl = np.zeros((self.middleDim), dtype='float32')
sr = np.zeros((self.middleDim), dtype='float32')
for j in range(self.paramDim):
sl *= 0
sl += temp
for k in node.left:
idx2 = min(k.idx, self.paramDim-1)
sl += dot(self.Ul[j][idx2], k.hActs2)
for k in node.right:
idx2 = min(k.idx, self.paramDim-1)
sl += dot(self.Vl[j][idx2], k.hActs2)
self.l[j] = sigmoid(sl)
for j in range(self.paramDim):
sr *= 0
sr += temp
for k in node.left:
idx2 = min(k.idx, self.paramDim-1)
sr += dot(self.Ur[j][idx2], k.hActs2)
for k in node.right:
idx2 = min(k.idx, self.paramDim-1)
sr += dot(self.Vr[j][idx2], k.hActs2)
self.r[j] = sigmoid(sr)
node.hActs1 = np.multiply(self.i, self.u)
for j in node.left:
idx = min(j.idx, self.paramDim-1)
node.hActs1 += np.multiply(self.l[idx], j.hActs1)
for j in node.right:
idx = min(j.idx, self.paramDim-1)
node.hActs1 += np.multiply(self.r[idx], j.hActs1)
node.hActs2 = np.multiply(self.o, tanh(node.hActs1))
return total + 1
def forward(self, x):
self.last_input = x
return np.tanh(x)
def tanh(self):
if self.autograd:
return Tensor(np.tanh(self.data),autograd=True,creators=[self],creation_op='tanh')
return Tensor(np.tanh(self.data))
def _logistic(self, x):
'''直接使用1.0 / (1.0 + np.exp(-x))容易发警告“RuntimeWarning: overflowencountered in exp”，
转换成如下等价形式后算法会更稳定
'''
return 0.5 * (1 + np.tanh(0.5 * x))
def tanh(self, Z):
A = np.tanh(Z)
cache = {}
cache["Z"] = Z
return A, cache
def sigmoid(x):
return (numpy.tanh(x / 2) + 1) / 2
def tanh_der(self, dA, cache):
Z = cache["Z"]
dZ = dA * (1 - np.tanh(Z)**2)
return dZ
def gfunc(x):
gx = np.tanh(x)
dg = 1 - gx**2
return gx, dg
def E_QHO_avg_theo(beta):
"""Uso: devuelve valor de energía interna para el QHO unidimensional"""
return 0.5 / np.tanh(0.5 * beta)
def fun_ed_aimless(s, d0, r):
# CC1/2 fitting equation used in Aimless, suggested by Ed Pozharski
return 0.5 * (1 - numpy.tanh((s - d0) / r))
def tanh(x, derive=False):
if derive:
return np.power(1 / np.cosh(x), 2)
return np.tanh(x)
def tanh_deriv(self, s):
return 1.0 - np.tanh(s)**2
"""
tanh
~~~~
Plots a graph of the tanh function."""
import numpy as np
import matplotlib.pyplot as plt
z = np.arange(-5, 5, .1)
t = np.tanh(z)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(z, t)
ax.set_ylim([-1.0, 1.0])
ax.set_xlim([-5,5])
ax.grid(True, which='major')
#grid x-axis line color
a = ax.get_xgridlines()
b = a[3]
b.set_color('black')
b.set_linewidth(1.5)
#grid y-axis line color
c = ax.get_ygridlines()
d = c[4]
d.set_color('black')
d.set_linewidth(1.5)
#labels
ax.set_xlabel('z')
ax.set_title('tanh function')
def __call__(self, x):
return np.log(abs(self.p*np.tanh(self.q*x*np.cos(self.r*x))))
def forward_cpu(self, x):
y = utils.force_array(numpy.tanh(x[0]))
self.retain_outputs((0,))
self._use_cudnn = False
return y,
def __activation_derivative(self, X):
return 1.0 - np.tanh(X)**2 #sigmoid-derivative: X * (1-X)
def forwardPropagate(self, X):
self.Z1 = np.add(np.matmul(self.W1, X), self.b1)
self.A1 = np.tanh(self.Z1)
self.Z2 = np.add(np.matmul(self.W2, self.A1), self.b2)
self.A2 = self.sigmoid(self.Z2)
return self.A2
def test_ampere_yee2D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
Bx = np.zeros([
layout.allocSize(tv.interpOrder, tv.BxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BxCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
By = np.zeros([
layout.allocSize(tv.interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ByCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Bz = np.zeros([
layout.allocSize(tv.interpOrder, tv.BzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jx = np.zeros([
layout.allocSize(tv.interpOrder, tv.JxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JxCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jy = np.zeros([
layout.allocSize(tv.interpOrder, tv.JyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JyCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jz = np.zeros([
layout.allocSize(tv.interpOrder, tv.JzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
w1 = np.zeros_like(Jz)
w2 = np.zeros_like(Jz)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[1])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[1])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
Bx = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_primal),
np.sin(2 * np.pi / tv.domainSize[1] * y_dual),
axes=0)
By = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_dual),
np.tanh(2 * np.pi / tv.domainSize[1] * y_primal),
axes=0)
Bz = np.tensordot(np.sin(2 * np.pi / tv.domainSize[0] * x_dual),
np.tanh(2 * np.pi / tv.domainSize[1] * y_dual),
axes=0)
# Jx = dyBz
# Jy = -dxBz
# Jz = dxBy - dyBx
Jx[:,
psi_p_Y:pei_p_Y + 1] = (Bz[:, psi_d_Y:pei_d_Y + 2] -
Bz[:, psi_d_Y - 1:pei_d_Y + 1]) / tv.meshSize[1]
Jy[psi_p_X:pei_p_X +
1, :] = -(Bz[psi_d_X:pei_d_X + 2, :] -
Bz[psi_d_X - 1:pei_d_X + 1, :]) / tv.meshSize[0]
w1[psi_p_X:pei_p_X +
1, :] = (By[psi_d_X:pei_d_X + 2, :] -
By[psi_d_X - 1:pei_d_X + 1, :]) / tv.meshSize[0]
w2[:, psi_p_Y:pei_p_Y +
1] = -(Bx[:, psi_d_Y:pei_d_Y + 2] -
Bx[:, psi_d_Y - 1:pei_d_Y + 1]) / tv.meshSize[1]
Jz = w1 + w2
filename_jx = "jx_yee_2D_order1.txt"
filename_jy = "jy_yee_2D_order1.txt"
filename_jz = "jz_yee_2D_order1.txt"
np.savetxt(os.path.join(path, filename_jx), Jx.flatten('C'), delimiter=" ")
np.savetxt(os.path.join(path, filename_jy), Jy.flatten('C'), delimiter=" ")
np.savetxt(os.path.join(path, filename_jz), Jz.flatten('C'), delimiter=" ")
def eval(self, values, x):
values[0] = (1.0 - np.tanh(x / (2.0 * np.sqrt(2.0 * lmbda)))) / 2.0
pi = np.pi omega = 1 kappa = 1 Nt = 4 T = np.linspace(0, np.pi/omega, Nt) eta = np.linspace(0, 2*np.pi/kappa, 300) xi = np.linspace(-1, 1, 299) epsilon = 0.3 gamma = np.sqrt(1j*omega/Sc) u_x = np.zeros((len(T), len(xi), len(eta)), dtype="complex") u_y = np.zeros((len(T), len(xi), len(eta)), dtype="complex") kappa_prime = np.sqrt(1j*omega/Sc + kappa*kappa) P1 = (gamma*F0*np.tanh(gamma)/(kappa*np.cosh(kappa)))/(1-kappa_prime*np.tanh(kappa)/(kappa*np.tanh(kappa_prime))) for t in range(len(T)): for x in range(len(xi)): u_x[t,x,:] = epsilon*np.sin(kappa*eta)*( (P1*kappa*np.cosh(kappa)/(gamma*gamma))*(np.cosh(kappa*xi[x])/np.cosh(kappa) - np.cosh(kappa_prime*xi[x])/np.cosh(kappa_prime)) + (F0*np.tanh(gamma)/(gamma))*(np.cosh(kappa_prime*xi[x])/np.cosh(kappa_prime) - xi[x]*np.sinh(gamma*xi[x])/np.sinh(gamma)) ) u_x[t,x,:] += F0*(1-np.cosh(gamma*xi[x])/np.cosh(gamma))/(gamma*gamma) u_x[t,x,:] *= np.exp(1j*omega*T[t]) u_y[t, x, :] = (np.exp(1j*omega*T[t])*np.cos(kappa*eta)*kappa*P1*np.sinh(kappa)/(gamma*gamma))*( np.sinh(kappa_prime*xi[x])/np.sinh(kappa_prime) - np.sinh(kappa*xi[x])/np.sinh(kappa)) #test boundary conditions """ for i in range(len(T)): plt.plot(xi, np.real(u_y[i, :, 150])) plt.plot(xi, np.real(u_y2[i, :, 150])) plt.show()
def __activation(self, X):
return np.tanh(X) #sigmoid: 1/(1 + np.exp(-X)
def tanh_deriv(x):
return 1.0 - np.tanh(x) * np.tanh(x)
def func_inter_dot_coupling(xdata, offset: float, slope: float, height: float,
position: float, width: float):
return offset + slope * xdata + .5 * height * (1 + np.tanh(
(xdata - position) / width))
def tanh(self, x, derivative=False):
if derivative == False:
return np.tanh(x)
else:
tanh_x = self.tanh(x)
return (1 - np.square(tanh_x))
def activation(x):
return np.tanh(x)
def tanh(x, Derivative=False):
if not Derivative:
return np.tanh(x)
else:
return 1.0 - np.tanh(x)**2
def _tanh(x):
return np.tanh(x)