@@ -11,28 +11,28 @@ def add_ones_axis(array):
1111
1212def compute_dot (array1 , array2 ):
1313 """
14+ Compute the dot product of two arrays.
15+
1416 Parameters
1517 ----------
1618 array1 : numpy array[..., 3]
17- First argument in the dot product.
18- The dot product axis is the last one.
19+ First argument in the dot product. The dot product axis is the last one.
1920 array2 : numpy array[..., 3]
20- Second argument in the dot product.
21- The dot product axis is the last one.
21+ Second argument in the dot product. The dot product axis is the last one.
2222 """
2323 return np .einsum ("...,i->...i" , np .einsum ("...i,...i->..." , array1 , array2 ), np .ones (3 ))
2424
2525
2626def compute_dot_deriv (array , deriv_array ):
2727 """
28+ Compute the derivative of the dot product.
29+
2830 Parameters
2931 ----------
3032 array : numpy array[..., 3]
31- The argument in the dot product we are not taking the derivatives for.
32- The dot product axis is the last one.
33+ The argument in the dot product we are not taking the derivatives for. The dot product axis is the last one.
3334 deriv_array : numpy array[..., 3, 3]
34- The derivatives of the argument in the dot product of interest.
35- The dot product axis is the last one.
35+ The derivatives of the argument in the dot product of interest. The dot product axis is the last one.
3636 """
3737 return np .einsum (
3838 "...j,i->...ij" ,
@@ -43,28 +43,28 @@ def compute_dot_deriv(array, deriv_array):
4343
4444def compute_cross (array1 , array2 ):
4545 """
46+ Compute the cross product of two arrays.
47+
4648 Parameters
4749 ----------
4850 array1 : numpy array[..., 3]
49- First argument in the cross product (order matters).
50- The cross product axis is the last one.
51+ First argument in the cross product (order matters). The cross product axis is the last one.
5152 array2 : numpy array[..., 3]
52- Second argument in the cross product (order matters).
53- The cross product axis is the last one.
53+ Second argument in the cross product (order matters). The cross product axis is the last one.
5454 """
5555 return np .cross (array1 , array2 , axis = - 1 )
5656
5757
5858def compute_cross_deriv1 (deriv_array , array ):
5959 """
60+ Compute the derivative of the cross product with respect to the first cross product argument.
61+
6062 Parameters
6163 ----------
6264 deriv_array : numpy array[..., 3, 3]
63- Derivatives of the first argument in the cross product.
64- The cross product axis is the second last one.
65+ Derivatives of the first argument in the cross product. The cross product axis is the second last one.
6566 array : numpy array[..., 3]
66- Second argument in the cross product (order matters).
67- The cross product axis is the last one.
67+ Second argument in the cross product (order matters). The cross product axis is the last one.
6868 """
6969 tmp_0 = np .einsum ("...i,j->...ij" , compute_cross (deriv_array [..., 0 ], array ), np .array ([1.0 , 0.0 , 0.0 ]))
7070 tmp_1 = np .einsum ("...i,j->...ij" , compute_cross (deriv_array [..., 1 ], array ), np .array ([0.0 , 1.0 , 0.0 ]))
@@ -74,14 +74,14 @@ def compute_cross_deriv1(deriv_array, array):
7474
7575def compute_cross_deriv2 (array , deriv_array ):
7676 """
77+ Compute the derivative of the cross product with respect to the second cross product argument.
78+
7779 Parameters
7880 ----------
7981 array : numpy array[..., 3]
80- First argument in the cross product (order matters).
81- The cross product axis is the last one.
82+ First argument in the cross product (order matters). The cross product axis is the last one.
8283 deriv_array : numpy array[..., 3, 3]
83- Derivatives of the second argument in the cross product.
84- The cross product axis is the second last one.
84+ Derivatives of the second argument in the cross product. The cross product axis is the second last one.
8585 """
8686 tmp_0 = np .einsum ("...i,j->...ij" , compute_cross (array , deriv_array [..., 0 ]), np .array ([1.0 , 0.0 , 0.0 ]))
8787 tmp_1 = np .einsum ("...i,j->...ij" , compute_cross (array , deriv_array [..., 1 ]), np .array ([0.0 , 1.0 , 0.0 ]))
@@ -91,6 +91,8 @@ def compute_cross_deriv2(array, deriv_array):
9191
9292def compute_norm (array ):
9393 """
94+ Compute the 2-norm of an array.
95+
9496 Parameters
9597 ----------
9698 array : numpy array[..., 3]
@@ -101,6 +103,8 @@ def compute_norm(array):
101103
102104def compute_norm_deriv (array , deriv_array ):
103105 """
106+ Compute the derivative of the 2-norm of an array.
107+
104108 Parameters
105109 ----------
106110 array : numpy array[..., 3]
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