From 66c3bbfa94d8a41e58adf154be25e6d86fee8e30 Mon Sep 17 00:00:00 2001 From: "martial.simon" Date: Sun, 13 Apr 2025 19:54:19 +0200 Subject: init: initial commit --- PVCM/cama/en/ma1 np02 Filtres.ipynb | 411 ++++++++++++++++++++++++++++++++++++ 1 file changed, 411 insertions(+) create mode 100644 PVCM/cama/en/ma1 np02 Filtres.ipynb (limited to 'PVCM/cama/en/ma1 np02 Filtres.ipynb') diff --git a/PVCM/cama/en/ma1 np02 Filtres.ipynb b/PVCM/cama/en/ma1 np02 Filtres.ipynb new file mode 100644 index 0000000..61d0454 --- /dev/null +++ b/PVCM/cama/en/ma1 np02 Filtres.ipynb @@ -0,0 +1,411 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 1, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let's look at how to extract pieces from an array or modify only some of its parts. For this, we\n", + "have two tools:\n", + " \n", + "* the extraction according to the indices\n", + "* the extraction by applying a logical filter on the values" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Filter by indices\n", + "\n", + "We can extract values from an array according to its indices as we did for lists. For each dimension of the table, you can indicate\n", + "\n", + "* the value of the desired index (an integer)\n", + "* a list of `start:end:jump` indices. Thus `1:6:2` means the odd values between index 1 and index 6 excluded. The `start`, `end` and `jump` values are optional:\n", + " * `:5` gives the first 5 values (indices 0,1,2,3 and 4)\n", + " * `3:` gives 4th to last values\n", + " * `::3` returns a value every 3 from the beginning to the end of the array.\n", + "* an explicit list of indices like `[1,3,-2]` (negative values means start from the end, hence `-2` is the penultimate index)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]] \n", + "\n", + "[4 5 6 7] \n", + "\n", + "[[0 1]\n", + " [4 5]] \n", + "\n", + "[ 3 11] \n", + "\n", + "[[ 0 3]\n", + " [ 4 7]\n", + " [ 8 11]]\n" + ] + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "print(a, '\\n')\n", + "print(a[1, :], '\\n') # 2nd line\n", + "print(a[0:2, 0:2], '\\n') # top left sub-matrix\n", + "print(a[::2, -1], '\\n') # even lines, last column\n", + "print(a[:, [0,-1]]) # first and last column" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is thus possible to indicate that an operation only applies to an extract from the table by indicating\n", + "which cells of the table will be modified:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 101, 2, 103],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 109, 10, 111]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[::2, 1::2] += 100\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It also makes it possible to simply write calculations such as extracting a grayscale image from a color image:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "image = np.random.randint(256, size=(800, 600, 3)) # RGB 800x600 image\n", + "gray_image = 0.2126 * image[:,:,0] + 0.7152 * image[:,:,1] + 0.0722 * image[:,:,2]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "You can also use `...` to replace multiple indices like `image[...,0] == image[:,:,0]`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Logical filters\n", + "\n", + "### A filter = a logical condition\n", + "\n", + "Numpy allows you to simply extract the values ​​that meet a logical condition.\n", + "\n", + "To do this, we use a filter, namely a Boolean array that is placed on an array of the same size, imagining that the True boxes are windows and False are walls. The result is the set of values ​​seen through the windows ordered by their index.\n", + "\n", + "The result is always a 1-dimensional array unless you use `where`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The filter a > 5 is\n", + " [[False False False False]\n", + " [False False True True]\n", + " [ True True True True]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "fil = a > 5 # a > 5 means all VALUES greater than 5\n", + "print(\"The filter a > 5 is\\n\", fil)\n", + "a[fil] # apply the filter and show the result (1D array)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is easier and more readable to write the logical condition where we normally put the indices, namely between the square brackets:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>5]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### When the goal is the filter\n", + "\n", + "The filter can be used for something other than selecting values ​​from our array. It can be the result on which we want to work, for example for a population `fil = (age == weight)`. It is an array of Boolean which gives true cases and other false cases i.e. 0s and 1s.\n", + "\n", + "Thus, with a `fil` filter, we can know\n", + "\n", + "| | | |\n", + "|:-|:-|:-|\n", + "| how many cases are true: |`fil.sum()` | |\n", + "| if there is at least one true case: |`fil.sum() > 0` | Numpy also offers `np.any(fil)` |\n", + "| if all cases are true: |`fil.prod() == 1` | Numpy also offers `np.all(fil)` |\n", + "| if at least one case is false: |`fil.prod() == 0` |\n", + "|if all cases are false:| `fil.sum() == 0` |" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### `where` to handle non-filter values\n", + "\n", + "To preserve the shape of the array, it is necessary to tell it what to do with the values that do not meet the condition. To do this, we use the [`where`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html) function:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 0, 0, 0],\n", + " [ 0, 0, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a > 5, a, 0) # if a > 5 then a else 0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We can make all imaginable filters that give a boolean array." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, -1, 6],\n", + " [-1, -1, 12, -1],\n", + " [-1, 18, -1, -1]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a%3 == 0, 2*a, -1) # if a modulo 3 is 0 then 2 times a else -1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Update a table with a filter\n", + "\n", + "Another way to maintain the shape of the array is to change only the values ​​that match the filter." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 200, 200],\n", + " [200, 200, 200, 200]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[a > 5] = 200\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here's how to add 100 to all values ​​in the array that are perfect squares as well as to the value 5:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[100, 101, 2, 3],\n", + " [104, 105, 6, 7],\n", + " [ 8, 109, 10, 11]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[(np.round(np.sqrt(a)) - np.sqrt(a) == 0) | (a==5)] += 100 # | is OR (AND is &)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "variables": { + " PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")": "                                                                                                                                                                                                                                                                                                                                                                                                               
np01 Numpy Introduction  ← △ →  np03 Manipulations

 " + } + }, + "source": [ + "{{ PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")}}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file -- cgit v1.2.3