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from math import *
import array
import sys
import random
def run_mvc(k, k1, k2, k3, C, n = 100, do_print = False):
cmd = 'moveto'
result = array.array('d')
cost = 0
th = 0
x = 0
y = 0
dt = 1.0 / n
for i in range(n):
k4 = -k * (k * k2 - .5 * k1 * k1 + C)
cost += dt * k1 * k1
x += dt * cos(th)
y += dt * sin(th)
th += dt * k
k += dt * k1
k1 += dt * k2
k2 += dt * k3
k3 += dt * k4
result.append(k)
if do_print: print 400 + 400 * x, 500 + 400 * y, cmd
cmd = 'lineto'
return result, cost, x, y, th
def run_mec_cos(k, lam1, lam2, n = 100, do_print = False):
cmd = 'moveto'
result = array.array('d')
cost = 0
th = 0
x = 0
y = 0
dt = 1.0 / n
for i in range(n):
k1 = lam1 * cos(th) + lam2 * sin(th)
cost += dt * k * k
x += dt * cos(th)
y += dt * sin(th)
th += dt * k
k += dt * k1
result.append(k)
if do_print: print 400 + 400 * x, 500 + 400 * y, cmd
cmd = 'lineto'
return result, cost, x, y, th
def descend(params, fnl):
delta = 1
for i in range(100):
best = fnl(params, i, True)
bestparams = params
for j in range(2 * len(params)):
ix = j / 2
sign = 1 - 2 * (ix & 1)
newparams = params[:]
newparams[ix] += delta * sign
new = fnl(newparams, i)
if (new < best):
bestparams = newparams
best = new
if (bestparams == params):
delta *= .5
print '%', params, delta
sys.stdout.flush()
params = bestparams
return bestparams
def descend2(params, fnl):
delta = 20
for i in range(5):
best = fnl(params, i, True)
bestparams = params
for j in range(100000):
newparams = params[:]
for ix in range(len(params)):
newparams[ix] += delta * (2 * random.random() - 1)
new = fnl(newparams, i)
if (new < best):
bestparams = newparams
best = new
if (bestparams == params):
delta *= .5
params = bestparams
print '%', params, best, delta
sys.stdout.flush()
return bestparams
def desc_eval(params, dfdp, fnl, i, x):
newparams = params[:]
for ix in range(len(params)):
newparams[ix] += x * dfdp[ix]
return fnl(newparams, i)
def descend3(params, fnl):
dp = 1e-6
for i in range(1000):
base = fnl(params, i, True)
dfdp = []
for ix in range(len(params)):
newparams = params[:]
newparams[ix] += dp
new = fnl(newparams, i)
dfdp.append((new - base) / dp)
print '% dfdp = ', dfdp
xr = 0.
yr = base
xm = -1e-3
ym = desc_eval(params, dfdp, fnl, i, xm)
if ym > yr:
while ym > yr:
xl, yl = xm, ym
xm = .618034 * xl
ym = desc_eval(params, dfdp, fnl, i, xm)
else:
xl = 1.618034 * xm
yl = desc_eval(params, dfdp, fnl, i, xl)
while ym > yl:
xm, ym = xl, yl
xl = 1.618034 * xm
yl = desc_eval(params, dfdp, fnl, i, xl)
# We have initial bracket; ym < yl and ym < yr
x0, x3 = xl, xr
if abs(xr - xm) > abs(xm - xl):
x1, y1 = xm, ym
x2 = xm + .381966 * (xr - xm)
y2 = desc_eval(params, dfdp, fnl, i, x2)
else:
x2, y2 = xm, ym
x1 = xm + .381966 * (xl - xm)
y1 = desc_eval(params, dfdp, fnl, i, x1)
for j in range(30):
if y2 < y1:
x0, x1, x2 = x1, x2, x2 + .381966 * (x3 - x2)
y0, y1 = y1, y2
y2 = desc_eval(params, dfdp, fnl, i, x2)
else:
x1, x2, x3 = x1 + .381966 * (x0 - x1), x1, x2
y1 = desc_eval(params, dfdp, fnl, i, x1)
if y1 < y2:
xbest = x1
ybest = y1
else:
xbest = x2
ybest = y2
for ix in range(len(params)):
params[ix] += xbest * dfdp[ix]
print '%', params, xbest, ybest
sys.stdout.flush()
return params
def mk_mvc_fnl(th0, th1):
def fnl(params, i, do_print = False):
k, k1, k2, k3, C = params
ks, cost, x, y, th = run_mvc(k, k1, k2, k3, C, 100)
cost *= hypot(y, x) ** 3
actual_th0 = atan2(y, x)
actual_th1 = th - actual_th0
if do_print: print '%', x, y, actual_th0, actual_th1, cost
err = (th0 - actual_th0) ** 2 + (th1 - actual_th1) ** 2
multiplier = 1000
return cost + err * multiplier
return fnl
def mk_mec_fnl(th0, th1):
def fnl(params, i, do_print = False):
k, lam1, lam2 = params
ks, cost, x, y, th = run_mec_cos(k, lam1, lam2)
cost *= hypot(y, x)
actual_th0 = atan2(y, x)
actual_th1 = th - actual_th0
if do_print: print '%', x, y, actual_th0, actual_th1, cost
err = (th0 - actual_th0) ** 2 + (th1 - actual_th1) ** 2
multiplier = 10
return cost + err * multiplier
return fnl
#ks, cost, x, y, th = run_mvc(0, 10, -10, 10, 200)
#print '%', cost, x, y
#print 'stroke showpage'
def mvc_test():
fnl = mk_mvc_fnl(-pi, pi/4)
params = [0, 0, 0, 0, 0]
params = descend3(params, fnl)
k, k1, k2, k3, C = params
run_mvc(k, k1, k2, k3, C, 100, True)
print 'stroke showpage'
print '%', params
def mec_test():
th0, th1 = pi/2, pi/2
fnl = mk_mec_fnl(th0, th1)
params = [0, 0, 0]
params = descend2(params, fnl)
k, lam1, lam2 = params
run_mec_cos(k, lam1, lam2, 1000, True)
print 'stroke showpage'
print '%', params
mvc_test()
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