def test_Div_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = (3 * x + 1) / (x - 2)
deriv = expr.diff(x)
ref = (3 * (3.14 - 2) - (3 * 3.14 + 1)) / ((3.14 - 2)**2)
assert abs(deriv.evalf(np.array([3.14])) - ref) < 1e-15
def test_Matrix():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
matrix = ns.Matrix(2, 2, [[x + 1, y - 2], [x - y, x * y]])
out = matrix.eval_float(np.array([2., 3.]))
assert np.allclose(out, [[3, 1], [-1, 6]])
def test_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = (3 * x)
deriv = expr.diff(x)
ref = ns.Number(3)
assert (deriv == ref) is True
assert (-x).diff(x) == ns.Number(-1)
def test_trigfuncs_evalf():
ns = NameSpace()
cos_pi = ns.cos(ns.pi)
sin_pi = ns.sin(ns.pi)
tan_pi = ns.tan(ns.pi)
assert abs(cos_pi.evalf(np.array([])) + 1) < 1e-15
assert abs(sin_pi.evalf(np.array([]))) < 1e-15
assert abs(tan_pi.evalf(np.array([]))) < 1e-15
def test_trigfuncs_evalf():
ns = NameSpace()
cos_pi = ns.cos(ns.pi)
sin_pi = ns.sin(ns.pi)
tan_pi = ns.tan(ns.pi)
assert abs(cos_pi.evalf(np.array([])) + 1) < 1e-15
assert abs(sin_pi.evalf(np.array([]))) < 1e-15
assert abs(tan_pi.evalf(np.array([]))) < 1e-15
def test_Lambdify():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
z = ns.Symbol('z')
u = ns.Symbol('u')
v = ns.Symbol('v')
w = ns.Symbol('w')
lmb0 = ns.Lambdify((x, y, z, u, v, w), [x, y, z, u, v, w])
out0 = lmb0(np.array([2., 3, 4, 5, 6, 7]))
ref0 = [2., 3, 4, 5, 6, 7]
assert np.allclose(out0.flatten(), ref0)
lmb3 = ns.Lambdify((z, y, x), [x, y, z])
out3 = lmb3(np.array([2., 3, 4]))
ref3 = [4, 3, 2]
assert np.allclose(out3.flatten(), ref3)
lmb1 = ns.Lambdify((x, y), [x + y, x - y, x * y, 13 * x + 2 * y])
out1 = lmb1(np.array([2.0, 3.0]))
ref1 = [5, -1, 6, 13 * 2 + 2 * 3]
assert np.allclose(out1.flatten(), ref1)
lmb2 = ns.Lambdify((y, x), [x + y, x - y, x * y])
out2 = lmb2(np.array([2.0, 3.0]))
ref2 = [5, 1, 6]
assert np.allclose(out2.flatten(), ref2)
def test_NameSpace_Symbol():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
add = x + y
result = add.evalf(np.array([3., 5.]))
assert abs(result - 8) < 1e-15
sub = x - y
result = sub.evalf(np.array([3., 5.]))
assert abs(result + 2) < 1e-15
def test_jacobian():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
my = ns.Matrix(2, 1, [x + y, x * y])
mx = ns.Matrix(1, 2, [x, y])
assert my.shape == (2, 1)
assert mx.shape == (1, 2)
J = my.jacobian(mx)
out = J.eval_float(np.array([2., 3.]))
assert np.allclose(out, [[1, 1], [3, 2]])
def test_has():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
add = x + y
assert add.has(x)
assert add.has(y)
mul = 2 * y
assert mul.has(y)
assert not mul.has(x)
expr = (1 + 3 / (1 + x))
assert expr.has(x)
assert not expr.has(y)
def test_division():
ns = NameSpace(2)
assert ns.symbol_names == []
x, y = map(ns.Symbol, 'x y'.split())
zero_over_x_1 = 0 / x
zero_over_x_2 = 0 / x
assert zero_over_x_1 == zero_over_x_2
expr = x / y
assert abs(expr.evalf(np.array([3., 7.])) - 3 / 7) < 1e-15
assert x / 3 == x / 3
assert 3 / y == 3 / y
assert 3 / x != 3 / y
def test_NameSpace_relational_equal():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
lt = ns.lt(x, y)
le = ns.le(x, y)
eq = ns.eq(x, y)
ne = ns.ne(x, y)
ge = ns.ge(x, y)
gt = ns.gt(x, y)
assert (x < y) == lt
assert (x < y) != le
assert (x <= y) == le
assert (x <= y) != eq
assert (x == y) == eq
assert (x == y) != ne
assert (x != y) == ne
assert (x != y) != ge
assert (x >= y) == ge
assert (x >= y) != gt
assert (x > y) == gt
assert (x > y) != lt
def test_NameSpace_relational():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
lt = ns.lt(x, y)
le = ns.le(x, y)
eq = ns.eq(x, y)
ne = ns.ne(x, y)
ge = ns.ge(x, y)
gt = ns.gt(x, y)
assert lt.evalb(np.array([3., 5.])) is True
assert lt.evalb(np.array([5., 5.])) is False
assert le.evalb(np.array([3., 5.])) is True
assert le.evalb(np.array([5., 5.])) is True
assert eq.evalb(np.array([3., 5.])) is False
assert eq.evalb(np.array([5., 5.])) is True
assert ne.evalb(np.array([3., 5.])) is True
assert ne.evalb(np.array([5., 5.])) is False
assert ge.evalb(np.array([3., 5.])) is False
assert ge.evalb(np.array([5., 5.])) is True
assert gt.evalb(np.array([3., 5.])) is False
assert gt.evalb(np.array([5., 5.])) is False
def test_NameSpace_relational_equal():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
lt = ns.lt(x, y)
le = ns.le(x, y)
eq = ns.eq(x, y)
ne = ns.ne(x, y)
ge = ns.ge(x, y)
gt = ns.gt(x, y)
assert (x < y) == lt
assert (x < y) != le
assert (x <= y) == le
assert (x <= y) != eq
assert (x == y) == eq
assert (x == y) != ne
assert (x != y) == ne
assert (x != y) != ge
assert (x >= y) == ge
assert (x >= y) != gt
assert (x > y) == gt
assert (x > y) != lt
def test_NameSpace_relational():
ns = NameSpace(2)
x = ns.Symbol('x')
y = ns.Symbol('y')
lt = ns.lt(x, y)
le = ns.le(x, y)
eq = ns.eq(x, y)
ne = ns.ne(x, y)
ge = ns.ge(x, y)
gt = ns.gt(x, y)
assert lt.evalb(np.array([3., 5.])) is True
assert lt.evalb(np.array([5., 5.])) is False
assert le.evalb(np.array([3., 5.])) is True
assert le.evalb(np.array([5., 5.])) is True
assert eq.evalb(np.array([3., 5.])) is False
assert eq.evalb(np.array([5., 5.])) is True
assert ne.evalb(np.array([3., 5.])) is True
assert ne.evalb(np.array([5., 5.])) is False
assert ge.evalb(np.array([3., 5.])) is False
assert ge.evalb(np.array([5., 5.])) is True
assert gt.evalb(np.array([3., 5.])) is False
assert gt.evalb(np.array([5., 5.])) is False
def test_expm1():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.expm1(3*x + 1e-16)
assert abs(expr.evalf(np.array([3.14e-17])) - 1.942e-16) < 1e-18
def test_tan_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.tan(3*x + 1)
ref = 3*(1 + math.tan(3*3.14 + 1)**2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_cbrt_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.cbrt(3 * x + 1)
ref = 1. / (3 * 3.14 + 1)**(2 / 3.)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_expm1_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.expm1(3 * x + 1e-16)
ref = 3 + 2.86e-14
assert abs(expr.diff(x).evalf(np.array([3.14e-15])) - ref) < 1e-15
def test_exp2_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.exp2(3 * x + 1)
ref = 3 * 2**(3 * 3.14 + 1) * math.log(2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-12
def test_atanh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.atanh(3 * x + 4)
ref = -0.0167507554590712
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_log10_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.log10(3*x + 1)
ref = 3/(3*3.14 + 1)/math.log(10)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_factor():
ns = NameSpace()
fortytwo = ns.Number(42)
factors = ns.factor(fortytwo)
ref = ns.mul(2, 3, 7)
assert ref == factors
def test_erfc_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.erfc(.1*x - 1)
ref = -.1*2*math.exp(-(.1*3.14-1)**2)/math.pi**.5
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_cbrt_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.cbrt(3*x + 1)
ref = 1./(3*3.14 + 1)**(2/3.)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_sqrt_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.sqrt(3*x + 1)
ref = .5*3/(3*3.14 + 1)**.5
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_expm1_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.expm1(3*x + 1e-16)
ref = 3 + 2.86e-14
assert abs(expr.diff(x).evalf(np.array([3.14e-15])) - ref) < 1e-15
def test_tanh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.tanh(.1 * x + .2)
ref = .1 * (1 - math.tanh(.1 * 3.14 + .2)**2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_acosh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.acosh(3 * x + 4)
ref = 0.224170172808993
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_atanh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.atanh(3*x + 4)
ref = -0.0167507554590712
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_asinh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.asinh(3 * x + 4)
ref = 0.222928886183630
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_asin_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.asin(.1*x + .2)
ref = 0.11657862476093600653
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_log10_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.log10(3 * x + 1)
ref = 3 / (3 * 3.14 + 1) / math.log(10)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_asinh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.asinh(3*x + 4)
ref = 0.222928886183630
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_expm1():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.expm1(3 * x + 1e-16)
assert abs(expr.evalf(np.array([3.14e-17])) - 1.942e-16) < 1e-18
def test_factor():
ns = NameSpace()
fortytwo = ns.Number(42)
factors = ns.factor(fortytwo)
ref = ns.mul(2, 3, 7)
assert ref == factors
def test_sqrt_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.sqrt(3 * x + 1)
ref = .5 * 3 / (3 * 3.14 + 1)**.5
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_acosh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.acosh(3*x + 4)
ref = 0.224170172808993
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_erfc_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.erfc(.1 * x - 1)
ref = -.1 * 2 * math.exp(-(.1 * 3.14 - 1)**2) / math.pi**.5
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_tanh_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.tanh(.1*x + .2)
ref = .1*(1 - math.tanh(.1*3.14 + .2)**2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_Pow_diff0():
ns = NameSpace(7)
x = ns.Symbol('x')
expr = (3 * x + 1)**(x - 2)
deriv = expr.diff(x)
assert abs(deriv.evalf(np.array([3.14])) - 38.6541588883393) < 1e-13
def test_exp2_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.exp2(3*x + 1)
ref = 3*2**(3*3.14 + 1)*math.log(2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-12
def test_equality():
ns = NameSpace()
p0 = ns.Symbol('p')
p1 = ns.Symbol('p')
assert p0 == p1
assert p1 == p1
def test_cos_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.cos(3 * x + 1)
ref = -3 * math.sin(3 * 3.14 + 1)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_Dummy():
ns = NameSpace()
d = ns.Dummy()
lmb = ns.Lambdify([d], [3 * d, 8])
assert np.allclose(lmb(np.array([7.0])), [21, 8])
def test_cos_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.cos(3*x + 1)
ref = -3*math.sin(3*3.14 + 1)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_asin_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.asin(.1 * x + .2)
ref = 0.11657862476093600653
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_atan_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.atan(.1 * x + .2)
ref = .1 / ((.1 * 3.14 + .2)**2 + 1)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_tan_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.tan(3 * x + 1)
ref = 3 * (1 + math.tan(3 * 3.14 + 1)**2)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15
def test_atan_diff0():
ns = NameSpace(1)
x = ns.Symbol('x')
expr = ns.atan(.1*x + .2)
ref = .1/((.1*3.14+.2)**2 + 1)
assert abs(expr.diff(x).evalf(np.array([3.14])) - ref) < 1e-15