2021 Training Courses

Table of Contents

• 2021 Training Courses
  • Packages
  • Q1
    • Prototype
    • Test Cases
  • Q2
    • Prototype
    • Test Cases

Packages

• NumPy
• Matplotlib
• pytest

Q1

Deadline: 2021-08-13

1. 設計一個多項式函數類別 Polynomial 和變數類別 Variable，支援以下功能：
   • 計算多項式函數
   • 對多項式函數進行微分
2. 實作 plot_polynomial(file, function, p_x, x, formula)，輸出一張 png 檔：
   • 畫出多項式函數圖形
   • 給定一個點，畫出經過該點的多項式函數的切線
   • 參數：
     • file: 輸出的檔案名稱
     • function: 多項式函數的 instance
     • p_x: 點坐標
     • x: 圖表的 x 軸
     • formula: 數學式描述

Prototype

In libs/functional.py:

from typing import List, Union

import numpy as np


class Variable:

    def __init__(self, value=None):
        self.value = value
        self.grad = None


class Polynomial:

    def __init__(self, a: List = None):
        self.a = np.array(a)

    def __call__(self, x: Union[float, np.ndarray]) -> Variable:
        pass

In libs/visualization.py:

from pathlib import Path

import numpy as np

from libs.functional import Polynomial
from libs.visualization import plot_polynomial


class TestPlotPolynomial:

    def test_plot_polynomial_1(self):
        f = Polynomial(a=[1., 2., 3.])  # 1 + 2x + 3x^2
        file = Path('test_plot_polynomial_1.png')
        x = np.linspace(-4.3, 3.7)
        plot_polynomial(file=file, function=f, p_x=1., x=x, formula='1 + 2x + 3x^2')
        assert file.exists()

    def test_plot_polynomial_2(self):
        f = Polynomial(a=[4., 1., 3., 1.2])  # 4 + x + 3x^2 + 1.2x^3
        file = Path('test_plot_polynomial_2.png')
        x = np.linspace(-2.5, 1.0)
        plot_polynomial(file=file, function=f, p_x=-1., x=x, formula='4 + x + 3x^2 + 1.2x^3')
        assert file.exists()

Test Cases

In tests/test_functional.py:

import numpy as np

from libs.functional import Polynomial


class TestPolynomial:

    def test_io(self):
        f = Polynomial(a=[1., 2., 3.])  # 1 + 2x + 3x^2
        assert f(4.).value == 57.
        assert f(5.).value == 86.

    def test_io_array(self):
        f = Polynomial(a=[1., 2., 3.])  # 1 + 2x + 3x^2
        x = np.array([4., 5.])
        y = np.array([57., 86.])
        assert np.all(f(x).value == y)

    def test_grad(self):
        f = Polynomial(a=[1., 2., 3.])  # 1 + 2x + 3x^2
        # gradient: <2 + 6x>
        assert f(4.).grad == 26.
        assert f(5.).grad == 32.

In tests/visualization.py:

from pathlib import Path

import numpy as np

from libs.functional import Polynomial
from libs.visualization import plot_polynomial


class TestPlotPolynomial:

    def test_plot_polynomial_1(self):
        f = Polynomial(a=[1., 2., 3.])  # 1 + 2x + 3x^2
        file = Path('test_plot_polynomial_1.png')
        x = np.linspace(-4.3, 3.7)
        plot_polynomial(file=file, function=f, p_x=1., x=x, formula='1 + 2x + 3x^2')
        assert file.exists()

    def test_plot_polynomial_2(self):
        f = Polynomial(a=[4., 1., 3., 1.2])  # 4 + x + 3x^2 + 1.2x^3
        file = Path('test_plot_polynomial_2.png')
        x = np.linspace(-2.5, 1.0)
        plot_polynomial(file=file, function=f, p_x=-1., x=x, formula='4 + x + 3x^2 + 1.2x^3')
        assert file.exists()

test_plot_polynomial_1.png:

test_plot_polynomial_2.png:

Q2

Deadline: 2021-08-20

給定 data points ，利用 SGD 解出 linear regression.

1. Linear regression model:
2. 隨機初始化
3. 計算 MSE Loss:
   
4. 計算參數的 gradients:
   • 
   • 
5. 利用 SGD 更新參數

Prototype

In libs/functional.py:

from typing import Tuple

import numpy as np


def regression_sgd(x, y, num_samples, num_iterations, batch_size, learning_rate) -> Tuple[np.ndarray, np.ndarray]:
    pass

In libs/visualization.py:

def plot_regression(file, x, y, prediction, groundtruth):
    pass

Test Cases

In tests/test_functional.py:

import numpy as np

from libs.functional import regression_sgd


def test_regression_solved_correctly():
    m_gt, b_gt = 2.4, 1.0
    num_samples = 100
    x = np.random.uniform(-10, 10, num_samples)
    noise = np.random.normal(0, 1, num_samples)
    y = m_gt * x + b_gt + noise
    num_iterations = 1000
    batch_size = 10
    learning_rate = 0.001

    m, b = regression_sgd(x, y, num_samples, num_iterations, batch_size, learning_rate)

    assert m.shape == (num_iterations + 1,) and b.shape == (num_iterations + 1,)
    assert np.isclose(m[-1], m_gt, 1e-01)

In tests/visualization.py:

from pathlib import Path

import numpy as np

from libs.functional import regression_sgd
from libs.visualization import plot_regression


def test_plot_regression():
    m_gt, b_gt = 2.4, 1.0
    num_samples = 100
    x = np.random.uniform(-10, 10, num_samples)
    noise = np.random.normal(0, 1, num_samples)
    y = m_gt * x + b_gt + noise
    num_iterations = 1000
    batch_size = 10
    learning_rate = 0.001

    m, b = regression_sgd(x, y, num_samples, num_iterations, batch_size, learning_rate)
    file = Path('test_plot_regression.png')
    plot_regression(file, x, y, prediction=(m, b), groundtruth=(m_gt, b_gt))

    assert file.exists()