def construct_array_contraction(contractions, points):
"""Return the evaluations of the given contractions at the given coordinates.
Parameters
----------
contractions : GeneralizedContractionShell
Contracted Cartesian Gaussians (of the same shell) that will be used to construct an
array.
points : np.ndarray(N, 3)
Coordinates of the points in space (in atomic units) where the basis functions are
evaluated.
Rows correspond to the points and columns correspond to the x, y, and z components.
Returns
-------
array_contraction : np.ndarray(M, L_cart, N)
Evaluations of the given Cartesian contractions at the given coordinates.
First index corresponds to segmented contractions within the given generalized
contraction (same exponents and angular momentum, but different coefficients). `M` is
the number of segmented contractions with the same exponents (and angular momentum).
Second index corresponds to angular momentum vector. `L_cart` is the number of Cartesian
contractions for the given angular momentum.
Third index corresponds to coordinates at which the contractions are evaluated. `N` is
the number of coordinates at which the contractions are evaluated.
Raises
------
TypeError
If contractions is not a GeneralizedContractionShell instance.
If points is not a two-dimensional numpy array with 3 columns.
Note
----
Since all of the keyword arguments of `construct_array_cartesian`,
`construct_array_spherical`, and `construct_array_lincomb` are ultimately passed
down to this method, all of the mentioned methods must be called with the keyword arguments
`points` and `orders`.
"""
if not isinstance(contractions, GeneralizedContractionShell):
raise TypeError(
"`contractions` must be a GeneralizedContractionShell instance."
)
if not (isinstance(points, np.ndarray) and points.ndim == 2
and points.shape[1] == 3):
raise TypeError(
"`points` must be given as a two-dimensional numpy array with 3 columnms."
)
alphas = contractions.exps
prim_coeffs = contractions.coeffs
angmom_comps = contractions.angmom_components_cart
center = contractions.coord
norm_prim_cart = contractions.norm_prim_cart
output = _eval_deriv_contractions(points, np.zeros(3), center,
angmom_comps, alphas, prim_coeffs,
norm_prim_cart)
return output
def test_evaluate_construct_array_contraction():
"""Test gbasis.evals.eval.Eval.construct_array_contraction."""
test = GeneralizedContractionShell(1, np.array([0.5, 1, 1.5]),
np.array([1.0, 2.0]),
np.array([0.1, 0.01]))
answer = np.array([
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
np.array([0, 0, 0]),
np.array([0.5, 1, 1.5]),
np.array([angmom_comp]),
np.array([0.1, 0.01]),
np.array([1, 2]),
np.array([[
(2 * 0.1 / np.pi)**(3 / 4) * (4 * 0.1)**(1 / 2) /
np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
(2 * 0.01 / np.pi)**(3 / 4) * (4 * 0.01)**(1 / 2) /
np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
]]),
) for angmom_comp in test.angmom_components_cart
]).reshape(3, 1)
assert np.allclose(
Eval.construct_array_contraction(points=np.array([[2, 3, 4]]),
contractions=test), answer)
with pytest.raises(TypeError):
Eval.construct_array_contraction(points=np.array([[2, 3, 4]]),
contractions=None)
with pytest.raises(TypeError):
Eval.construct_array_contraction(points=np.array([[2, 3, 4]]),
contractions={1: 2})
with pytest.raises(TypeError):
Eval.construct_array_contraction(points=np.array([2, 3, 4]),
contractions=test)
with pytest.raises(TypeError):
Eval.construct_array_contraction(points=np.array([[3, 4]]),
contractions=test)
def evaluate_deriv_prim(coord, orders, center, angmom_comps, alpha):
"""Return the evaluation of the derivative of a Gaussian primitive.
Parameters
----------
coord : np.ndarray(3,)
Point in space where the derivative of the Gaussian primitive is evaluated.
orders : np.ndarray(3,)
Orders of the derivative.
Negative orders are treated as zero orders.
center : np.ndarray(3,)
Center of the Gaussian primitive.
angmom_comps : np.ndarray(3,)
Component of the angular momentum that corresponds to this dimension.
alpha : float
Value of the exponential in the Guassian primitive.
Returns
-------
derivative : float
Evaluation of the derivative.
Note
----
If you want to evaluate the derivative of the contractions of the primitive, then use
`gbasis.evals._deriv.evaluate_deriv_contraction` instead.
"""
return _eval_deriv_contractions(
coord.reshape(1, 3),
orders,
center,
angmom_comps.reshape(1, 3),
np.array([alpha]),
np.array([1.0]),
np.array([[1]]),
)[0]
def test_evaluate_deriv_construct_array_contraction():
"""Test gbasis.evals.evaluate_deriv.EvalDeriv.construct_array_contraction."""
points = np.array([[2, 3, 4]])
orders = np.array([0, 0, 0])
contractions = GeneralizedContractionShell(
1, np.array([0.5, 1, 1.5]), np.array([1.0, 2.0]), np.array([0.1, 0.01])
)
with pytest.raises(TypeError):
EvalDeriv.construct_array_contraction(
points=[[2, 3, 4]], orders=orders, contractions=contractions
)
with pytest.raises(TypeError):
EvalDeriv.construct_array_contraction(
points=points, orders=[0, 0, 0], contractions=contractions
)
with pytest.raises(TypeError):
EvalDeriv.construct_array_contraction(
points=points, orders=orders, contractions=contractions.__dict__
)
with pytest.raises(TypeError):
EvalDeriv.construct_array_contraction(
points=points.reshape(3, 1), orders=orders, contractions=contractions
)
with pytest.raises(TypeError):
EvalDeriv.construct_array_contraction(
points=points, orders=orders.reshape(1, 3), contractions=contractions
)
with pytest.raises(ValueError):
EvalDeriv.construct_array_contraction(
points=points, orders=np.array([-1, 0, 0]), contractions=contractions
)
with pytest.raises(ValueError):
EvalDeriv.construct_array_contraction(
points=points, orders=np.array([0.0, 0, 0]), contractions=contractions
)
# first order
for k in range(3):
orders = np.zeros(3, dtype=int)
orders[k] = 1
test = GeneralizedContractionShell(
1, np.array([0.5, 1, 1.5]), np.array([1.0, 2.0]), np.array([0.1, 0.01])
)
answer = np.array(
[
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([angmom_comp]),
np.array([0.1, 0.01]),
np.array([1, 2]),
np.array(
[
[
(2 * 0.1 / np.pi) ** (3 / 4)
* (4 * 0.1) ** (1 / 2)
/ np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
(2 * 0.01 / np.pi) ** (3 / 4)
* (4 * 0.01) ** (1 / 2)
/ np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
]
]
),
)
for angmom_comp in test.angmom_components_cart
]
).reshape(3, 1)
assert np.allclose(
EvalDeriv.construct_array_contraction(
points=np.array([[2, 3, 4]]), orders=orders, contractions=test
),
answer,
)
# second order
for k, l in it.product(range(3), range(3)):
orders = np.zeros(3, dtype=int)
orders[k] += 1
orders[l] += 1
test = GeneralizedContractionShell(
1, np.array([0.5, 1, 1.5]), np.array([1.0, 2.0]), np.array([0.1, 0.01])
)
answer = np.array(
[
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([angmom_comp]),
np.array([0.1, 0.01]),
np.array([1, 2]),
np.array(
[
[
(2 * 0.1 / np.pi) ** (3 / 4)
* (4 * 0.1) ** (1 / 2)
/ np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
(2 * 0.01 / np.pi) ** (3 / 4)
* (4 * 0.01) ** (1 / 2)
/ np.sqrt(np.prod(factorial2(2 * angmom_comp - 1))),
]
]
),
)
for angmom_comp in test.angmom_components_cart
]
).reshape(3, 1)
assert np.allclose(
EvalDeriv.construct_array_contraction(
points=np.array([[2, 3, 4]]), orders=orders, contractions=test
),
answer,
)
def construct_array_contraction(contractions, points, orders):
r"""Return the array associated with a set of contracted Cartesian Gaussians.
Parameters
----------
contractions : GeneralizedContractionShell
Contracted Cartesian Gaussians (of the same shell) that will be used to construct an
array.
points : np.ndarray(N, 3)
Cartesian coordinates of the points in space (in atomic units) where the basis
functions are evaluated.
Rows correspond to the points and columns correspond to the :math:`x, y, \text{and} z`
components.
orders : np.ndarray(3,)
Orders of the derivative.
Returns
-------
array_contraction : np.ndarray(M, L_cart, N)
Array associated with the given instance(s) of GeneralizedContractionShell.
Dimension 0 corresponds to segmented contractions within the given generalized
contraction (same exponents and angular momentum, but different coefficients). `M` is
the number of segmented contractions with the same exponents (and angular momentum).
Dimension 1 corresponds to angular momentum vector. `L_cart` is the number of Cartesian
contractions for the given angular momentum.
Dimension 2 corresponds to coordinates at which the contractions are evaluated. `N` is
the number of coordinates at which the contractions are evaluated.
Raises
------
TypeError
If contractions is not a `GeneralizedContractionShell` instance.
If points is not a two-dimensional `numpy` array with 3 columns.
If orders is not a one-dimensional `numpy` array with 3 elements.
ValueError
If orders has any negative numbers.
If orders does not have `dtype` int.
Note
----
Since all of the keyword arguments of `construct_array_cartesian`,
`construct_array_spherical`, and `construct_array_lincomb` are ultimately passed
down to this method, all of the mentioned methods must be called with the keyword arguments
`points` and `orders`.
"""
if not isinstance(contractions, GeneralizedContractionShell):
raise TypeError(
"`contractions` must be a `GeneralizedContractionShell` instance."
)
if not (isinstance(points, np.ndarray) and points.ndim == 2
and points.shape[1] == 3):
raise TypeError(
"`points` must be given as a two-dimensional `numpy` array with 3 columns."
)
if not (isinstance(orders, np.ndarray) and orders.shape == (3, )):
raise TypeError(
"Orders of the derivatives must be a one-dimensional `numpy` array with 3 elements."
)
if np.any(orders < 0):
raise ValueError("Negative order of derivative is not supported.")
if orders.dtype != int:
raise ValueError(
"Orders of the derivatives must be given as integers.")
alphas = contractions.exps
prim_coeffs = contractions.coeffs
angmom_comps = contractions.angmom_components_cart
center = contractions.coord
norm_prim_cart = contractions.norm_prim_cart
output = _eval_deriv_contractions(points, orders, center, angmom_comps,
alphas, prim_coeffs, norm_prim_cart)
return output
def test_evaluate_deriv_generalized_contraction():
"""Test gbasis.evals._deriv._eval_deriv_contractions for generalized contractions."""
for k, l in it.product(range(3), range(3)):
orders = np.zeros(3, dtype=int)
orders[k] += 1
orders[l] += 1
for x, y, z in it.product(range(4), range(4), range(4)):
# only contraction
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z]]),
np.array([1, 2]),
np.array([[3, 4, 5], [6, 7, 8]]),
np.array([[1, 1]]),
),
np.array(
[
3
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 6
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
4
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 7
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
5
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 8
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
]
).reshape(3, 1, 1),
)
# contraction + multiple angular momentums
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z], [x - 1, y + 2, z + 1]]),
np.array([1, 2]),
np.array([[3, 4, 5], [6, 7, 8]]),
np.array([[1, 1]]),
),
np.array(
[
[
3
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 6
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
3
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
1,
)
+ 6
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
2,
),
],
[
4
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 7
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
4
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
1,
)
+ 7
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
2,
),
],
[
5
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
1,
)
+ 8
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x, y, z]),
2,
),
5
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
1,
)
+ 8
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
2,
),
],
]
),
)
def test_eval_deriv_contractions():
"""Test gbasis.evals._deriv._eval_deriv_contractions."""
# first order
for k in range(3):
orders = np.zeros(3, dtype=int)
orders[k] = 1
for x, y, z in it.product(range(3), range(3), range(3)):
# only contraction
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z]]),
np.array([1, 2]),
np.array([3, 4]),
np.array([[1, 1]]),
),
3
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 1
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 2
),
)
# contraction + multiple angular momentums
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z], [x - 1, y + 2, z + 1]]),
np.array([1, 2]),
np.array([3, 4]),
np.array([[1, 1]]),
),
[
3
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 1
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 2
),
3
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
1,
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
2,
),
],
)
# second order
for k, l in it.product(range(3), range(3)):
orders = np.zeros(3, dtype=int)
orders[k] += 1
orders[l] += 1
for x, y, z in it.product(range(4), range(4), range(4)):
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z]]),
np.array([1]),
np.array([1]),
np.array([[1]]),
),
evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 1
),
)
# only contraction
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z]]),
np.array([1, 2]),
np.array([3, 4]),
np.array([[1, 1]]),
),
3
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 1
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 2
),
)
# contraction + multiple angular momentums
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 3, 4]]),
orders,
np.array([0.5, 1, 1.5]),
np.array([[x, y, z], [x - 1, y + 2, z + 1]]),
np.array([1, 2]),
np.array([3, 4]),
np.array([[1, 1]]),
),
[
3
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 1
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]), orders, np.array([0.5, 1, 1.5]), np.array([x, y, z]), 2
),
3
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
1,
)
+ 4
* evaluate_deriv_prim(
np.array([2, 3, 4]),
orders,
np.array([0.5, 1, 1.5]),
np.array([x - 1, y + 2, z + 1]),
2,
),
],
)
def test_evaluate_contractions():
"""Test gbasis.evals._deriv._evaluate_deriv_contraction without derivatization."""
# angular momentum: 0
assert np.allclose(
_eval_deriv_contractions(
np.array([[0, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 0, 0]),
np.array([[0, 0, 0]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
1,
)
assert np.allclose(
_eval_deriv_contractions(
np.array([[1.0, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 0, 0]),
np.array([[0, 0, 0]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
np.exp(-1),
)
assert np.allclose(
_eval_deriv_contractions(
np.array([[1.0, 2.0, 0]]),
np.array([0, 0, 0]),
np.array([0, 0, 0]),
np.array([[0, 0, 0]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
np.exp(-1) * np.exp(-4),
)
assert np.allclose(
_eval_deriv_contractions(
np.array([[1.0, 2.0, 3.0]]),
np.array([0, 0, 0]),
np.array([0, 0, 0]),
np.array([[0, 0, 0]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
np.exp(-1) * np.exp(-4) * np.exp(-9),
)
# angular momentum 1
assert np.allclose(
_eval_deriv_contractions(
np.array([[2.0, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 0, 0]),
np.array([[1, 0, 0]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
2 * np.exp(-2 ** 2),
)
# other angular momentum
assert np.allclose(
_eval_deriv_contractions(
np.array([[2.0, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 3, 4]),
np.array([[2, 1, 3]]),
np.array([1.0]),
np.array([1.0]),
np.array([[1.0]]),
),
4 * 3 * 4 ** 3 * np.exp(-(2 ** 2 + 3 ** 2 + 4 ** 2)),
)
# contraction
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 3, 4]),
np.array([[2, 1, 3]]),
np.array([0.1, 0.001]),
np.array([3, 4]),
np.array([[1.0, 1.0]]),
),
3 * (2 ** 2 * (-3) ** 1 * (-4) ** 3 * np.exp(-0.1 * (2 ** 2 + 3 ** 2 + 4 ** 2)))
+ 4 * (2 ** 2 * (-3) ** 1 * (-4) ** 3 * np.exp(-0.001 * (2 ** 2 + 3 ** 2 + 4 ** 2))),
)
# contraction + multiple angular momentums
assert np.allclose(
_eval_deriv_contractions(
np.array([[2, 0, 0]]),
np.array([0, 0, 0]),
np.array([0, 3, 4]),
np.array([[2, 1, 3], [1, 3, 4]]),
np.array([0.1, 0.001]),
np.array([3, 4]),
np.array([[1.0, 1.0], [1.0, 1.0]]),
),
[
[
3 * (2 ** 2 * (-3) ** 1 * (-4) ** 3 * np.exp(-0.1 * (2 ** 2 + 3 ** 2 + 4 ** 2)))
+ 4 * (2 ** 2 * (-3) ** 1 * (-4) ** 3 * np.exp(-0.001 * (2 ** 2 + 3 ** 2 + 4 ** 2)))
],
[
3 * (2 ** 1 * (-3) ** 3 * (-4) ** 4 * np.exp(-0.1 * (2 ** 2 + 3 ** 2 + 4 ** 2)))
+ 4 * (2 ** 1 * (-3) ** 3 * (-4) ** 4 * np.exp(-0.001 * (2 ** 2 + 3 ** 2 + 4 ** 2)))
],
],
)
