def test_f4():
f1 = "SIN(2.0/X)-COS(3*X)"
vd = "X:5.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 1.1491062551674717) < 1e-7
assert math.fabs(F1.diff("X") - 1.877178640951119) < 1e-7
def test_f1():
f1 = "POW(x, POW(x, x))"
vd = "x:2.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 16) < 1e-7
assert math.fabs(F1.diff("x") - 107.1104124466013909) < 1e-7
def test_f6():
f1 = "POW(2, X)"
vd = "X:2.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 4) < 1e-7
assert math.fabs(F1.diff("X") - 2.772588722239781) < 1e-7
def test_f3():
f1 = "EXP(3+LOG(POW(X,2)))"
vd = "X:2.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 80.342147692750670) < 1e-7
assert math.fabs(F1.diff("X") - 80.342147692750670) < 1e-7
def test_4():
# Example using exp
# dx of e^x = e^x
f1 = "EXP(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='default')) == 'exp(x)'
def test_3():
# Example using sin, cos and pow:
# sin(x)^2+cos(x)^2 = 1 thus the x-derivative=0
f1 = "SIN(x) + COS(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='default')) == '-sin(x) + cos(x)'
def test_2():
# Example using exp and log:
# e^(log(5x)) = 5x thus the x-derivative=5
f1 = "EXP(LOG(5*x))"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='default')) == '5.00000000000000'
def test_1():
# Long expression simplifying in: 6xy^2 thus the dx should be 6y^2 or '6.0*y**2'
# Example using power:
f1 = "(((((POW(x,3.0)*(3.0/x))*(3.0/x))+(POW(x,3.0)*((-3.0)/(x*x))))*y)*y)"
vd = "x:2,y:3"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='default')) == '6.0*y**2'
def test_8():
# Example using arctan
# dx of atan(x) = 1/(x^2+1)
f1 = "ARCTAN(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='all')) == '(x**2 + 1)**(-1.0)'
def test_9():
# Example using hyperbolic sine
# dx of sinh(x) = (e^(-x)+e^(x))/2 = cosh(x)
f1 = "SINH(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x")) == 'cosh(x)'
def test_11():
# Example using hyperbolic tan
# dx of tanh(x) = 4/(e^(x)+e^(-x))^2 =sech^2(x) = 1/cosh^2(x)
f1 = "TANH(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x")) == '1.0/cosh(x)**2'
def test_f5():
f1 = "SIN(POW(X, 2))*EXP(COS(3.0*Y))"
vd = "X:2.0,Y:3.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - -0.30428721849) < 1e-7
assert math.fabs(F1.diff("X") - -1.05124071609) < 1e-7
assert math.fabs(F1.diff("Y") - 0.37620716268) < 1e-7
def test_10():
# Example using hyperbolic cose
# dx of cosh(x) = (e^(x)-e^(-x))/2 = sinh(x)
f1 = "COSH(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x")) == 'sinh(x)'
def test_7():
# Example using arccos
# dx of acos(x) = -1/sqrt(1-x^2)
f1 = "ARCCOS(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x")) == '-(-x**2 + 1)**(-0.5)'
def test_6():
# Example using arcsin
# dx of asin(x) = 1/sqrt(1-x^2)
f1 = "ARCSIN(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", output='pretty')) == '(-x**2 + 1)**(-0.5)'
def test_f11():
f1 = "(3)+x"
vd = "x:1.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 4) < 1e-7
assert math.fabs(F1.diff("x") - 1) < 1e-7
assert math.fabs(F1.diff("x", order=1) - 1) < 1e-7
assert math.fabs(F1.diff("x", order=2) - 0) < 1e-7
def test_f2():
f1 = "EXP(3.0*X+X*POW(Y,2))"
vd = "X:1.0,Y:2.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
math.fabs(F1.val() - 1096.6331584284585992) < 1e-7
assert math.fabs(F1.diff("X") - 7676.432108999210194) < 1e-7
assert math.fabs(F1.diff("Y") - 4386.532633713834397) < 1e-7
def test_smallVd():
F1 = symdif.SD("x")
f2 = "x*y"
vd = "x:3"
F1.new_formula(f2)
with pytest.raises(NameError) as e:
F1.val(vd)
assert (F1.val("x:3,y:2") == 6)
return
def test_5():
# Example using tan and the latex formula
# dx of tan(x) = 1/cos^2(x)
f1 = "TAN(x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff(
"x", output='latex')) == '\\frac{1}{\\cos^{2}{\\left (x \\right )}}'
def test_noVd():
f1 = "x+y"
vd = "x:1,y:1"
F1 = symdif.SD(f1)
with pytest.raises(NameError) as e:
F1.diff_all()
assert (str(e.value) == 'Must set point to evaluate')
ret = F1.diff_all(vd)
for k, v in ret.items():
assert (v == 1)
def test_4_order():
# Example using exp
# dx of e^(2x) = 2*e^(2*x)
f1 = "EXP(2*x)"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert str(F1.symbolic_diff("x", order=1,
output='default')) == '2.0*exp(2.0*x)'
assert str(F1.symbolic_diff("x", order=2,
output='default')) == '4.0*exp(2.0*x)'
assert str(F1.symbolic_diff("x", order=3,
output='default')) == '8.0*exp(2.0*x)'
def test_f12():
f1 = "x+3)))"
vd = "x:1.0"
with pytest.raises(NameError) as e:
F1 = symdif.SD(f1)
assert (str(e.value) == "Invalid syntax")
def test_float3():
f1 = "e*pi"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - math.e * math.pi) < 1e-7
def test_float2():
f1 = "5.111"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 5.111) < 1e-7
def test_float():
f1 = "5e-10"
vd = "x:2"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 5e-10) < 1e-7
def test_f10():
f1 = "-3+x"
vd = "x:1.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() + 2) < 1e-7
def test_f8():
f1 = "x#y"
vd = "x:1.0"
with pytest.raises(NameError) as e:
F1 = symdif.SD(f1)
assert (str(e.value) == "Invalid character")
def test_f9():
f1 = "+3+x"
vd = "x:1.0"
F1 = symdif.SD(f1)
F1.set_point(vd)
assert math.fabs(F1.val() - 4) < 1e-7
