def test_matrix_circle_times_operations(reset_NodeDict):
va = np.matrix([[1, 2, 3], [2, 3, 4]])
vb = np.matrix([[2, 3, 4], [3, 2, 1]])
vx = np.matrix([5, 1, 2])
vy = np.matrix([[5], [1], [2]])
a, b, x, y = Var('a', va), Var('b', vb), Var('x', vx), Var('y', vy)
with pytest.raises(ValueError):
va * vx
with pytest.raises(ValueError):
va.dot(vx)
with pytest.raises(ValueError):
Mul(a, x).val
assert_all(va * vy == va.dot(vy))
assert_all(va * vy == Mul(a, y).val)
assert_all(va * vy == [[13], [21]])
assert_all(CTimes(a, a).val == np.array([[1, 4, 9], [4, 9, 16]]))
assert_all(CTimes(a, b).val == np.array([[2, 6, 12], [6, 6, 4]]))
assert_all(CTimes(b, a).val == np.array([[2, 6, 12], [6, 6, 4]]))
vd = np.matrix([1, 3])
ve = np.matrix([[1], [2], [4]])
vf = np.matrix([1, 2, 4])
d, e, f = Var('d', vd), Var('e', ve), Var('f', vf)
with pytest.raises(ValueError):
Mul(d, e).val
assert (np.all(CTimes(d, e).val == np.array([[1, 3], [2, 6], [4, 12]])))
assert (np.all(CTimes(e, d).val == np.array([[1, 3], [2, 6], [4, 12]])))
with pytest.raises(ValueError):
CTimes(d, f).val
def test_CacheKnownValues(reset_NodeDict):
x = Var('x')
fx = VSF('cos', x, np.cos)
gfx = VSF('exp', fx, np.exp)
gfx.cache()
exp_cos = lambda x: np.exp(np.cos(x))
for v in np.random.random(10):
x.val = v
assert (gfx.val == exp_cos(v))
for i in range(100):
assert (gfx.val == exp_cos(v))
y = Var('y')
hy = VSF('tanh', y, np.tanh)
hy.cache()
for v in np.random.random(10):
y.val = v
assert (hy.val == np.tanh(v))
gfx_hy = CTimes(gfx, hy)
gfx_hy.cache()
exp_cos_x_times_tanh_y = lambda x, y: exp_cos(x) * np.tanh(y)
vx = 5.7
vy = np.array([1.1, 2.1, 0.5])
x.val = vx
y.val = vy
print gfx_hy.val / exp_cos_x_times_tanh_y(vx, vy)
assert_all(gfx_hy.val == exp_cos_x_times_tanh_y(vx, vy))
print "Change x only:"
#TODO: verify hy will not be evaluated, but use cache, instead.
vx = 1.0
x.val = vx
assert_all(gfx_hy.val == exp_cos_x_times_tanh_y(vx, vy))
print "Change y only:"
#TODO: verify gfx will not be evaluated, but use cache, instead.
vy = 1.0
y.val = vy
assert_all(gfx_hy.val == exp_cos_x_times_tanh_y(vx, vy))
#Instance of Var must be single-assigned,
#but it is not yet enforced by code.
a = Var('a')
b = Var('b')
ab = Mul(a, b)
ab.cache()
assert (np.isnan(ab.val))
a.val = 1.0
assert (np.isnan(ab.val))
b.val = 2.0
assert (ab.val == 2.0)
def test_DiffKnownFunctions(reset_NodeDict):
x = Var('x')
fx = VSF('sin', x)
dfx = fx.diff(x)
dfx.cache()
#dfx is used in dgfx again. Forgetting to cache fx may casue subtle errors.
assert (dfx.expression() == 'cos(x)')
gfx = VSF('exp', Mul(Val(3), fx))
dgfx = gfx.diff(x)
assert (dgfx.expression() == u'exp(3*sin(x))⨯3⨯cos(x)')
#Caching top expressions only is enough
gfx.cache()
dgfx.cache()
for v in [1.0, 2.0, 14.2, 5.1, 5.72341]:
x.val = v
assert (dfx.val == np.cos(v))
assert (gfx.val == np.exp(3 * np.sin(v)))
#Allow slight difference for complex numpy expressions.
np.testing.assert_allclose(dgfx.val,
np.exp(3 * np.sin(v)) * 3 * np.cos(v),
rtol=1e-10,
atol=0)
hfx = VSF('log', fx)
dhfx = hfx.diff(x)
assert (dhfx.expression() == u'1/(sin(x))⨯cos(x)')
hx = VSF('log', Add(fx, VSF('exp', x)))
dhx = hx.diff(x)
assert (dhx.expression() == u'1/(sin(x)+exp(x))⨯{cos(x)+exp(x)}')
def test_ElementaryTypes(reset_NodeDict):
val0 = Val(0)
val2 = Val(2)
val10 = Val(10)
val = Mul(Val(2), Val(10))
assert (unicode(val) == '2*10')
assert (unicode(val0) == '0')
assert (unicode(val10) == '10')
def test_DiffOperations(reset_NodeDict):
x = Var('x')
y = Var('y')
fx = VSF('f', x)
fy = VSF('f', y)
gx = VSF('g', x)
gy = VSF('g', y)
gfx = VSF('g', fx)
zero = Val(0)
one = Val(1)
assert (zero == Val(0))
assert (zero != one)
assert (fx != gx)
assert (unicode(Var('x')) == 'x')
assert (unicode(fx) == 'f(x)')
assert (unicode(gfx) == 'g(f(x))')
assert (unicode(Mul(fx, gx)) == 'f(x)*g(x)')
assert (unicode(Mul(fx, gy)) == 'f(x)*g(y)')
assert (unicode(Mul(gfx, gy)) == 'g(f(x))*g(y)')
z = '0.0'
i = '1.0'
assert (unicode(Mul(
fx,
gx).diff_no_simplify(x)) == u"f`(x)⨯%s⨯g(x)+f(x)⨯g`(x)⨯%s" % (i, i))
assert (unicode(Mul(
fx,
gy).diff_no_simplify(x)) == u"f`(x)⨯%s⨯g(y)+f(x)⨯g`(y)⨯%s" % (i, z))
assert (unicode(fx.diff_no_simplify(x)) == u"f`(x)⨯%s" % i)
assert (unicode(gfx.diff_no_simplify(x)) == u"g`(f(x))⨯f`(x)⨯%s" % i)
assert (unicode(gfx.diff_no_simplify(y)) == u"g`(f(x))⨯f`(x)⨯%s" % z)
assert(unicode(Mul(gfx,gy).diff_no_simplify(x)) ==\
u'g`(f(x))⨯f`(x)⨯%s⨯g(y)+g(f(x))⨯g`(y)⨯%s'%(i,z))
assert(unicode(Mul(gfx,gy).diff_no_simplify(y)) ==\
u'g`(f(x))⨯f`(x)⨯%s⨯g(y)+g(f(x))⨯g`(y)⨯%s'%(z,i))
def test_Transpose(reset_NodeDict):
vx = np.matrix([5, 1, 2])
vy = np.matrix([1, 3, 2]).T
x = Var('x', vx)
y = Var('y', vy)
fy = VSF('f', y)
gx = VSF('g', x)
fygx = Mul(fy, gx)
assert (unicode(Transpose(fygx).simplify()) == u'[f(y)*g(x)]ᵀ')
assert (unicode(Transpose(Var('z', 2)).simplify()) == 'z')
assert (Transpose(Var('z', 2)).val == 2)
assert_all(Transpose(x).val == vx.T)
assert_all(Transpose(Transpose(x)).val == x.val)
y.val = vy.T
xyt = Mul(x, Transpose(y))
assert (unicode(Transpose(xyt)) == u'[x*yᵀ]ᵀ')
assert (xyt.val == 12)
def test_ParentsSettingOfCache():
x = Var('x')
fx = VSF('sin', x)
dfx = fx.diff(x)
gfx = VSF('exp', Mul(Val(3), fx))
dgfx = gfx.diff(x)
dgfx.cache()
assert fx in x.parents and dfx in x.parents
for expr in dgfx.children:
assert dgfx in expr.parents
def test_Evaluation(reset_NodeDict):
vx = np.array([1.0, 2.0, 3.0]).reshape(1, 3)
vy = np.array([2.0, 3.0, 4.0]).reshape(3, 1)
vz = np.array([3.0, 5.0, 7.0]).reshape(1, 3)
x = Var('x')
x.val = vx
y = Var('y', vy)
z = Var('z', vz)
with pytest.raises(ValueError):
Dot(x, Var('t', vy.T)).val
xy = Mul(x, y)
assert (unicode(xy) == 'x*y')
assert_all(xy.val == vx.dot(vy))
x_plus_z = Add(x, z)
assert (unicode(x_plus_z) == 'x+z')
assert_all(x_plus_z.val == vx + vz)
assert_all(CTimes(xy, z).val == CTimes(z, xy).val)
assert_all(CTimes(xy, z).val == vx.dot(vy) * vz)
s0 = 1.57
s = Var('s', s0)
fs = VSF('cos', s, np.cos)
assert (unicode(fs) == 'cos(s)')
assert (fs.val == np.cos(s0))
def test_SimplifyZeroAndOne(reset_NodeDict):
assert (IsIdentity(Val(1)))
assert (Mul(Val(1), Val(1)).simplify() == Val(1))
assert (Mul(Mul(Val(1), Val(1)),
Mul(Val(1), Mul(Val(1), Mul(Val(1),
Val(1))))).simplify() == Val(1))
assert (Mul(Mul(Val(1), Val(1)),
Mul(Val(1), Mul(Val(1), Mul(Val(1),
Val(0))))).simplify() == Val(0))
x = Var('x')
y = Var('y')
fx = VSF('f', x)
fy = VSF('f', y)
gx = VSF('g', x)
gy = VSF('g', y)
hx = VSF('h', x)
gfx = VSF('g', fx)
zero = Val(0)
one = Val(1)
assert (unicode(Mul(one, Add(x, y))) == '1*{x+y}')
assert (Mul(one, Add(x, y)).expression() == '1*{x+y}')
assert (unicode(Mul(one, Add(x, y)).simplify()) == 'x+y')
assert (Add(fx, zero).simplify() == fx)
assert (Mul(fx, zero).simplify() == zero)
assert (Mul(fx, one).simplify() == fx)
assert (Mul(zero, gy).simplify() == zero)
assert (Mul(gx, Mul(fx, zero)).simplify() == zero)
assert (Mul(gy, Mul(gx, Mul(fx, zero))).simplify() == zero)
assert (unicode(fx.diff(x)) == 'f`(x)')
assert (unicode(Mul(gfx, gy).diff(x)) == u'g`(f(x))⨯f`(x)⨯g(y)')
assert (unicode(Mul(gfx, gy).diff(y)) == u'g(f(x))⨯g`(y)')
assert (unicode(Mul(hx, Mul(gx, fx))) == u'h(x)*g(x)*f(x)')
assert (unicode(Mul(hx, Mul(
gx, fx)).diff(x)) == u'h`(x)⨯g(x)*f(x)+h(x)⨯{g`(x)⨯f(x)+g(x)⨯f`(x)}')
assert (unicode(Mul(hx, Mul(gx, fx)).diff(y)) == '0.0')
def test_SimplifyZeroAndIdentityMatrix(reset_NodeDict):
i = np.identity(5)
z = np.zeros((5, 5))
assert (IsIdentity(Val(i)))
assert (Mul(Val(i), Val(i)).simplify() == Val(i))
assert (Mul(Mul(Val(i), Val(i)),
Mul(Val(i), Mul(Val(i), Mul(Val(i),
Val(i))))).simplify() == Val(i))
assert (Mul(Mul(Val(i), Add(Add(Val(z), Val(z)), Val(i))),
Mul(Val(i), Mul(Val(i), Mul(Val(i),
Val(i))))).simplify() == Val(i))
assert (Mul(Mul(Val(i), Val(i)),
Mul(Val(i), Mul(Val(i), Mul(Val(i),
Val(z))))).simplify() == Val(z))