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79 lines
2.2 KiB
Python
79 lines
2.2 KiB
Python
6 years ago
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"""
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Lists as Vectors is actually not that performant. Numpy gives all of these features straight out of the box.
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"""
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import math
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from typing import List
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from functools import reduce
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def vector_add(v: List[float], w: List[float]) -> List[float]:
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"""Adds corresponding elements of two Vectors."""
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return [v_i + w_i
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for v_i, w_i in zip(v, w)]
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def vector_subtract(v: List[float], w: List[float]) -> List[float]:
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"""Subtracts corresponding elements of two Vectors."""
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return [v_i - w_i
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for v_i, w_i in zip(v, w)]
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def vector_sum(vectors: List[List[float]]) -> List[float]:
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"""Sums all corresponding elements."""
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# result = vectors[0]
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# for vector in vectors[1:0]:
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# result = vector_add(result, vector)
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# return result
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return reduce(vector_add, vectors)
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def scalar_multiple(c: float, v: List[float]) -> List[float]:
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"""Scales a vector by a multiplier."""
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return [c * vi for vi in v]
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def vector_mean(vectors) -> List[float]:
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"""Compute the vector whose ith element is the mean of the ith element
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of the input vectors.
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Allows us to calculate the component-wise means of a list of (same-sized)
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vectors.
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"""
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n = len(vectors)
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return scalar_multiple(1 / n, vector_sum(vectors))
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def dot_product(v: List[float], w: List[float]) -> float:
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"""The dot product of two vectors is the sum of their component wise
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products.
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The dot product measures how far vector v extends in the w direction.
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"""
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return sum(v_i * w_i for v_i, w_i in zip(v, w))
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def sum_of_squares(v: List[float]) -> float:
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return dot_product(v, v)
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def magnitude(v: List[float]) -> float:
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"""Calculates the magnitude (length) of a vector.
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The pythagorean theorem a**2 + b**2 = c**2 actually is an example
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of calculating the magnitude of a vector of length 2.
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"""
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return math.sqrt(sum_of_squares(v))
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# def squared_distance(v: List[float], w: List[float]) -> float:
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# """Calculates t
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#
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# """
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# return sum_of_squares(vector_subtract(v, w))
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def vector_distance(v: List[float], w: List[float]) -> float:
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"""Calculates the distance between vectors."""
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# return math.sqrt(squared_distance(v, w))
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return magnitude(vector_subtract(v, w))
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