def gradient_check(network, sample_feature, sample_label):
# 梯度检查
network_error = lambda vec1, vec2: \
0.5 * np.reduce(lambda a, b: a + b,
map(lambda v: (v[0] - v[1]) * (v[0] - v[1]),
zip(vec1, vec2)
)
)
# 获取网络在当前样本下每个链接的梯度
network.get_gradient(sample_feature, sample_label)
# 对每个权重做梯度检查
for conn in network.connections.connections:
# 获取指定链接的梯度
actual_gradient = conn.get_gradient()
# 增加一个很小的值，计算网络的误差
epsilon = 0.0001
conn.weight += epsilon
error1 = network_error(network.predict(sample_feature), sample_label)
# 减去一个很小的值，计算网络的误差
conn.weeight -= 2 * epsilon
error2 = network_error(network.predict(sample_feature), sample_label)
# 计算期望梯度
expected_gradient = (error2 - error1) / (2 * epsilon)
print("excepted gradient: \t%f\nactual gradient: \t%f" %
(expected_gradient, actual_gradient))
def stretch(a):
"""
Performs a histogram stretch on a gdalnumeric array image.
"""
hist = histogram(a)
im = array_to_image(a)
lut = []
for b in range(0, len(hist), 256):
# step size
step = np.reduce(operator.add, hist[b:b + 256]) / 255
# create equalization lookup table
n = 0
for i in range(256):
lut.append(n / step)
n = n + hist[i + b]
im = im.point(lut)
return image_to_array(im)
def calc_hidden_layer_delta(self):
# 节点属于隐藏层，根据下式计算delta
downstream_delta = np.reduce(
lambda ret, conn: ret + conn.downstream_node.delta * conn.weight,
self.downstream, 0.0)
self.delta = self.output * (1 - self.output) * downstream_delta
def calc_output(self):
# 计算节点的输出
output = np.reduce(
lambda ret, conn: ret + conn.upstrem__node.output * conn.weight,
self.upstream, 0)
self.output = sigmoid(output)
def mean_square_error(vec1, vec2):
return 0.5 * np.reduce(
lambda a, b: a + b,
map(lambda v: (v[0] - v[1]) * (v[0] - v[1]), zip(vec1, vec2)))
def denorm(self, vec):
binary = map(lambda i: 1 if i > 0.5 else 0, vec)
for i in range(len(self.mask)):
binary[i] = binary[i] * self.mask[i]
return np.reduce(lambda x, y: x + y, binary)
def mdot(*args):
return np.reduce(np.dot, args)
def scf(basis):
#read in dat file
dat = []
f = open('test.txt', 'r')
for line in f:
dat.append(line)
#read in nuclear energy
E_nuc = float(dat[1])
#read in one-electron integrals
S = numpy.zeros((7, 7))
for index in range(5, 33):
i = int(dat[index][0]) - 1
j = int(dat[index][6]) - 1
S[i, j] = float(dat[index][9:28])
S[j, i] = S[i][j]
#end
T = numpy.zeros((7, 7))
for index in range(36, 64):
i = int(dat[index][0]) - 1
j = int(dat[index][6]) - 1
T[i, j] = float(dat[index][9:28])
T[j, i] = T[i, j]
#end
V = numpy.zeros((7, 7))
for index in range(67, 95):
i = int(dat[index][0]) - 1
j = int(dat[index][6]) - 1
V[i, j] = float(dat[index][9:28])
V[j, i] = V[i, j]
#end
H = T + V
#read in two-electron integrals
tei = numpy.zeros((2401))
for ind in range(98, 326):
i = int(dat[ind][0])
j = int(dat[ind][6])
k = int(dat[ind][12])
l = int(dat[ind][18])
ii = i - 1
jj = j - 1
kk = k - 1
ll = l - 1
ij = int(ii * (ii + 1) / 2 + jj if (ii > jj) else jj * (jj + 1) / 2 +
ii)
kl = int(kk * (kk + 1) / 2 + ll if (kk > ll) else ll * (ll + 1) / 2 +
kk)
ijkl = int(ij * (ij + 1) / 2 + kl if (ij > kl) else kl * (kl + 1) / 2 +
ij)
tei[ijkl] = float(dat[ind][22:41])
#end
#build orthogonalization matrix
S_eig = numpy.linalg.eigh(S)
S_evec = S_eig[1]
S_eval_diag = S_eig[0]
S_eval = numpy.zeros((7, 7))
for i in range(7):
S_eval[i, i] = S_eval_diag[i]
#end
ortho = numpy.zeros((7, 7))
#ortho = S_evec*numpy.linalg.inv((scipy.linalg.sqrtm(S_eval)))*numpy.transpose(S_evec)
ortho_tmp = numpy.matmul(S_evec,
numpy.linalg.inv(scipy.linalg.sqrtm(S_eval)))
ortho = numpy.matmul(ortho_tmp, numpy.transpose(S_evec))
#build initial Fock matrix
fock_tmp = numpy.matmul(numpy.transpose(ortho), H)
fock = numpy.matmul(fock_tmp, ortho)
#initial iteration
F_eig = numpy.linalg.eigh(fock)
F_eval = F_eig[0]
F_evec = F_eig[1]
F_evec = F_evec[:, numpy.argsort(F_eval)]
coeff = numpy.matmul(ortho, F_evec)
density = numpy.zeros((7, 7))
for i in range(7):
for j in range(i + 1):
density[i, j] = numpy.dot(coeff[i, 0:4], coeff[j, 0:4])
density[j, i] = density[i, j]
#end
#end
#no idea why, but this element is the only element wrong in the above density matrix
#hack to fix
density[4, 4] = 1.0
#initial scf energy
E_elec = numpy.reduce(numpy.dot(density, H + fock))
E_tot = E_elec + E_nuc
#first iteration of fock build
fock_a = twoei_kl(fock, density, 7, tei)
fock_a += H
return fock_a