def test_10(self):
#(3x+2)^4
print("****Unit Test 10********")
fex0 = make_prod(make_const(3.0), make_pwr('x', 1.0))
fex1 = make_plus(fex0, make_const(2.0))
fex = make_pwr_expr(fex1, 4.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
print(afex)
afexf = tof(afex)
err = 0.0001
def gt(x):
return (1.0 / 15) * ((3 * x + 2.0)**5)
for i in range(1, 10):
assert abs(afexf(i) - gt(i)) <= err
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print(fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 1000):
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 10:pass')
def test_09(self):
#3*(x+2)^-1 => 3*ln|x+2|
print("****Unit Test 09********")
fex0 = make_plus(make_pwr('x', 1.0), make_const(2.0))
fex1 = make_pwr_expr(fex0, -1.0)
fex = make_prod(make_const(3.0), fex1)
print(fex)
afex = antideriv(fex)
print("antideriv: ", afex)
err = 0.0001
afexf = tof(afex)
def gt(x):
return 3.0 * math.log(abs(2.0 + x), math.e)
for i in range(1, 101):
assert abs(afexf(i) - gt(i)) <= err
assert not afex is None
print(afex)
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print(fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 1000):
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 09:pass')
def test_08(self):
#(5x-7)^-2 => -1/5 * (5x-7)^-1
print("****Unit Test 08********")
fex1 = make_plus(make_prod(make_const(5.0), make_pwr('x', 1.0)),
make_const(-7.0))
fex = make_pwr_expr(fex1, -2.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
print("antideriv: ", afex)
afexf = tof(afex)
err = 0.0001
def gt(x):
return (-1.0 / 5.0) * ((5 * x - 7.0)**-1)
for i in range(1, 100):
assert abs(afexf(i) - gt(i)) <= err
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print("deriv fex2: ", fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 100):
print(fexf(i), " ", fex2f(i))
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 08:pass')
def test_06(self):
#x^-3+7e^(5x)+4*x^-1 => (1/-2)*(x^-2)+0 +(7*(1/5)*e(5x)+ (4*ln|x|)
print("****Unit Test 06********")
fex1 = make_pwr('x', -3.0)
fex2 = make_prod(
make_const(7.0),
make_e_expr(make_prod(make_const(5.0), make_pwr('x', 1.0))))
fex3 = make_prod(make_const(4.0), make_pwr('x', -1.0))
fex4 = make_plus(fex1, fex2)
fex = make_plus(fex4, fex3)
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
v1 = -0.5 * (x**(-2.0))
v2 = (7.0 / 5.0) * (math.e**(5.0 * x))
v3 = 4.0 * (math.log(abs(x), math.e))
return v1 + v2 + v3
afexf = tof(afex)
assert not afexf is None
err = 0.001
for i in range(1, 10):
print(afexf(i), gt(i))
assert abs(afexf(i) - gt(i)) <= err * gt(i)
print("Unit Test 06 pass")
def consumer_surplus(dexpr, a):
assert isinstance(a, const)
B = const(-1 * tof(dexpr)(a.get_val()))
f = make_plus(dexpr, B)
surplus = tof(antideriv(f))
return surplus(a.get_val()) - surplus(0)
def net_change(mrexpr, pl1, pl2):
assert isinstance(pl1, const)
assert isinstance(pl2, const)
#F(b) - F(a)
a = pl1
b = pl2
F = tof(antideriv(mrexpr))
return F(b.get_val()) - F(a.get_val())
def test_04(self):
#1/(x^2)=> -1.0/x
print("****Unit Test 04********")
fex = make_pwr('x', -2.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
return -1.0 / x
afexf = tof(afex)
assert not afexf is None
err = 0.0001
for i in range(1, 101):
assert abs(afexf(i) - gt(i)) <= err
print(afex)
print("Unit Test 04 pass")
def test_03(self):
#x^0.5 => (2/3)*x^(3/2)
print("****Unit Test 03********")
fex = make_pwr('x', 0.5)
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
return (2.0 / 3.0) * (x**(3.0 / 2.0))
afexf = tof(afex)
assert not afexf is None
err = 0.0001
for i in range(1, 101):
assert abs(afexf(i) - gt(i)) <= err
print(afex)
print("Unit Test 03: pass")
def test_02(self):
#e^(-2x)=> -0.5e^(-2x)
print("****Unit Test 02********")
fex = make_e_expr(make_prod(make_const(-2.0), make_pwr('x', 1.0)))
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
return (-0.5) * (math.e**(-2.0 * x))
afexf = tof(afex)
assert not afexf is None
err = 0.0001
for i in range(0, 101):
assert abs(afexf(i) - gt(i)) <= err
print(afex)
print("Unit Test 02: pass")
def test_01(self):
#x^2 => (1/3)x^3
print("****Unit Test 01********")
fex = make_pwr('x', 2.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
return (1.0 / 3.0) * (x**3.0)
afexf = tof(afex)
assert not afexf is None
err = 0.0001
for i in range(101):
assert abs(afexf(i) - gt(i)) <= err
print(afex)
print("Unit Test 01: pass")
def test_07(self):
# 4x^3 find antideriv and then plug it into deriv to get 4x^3 back
print("****Unit Test 07********")
fex = make_prod(make_const(4.0), make_pwr('x', 3.0))
print(fex)
afex = antideriv(fex)
assert not afex is None
print(afex)
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print(fex2)
fex2f = tof(fex2)
assert not fex2f is None
err = 0.0001
for i in range(11):
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 07:pass')
def test_05(self):
#1/(x)=> ln|x|
print("****Unit Test 05********")
fex = make_pwr('x', -1.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
def gt(x):
return math.log(abs(x), math.e)
afexf = tof(afex)
assert not afexf is None
err = 0.0001
for i in range(2, 101):
assert abs(afexf(i) / gt(i) - 1) <= err
for i in range(-100, 0):
assert abs(afexf(i) - gt(i)) <= err
print(afex)
print("Unit Test 05 pass")