491 lines
9.4 KiB
Plaintext
Executable File
491 lines
9.4 KiB
Plaintext
Executable File
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# NumPy - Numeric Python\n",
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"NumPy is the core library for scientifc computing Python. The module provides high-performance implementations for dealing with n-dimensional arrays and tools for working with these arrays."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## How to work with NumPy\n",
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"The fundamental data structure in NumPy is called _array_. An array is a n-dimensional container. It can be used for \n",
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"\n",
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"* vectors\n",
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"* matrices\n",
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"* n-dimensional data\n",
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"\n",
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"Internally a NumPy array is stored row major (C order) by default. Note that this is different to Matlab where arrays are stored column major."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Import NumPy"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib notebook\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Creating NumPy arrays"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# integer vector, 1D array\n",
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"v = np.array([1, 2, 3])\n",
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"v"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# matrix, 2D array\n",
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"M = np.array([[1, 2], \n",
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" [3, 4]], dtype=float)\n",
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"M"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# volume, 3D array\n",
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"V = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8 , 9], [10, 11, 12]]])\n",
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"V"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Initial placeholders"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create array of zeros with 3 rows and 4 columns\n",
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"np.zeros((3, 4))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create array of ones \n",
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"np.ones((2, 3, 4), dtype=np.int16)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create array of evenly spaced values\n",
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"# args: start, stop, step: inclusive start, exclusive stop\n",
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"np.arange(3, 11, 2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create array with evenly spaced values using number of samples\n",
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"# start, stop, num_samples\n",
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"x = np.linspace(-1, 4, 20)\n",
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"\n",
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"_, ax = plt.subplots(figsize=(5, 3.5))\n",
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"ax.plot(x, np.sin(x))\n",
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"\n",
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"_, ax = plt.subplots(figsize=(5, 3.5))\n",
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"ax.plot(np.sin(x))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create a constant array \n",
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"np.full((2, 3), 7)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create a n x n identity matrix\n",
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"np.eye(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create an array with random values\n",
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"np.random.random((2, 3))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create an empty array (attention: memory is uninitialized!)\n",
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"np.empty((3, 2))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"base = np.array([1, 2, 3])\n",
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"\n",
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"a = []\n",
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"for i in range(10):\n",
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" a.append(base.copy())\n",
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"a = np.array(a)\n",
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" \n",
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"b = np.stack([base.copy()] * 10)\n",
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"c = np.repeat(base[None], 10, axis=0)\n",
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"d = np.tile(base, (10, 1))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"print(a)\n",
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"assert np.allclose(a, b) and np.allclose(b, c) and np.allclose(c, d)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Inspecting array"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# array dimensions\n",
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"V.shape"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# number of dimensions\n",
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"V.ndim"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# number of elements\n",
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"V.size"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# data type of array elements\n",
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"V.dtype"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Array operations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# sum\n",
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"V.sum()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# min\n",
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"V.min()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# max\n",
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"V.max()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# mean\n",
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"V.mean()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# standard deviation\n",
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"V.std()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Arithmetic Operations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"a = np.arange(3)\n",
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"a"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# addition\n",
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"a + a"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"a + 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# exp\n",
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"np.exp(a)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# * is elementwise multiplication\n",
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"# @ is __matmul__\n",
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"# a is one-dimensional\n",
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"for inner in [(a * a).sum(), a @ a, a.dot(a), a.T.dot(a)]:\n",
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" print(inner)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"for outer in [np.outer(a, a), a[None] * a[:, None]]:\n",
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" print(outer)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Slicing, Indexing\n",
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"In python indexing starts at 0!"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# get first element\n",
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"a\n",
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"a[0]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"M"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# get 1st row\n",
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"M[0] # = M[0,:]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# get last column\n",
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"M[:,-1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"v = np.arange(10)\n",
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"v"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# get every second element\n",
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"# [start:stop:step]\n",
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"v[1::2]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# boolean indexing\n",
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"v[v > 3]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"v > 3"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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