def test_04():
ln1 = make_line_eq(make_var('y'), make_const(2.0))
ln2 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(2.0),
make_pwr('x', 1.0)),
make_const(-6.0)))
print(line_intersection(ln1, ln2))
print(line_intersection(ln2, ln1))
def test_09(): #y = 5; y = -x +6
ln1 = make_line_eq(make_var('y'), make_const(5.0))
ln2 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(-1.0), make_pwr('x', 1.0)),
make_const(6.0)))
print(line_intersection(ln1, ln2))
def opt_prob_1c():
f1 = lambda x, y: 3*x - 2*y
#find corner points:
ln1 = make_line_eq(make_plus(make_var('x'),make_var('y')), make_const(0.0))# x+y=0
ln2 = make_line_eq(make_var('x'),make_var('y'))# x-y=0 => x=y
ln3 = make_line_eq(make_plus(make_prod(make_const(-2.0), make_var('x')),make_prod(make_const(4.0), make_var('y'))), make_const(5.0))# -2x+4y=5
p12 = line_intersection(ln1, ln2)
p13 = line_intersection(ln1, ln3)
p23 = line_intersection(ln2, ln3)
possible_cps = [p12,p13,p23]
corner_points = [pt for pt in possible_cps if -2*pt.get_x().get_val() + 4*pt.get_y().get_val() <= 5] # -2x+4y<=5
corner_points = [pt for pt in corner_points if pt.get_x().get_val() + pt.get_y().get_val() >= 0] #x+y>=0
corner_points = [pt for pt in corner_points if pt.get_x().get_val() - pt.get_y().get_val() <= 0] #x-y<=0
# for pt in corner_points:
# print(pt.get_x().get_val(), pt.get_y().get_val())
print '1c: ',maximize_obj_fun(f1, corner_points)
def opt_prob_1a():
f1 = lambda x, y: 2*x + y
#find corner points:
ln1 = make_line_eq(make_var('x'), make_const(1.0))
ln2 = make_line_eq(make_var('y'), make_const(1.0))
ln3 = make_line_eq(make_var('x'), make_const(5.0))
ln4 = make_line_eq(make_var('y'), make_const(5.0))
p12 = line_intersection(ln1, ln2)
# p13 = line_intersection(ln1, ln3) #parallel lines
p14 = line_intersection(ln1, ln4)
p23 = line_intersection(ln2, ln3)
# p24 = line_intersection(ln2, ln4) #parallel lines
p34 = line_intersection(ln3, ln4)
possible_cps = [p12,p14,p23,p34]
corner_points = [pt for pt in possible_cps if pt.get_x().get_val() + pt.get_y().get_val() <= 6] #x+y <= 6
# for pt in corner_points:
# print(pt.get_x().get_val(), pt.get_y().get_val())
print '1a: ',maximize_obj_fun(f1, corner_points)
def test_07():
ln1 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(-1.0/5.0),
make_pwr('x', 1.0)),
make_const(10.0)))
ln2 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(1.0/5.0),
make_pwr('x', 1.0)),
make_const(5.0)))
print(line_intersection(ln1, ln2))
def test_11():
ln1 = make_line_eq(make_var('x'), make_const(1.0))
ln2 = make_line_eq(make_var('y'), make_prod(make_const(0.5),
make_pwr('x', 1.0)))
print(line_intersection(ln1, ln2))
ln3 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(-3.0/4),
make_pwr('x', 1.0)),
make_const(3.0)))
print(line_intersection(ln1, ln3))
print(line_intersection(ln2, ln3))
def test_05(): #y = x; y = 2x; y = 3x-10
ln1 = make_line_eq(make_var('y'), make_pwr('x', 1.0))
ln2 = make_line_eq(make_var('y'),
make_prod(make_const(2.0), make_pwr('x', 1.0)))
ln3 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(3.0), make_pwr('x', 1.0)),
make_const(-10.0)))
print(get_line_coeffs(ln1))
print(get_line_coeffs(ln2))
print(get_line_coeffs(ln3))
def test_05():
ln1 = make_line_eq(make_var('y'), make_pwr('x', 1.0))
ln2 = make_line_eq(make_var('y'), make_prod(make_const(2.0),
make_pwr('x', 1.0)))
ln3 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(3.0),
make_pwr('x', 1.0)),
make_const(-10.0)))
print(get_line_coeffs(ln1))
print(get_line_coeffs(ln2))
print(get_line_coeffs(ln3))
print(line_intersection(ln1, ln2))
print(line_intersection(ln2, ln3))
print(line_intersection(ln1, ln3))
def test_12():
ln1 = make_line_eq(make_var('x'), make_const(0.0))
ln2 = make_line_eq(make_var('y'), make_const(0.0))
ln3 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(-4.0/3),
make_pwr('x', 1.0)),
make_const(160.0)))
ln4 = make_line_eq(make_var('y'), make_plus(make_prod(make_const(-0.5),
make_pwr('x', 1.0)),
make_const(120.0)))
print(ln1)
print(ln3)
print(line_intersection(ln1, ln3))
print(ln2)
print(ln3)
print(line_intersection(ln2, ln3))
print(line_intersection(ln3, ln4))
def opt_prob_1c():
f1 = lambda x, y: 3 * x - 2 * y
ln1 = make_line_eq(make_var('y'),
make_prod(make_const(-1.0), make_pwr('x', 1.0)))
ln2 = make_line_eq(make_var('y'), make_pwr('x', 1.0))
ln3 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(1.0 / 2.0), make_pwr('x', 1.0)),
make_const(5.0 / 4.0)))
cp_1 = line_intersection(ln1, ln2) #y = -x; y = x
cp_2 = line_intersection(ln1, ln3)
cp_3 = line_intersection(ln2, ln3)
corner_points = [cp_1, cp_2, cp_3]
max_xy = maximize_obj_fun(f1, corner_points)
max_val = f1(max_xy.get_x().get_val(), max_xy.get_y().get_val())
print(max_xy, max_val)
def opt_prob_1b():
f1 = lambda x, y: x / 2 + y
ln1 = make_line_eq(make_var('y'), make_const(2.0))
ln2 = make_line_eq(make_var('x'), make_const(0.0))
ln3 = make_line_eq(make_var('y'), make_pwr('x', 1.0))
ln4 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(-1.0), make_pwr('x', 1.0)),
make_const(6.0)))
cp_1 = line_intersection(ln3, ln4)
cp_2 = line_intersection(ln1, ln3)
cp_3 = line_intersection(ln1, ln4)
corner_points = [cp_1, cp_2, cp_3]
min_xy = minimize_obj_fun(f1, corner_points)
min_val = f1(min_xy.get_x().get_val(), min_xy.get_y().get_val())
print(min_xy, min_val)
def opt_prob_1a():
f1 = lambda x, y: 2 * x + y
ln1 = make_line_eq(make_var('x'), make_const(1.0))
ln2 = make_line_eq(make_var('y'), make_const(1.0))
ln3 = make_line_eq(make_var('x'), make_const(5.0))
ln4 = make_line_eq(make_var('y'), make_const(5.0))
ln5 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(-1.0), make_pwr('x', 1.0)),
make_const(6.0)))
cp_1 = line_intersection(ln1, ln5)
cp_2 = line_intersection(ln1, ln2)
cp_3 = line_intersection(ln4, ln5)
corner_points = [cp_1, cp_2, cp_3]
max_xy = maximize_obj_fun(f1, corner_points)
max_val = f1(max_xy.get_x().get_val(), max_xy.get_y().get_val())
print(max_xy, max_val)
def opt_prob_1b():
f1 = lambda x, y: x/2 + y
#find corner points:
ln1 = make_line_eq(make_var('x'), make_const(0.0))
ln2 = make_line_eq(make_var('y'), make_const(2.0))
ln3 = make_line_eq(make_var('x'), make_var('y'))#x=y
ln4 = make_line_eq(make_plus(make_var('x'),make_var('y')), make_const(6.0))# x+y=6
p12 = line_intersection(ln1, ln2)
p13 = line_intersection(ln1, ln3)
p14 = line_intersection(ln1, ln4)
p23 = line_intersection(ln2, ln3)
p24 = line_intersection(ln2, ln4)
p34 = line_intersection(ln3, ln4)
possible_cps = [p12,p13,p14,p23,p24,p34]
# for pt in possible_cps:
# print pt
corner_points = [pt for pt in possible_cps if pt.get_x().get_val() + pt.get_y().get_val() <= 6] #x+y <= 6
corner_points = [pt for pt in corner_points if pt.get_x().get_val() >= pt.get_y().get_val()] #x>=y
corner_points = [pt for pt in corner_points if pt.get_x().get_val() >= 0] #x>=0
corner_points = [pt for pt in corner_points if pt.get_y().get_val() >= 2] #y>=2
# for pt in corner_points:
# print(pt.get_x().get_val(), pt.get_y().get_val())
print '1b: ',minimize_obj_fun(f1, corner_points)
def linear_programming_prob1():
f1 = lambda x, y: 5 * x + 4 * y
ln1 = make_line_eq(
make_var('y'),
make_plus(make_prod(const(-4.0 / 3.0), make_pwr('x', 1.0)),
make_const(160)))
ln2 = make_line_eq(
make_var('y'),
make_plus(make_prod(const(-3.0 / 6.0), make_pwr('x', 1.0)),
make_const(120)))
ln3 = make_line_eq(make_var('x'), make_const(0.0))
ln4 = make_line_eq(make_var('y'), make_const(0.0))
cp_1 = line_intersection(ln2, ln3)
cp_2 = line_intersection(ln1, ln2)
cp_3 = line_intersection(ln1, ln4)
corner_points = [cp_1, cp_2, cp_3]
max_xy = maximize_obj_fun(f1, corner_points)
max_val = f1(max_xy.get_x().get_val(), max_xy.get_y().get_val())
print(max_xy, max_val)
def test_03(): #y = -2; y = x +10
ln1 = make_line_eq(make_var('y'), make_const(-2.0))
ln2 = make_line_eq(make_var('y'),
make_plus(make_pwr('x', 1.0), make_const(10.0)))
print(line_intersection(ln1, ln2))
print(line_intersection(ln2, ln1))
def test_01():
ln1 = make_line_eq(make_var('y'), make_const(1.0))
ln2 = make_line_eq(make_var('x'), make_const(1.0))
assert is_const_line(ln1)
assert is_const_line(ln2)
print(line_intersection(ln1, ln2))
from maker import make_line_eq
from maker import make_var, make_const, make_prod
from maker import make_pwr, make_plus
from maker import make_point2d
from const import const
from var import var
from prod import prod
from pwr import pwr
# from poly12 import is_pwr_1
from plus import plus
from tof import tof
from consts import is_const_line
import sys
### sample line equations
lneq1 = make_line_eq(make_var('y'), make_const(2))
lneq2 = make_line_eq(make_var('y'), make_var('x'))
lneq3 = make_line_eq(make_var('y'), make_var('y'))
lneq4 = make_line_eq(make_var('y'),
make_prod(make_const(2.0), make_pwr('x', 1.0)))
lneq5 = make_line_eq(make_var('y'),
make_prod(make_const(5.0), make_pwr('y', 1.0)))
lneq6 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(5.0), make_pwr('x', 1.0)), make_const(4.0)))
lneq7 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(5.0), make_pwr('y', 1.0)), make_const(4.0)))
lneq8 = make_line_eq(
make_var('y'),
make_plus(make_prod(make_const(3.0), make_pwr('x', 1.0)),
from maker import make_point2d
from const import const
from var import var
from prod import prod
from pwr import pwr
# from poly12 import is_pwr_1
from plus import plus
from tof import tof
import sys
import numpy as np
'''
'''
### sample line equations
lneq1 = make_line_eq(make_var('y'),
make_const(2))
lneq2 = make_line_eq(make_var('y'),
make_var('x'))
lneq3 = make_line_eq(make_var('y'),
make_var('y'))
lneq4 = make_line_eq(make_var('y'),
make_prod(make_const(2.0),
make_pwr('x', 1.0)))
lneq5 = make_line_eq(make_var('y'),
make_prod(make_const(5.0),
make_pwr('y', 1.0)))
lneq6 = make_line_eq(make_var('y'),
make_plus(make_prod(make_const(5.0),
make_pwr('x', 1.0)),
make_const(4.0)))
