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# util.py

# From Classic Computer Science Problems in Python Chapter 7

# Licensed under the Apache License, Version 2.0 (the "License");

# you may not use this file except in compliance with the License.

# You may obtain a copy of the License at

# http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software

# distributed under the License is distributed on an "AS IS" BASIS,

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

# See the License for the specific language governing permissions and

# limitations under the License.

from typing import List

from math import exp

# dot product of two vectors

def dot_product(xs: List[float], ys: List[float]) -> float:

return sum(x * y for x, y in zip(xs, ys))

# the classic sigmoid activation function

def sigmoid(x: float) -> float:

return 1.0 / (1.0 + exp(-x))

def derivative_sigmoid(x: float) -> float:

sig: float = sigmoid(x)

return sig * (1 - sig)

# assume all rows are of equal length

# and feature scale each column to be in the range 0 - 1

def normalize_by_feature_scaling(dataset: List[List[float]]) -> None:

for col_num in range(len(dataset[0])):

column: List[float] = [row[col_num] for row in dataset]

maximum = max(column)

minimum = min(column)

for row_num in range(len(dataset)):

dataset[row_num][col_num] = (dataset[row_num][col_num] - minimum) / (maximum - minimum)