Vector: (1) scalar division, (2) average, (3) collinearity, (4) linea…

…r independence

README.md

@@ -30,6 +30,7 @@ assert b - a == Vector([2, 2])
 ```python
 assert a * 5 == Vector([5, 10])
 assert 5 * a == Vector([5, 10])
+assert a / 2 == Vector([0.5, 1.0])
 ```
 
 #### Dot (inner) product
@@ -75,4 +76,30 @@ assert Vector.scalproj(b, b) - 5 < 0.1
 
 ```python
 assert Vector.cross(c, d) == Vector([-3, 6, -3])
+```
+
+#### Average (arithmetic mean)
+
+```python
+assert Vector.average(Vector([2, 1]), Vector([4, 2])) == Vector([3.0, 1.5])
+```
+
+#### Collinearity
+
+Vectors are collinear iff one is a scalar multiple of the other.
+
+```python
+assert Vector.collinear(Vector([2, 1]), Vector([4, 2]))
+assert Vector.collinear(Vector([-3, 4, 1]), Vector([-15, 20, 5]))
+assert not Vector.collinear(Vector([0, 1]), Vector([1, 0]))
+```
+
+#### Linear independence
+
+A set of vectors is linearly independent iff all vectors in it are pairwise non-collinear.
+
+```python
+assert Vector.linindep(Vector([0, 1]), Vector([1, 0]))
+assert Vector.linindep(Vector([1, 1]), Vector([2, 1]))
+assert not Vector.linindep(Vector([1, 2, 3]), Vector([0, 0, 1]), Vector([0, 0, 2]))
 ```

abel/linalg/test_vector.py

@@ -24,6 +24,9 @@ def test_scal_mult():
     assert a * 5 == Vector([5, 10])
     assert 5 * a == Vector([5, 10])
 
+def test_scal_div():
+    assert a / 2 == Vector([0.5, 1.0])
+
 def test_matmul():
     assert a @ b == 11
     assert b @ a == a @ b
@@ -52,3 +55,17 @@ def test_scalproj():
 def test_cross():
     A, B = Vector([1, 2, 3]), Vector([4, 5, 6])
     assert Vector.cross(A, B) == Vector([-3, 6, -3])
+
+def test_average():
+    assert Vector.average(Vector([2, 1]), Vector([4, 2])) == Vector([3.0, 1.5])
+
+def test_collinear():
+    assert Vector.collinear(Vector([2, 1]), Vector([4, 2]))
+    assert Vector.collinear(Vector([-3, 4, 1]), Vector([-15, 20, 5]))
+    assert not Vector.collinear(Vector([0, 1]), Vector([1, 0]))
+
+def test_linindep():
+    assert Vector.linindep(Vector([0, 1]), Vector([1, 0]))
+    assert Vector.linindep(Vector([1, 1]), Vector([2, 1]))
+    assert not Vector.linindep(
+        Vector([1, 2, 3]), Vector([0, 0, 1]), Vector([0, 0, 2]))

abel/linalg/vector.py

@@ -36,6 +36,10 @@ def __mul__(self, k):
     def __rmul__(self, k):
         return self * k
 
+    def __truediv__(self, k):
+        """Scalar division."""
+        return self * (1 / k)
+
     def __matmul__(self, B):
         """Dot product."""
         xs, ys = self._contents, B._contents
@@ -70,3 +74,28 @@ def cross(A, B):
             A_z * B_x - A_x * B_z,
             A_x * B_y - A_y * B_x
         ])
+
+    @staticmethod
+    def average(A, B):
+        """The average or arithmetic mean of A and B."""
+        return (A + B) / A.shape[1]
+
+    @staticmethod
+    def collinear(A, B):
+        """Whether two vectors are collinear."""
+        def find_n(A_cont, B_cont):
+            for a, b in zip(A_cont, B_cont):
+                if a != 0:
+                    return b / a
+                if b != 0:
+                    return a / b
+        n = find_n(A._contents, B._contents)
+        return (n * A == B) or (n * B == A)
+
+    @staticmethod
+    def linindep(*vs):
+        for i, v in enumerate(vs):
+            for j in range(i + 1, len(vs)):
+                if Vector.collinear(vs[i], vs[j]):
+                    return False
+        return True

setup.py

@@ -7,7 +7,7 @@
 
 setuptools.setup(
     name='abel',
-    version='0.0.5',
+    version='0.0.6',
     author='Hunan Rostomyan',
     author_email='[email protected]',
     description='Machine learning components',