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GradientDescent.py
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import GeomTool
import Explainer
import Pathfinder
def get_value(vl, vnl):
outlst = []
for obj_num in range(len(vl)):
if vnl[obj_num] == 0:
outlst.append(vl[obj_num].freec)
if vnl[obj_num] == 1:
outlst.append(vl[obj_num].freec[0])
if vnl[obj_num] == 2:
outlst.append(vl[obj_num].freec[1])
return outlst
def cyclic_det(x1, y1, x2, y2, x3, y3):
# Determine whether the four points (0, 0), (xi, yi) are cyclic
return x2**2 * (x3 * y1 - x1 * y3) + x2 * (-x3**2 * y1 + y3 * (x1**2 + y1**2 - y1 * y3)) + y2 * (-x1**2 * x3 + x3 * y1 * (-y1 + y2) + x1 * (x3**2 - y2 * y3 + y3**2))
def calc_datum(descent_datum, in_geom_list):
# Calculate the descent datum. -- To minimize what?
outsum = 0
for data in descent_datum:
if data[0] == "eq":
if data[1].type == "Point":
outsum += (data[1].c[0] - data[2].c[0]) **2 + (data[1].c[1] - data[2].c[1]) **2
if data[1].type == "Circle":
outsum += (data[1].c[0] - data[2].c[0]) **2 + (data[1].c[1] - data[2].c[1]) **2 + (data[1].c[2] - data[2].c[2]) **2
if data[1].type == "Line":
outsum += (data[1].c[0] * data[2].c[1] - data[2].c[0] * data[1].c[1]) **2 + (data[1].c[1] * data[2].c[2] - data[2].c[1] * data[1].c[2]) **2 + (data[1].c[2] * data[2].c[0] - data[2].c[2] * data[1].c[0]) **2
continue
if data[0] == "eqdist":
if data[1].type == "Line":
d1 = (data[1].c[0] * data[2].c[0] + data[1].c[1] * data[2].c[1] + data[1].c[2])**2 / (data[1].c[0] ** 2 + data[1].c[1] ** 2)
elif data[2].type == "Line":
d1 = (data[2].c[0] * data[1].c[0] + data[2].c[1] * data[1].c[1] + data[2].c[2])**2 / (data[2].c[0] ** 2 + data[2].c[1] ** 2)
else:
d1 = (data[1].c[0] - data[2].c[0]) **2 + (data[1].c[1] - data[2].c[1]) **2
if data[3].type == "Line":
d2 = (data[3].c[0] * data[4].c[0] + data[3].c[1] * data[4].c[1] + data[3].c[2])**2 / (data[3].c[0] ** 2 + data[3].c[1] ** 2)
elif data[4].type == "Line":
d2 = (data[4].c[0] * data[3].c[0] + data[4].c[1] * data[3].c[1] + data[4].c[2])**2 / (data[4].c[0] ** 2 + data[4].c[1] ** 2)
else:
d2 = (data[3].c[0] - data[4].c[0]) **2 + (data[3].c[1] - data[4].c[1]) **2
outsum += (d1 - d2) **2
continue
if data[0] == "col":
outsum += (data[1].c[0] * data[2].c[1] + data[2].c[0] * data[3].c[1] + data[3].c[0] * data[1].c[1] - data[1].c[1] * data[2].c[0] - data[2].c[1] * data[3].c[0] - data[3].c[1] * data[1].c[0]) ** 2
continue
if data[0] == "cyc":
outsum += (cyclic_det(data[2].c[0]-data[1].c[0], data[2].c[1]-data[1].c[1], data[3].c[0]-data[1].c[0], data[3].c[1]-data[1].c[1], data[4].c[0]-data[1].c[0], data[4].c[1]-data[1].c[1])) ** 2
continue
if data[0] == "para":
outsum += ((data[1].c[1] - data[2].c[1]) * (data[3].c[0] - data[4].c[0]) - (data[3].c[1] - data[4].c[1]) * (data[1].c[0] - data[2].c[0])) ** 2
continue
if data[0] == "perp":
outsum += ((data[1].c[1] - data[2].c[1]) * (data[3].c[1] - data[4].c[1]) + (data[3].c[0] - data[4].c[0]) * (data[1].c[0] - data[2].c[0])) ** 2
continue
if data[0] == "online":
outsum += (data[1].c[0] * data[2].c[0] + data[1].c[1] * data[2].c[1] + data[2].c[2]) ** 2
continue
if data[0] == "oncirc":
outsum += ((data[1].c[0] - data[2].c[0])**2 + (data[1].c[1] - data[2].c[1])**2 - data[2].c[2]**2) ** 2
continue
if data[0] == "simtri":
re1, im1 = Pathfinder.complexdiv(data[2].c[0] - data[1].c[0], data[2].c[1] - data[1].c[1], data[3].c[0] - data[1].c[0], data[3].c[1] - data[1].c[1])
re2, im2 = Pathfinder.complexdiv(data[5].c[0] - data[4].c[0], data[5].c[1] - data[4].c[1], data[6].c[0] - data[4].c[0], data[6].c[1] - data[4].c[1])
outsum += (re1 - re2)**2 + (im1 - im2)**2
continue
if data[0] == "eqangle":
dx1 = data[2].c[0] - data[1].c[0]
dy1 = data[2].c[1] - data[1].c[1]
dx2 = data[4].c[0] - data[3].c[0]
dy2 = data[4].c[1] - data[3].c[1]
dx3 = data[6].c[0] - data[5].c[0]
dy3 = data[6].c[1] - data[5].c[1]
dx4 = data[8].c[0] - data[7].c[0]
dy4 = data[8].c[1] - data[7].c[1]
outsum += ((dy1 * dx2 - dy2 * dx1) * (dy3 * dy4 + dx3 * dx4) - (dy3 * dx4 - dy4 * dx3) * (dy1 * dy2 + dx1 * dx2)) ** 2
continue
if data[0] == "Formula":
outsum += Explainer.calculate(data[1], in_geom_list) ** 2
return outsum
def update_and_calc_value(datum, inlst, vl, vnl):
for obj_num in range(len(vl)):
if vnl[obj_num] == 0:
vl[obj_num].freec = inlst[obj_num]
if vnl[obj_num] == 1:
vl[obj_num].freec = (inlst[obj_num], inlst[obj_num + 1])
vl[0].tree.calc_all()
return calc_datum(datum, vl[0].tree.obj_list)
def update_value(inlst, vl, vnl):
for obj_num in range(len(vl)):
if vnl[obj_num] == 0:
vl[obj_num].freec = inlst[obj_num]
if vnl[obj_num] == 1:
vl[obj_num].freec = (inlst[obj_num], inlst[obj_num + 1])
vl[0].tree.calc_all()
DERIVATIVE_DELTA = 3e-5
FIRST_STEP = 1e-6
BIGTIMES = 3
TIMES = 70
STEP = FIRST_STEP
def descent(in_datum, in_tree):
datum = in_datum
# Create a list of objects with free variables
# Variable_num_list: 0 if degree_of_freedom == 1; 1, 2 the freec tuple when degree_of_freedom == 2
variable_list = []
variable_num_list = []
for obj in in_tree.get_movable():
if obj.method.name == "free_pt":
variable_list += [obj, obj]
variable_num_list += [1, 2]
else:
variable_list += [obj]
variable_num_list += [0]
for bigtimer in range(BIGTIMES):
# The list of values of the free variables
value_list = get_value(variable_list, variable_num_list)
last_grad_list = []
last_value_list = []
for timer in range(TIMES):
if timer > 0:
last_grad_list = grad_list.copy()
grad_list = []
for obj_num in range(len(value_list)):
# Calculate the partial derivatives using values at 4 points
value_list_shifted = value_list.copy()
value_list_shifted[obj_num] -= DERIVATIVE_DELTA * 2
fmm = update_and_calc_value(datum, value_list_shifted, variable_list, variable_num_list)
value_list_shifted = value_list.copy()
value_list_shifted[obj_num] -= DERIVATIVE_DELTA
fm = update_and_calc_value(datum, value_list_shifted, variable_list, variable_num_list)
value_list_shifted = value_list.copy()
value_list_shifted[obj_num] += DERIVATIVE_DELTA
fp = update_and_calc_value(datum, value_list_shifted, variable_list, variable_num_list)
value_list_shifted = value_list.copy()
value_list_shifted[obj_num] += DERIVATIVE_DELTA * 2
fpp = update_and_calc_value(datum, value_list_shifted, variable_list, variable_num_list)
der = ((fmm - fpp) - (fm - fp)*8) / (12 * DERIVATIVE_DELTA)
grad_list.append(der)
update_value(value_list, variable_list, variable_num_list)
if timer == 0:
STEP = FIRST_STEP
else:
# The Barzilar-Borwein Step
delta_value_list = []
for obj_num in range(len(value_list)):
delta_value_list.append(value_list[obj_num] - last_value_list[obj_num])
delta_grad_list = []
for obj_num in range(len(grad_list)):
delta_grad_list.append(grad_list[obj_num] - last_grad_list[obj_num])
A = sum(delta_value_list[_] * delta_grad_list[_] for _ in range(len(value_list)))
if A == 0:
return timer + bigtimer * TIMES
B = sum(delta_grad_list[_] * delta_grad_list[_] for _ in range(len(grad_list)))
STEP = abs(A / B)
# Update values of free variables
last_value_list = value_list.copy()
for obj_num in range(len(value_list)):
value_list[obj_num] -= STEP * grad_list[obj_num]
update_value(value_list, variable_list, variable_num_list)
return BIGTIMES * TIMES