def TrainNetwork(sample, lebal):
sample_num = len(sample)
sample_len = len(sample[0])
import math
out_num = 10
hid_num = 8
w1 = 0.2 * math.random.random((sample_len, hid_num)) - 0.1
w2 = 0.2 * math.random.random((hid_num, out_num)) - 0.1
hid_offset = math.zeros(hid_num)
out_offset = math.zeros(out_num)
input_learnrate = 0.2
hid_learnrate = 0.2
for i in range(0, len(sample)):
t_label = math.zeros(out_num)
t_label[label[i]] = 1
# 前向的过程
hid_value = math.dot(sample[i], w1) + hid_offset # 隐层的输入
hid_act = get(hid_value) # 隐层对应的输出
out_value = math.dot(hid_act, w2) + out_offset
out_act = get(out_value) # 输出层最后的输出
# 后向过程
err = t_label - out_act
out_delta = err * out_act * (1 - out_act) # 输出层的方向梯度方向
hid_delta = hid_act * (1 - hid_act) * math.dot(w2, out_delta)
for j in range(0, out_num):
w2[:, j] += hid_learnrate * out_delta[j] * hid_act
for k in range(0, hid_num):
w1[:, k] += input_learnrate * hid_delta[k] * sample[i]
out_offset += hid_learnrate * out_delta # 阈值的更新
hid_offset += input_learnrate * hid_delta
return w1, w2, hid_offset, out_offset
def crosspos(self, p0):
x, y = p0
x0, y0 = view.to0plane(self.x, self.y, self.z)
cx, cy = x - x0, y - y0
a = math.dot((cx, cy), self.dhat) / self.d0
b = self.dhatx * cy - self.dhaty * cx
return a, b
def cvt_c1c2_using_body2inertial_Q_to_v2v3pa_tuple(Q, coord1, coord2):
"""Given Q and a position, returns v2, v3, V3PA tuple """
Vp_eci = Vector(1., 0., 0.)
Vp_eci.set_xyz_from_angs(coord1, coord2)
Vp_body_pt = Q.inv_cnvrt(Vp_eci)
v2 = math.atan2(Vp_body_pt.y, Vp_body_pt.x)
v3 = math.asin(unit_limit(Vp_body_pt.z))
V3_body = Vector(0., 0., 1.)
V3_eci_pt = self.cnvrt(V3_body)
NP_eci = Vector(0., 0., 1.)
V_left = math.cross(NP_eci, Vp_eci)
if V_left.length() > 0.:
V_left = V_left / V_left.length()
NP_in_plane = math.cross(Vp_eci, V_left)
x = math.dot(V3_eci_pt, NP_in_plane)
y = math.dot(V3_eci_pt, V_left)
pa = math.atan2(y, x)
if pa < 0.: pa += PI2
return (v2, v3, pa)
def polygon(self, f=1):
theta = 30 if math.dot(self.pos, (C15, -S15)) < 0 else -60
theta = -60
R = math.R(math.radians(theta))
w, h = self.size
w *= f
h *= f
sx, sy = self.pos
ds = [R(p) for p in ((0, h), (w, 0), (w, -0.8), (-w, -0.8), (-w, 0))]
return [(sx + dx, sy + dy) for dx, dy in ds]
def cvt_c1c2_using_body2inertial_Q_to_v2v3pa_tuple(Q, coord1, coord2):
"""Given Q and a position, returns v2, v3, V3PA tuple """
Vp_eci = Vector(1., 0., 0.)
Vp_eci.set_xyz_from_angs(coord1, coord2)
Vp_body_pt = Q.inv_cnvrt(Vp_eci)
v2 = math.atan2(Vp_body_pt.y, Vp_body_pt.x)
v3 = math.asin(unit_limit(Vp_body_pt.z))
V3_body = Vector(0., 0., 1.)
V3_eci_pt = self.cnvrt(V3_body)
NP_eci = Vector(0., 0., 1.)
V_left = math.cross(NP_eci, Vp_eci)
if V_left.length()>0.:
V_left = V_left / V_left.length()
NP_in_plane = math.cross(Vp_eci, V_left)
x = math.dot(V3_eci_pt, NP_in_plane)
y = math.dot(V3_eci_pt, V_left)
pa = math.atan2(y, x)
if pa < 0. : pa += PI2
return (v2, v3, pa)
def dof(j0, j1, jc=None):
x0, y0 = ps[j0]
x1, y1 = ps[j1]
f = 1
if jc is not None:
xc, yc = ps[jc]
a = math.clamp(
math.dot(math.norm((xc - x0, yc - y0)),
math.norm((x1 - xc, y1 - yc))), -0.999, 0.999)
f = 1 / math.cos(math.acos(a) / 2)
return math.norm((x1 - x0, y1 - y0), w * f)
def constrain(self, pos, j):
if pos[1] < 0.0001:
pos = pos[0], 0.0001
if pos[0] < 0:
pos = 0, pos[1]
if math.dot(pos, (C30, -S30)) > 0:
pos, _ = ptoline(pos, (S30, C30))
a = math.length(pos)
if a > 1 - self.r:
pos = math.norm(pos, 1 - self.r)
return pos
def constrain(self, pos, j):
if pos[1] < 0.0001:
pos = pos[0], 0.0001
if pos[0] < self.width:
pos = self.width, pos[1]
if math.dot(math.norm(pos), (C30, -S30)) > -self.width:
pos, _ = ptoline(pos, (S30, C30))
pos = pos[0] - self.width * C30, pos[1] + self.width * S30
a = math.length(pos)
if a > 1 - self.width:
pos = math.norm(pos, 1 - self.width)
return pos
def cvt_v2v3_using_body2inertial_Q_to_c1c2pa_tuple(Q, v2, v3):
"""Given Q and v2, v3 gives pos on sky and V3 PA """
Vp_body = Vector(0., 0., 0.)
Vp_body.set_xyz_from_angs(v2, v3)
Vp_eci_pt = Q.cnvrt(Vp_body)
coord1 = math.atan2(Vp_eci_pt.y, Vp_eci_pt.x)
if coord1 < 0.: coord1 += PI2
coord2 = math.asin(unit_limit(Vp_eci_pt.z))
V3_body = Vector(0., 0., 1.)
V3_eci_pt = Q.cnvrt(V3_body)
NP_eci = Vector(0., 0., 1.)
V_left = math.cross(NP_eci, Vp_eci_pt)
if V_left.length() > 0.:
V_left = V_left / V_left.length()
NP_in_plane = math.cross(Vp_eci_pt, V_left)
x = math.dot(V3_eci_pt, NP_in_plane)
y = math.dot(V3_eci_pt, V_left)
pa = math.atan2(y, x)
if pa < 0.: pa += PI2
return (coord1, coord2, pa)
def cvt_v2v3_using_body2inertial_Q_to_c1c2pa_tuple(Q, v2, v3):
"""Given Q and v2, v3 gives pos on sky and V3 PA """
Vp_body = Vector(0., 0., 0.)
Vp_body.set_xyz_from_angs(v2, v3)
Vp_eci_pt = Q.cnvrt(Vp_body)
coord1 = math.atan2(Vp_eci_pt.y, Vp_eci_pt.x)
if coord1 < 0. : coord1 += PI2
coord2 = math.asin(unit_limit(Vp_eci_pt.z))
V3_body = Vector(0., 0., 1.)
V3_eci_pt = Q.cnvrt(V3_body)
NP_eci = Vector(0., 0., 1.)
V_left = math.cross(NP_eci, Vp_eci_pt)
if V_left.length()>0.:
V_left = V_left/V_left.length()
NP_in_plane = math.cross(Vp_eci_pt, V_left)
x = math.dot(V3_eci_pt, NP_in_plane)
y = math.dot(V3_eci_pt, V_left)
pa = math.atan2(y, x)
if pa < 0. : pa += PI2
return (coord1, coord2, pa)
def Test():
train_sample = LoadFile('mnist_train.mat')
train_sample = train_sample / 256.0
train_label = LoadFile('mnist_train_labels.mat')
test_sample = LoadFile('mnist_test.mat')
test_sample = test_sample / 256.0
test_label = LoadFile('mnist_test_labels.mat')
w1, w2, hid_offset, out_offset = TrainNetwork(train_sample, train_label)
import math
right = math.zeros(10)
numbers = math.zeros(10)
for i in test_label:
numbers[i] += 1
print(numbers)
for i in range(0, len(test_label)):
hid_value = math.dot(test_sample[i], w1) + hid_offset
hid_act = get(hid_value)
out_value = math.dot(hid_act, w2) + out_offset
out_act = get(out_value)
if math.argmax(out_act) == test_label[i]:
right[test_label[i]] += 1
print(right.sum() / len(test_label))
def ptoline(p, n):
pproj = math.dot(p, n)
nx, ny = n
proj = nx * pproj, ny * pproj
return proj, math.distance(proj, p)
def constrain(self, pos, j):
a = math.clamp(math.dot(pos, (S15, C15)), self.width, 1 - self.width)
return a * S15, a * C15
