def test_reuse_of_expr():
x = cg.Symbol('x')
y = cg.Symbol('y')
xy = x * y
f = (xy + 1) * xy
checkf(f, {x: 2, y: 3}, value=42, ngrad={x: 39, y: 26})
def test_exp():
x = cg.Symbol('x')
f = cg.sym_exp(x)
checkf(f, {x: 2}, value=math.exp(2), ngrad={x: math.exp(2)})
checkf(f, {x: [1, 0]},
value=[math.exp(1), math.exp(0)],
ngrad={x: [math.exp(1), math.exp(0)]})
def test_pow():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = x**y
checkf(f, {x: 2, y: 3}, value=8, ngrad={x: 12, y: math.log(256)})
d = cg.symbolic_gradient(f)
checkf(d[x], {
x: 2,
y: 3
}, value=12, ngrad={
x: 12,
y: 4 + math.log(4096)
}) # ddf/dxdx and ddf/dxdy
checkf(d[y], {
x: 2,
y: 3
},
value=math.log(256),
ngrad={
x: 4 + math.log(4096),
y: 8 * math.log(2) * math.log(2)
}) # ddf/dydx and ddf/dydy
f = (x * 2 + y)**2
checkf(f, {x: 2, y: 3}, value=7**2, ngrad={x: 2 * 7 * 2, y: 2 * 7 * 1})
def test_add():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = x + y
checkf(f, {x: 2, y: 3}, value=5, ngrad={x: 1, y: 1})
checkf(f, {
x: [2, 3],
y: [4, 5]
},
value=[6, 8],
ngrad={
x: [1, 1],
y: [1, 1]
})
def test_sub():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = x - y
checkf(f, {x: 2, y: 3}, value=-1, ngrad={x: 1, y: -1})
checkf(f, {
x: [2, 3],
y: [4, 5]
},
value=[-2, -2],
ngrad={
x: [1, 1],
y: [-1, -1]
})
def test_complex_expr():
x = cg.Symbol('x')
y = cg.Symbol('y')
z = cg.Symbol('z')
f = (x * y + 3) / (z - 2)
checkf(f, {x: 3, y: 4, z: 4}, value=7.5, ngrad={x: 2., y: 1.5, z: -3.75})
k = x * 3 - math.pi
m = f / k
checkf(m, {
x: 3,
y: 4,
z: 4
},
value=1.28021142206776,
ngrad={
x: -0.314186801525697,
y: 0.2560422844135512,
z: -0.64010571103387
})
def test_circle():
x = cg.Symbol('x')
y = cg.Symbol('y')
c = sdf.Circle(center=[1, 1], radius=1.)
checkf(c.sdf, {x: 2, y: 1}, value=0., ngrad={x: 1, y: 0})
checkf(c.sdf, {
x: 0.9,
y: 0.7
},
value=-0.683772,
ngrad={
x: -0.316228,
y: -0.948683
})
checkf(c.sdf, {x: 5, y: 4}, value=4, ngrad={x: 0.8, y: 0.6})
def test_halfspace():
x = cg.Symbol('x')
y = cg.Symbol('y')
c = sdf.Halfspace(normal=[0, 1], d=1)
checkf(c.sdf, {x: 0, y: 0}, value=-1., ngrad={x: 0, y: 1})
def test_sqrt():
x = cg.Symbol('x')
f = cg.sym_sqrt(x)
checkf(f, {x: 4}, value=2, ngrad={x: 0.25})
def test_neg():
x = cg.Symbol('x')
f = -x
checkf(f, {x: 2}, value=-2, ngrad={x: -1})
def test_log():
x = cg.Symbol('x')
f = cg.sym_log(x)
checkf(f, {x: 2}, value=math.log(2), ngrad={x: 1 / 2})
def test_div():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = x / y
checkf(f, {x: 2, y: 3}, value=2 / 3, ngrad={x: 1 / 3, y: -2 / 9})
def test_mul():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = x * y
checkf(f, {x: 2, y: 3}, value=6, ngrad={x: 3, y: 2})
def test_sum():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = cg.sym_sum([x, y, x, y])
checkf(f, {x: 2, y: 3}, value=10, ngrad={x: 2, y: 2})
def test_min():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = cg.sym_min(x, y)
checkf(f, {x: 2, y: 1}, value=1, ngrad={x: 0, y: 1}, with_sgrad=False)
def test_cos():
x = cg.Symbol('x')
f = cg.sym_cos(x)
checkf(f, {x: 2}, value=math.cos(2), ngrad={x: -math.sin(2)})
def test_max():
x = cg.Symbol('x')
y = cg.Symbol('y')
f = cg.sym_max(x, y)
checkf(f, {x: 2, y: 1}, value=2, ngrad={x: 1, y: 0}, with_sgrad=False)