More comprehensive primitive generation (#314)

* initial commit

* second commit

* second commit

* simplify code

* linear angle

* linear angle

* test update, more fixes needed

* unifinished update

* linear angle update

* unfinished update

* unfinished update

* unifinished update

* unfinished update

* better linear angles

* better linear angles

* minor change

* fix linear bend code

* fix some tests

* add tests

* fix failing test

* add tests

* minor dihedral fix

* dihedral code fix

* add test for linear bend with ref

* add test for linear bend with ref

* add tests

* make bond angle consistent

* add tests and fix value bug

* add tests

* fix test

* change backup hessian update scheme for crfo

* revert change to hessian update scheme

* correction to angle code

* assert only for graph

* fix tests

* pr suggestions 1

* pr suggestions 2 partial

* test fix

* put methods into anypic class

* pr update 3

* pr update 4

* pr update 5

* pr update 6

* pr update 7

* pr update 8

* pr update

* pr update, changelog update

autode/atoms.py

@@ -1041,9 +1041,10 @@ def angle(self, i: int, j: int, k: int) -> Angle:
                 f"least one zero vector"
             )
 
-        value = np.arccos(np.dot(vec1, vec2) / norms)
+        # Cos(theta) must lie within [-1, 1]
+        cos_value = np.clip(np.dot(vec1, vec2) / norms, a_min=-1, a_max=1)
 
-        return Angle(value)
+        return Angle(np.arccos(cos_value))
 
     def dihedral(self, w: int, x: int, y: int, z: int) -> Angle:
         r"""

autode/mol_graphs.py

@@ -115,6 +115,15 @@ def node_matcher(self):
 
         return matcher
 
+    @property
+    def is_connected(self) -> bool:
+        """Is this graph fully connected (i.e. not separate parts)"""
+        return nx.is_connected(self)
+
+    def connected_components(self):
+        """Generate the separate connected components"""
+        return nx.connected_components(self)
+
 
 def make_graph(
     species: "Species",

autode/opt/coordinates/__init__.py

@@ -1,3 +1,3 @@
-from autode.opt.coordinates.base import OptCoordinates, CartesianComponent
+from autode.opt.coordinates.base import OptCoordinates
 from autode.opt.coordinates.cartesian import CartesianCoordinates
 from autode.opt.coordinates.dic import DIC, DICWithConstraints

autode/opt/coordinates/_autodiff.py

@@ -580,7 +580,9 @@ class DifferentiableVector3D:
     hyper-dual numbers
     """
 
-    def __init__(self, items: Sequence["VectorHyperDual"]):
+    def __init__(
+        self, items: Sequence[Union["VectorHyperDual", numeric_type]]
+    ):
         """
         Initialise the 3D vector from a list of 3 hyperdual numbers
 
@@ -590,7 +592,9 @@ def __init__(self, items: Sequence["VectorHyperDual"]):
         items = list(items)
         if len(items) != 3:
             raise ValueError("A 3D vector must have only 3 components")
-        assert all(isinstance(item, VectorHyperDual) for item in items)
+        assert all(
+            isinstance(item, (VectorHyperDual, *numeric)) for item in items
+        )
         self._data = items
 
     @staticmethod
@@ -600,7 +604,9 @@ def _check_same_type(other) -> None:
             raise ValueError("Operation must be done with another 3D vector!")
         return None
 
-    def dot(self, other: "DifferentiableVector3D") -> "VectorHyperDual":
+    def dot(
+        self, other: "DifferentiableVector3D"
+    ) -> Union["VectorHyperDual", numeric_type]:
         """
         Dot product of two 3D vectors
 
@@ -611,13 +617,12 @@ def dot(self, other: "DifferentiableVector3D") -> "VectorHyperDual":
             (VectorHyperDual): A scalar number (with derivatives)
         """
         self._check_same_type(other)
-        dot = 0
+        dot: Union[VectorHyperDual, numeric_type] = 0
         for k in range(3):
             dot = dot + self._data[k] * other._data[k]
-        assert isinstance(dot, VectorHyperDual)
         return dot
 
-    def norm(self) -> "VectorHyperDual":
+    def norm(self) -> Union["VectorHyperDual", numeric_type]:
         """
         Euclidean (l2) norm of this 3D vector
 
@@ -627,7 +632,6 @@ def norm(self) -> "VectorHyperDual":
         norm = DifferentiableMath.sqrt(
             self._data[0] ** 2 + self._data[1] ** 2 + self._data[2] ** 2
         )
-        assert isinstance(norm, VectorHyperDual)
         return norm
 
     def __add__(
@@ -690,6 +694,18 @@ def __rmul__(self, other):
         """Multiplication of scalar and vector is commutative"""
         return self.__mul__(other)
 
+    def __truediv__(self, other: Union[VectorHyperDual, numeric_type]):
+        """
+        Division of a 3D vector with a scalar
+
+        Args:
+            other (VectorHyperDual|float|int):
+
+        Returns:
+            (DifferentiableVector3D):
+        """
+        return self.__mul__(1 / other)
+
     def cross(
         self, other: "DifferentiableVector3D"
     ) -> "DifferentiableVector3D":
@@ -702,6 +718,7 @@ def cross(
         Returns:
             (DifferentiableVector3D):
         """
+        self._check_same_type(other)
         return DifferentiableVector3D(
             [
                 self._data[1] * other._data[2]

autode/opt/coordinates/base.py

@@ -1,7 +1,6 @@
 # mypy: disable-error-code="has-type"
 import numpy as np
 from copy import deepcopy
-from enum import IntEnum, unique
 from typing import Optional, Union, Sequence, List, TYPE_CHECKING
 from abc import ABC, abstractmethod
 
@@ -15,15 +14,6 @@
     from autode.hessians import Hessian
 
 
-@unique
-class CartesianComponent(IntEnum):
-    """Cartesian component in 3D space"""
-
-    x = 0
-    y = 1
-    z = 2
-
-
 class OptCoordinates(ValueArray, ABC):
     """Coordinates used to perform optimisations"""