def test_GaussOverlap():
b1 = 10.0
b2 = 20.0
r1 = [0.00, 0.00, 0.00]
r2 = [0.25, 0.25, 0.25]
f1 = vp.GaussFunc(exp=b1, pos=r1)
f2 = vp.GaussFunc(exp=b2, pos=r2)
p = b1 + b2
mu = b1 * b2 / p
R12 = sum([(x1 - x2) ** 2 for x1, x2 in zip(r1, r2)])
ref = (np.pi / p) ** (3.0 / 2.0) * np.exp(-mu * R12)
assert f1.overlap(f2) == pytest.approx(ref, rel=numprec)
def test_GaussExpNorm():
b0 = 10.0
b1 = 20.0
r0 = [0.1, 0.1, 0.1]
r1 = [-0.1, -0.1, -0.1]
f0 = vp.GaussFunc(exp=b0, pos=r0)
f1 = vp.GaussFunc(exp=b1, pos=r1)
fexp = vp.GaussExp()
fexp.append(f0)
fexp.append(f1)
ref = f0.squaredNorm() + 2.0 * f0.overlap(f1) + f1.squaredNorm()
assert fexp.squaredNorm() == pytest.approx(ref, rel=numprec)
def test_GaussExpEnergy():
b0 = 10.0
b1 = 20.0
r0 = [0.1, 0.1, 0.1]
r1 = [-0.1, -0.1, -0.1]
f0 = vp.GaussFunc(exp=b0, pos=r0)
f1 = vp.GaussFunc(exp=b1, pos=r1)
fexp = vp.GaussExp()
fexp.append(f0)
fexp.append(f1)
ref = f0.calcCoulombEnergy(f0)
ref += f0.calcCoulombEnergy(f1)
ref += f1.calcCoulombEnergy(f0)
ref += f1.calcCoulombEnergy(f1)
assert fexp.calcCoulombEnergy() == pytest.approx(ref, rel=numprec)
def test_GaussExp():
b0 = 10.0
b1 = 20.0
r0 = [0.1, 0.1, 0.1]
r1 = [-0.1, -0.1, -0.1]
f0 = vp.GaussFunc(exp=b0, pos=r0)
f1 = vp.GaussFunc(exp=b1, pos=r1)
fexp = vp.GaussExp()
fexp.append(f0)
fexp.append(f1)
ref = f0(r0) + f1(r0)
assert fexp.size() == 2
assert fexp.func(term=0).exp() == b0
assert fexp.func(term=1).exp() == b1
assert fexp(r0) == pytest.approx(ref, rel=numprec)
def test_GaussExpDerivative():
b0 = 10.0
b1 = 20.0
r0 = [0.1, 0.1, 0.1]
r1 = [-0.1, -0.1, -0.1]
r2 = [0.0, 0.0, 0.0]
f0 = vp.GaussFunc(exp=b0, pos=r0)
f1 = vp.GaussFunc(exp=b1, pos=r1)
fexp = vp.GaussExp()
fexp.append(f0)
fexp.append(f1)
df0 = f0.differentiate(dir=2)
df1 = f1.differentiate(dir=2)
dfexp = fexp.differentiate(dir=2)
ref = df0(r2) + df1(r2)
assert dfexp(r2) == pytest.approx(ref, rel=numprec)
def test_GaussDerivative():
beta = 100.0
alpha = (np.pi / beta) ** (3.0 / 2.0)
r_0 = [0.25, 0.25, 0.25]
r_1 = [0.25, 0.25, 0.35]
f = vp.GaussFunc(coef=alpha, exp=beta, pos=r_0)
df = f.differentiate(dir=2)
ref = -(2.0 / 10.0) * alpha * beta * np.exp(-1.0)
assert df(r_0) == 0.0
assert df(r_1) == pytest.approx(ref, rel=numprec)
def test_GaussFunc():
beta = 100.0
alpha = (np.pi / beta) ** (3.0 / 2.0)
r_0 = [0.25, 0.25, 0.25]
r_1 = [0.25, 0.25, 0.35]
f = vp.GaussFunc(coef=alpha, exp=beta, pos=r_0)
ref = alpha * np.exp(-1.0)
assert f(r_0) == alpha
assert f(r_1) == pytest.approx(ref, rel=numprec)
assert f.coef() == alpha
assert f.pos() == r_0
assert f.exp() == beta
assert f.pow(dim=2) == 0
from vampyr import vampyr3d as vp
epsilon = 1.0e-3
mu = epsilon / 10
D = 3
k = 5
N = -2
world = vp.BoundingBox(scale=N)
mra = vp.MultiResolutionAnalysis(box=world, order=k)
r0 = [0.8, 0.8, 0.8]
beta = 10.0
alpha = (beta / np.pi)**(D / 2.0)
ffunc = vp.GaussFunc(coef=alpha, exp=beta, pos=r0)
ref_energy = ffunc.calcCoulombEnergy(ffunc)
ftree = vp.FunctionTree(mra)
vp.advanced.build_grid(out=ftree, inp=ffunc)
vp.advanced.project(prec=epsilon, out=ftree, inp=ffunc)
def test_Identity():
I = vp.IdentityConvolution(mra, prec=epsilon)
gtree = vp.FunctionTree(mra)
vp.advanced.apply(prec=epsilon, out=gtree, oper=I, inp=ftree)
assert gtree.integrate() == pytest.approx(ftree.integrate(), rel=epsilon)
gtree2 = I(ftree)
def test_GaussEnergy():
beta = 100.0
alpha = (np.pi / beta) ** (3.0 / 2.0)
f = vp.GaussFunc(coef=alpha, exp=beta)
ref = np.sqrt(2.0 * beta / np.pi)
assert f.calcCoulombEnergy(f) == pytest.approx(ref, rel=numprec)
def test_GaussNorm():
beta = 10.0
f = vp.GaussFunc(exp=beta)
ref = (np.pi / (2.0 * beta)) ** (3.0 / 2.0)
assert f.squaredNorm() == pytest.approx(ref, rel=numprec)
assert f.squaredNorm() == f.overlap(f)