def test_power(self):
val_dict = {'x' : 10.0, 'y' : 3.0}
x = Variable('x')
y = Variable('y')
c1 = 2.0
c2 = -2.0
c3 = 0.0
f0 = x**c1
assert(f0.get_val(val_dict) ==100)
assert(f0.get_der(val_dict)['x'] == 20)
f1 = x**c2
assert(f1.get_val(val_dict) ==0.01)
assert(f1.get_der(val_dict)['x'] == -0.002)
f2 = x**c3
assert(f2.get_val(val_dict) ==1)
assert(f2.get_der(val_dict)['x'] == 0)
f3 = x**y
assert(f3.get_val(val_dict) ==1000)
assert(f3.get_der(val_dict)['x'] == 300)
assert(f3.get_der(val_dict)['y'] == math.log(10.0)*1000)
f4 = f0 ** f1
assert(f2.get_val(val_dict) ==1)
assert(f2.get_der(val_dict)['x'] == 0)
f5 = 2.0**y
assert(f5.get_der(val_dict)['y'] == 8*math.log(2))
f5 = y**2.0
assert(f5.get_der(val_dict)['y'] == 6.0)
def test_trig(self):
val_dict = {'x' : 0, 'y' : math.pi/2}
x = Variable('x')
y = Variable('y')
c1 = 2.0
c2 = -2.0
c3 = 0.0
f0 = mo.sin(x)
assert(f0.get_val(val_dict) ==0)
assert(f0.get_der(val_dict)['x'] == 1.0)
f1 = c1*f0
assert(f1.get_val(val_dict) ==0)
assert(f1.get_der(val_dict)['x'] == 2.0)
f2 = c1+f0
assert(f2.get_val(val_dict) ==2.0)
assert(f2.get_der(val_dict)['x'] == 1.0)
f3 = mo.sin(y)
assert(f3.get_val(val_dict) ==1.0)
assert(f3.get_der(val_dict)['y'] == math.cos(math.pi/2))
f4 = mo.cos(f3)
assert(f4.get_val(val_dict) ==math.cos(math.sin(math.pi/2)))
assert(f4.get_der(val_dict)['y'] == -math.sin(math.sin(math.pi/2))*math.cos(math.pi/2))
f5 = mo.tan(x)
assert(f5.get_val(val_dict)) == math.tan(0)
assert(f5.get_der(val_dict)['x']) == 1/math.cos(0)**2
def test_multiply(self):
val_dict = {'x' : 10, 'y' : 20}
x = Variable('x')
y = Variable('y')
c1 = 5
f0 = x*y
assert(f0.get_val(val_dict) ==200)
assert(f0.get_der(val_dict)['x'] == 20)
assert(f0.get_der(val_dict)['y'] == 10)
f1 = y*x
assert(f1.get_val(val_dict) ==200)
assert(f1.get_der(val_dict)['x'] == 20)
assert(f1.get_der(val_dict)['y'] == 10)
f2 = f0*f1
assert(f2.get_val(val_dict) ==40000)
assert(f2.get_der(val_dict)['x'] == 8000)
assert(f2.get_der(val_dict)['y'] == 4000)
f3 = f0*c1
assert(f3.get_val(val_dict) ==1000)
assert(f3.get_der(val_dict)['x'] == 100)
assert(f3.get_der(val_dict)['y'] == 50)
f4 = c1*f0
assert(f4.get_val(val_dict) ==1000)
assert(f4.get_der(val_dict)['x'] == 100)
assert(f4.get_der(val_dict)['y'] == 50)
def test_no_roots(self):
x = Variable('x')
y = Variable('y')
z = Variable('z')
f_1 = (x-1)**2*(x-2)*2
f_2 = (x-3)**3*(x-4)*4
f_3 = (x-5)**3*(x-5)*4
roots=root_finder_multiple([f_1,f_2,f_3])
assert(len(roots)==0)
def test_divide_by_zero_dir(self):
val_dict = {'x' : 0}
x = Variable('x')
y = Variable('y')
c1 = 1/3
f0 = x**c1
with pytest.raises(ZeroDivisionError):
f0.get_der(val_dict)['x']
def test_multiple_roots(self):
x = Variable('x')
y = Variable('y')
z = Variable('z')
f_1 = (x-1)**3*(x-2)
f_2 = (x-1)**4*(x-2)
f_3 = (x-1)**5*(x-2)
roots=root_finder_multiple([f_1,f_2,f_3])
assert(len(roots)==2)
assert((((abs(roots[0]-2)<TOL) and (abs(roots[1]-1)<TOL)) or ((abs(roots[0]-1)<TOL) and (abs(roots[1]-2)<TOL))))
def test_single_root(self):
x = Variable('x')
y = Variable('y')
z = Variable('z')
f_1 = (x-1)**2*(x-2)*2
f_2 = (x-2)**3*(x-4)*4
f_3 = (x-5)**3*(x-2)*4
roots=root_finder_multiple([f_1,f_2,f_3])
assert(len(roots)==1)
assert(abs(roots[0]-2)<TOL)
def test_neg(self):
val_dict = {'x' : 10, 'y' : 5}
x = Variable('x')
y = Variable('y')
c1 = 2.0
f1 = c1*x
f2 = -f1
assert(f2.get_val(val_dict) == -20.0)
f3 = x*y
f4 = -f3
assert(f4.get_val(val_dict) == -50.0)
assert(f4.get_der(val_dict)['x']==-5)
assert(f4.get_der(val_dict)['y']==-10)
def test_exp(self):
val_dict = {'x' : 10, 'y' : 5}
x = Variable('x')
y = Variable('y')
c1 = 2.0
c2 = 0.0
f0 = mo.exp(x)
assert(f0.get_val(val_dict) == math.exp(10))
assert(f0.get_der(val_dict)['x'] == math.exp(10))
f1 = c1*f0
assert(f1.get_val(val_dict)==2.0*math.exp(10))
assert(f1.get_der(val_dict)['x'] == 2.0*math.exp(10))
def test_hyperbolic_trig(self):
val_dict = {'x' : 0, 'y' : math.pi/2}
x = Variable('x')
y = Variable('y')
f1 = mo.tanh(x)
assert(f1.get_val(val_dict) == 0)
assert(f1.get_der(val_dict)['x'] == 1)
f2 = mo.cosh(x)
assert(f2.get_val(val_dict) == 1)
assert(f2.get_der(val_dict)['x'] == 0)
f3 = mo.sinh(x)
assert(f3.get_val(val_dict) == 0)
assert(f3.get_der(val_dict)['x'] == 1)
def DeclareVariables(self, base_name, dim):
var = [{base_name + '_' + str(i+1) + ('_' + str(j+1) if dim[1] > 1 else '') : \
Variable(base_name + '_' + str(i+1) + ('_' + str(j+1) if dim[1] > 1 else '')) \
for j in range(dim[1])} for i in range(dim[0])]
val_dict = [{base_name + '_' + str(i+1) + ('_' + str(j+1) if dim[1] > 1 else '') : np.random.randn()\
for j in range(dim[1])} for i in range(dim[0])]
return var, val_dict
def test_sqrt(self):
val_dict = {'x' : 10, 'y' : 4, 'z':-5}
x = Variable('x')
y = Variable('y')
z = Variable('z')
c1 = 2.0
c2 = 0.0
f = mo.sqrt(y)
g = mo.sqrt(z)
assert(f.get_val(val_dict) == 2)
assert(f.get_der(val_dict)['y'] == 0.25)
with pytest.raises(ValueError):
g.get_der(val_dict)['z']
with pytest.raises(ValueError):
g.get_val(val_dict)['z']
def test_exceptions(self):
val_dict = {'x' : 10, 'y' : 5}
x = Variable('x')
y = Variable('y')
c1 = 2.0
c2 = 0.0
f = 5
with pytest.raises(ValueError):
f0 = x/c2
f0.get_val(val_dict)
with pytest.raises(ValueError):
f0.get_der(val_dict)['p']
with pytest.raises(ValueError):
f0.get_val({'p':5})
with pytest.raises(TypeError):
f0.get_val({'x':'hello'})
with pytest.raises(TypeError):
mo.sin("hello")
def test_inverse_trig(self):
val_dict = {'x' : 0, 'y' : -1}
x = Variable('x')
y = Variable('y')
f1 = mo.arctan(x)
assert(f1.get_val(val_dict) == 0)
assert(f1.get_der(val_dict)['x'] == 1)
f2 = mo.arccos(x)
f21 = mo.arccos(y)
assert(f2.get_val(val_dict) == math.pi/2)
assert(f2.get_der(val_dict)['x'] == -1)
with pytest.raises(ValueError):
f21.get_der(val_dict)
f3 = mo.arcsin(x)
f31 = mo.arcsin(y)
assert(f3.get_val(val_dict) == 0)
assert(f3.get_der(val_dict)['x'] == 1)
with pytest.raises(ValueError):
f31.get_der(val_dict)
def test_divide(self):
val_dict = {'x' : 10, 'y' : 20, 'z':2}
x = Variable('x')
y = Variable('y')
c1 = 5
z = Variable('z')
f0 = x/y
assert(f0.get_val(val_dict) ==0.5)
assert(f0.get_der(val_dict)['x'] == 0.05)
assert(f0.get_der(val_dict)['y'] == -0.025)
f1 = y/x
assert(f1.get_val(val_dict) ==2.0)
assert(f1.get_der(val_dict)['x'] == -0.2)
assert(f1.get_der(val_dict)['y'] == 0.1)
f2 = f1/y
assert(f2.get_val(val_dict) ==0.1)
assert(f2.get_der(val_dict)['x'] == -0.01)
assert(f2.get_der(val_dict)['y'] == 0.00)
f3 = f0/f1
assert(f3.get_val(val_dict) ==0.25)
assert(f3.get_der(val_dict)['x'] == 0.05)
assert(f3.get_der(val_dict)['y'] == -0.025)
f4 = f0/c1
assert(f4.get_val(val_dict) ==0.1)
assert(f4.get_der(val_dict)['x'] == 0.01)
assert(f4.get_der(val_dict)['y'] == -0.005)
f5 = 5/x
assert(f5.get_val(val_dict)==0.5)
assert(f5.get_der(val_dict)['x']==-.05)
f6 = 5**z
assert(f6.get_val(val_dict) == 25)
assert(f6.get_der(val_dict)['z'] == 5**2*math.log(5))
def test_log(self):
val_dict = {'x' : 10, 'y' : 5, 'z' : -1, 'a' : 0}
x = Variable('x')
y = Variable('y')
z = Variable('z')
a = Variable('a')
c1 = 2.0
f0 = mo.log(x)
assert(f0.get_val(val_dict) ==math.log(10))
assert(f0.get_der(val_dict)['x'] == 0.10)
f1 = f0**c1
assert(f1.get_val(val_dict) ==math.log(10)**2.0)
assert(f1.get_der(val_dict)['x'] == 2*math.log(10)*0.1)
f2 = mo.log(y)*f0
assert(f2.get_val(val_dict) ==math.log(5)*math.log(10))
assert(f2.get_der(val_dict)['x'] == math.log(5)*(1/10))
assert(f2.get_der(val_dict)['y'] == math.log(10)*(1/5))
with pytest.raises(ValueError):
f2 = mo.log(z)
f2.get_val(val_dict)['z']
with pytest.raises(ValueError):
f2 = mo.log(a)
f2.get_der(val_dict)['a']
with pytest.raises(ValueError):
f3 = mo.log(x,-5)
f3 = mo.log(x,10)
assert(f3.get_val(val_dict) ==1)
# issue with rounding
assert(f3.get_der(val_dict)['x']-(1.0/(10.0*math.log(10)))<1e-10)
f4 = mo.loge(x)
assert(f4.get_val(val_dict) == math.log(10))
def test_subtract(self):
val_dict = {'x' : 10, 'y' : 20}
x = Variable('x')
y = Variable('y')
f0 = x - y
c1 = 5
assert(f0.get_val(val_dict) ==-10)
assert(f0.get_der(val_dict)['x'] == 1)
assert(f0.get_der(val_dict)['y'] == -1)
f1 = y - x
assert(f1.get_val(val_dict) ==10)
assert(f1.get_der(val_dict)['x'] == -1)
assert(f1.get_der(val_dict)['y'] == 1)
f2 = f0 + f1 - x
assert(f2.get_val(val_dict) ==-10)
assert(f2.get_der(val_dict)['x'] == -1)
assert(f2.get_der(val_dict)['y'] == 0)
f3 = f0 - c1
assert(f3.get_val(val_dict) == -15)
assert(f3.get_der(val_dict)['x'] == 1)
assert(f3.get_der(val_dict)['y'] == -1)
f4 = c1 - f0
assert(f4.get_val(val_dict) == 15)
assert(f4.get_der(val_dict)['x'] == -1)
assert(f4.get_der(val_dict)['y'] == 1)
f5 = x + y - y
assert(f5.get_val(val_dict) ==10)
assert(f5.get_der(val_dict)['x'] == 1)
assert(f5.get_der(val_dict)['y'] == 0)
f6 = 6 - x
assert(f6.get_val(val_dict)==-4)
def test_add(self):
val_dict = {'x' : 10, 'y' : 20, 'z':1}
x = Variable('x')
y = Variable('y')
z = Variable('z')
c1 = 5
f0 = x + y
assert(f0.get_val(val_dict) ==30)
assert(f0.get_der(val_dict)['x'] == 1)
assert(f0.get_der(val_dict)['y'] == 1)
f1 = y + x
assert(f1.get_val(val_dict) ==30)
assert(f1.get_der(val_dict)['x'] == 1)
assert(f1.get_der(val_dict)['y'] == 1)
f2 = f0 + f1 + x
assert(f2.get_val(val_dict) ==70)
assert(f2.get_der(val_dict)['x'] == 3)
assert(f2.get_der(val_dict)['y'] == 2)
f3 = f0 + c1
assert(f3.get_val(val_dict) ==35)
assert(f3.get_der(val_dict)['x'] == 1)
assert(f3.get_der(val_dict)['y'] == 1)
f4 = c1 + f0
assert(f4.get_val(val_dict) ==35)
assert(f4.get_der(val_dict)['x'] == 1)
assert(f4.get_der(val_dict)['y'] == 1)
with pytest.raises(AttributeError):
assert(c1.get_der(val_dict, ['x', 'y'])['x'] == 0)
with pytest.raises(AttributeError):
assert(c1.get_der(val_dict, ['x', 'y'])['y'] == 0)
def test_get_dict_val(self):
val_dict = {'x' : 0, 'y':5}
x = Variable('x', 5)
y = Variable('y', 7)
z = Variable('x', 7)
w = 5
p = Variable('x')
f = 2*x*y
g = 2*x*z
assert(f.get_dict_val() == {'x':5, 'y':7})
with pytest.raises(ValueError):
g.get_dict_val()
assert(p.get_der(val_dict)['x'] == 1)
def test_equalities(self):
x = Variable('x', 5)
y = Variable('y', 7)
z = Variable('x', 5)
w = Variable('y',5)
assert(not x==y)
assert(not 'a'==y)
assert(x!=y)
assert(x==z)
assert(x<y)
assert(x<=y)
assert(x>=z)
assert(x!=w)
assert(y>x)
with pytest.raises(ValueError):
assert(x > "hi")
with pytest.raises(ValueError):
assert(x < "hi")
with pytest.raises(ValueError):
assert(x >= "hi")
with pytest.raises(ValueError):
assert(x <= "hi")
f = 5*x
g = 10*x
h = 5*w
assert(not f==g)
assert(not 'a'==f)
assert(f!=g)
assert(f<=g)
assert(f<g)
assert(f!=h)
assert(h>=f)
assert(g>f)
with pytest.raises(ValueError):
assert(f > 2)
with pytest.raises(ValueError):
assert(f < 2)
with pytest.raises(ValueError):
assert(f >= 2)
with pytest.raises(ValueError):
assert(f <= 2)
f1 = VectorFunction([f,g])
f2 = VectorFunction([f,g])
f3 = VectorFunction([f,h])
t1 = 0
t2 = 1
f4 = VectorFunction([t1*f,t1*g])
f5 = VectorFunction([t2*f,t2*g])
assert(f1==f2)
assert(f1!=f3)
assert(f3<=f2)
assert(f1>=f2)
assert(f5>f4)
assert(f4<f5)
a = mo.sin(x)
b = mo.sin(y)
c = mo.sin(z)
assert(not a==b)
assert(a!=h)
assert(a<=b)
assert(a<b)
assert(b>c)
assert(b>=c)
with pytest.raises(ValueError):
assert(a > 2)
with pytest.raises(ValueError):
assert(a < 2)
with pytest.raises(ValueError):
assert(a >= 2)
with pytest.raises(ValueError):
assert(a <= 2)
def root_finder_multiple(list_of_f):
final_list = []
root_list = [denoise_root_finder(f) for f in list_of_f]
# print(root_list)
for candidates in root_list[0]:
count = 0
for compare_group in root_list[1:]:
for compare_item in compare_group:
if abs(compare_item - candidates) < TOL:
count += 1
break
if count == len(list_of_f) - 1:
final_list.append(candidates)
return final_list
# quasi newton method
if __name__ == '__main__':
x = Variable('x')
y = Variable('y')
z = Variable('z')
f_1 = (x - 1)**3 * (x - 2)
f_2 = (x - 1)**4 * (x - 2)
f_3 = (x - 1)**5 * (x - 2)
# print(root_finder.vectorNewton(VectorFunction([f_1]), verbose=False))
roots = root_finder_multiple([f_1, f_2, f_3])
print(roots)
# assert(len(roots)==2)
# assert((((abs(roots[0]-2)<TOL) and (abs(roots[1]-3)<TOL)) or ((abs(roots[0]-3)<TOL) and (abs(roots[1]-2)<TOL))))
def test_logistic(self):
val_dict = {'x' : 10, 'y' : 5}
x = Variable('x')
f = mo.logistic(x)
assert(f.get_val(val_dict) == 1/(1+math.exp(-10)))