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IDSUP programs (chapterwise)
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Chapter 3 Visualizing Data.ipynb
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Chapter 4 - Linear Algebra.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 4 - Linear Algebra"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is no native vector data type in Python \n",
"\n",
"Representation of a vector in python - list \n",
"vec = [1, 2, 3]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using add function\n",
"[5, 7, 9]\n",
"Example of using subtract function\n",
"[-3, -3, -3]\n",
"Example of using dot function\n",
"32\n"
]
}
],
"source": [
"# to add 2 vectors v and w\n",
"from typing import List\n",
"# custom data type for a vector\n",
"vector = List[float]\n",
"\n",
"# addition of 2 vectors\n",
"def add(v: vector, w: vector) -> vector:\n",
" assert len(v) == len(w), \"vectors must be the same length\"\n",
" return [v_i + w_i for v_i, w_i in zip(v, w)]\n",
"\n",
"# example of using the function\n",
"print(\"Example of using add function\")\n",
"a = [1, 2, 3]\n",
"b = [4, 5, 6]\n",
"print(add(a, b))\n",
"\n",
"# subtraction of 2 vectors\n",
"def subtract(v: vector, w: vector) -> vector:\n",
" assert len(v) == len(w), \"vectors must be the same length\"\n",
" return [v_i - w_i for v_i, w_i in zip(v, w)]\n",
"\n",
"# example of using the function\n",
"print(\"Example of using subtract function\")\n",
"a = [1, 2, 3]\n",
"b = [4, 5, 6]\n",
"print(subtract(a, b))\n",
"\n",
"# dot product of 2 vectors\n",
"# let v = [v1, v2, v3] and w = [w1, w2, w3]\n",
"# v dot w = v1w1 + v2w2 + v3w3\n",
"def dot_product(v: vector, w: vector) -> float:\n",
" assert len(v) == len(w), \"vectors must be the same length\"\n",
" product = [v_i * w_i for v_i, w_i in zip(v, w)]\n",
" return sum(product)\n",
"\n",
"# example of using the function\n",
"print(\"Example of using dot function\")\n",
"a = [1, 2, 3]\n",
"b = [4, 5, 6]\n",
"print(dot_product(a, b))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Length of a vector in python \n",
"let v = [v1, v2, v3] \n",
"|v| = sqrt(v1^2 + v2^2 + v3^2) \n",
"\n",
"Length in vector means its magnitude"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using len_of_vector function\n",
"3.7416573867739413\n"
]
}
],
"source": [
"from typing import List\n",
"import math\n",
"\n",
"def len_of_vector(v: List[float]) -> float:\n",
" return math.sqrt(sum(v_i * v_i for v_i in v))\n",
"\n",
"# Example of using the function\n",
"print(\"Example of using len_of_vector function\")\n",
"a = [1, 2, 3]\n",
"print(len_of_vector(a))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Q. Get the distance between any 2 vectors."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# let v = [x1, y1] and w = [x2, y2]\n",
"# distance = sqrt((x2-x1)^2 + (y2-y1)^2)\n",
"# or simply, distance = len_of_vector(subtract(v, w))\n",
"\n",
"from typing import List\n",
"\n",
"vector = List[float]\n",
"\n",
"def distance(v: vector, w: vector) -> float:\n",
" assert len(v) == len(w) and len(v) > 0 and len(w) > 0, \"vectors must be the same length\"\n",
" return len_of_vector(subtract(v, w))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Matrix in python\n",
"\n",
"3x3 matrix in python \n",
"\n",
"matrix = [ \n",
" [1, 2, 3], \n",
" [4, 5, 6], \n",
" [7, 8, 9] \n",
" ] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Find Average Of Vectors In Python\n",
"\n",
"Let V1 = [1, 2, 3], V2 = [4, 5, 6], V3 = [7, 8, 9]\n",
"\n",
"Average Of Vectors = (V1 + V2 + V3) / 3"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using avg_of_vectors function\n",
"[4.0, 5.0, 6.0]\n"
]
}
],
"source": [
"from typing import List\n",
"\n",
"vector = List[float]\n",
"\n",
"def avg_of_vectors(vectors: List[vector]) -> vector:\n",
" \n",
" # check if all vectors have the same length\n",
" len_all = len(vectors[0])\n",
" assert all(len(v) == len_all for v in vectors), \"vectors must be the same length\"\n",
" \n",
" return [(sum(v[i] for v in vectors) / len(vectors)) for i in range(len_all)]\n",
"\n",
"print(\"Example of using avg_of_vectors function\")\n",
"a = [1, 2, 3]\n",
"b = [4, 5, 6]\n",
"c = [7, 8, 9]\n",
"print(avg_of_vectors([a, b, c]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Shape Of A Matrix In Python\n",
"\n",
"Returns the shape of a matrix i.e number of rows and columns"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using shape_of_matrix function\n",
"(3, 3)\n"
]
}
],
"source": [
"# Shape Of A Matrix In Python\n",
"\n",
"def shape_of_matrix(matrix: List[List[float]]) -> tuple:\n",
" return (len(matrix), len(matrix[0]))\n",
"\n",
"print(\"Example of using shape_of_matrix function\")\n",
"a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]\n",
"print(shape_of_matrix(a))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Q. Create a matrix with 3 rows and 4 columns."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using create_matrix function\n",
"[['00', '01', '02', '03'], ['10', '11', '12', '13'], ['20', '21', '22', '23']]\n"
]
}
],
"source": [
"# Create a matrix with 3 rows and 4 columns.\n",
"\n",
"from typing import List\n",
"matrix_type = List[List[float]]\n",
"\n",
"def create_matrix(rows: int, cols: int) -> matrix_type:\n",
" matrix = []\n",
" for i in range(rows):\n",
" row = []\n",
" for j in range(cols):\n",
" s_i = str(i)\n",
" s_j = str(j)\n",
" row.append(s_i + s_j)\n",
" matrix.append(row)\n",
" return matrix\n",
"\n",
"print(\"Example of using create_matrix function\")\n",
"a = create_matrix(3, 4)\n",
"print(a)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Q. Create identity matrix of n x n."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Example of using identity_matrix function\n",
"[[1, 0], [0, 1]]\n",
"[[1, 0, 0], [0, 1, 0], [0, 0, 1]]\n",
"[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]\n"
]
}
],
"source": [
"# Q. Create identity matrix of n x n.\n",
"\n",
"def identity_matrix(n: int):\n",
" matrix = []\n",
" for i in range(n):\n",
" row = []\n",
" for j in range(n):\n",
" if i == j:\n",
" row.append(1)\n",
" else:\n",
" row.append(0)\n",
" matrix.append(row)\n",
" return matrix\n",
"\n",
"print(\"Example of using identity_matrix function\")\n",
"# 2 x 2\n",
"a = identity_matrix(2)\n",
"print(a)\n",
"\n",
"# 3 x 3\n",
"a = identity_matrix(3)\n",
"print(a)\n",
"\n",
"# 4 x 4\n",
"b = identity_matrix(4)\n",
"print(b)\n"
]
}
],
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"display_name": ".venv",
"language": "python",
"name": "python3"
},
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"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.2"
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"nbformat": 4,
"nbformat_minor": 2
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Chapter 5 - Statistics.ipynb
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Chapter 6 - Probability.ipynb
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