{ "cells": [ { "cell_type": "markdown", "id": "e2362e9d-042e-4e26-82ad-517722f21d55", "metadata": {}, "source": [ "# DATA 311 Lecture 2 - `numpy` demo\n" ] }, { "cell_type": "markdown", "id": "20d0f1e8-e323-436e-87a4-b4fad4a03c78", "metadata": { "id": "4tRd3rnn5YHf" }, "source": [ "\n", "\n", "## Markdown Demo (this is a level 2 heading)\n", "\n", "### Lists\n", "* bulleted lists\n", "* another item\n", "\n", "1. numbered lists\n", "2. another item\n", "\n", "### Text formatting\n", "**bold**, *italics*, `monospace`\n", "\n", "A code block:\n", "```python\n", "a = 4\n", "b = 7\n", "```\n", "### Links and images:\n", "\n", "[link text](https://facultyweb.cs.wwu.edu/~wehrwes/courses/data311_26s/)\n", "\n", "![alt text](https://facultyweb.cs.wwu.edu/~wehrwes/courses/data311_25f/lab1/diagonal_example.png)\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "478eb7e7-029f-41c4-9349-89c3d7e4a727", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import random\n", "import matplotlib.pyplot as plt\n", "import imageio.v3 as imageio" ] }, { "cell_type": "markdown", "id": "e77cab94-293a-4a71-b3aa-5d7d5471f7fb", "metadata": {}, "source": [ "### Creating Arrays\n", "* `array`, `zeros`, `ones`, `*_like`\n", " * `dtype` argument" ] }, { "cell_type": "code", "execution_count": 2, "id": "9327ac12-6e94-47ea-a48f-01cadc3a12b8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create a python list with 0..9\n", "a = list(range(10))\n", "a\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "0a95dc4d-6489-4e52-89fc-ee8d79e82a68", "metadata": {}, "outputs": [], "source": [ "# create a numpy array with the list's contents\n", "a = np.array(a)" ] }, { "cell_type": "code", "execution_count": 4, "id": "20d562b2-0563-4ae2-8778-8d8f1d2c5a0b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dtype('int64')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# show the array's data type\n", "a.dtype" ] }, { "cell_type": "code", "execution_count": 5, "id": "2709d96d-d7d1-4ea6-80e9-c45528f30afa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.int64(1)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# get the element at index 1\n", "a[1]" ] }, { "cell_type": "code", "execution_count": 6, "id": "b5ac609c-b331-4984-96bb-8ef813f1ab9d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10,)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# get the shape of the array\n", "a.shape" ] }, { "cell_type": "markdown", "id": "e116f13f-de96-4ba0-9183-f4c73f1e9c32", "metadata": {}, "source": [ "### Basic list-like slicing" ] }, { "cell_type": "code", "execution_count": 7, "id": "04e7936a-9655-411b-8ee0-c64fcfe79262", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3, 4, 5])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# slice with beginning and end\n", "a[3:6]" ] }, { "cell_type": "code", "execution_count": 8, "id": "b84e5597-b0a4-4802-ba0b-a90d67a93d52", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 2, 3])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# slice with implicit start (0)\n", "a[:4]" ] }, { "cell_type": "code", "execution_count": 9, "id": "b57d654c-4458-40ac-bdec-e169f3a10599", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5, 6, 7, 8, 9])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# slice with implicit end (len)\n", "a[5:]" ] }, { "cell_type": "code", "execution_count": 10, "id": "a5050fcd-ddef-4b7c-a010-169b3c77c959", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# slice with implicit start and end\n", "a[:]" ] }, { "cell_type": "code", "execution_count": 11, "id": "bd646389-5025-46c5-b5f2-2e60682eed95", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 3, 5])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# slice with a step size\n", "a[1:7:2]" ] }, { "cell_type": "markdown", "id": "2326dcaf-8551-4557-8433-ce6aa3aceab7", "metadata": {}, "source": [ "### Elementwise Operations\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "be7ae120-a010-41e8-a564-f304fd002e2f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a" ] }, { "cell_type": "code", "execution_count": 13, "id": "f6fec9ad-44cb-4812-8799-b6ed556ec2e7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# array + scalar\n", "a + 4" ] }, { "cell_type": "code", "execution_count": 14, "id": "4f5cb864-b68a-43de-8e3b-d93b93ac479a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# array + array\n", "a + a" ] }, { "cell_type": "code", "execution_count": 15, "id": "d6d52581-cc25-415a-b66f-f84a8dc6c7b7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# scalar * array\n", "2 * a" ] }, { "cell_type": "code", "execution_count": 16, "id": "fb52730e-9f0c-48e4-a48f-39aa35b8b0ba", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "operands could not be broadcast together with shapes (10,) (4,) ", "output_type": "error", "traceback": [ "\u001b[31m---------------------------------------------------------------------------\u001b[39m", "\u001b[31mValueError\u001b[39m Traceback (most recent call last)", "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[16]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# array + array dimension matching\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m a + a[:\u001b[32m4\u001b[39m]\n", "\u001b[31mValueError\u001b[39m: operands could not be broadcast together with shapes (10,) (4,) " ] } ], "source": [ "# array + array dimension matching\n", "a + a[:4]" ] }, { "cell_type": "markdown", "id": "66a9ec63-8bd2-4a6b-ae01-ca0182c1ff82", "metadata": {}, "source": [ "### Exercise 1: Speed Check\n", "\n", "**In pairs**: I've claimed `numpy` is faster than native Python. Let's find out how much faster. \n", "\n", "1. In the cell below, create a Python list (not a numpy array!) of 10,000 random floating-point numbers between 0.0 and 1.0. Useful tools: `import random`, `random.random()`." ] }, { "cell_type": "code", "execution_count": 17, "id": "b236aa94-ef90-4764-9e2e-901e3043d8db", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.8437826572010122,\n", " 0.6696759345208393,\n", " 0.14343354017923993,\n", " 0.8904407099190859,\n", " 0.2182667489356157]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import random\n", "\n", "b = []\n", "for i in range(1_000_000):\n", " b.append(random.random())\n", "b[:5]" ] }, { "cell_type": "markdown", "id": "472e5cdf-0425-4dfa-9268-7a12ebf50e16", "metadata": {}, "source": [ "2. In the next cell, create a new Python list containing the same numbers as the original, but with 0.5 subtracted from each. Don't modify the original list. I've added the ipython magic command `%%time` to the top of the cell to measure and report the time it takes to execute that cell." ] }, { "cell_type": "code", "execution_count": 18, "id": "5b5a1d84-821c-48db-8b1c-0c8ad5a73ff4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 83.7 ms, sys: 16.1 ms, total: 99.8 ms\n", "Wall time: 99.4 ms\n" ] } ], "source": [ "%%time\n", "\n", "c = []\n", "for v in b:\n", " c.append(v - 0.5) \n", "\n" ] }, { "cell_type": "markdown", "id": "ebd4d06a-5b28-4de7-8c99-9910a5e1b148", "metadata": {}, "source": [ "3. In the next cell, create a numpy array `np_nums` containing the same numbers as your original (0.0 to 0.1) list.\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "9dd7bc63-1d0f-4ae0-9f13-e4ad6e862afc", "metadata": {}, "outputs": [], "source": [ "np_nums = np.array(b)" ] }, { "cell_type": "markdown", "id": "ce97493a-60a5-4087-9ce8-86fb3334e3e4", "metadata": {}, "source": [ "4. In the cell below, create a new numpy array `np_result` by subtracting 0.5 from `np_nums` (i.e., using elementwise operations). Time this cell's execution. How much faster is the numpy version than the native python version?" ] }, { "cell_type": "code", "execution_count": 20, "id": "cd0b7e95-fb75-48de-b9c9-6c374007b117", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 1.84 ms, sys: 2.96 ms, total: 4.8 ms\n", "Wall time: 4.14 ms\n" ] } ], "source": [ "%%time\n", "np_result = np_nums - 0.5\n", "# your code here" ] }, { "cell_type": "markdown", "id": "6d49c281-2964-42b0-b870-d18f962ee67e", "metadata": {}, "source": [ "### Multidimensional Arrays\n", "* 2D arrays, slicing across dimensions\n", "* elementwise operations\n", " * comparisons / boolean dtype, masking\n", "* visualizing as an image" ] }, { "cell_type": "markdown", "id": "06d0c62a-99f4-4d2e-bdf2-a12b3c4bcd36", "metadata": {}, "source": [ "More ways of making arrays:\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "b7829fb1-2ebc-4f34-9b98-6ef3aee9241c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 2, 3])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create an array from [1, 2, 3]\n", "np.array([1, 2, 3])" ] }, { "cell_type": "code", "execution_count": 22, "id": "629cf52c-1ce9-4758-b1dd-6cc547faded0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 0., 0., 0., 0., 0.])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create an array of 6 zeros\n", "np.zeros((6,))\n" ] }, { "cell_type": "code", "execution_count": 23, "id": "64ee80f6-b629-4910-b9f3-4de43a7c8724", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 0, 0, 0, 0, 0])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create an array of 6 ones with 64-bit integer datatype\n", "np.zeros((6,), dtype=np.int64)" ] }, { "cell_type": "code", "execution_count": 24, "id": "8098011e-8960-45ab-987d-387ea8471099", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0., 0., 0.],\n", " [0., 0., 0.]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create a 2-by-3 array of zeros\n", "np.zeros((2, 3))" ] }, { "cell_type": "code", "execution_count": null, "id": "1e64d8ce-ff59-40f8-aebc-d1fe55613bcd", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "b99c4784-9470-4687-9055-026f9038b0c7", "metadata": {}, "source": [ "### Reshaping\n", "* more than 2 dimensions" ] }, { "cell_type": "code", "execution_count": 25, "id": "e7078b4f-777d-40ae-b80b-8d0d8a136918", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 1, 2],\n", " [3, 4, 5]])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# set b to an array of 0..5, reshaped to 2-by-3\n", "b = np.array(range(6)).reshape((2, 3))\n", "b" ] }, { "cell_type": "code", "execution_count": 26, "id": "b1dab6f1-7ebb-4087-8737-9be85a7b9277", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.int64(5)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# demo indexing into b\n", "b[1,2]" ] }, { "cell_type": "markdown", "id": "32a9e33e-3b95-41b1-a98e-e482047bb088", "metadata": {}, "source": [ "### Aggregation / Projection\n" ] }, { "cell_type": "code", "execution_count": 27, "id": "550de3a9-103e-4e01-a9c6-71ede2ff1f26", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.int64(15)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# find the sum of all elements in b\n", "b.sum()" ] }, { "cell_type": "code", "execution_count": 28, "id": "77946e7d-a010-41a9-a5f9-981c282efed4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.int64(0)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# find the minimum value in b\n", "b.min()" ] }, { "cell_type": "code", "execution_count": 29, "id": "2e3bdd9e-6496-48e4-87dc-f08f0c2a1745", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 1, 2],\n", " [3, 4, 5]])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# display b, just for reference\n", "b" ] }, { "cell_type": "code", "execution_count": 30, "id": "0bf92ee6-63f0-4e12-831e-e880da468d36", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3, 5, 7])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# sum the elements of b along axis 0 (the row dimension)\n", "b.sum(axis=0)" ] }, { "cell_type": "code", "execution_count": 31, "id": "4ebc1ad7-998b-48d1-b285-7ebeb9de032e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 3, 12])" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# sum the elements of b along axis 1 (the column dimension)\n", "b.sum(axis=1)" ] }, { "cell_type": "markdown", "id": "f4f4d18c-146b-4cd8-be3a-828639c81977", "metadata": {}, "source": [ "### Exercise 2 - Broadcasting\n", "\n", "**In pairs**: We've seen that, to perform elementwise operations, the dimensions of the arrays must match. There's one convenient exception to this. Let's see it in action below:" ] }, { "cell_type": "code", "execution_count": 32, "id": "593ae1a4-2b7d-4f5d-b6c2-8965d8330ab3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2, 3)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = np.array(range(6)).reshape((2, 3))\n", "b.shape" ] }, { "cell_type": "code", "execution_count": 33, "id": "48b40f87-c4e6-4ced-9b07-2237e576e475", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2,)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = np.array([2, 4])\n", "c.shape" ] }, { "cell_type": "code", "execution_count": 34, "id": "f7fa7e24-4232-4d1f-9d5b-40e3f7a163a8", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "operands could not be broadcast together with shapes (2,3) (2,) ", "output_type": "error", "traceback": [ "\u001b[31m---------------------------------------------------------------------------\u001b[39m", "\u001b[31mValueError\u001b[39m Traceback (most recent call last)", "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[34]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# dimension mismatch\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m b * c\n", "\u001b[31mValueError\u001b[39m: operands could not be broadcast together with shapes (2,3) (2,) " ] } ], "source": [ "# dimension mismatch\n", "b * c" ] }, { "cell_type": "code", "execution_count": 35, "id": "bd5f466f-2c27-4693-9d7c-a8a973cd6234", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2, 1)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# reshape c to be 2D\n", "c_2x1 = c.reshape((2, 1))\n", "c_2x1.shape" ] }, { "cell_type": "code", "execution_count": 36, "id": "e1b166ff-d01d-40cd-89e0-8aee8992953d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 1, 2],\n", " [3, 4, 5]])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b" ] }, { "cell_type": "code", "execution_count": 37, "id": "f938a358-fb29-491c-b956-8f93171d86d6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[2],\n", " [4]])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_2x1" ] }, { "cell_type": "code", "execution_count": 38, "id": "6171b36d-f9aa-4bc3-a0c5-8f69b918873a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0, 2, 4],\n", " [12, 16, 20]])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# example of broadcasting:\n", "b * c_2x1" ] }, { "cell_type": "markdown", "id": "c70aab89-024d-4abd-baf6-795e43b14713", "metadata": {}, "source": [ "1. This is called **broadcasting**. Explain what happened here." ] }, { "cell_type": "markdown", "id": "1d7d726d-65ef-4ed8-b391-647fc3e94b27", "metadata": {}, "source": [ "The values in `c_2x1` got repeated across the column dimension to match the column dimension of b." ] }, { "cell_type": "markdown", "id": "282e8a06-4b9d-4c19-aa39-3f9e687d3c31", "metadata": {}, "source": [ "Now, run the following cells to see another example." ] }, { "cell_type": "code", "execution_count": 39, "id": "c1647f22-5f79-439f-9fc8-aca6ef54b3be", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 3)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = np.array([1, 0, 1]).reshape(1, 3)\n", "d.shape" ] }, { "cell_type": "code", "execution_count": 40, "id": "453a956c-ca42-4ed9-af2a-5a708b1d8963", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 1, 2],\n", " [3, 4, 5]])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b" ] }, { "cell_type": "code", "execution_count": 41, "id": "3e4a0d0a-2341-4c3d-a836-cbaa02b43f93", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1, 0, 1]])" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d" ] }, { "cell_type": "code", "execution_count": 42, "id": "e43a3fce-f968-4e06-8ac6-acc16ef19b6f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 0, 2],\n", " [3, 0, 5]])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b * d" ] }, { "cell_type": "markdown", "id": "02ac0f5e-ae25-4e23-91db-456a1f3b6277", "metadata": {}, "source": [ "Now, explain the general rule for:\n", "\n", "2. What kind of dimension mismatches are allowed?" ] }, { "cell_type": "markdown", "id": "efb05e2c-b9a0-409c-ba8f-4a563938391c", "metadata": {}, "source": [ "Dimensions must match exactly, unless one array has a 1 in a given dimension." ] }, { "cell_type": "markdown", "id": "87b61a43-8b95-4666-be4c-cc08fe054f59", "metadata": {}, "source": [ "\n", "3. How do elementwise operations behave when such a mismatch is present?\n" ] }, { "cell_type": "markdown", "id": "e96e90cf-2b43-4eb7-842f-6ecc838068ad", "metadata": {}, "source": [ "The elements will be repeated across the singleton dimension." ] }, { "cell_type": "markdown", "id": "390d84d5-f605-444b-9775-a81d5fb893de", "metadata": {}, "source": [ "## Numpy, Continued\n" ] }, { "cell_type": "markdown", "id": "4e100472-fb81-49d6-84aa-07abf1aadec2", "metadata": {}, "source": [ "### Fancy indexing\n", "* Integer indexing: `a[ list or ndarray of integer indices ]`\n", "* Boolean indexing: `a[ list or ndarray of booleans ]` where the list/ndarray's shape matches a's\n", "\n", "\n", "See for much more." ] }, { "cell_type": "markdown", "id": "43dc1963-2476-4777-891f-d454f608b996", "metadata": {}, "source": [ "#### Integer indexing" ] }, { "cell_type": "code", "execution_count": null, "id": "e4fd4822-e274-42e5-a8ab-4b143f83b1a7", "metadata": {}, "outputs": [], "source": [ "a = np.array(range(10, 20))\n", "a" ] }, { "cell_type": "markdown", "id": "4aea9397-4e35-4e5c-a64d-f0253b6339a1", "metadata": {}, "source": [ "Indexing with a list or array of integers pulls out only the elements at those indices:" ] }, { "cell_type": "code", "execution_count": null, "id": "da64fe99-4432-4a59-ab15-eb6286ea6c13", "metadata": {}, "outputs": [], "source": [ "# get the first, third, and fifth elements:\n" ] }, { "cell_type": "code", "execution_count": null, "id": "e16212b1-9d14-4b45-93de-1aa048bb2171", "metadata": {}, "outputs": [], "source": [ "# get the fourth, second, and second elements (!):\n" ] }, { "cell_type": "markdown", "id": "39a4a73c-c7f5-4e0f-8ae5-1e473e6beaf4", "metadata": {}, "source": [ "#### Boolean Indexing\n" ] }, { "cell_type": "code", "execution_count": null, "id": "faf2fba9-b205-46a7-b150-449eed3016d9", "metadata": {}, "outputs": [], "source": [ "b = np.ones((2, 2))\n", "b[0,0] = 2\n", "b[1,1] = 0" ] }, { "cell_type": "markdown", "id": "f8fd9d3c-13c9-4700-b842-0d54ff406b9d", "metadata": {}, "source": [ "**Quick quiz: what does b look like now?**" ] }, { "cell_type": "code", "execution_count": null, "id": "354df772-c6e9-4dea-916d-1a39f919f183", "metadata": {}, "outputs": [], "source": [ "b" ] }, { "cell_type": "markdown", "id": "9fafec39-69ea-4a80-8928-f8ccd6a16e98", "metadata": {}, "source": [ "Make a \"mask\" of booleans that's the same shape as `b`:" ] }, { "cell_type": "code", "execution_count": null, "id": "44ad98a0-75e0-4ff0-b092-fa23eb6cdc6b", "metadata": {}, "outputs": [], "source": [ "mask = np.array([\n", " [True, False],\n", " [False, True]\n", "])\n", "mask" ] }, { "cell_type": "code", "execution_count": null, "id": "7e93f608-d307-4c67-b9ba-ce2d2cd3dbbe", "metadata": {}, "outputs": [], "source": [ "# index b with the boolean mask:\n" ] }, { "cell_type": "markdown", "id": "387408d1-0ccf-4298-bb48-1ed23f24bdcf", "metadata": {}, "source": [ "A common pattern - comparison operators to generate a mask:" ] }, { "cell_type": "code", "execution_count": null, "id": "c53f5345-acbe-4fc9-987f-bb4c44436389", "metadata": {}, "outputs": [], "source": [ "# get an array of only the elements of b that are greater than zero:\n" ] }, { "cell_type": "markdown", "id": "43acafdd-a851-440e-9d83-869525b66c67", "metadata": {}, "source": [ "#### Tips for multidimensional arrays\n", "\n", "* I never display anything that's more than 2D.\n", "* I never try to visualize anything that's more than 3D." ] }, { "cell_type": "code", "execution_count": null, "id": "d1bfce3c-7b1a-4db4-a872-5460342eb9bf", "metadata": {}, "outputs": [], "source": [ "c = np.array(range(24)).reshape(2, 4, 3)\n", "c" ] }, { "cell_type": "code", "execution_count": null, "id": "d363f7db-1af7-4b2d-8b3a-2c482140d23d", "metadata": {}, "outputs": [], "source": [ "# take one 2D slice\n" ] }, { "cell_type": "code", "execution_count": null, "id": "e14d5322-bb1f-4350-ac34-f9bb1dc2b45b", "metadata": {}, "outputs": [], "source": [ "# take another 2D slice along a different axis\n" ] }, { "cell_type": "markdown", "id": "c913c407-2ebb-464b-883a-7459316fe19a", "metadata": {}, "source": [ "### Exercise 3 Play with my cat\n", "\n", "**In pairs**: In this exercise, we'll manipulate an image as a 2D array.\n", "\n", "We'll start by loading a picture of my cat, Beans:" ] }, { "cell_type": "code", "execution_count": null, "id": "a94298d7-179a-4c1e-9ad9-3cfb2c4f09ac", "metadata": {}, "outputs": [], "source": [ "beans = imageio.imread(\"/cluster/academic/DATA311/202620/beans_gray.jpeg\")" ] }, { "cell_type": "markdown", "id": "5f49a796-3ecc-4bbf-988b-ef52330654f8", "metadata": {}, "source": [ "We'll use `plt.imshow` to visualize the image:" ] }, { "cell_type": "code", "execution_count": null, "id": "5d461096-969c-4217-840e-3136b6273900", "metadata": {}, "outputs": [], "source": [ "plt.imshow(beans, cmap='gray')" ] }, { "cell_type": "markdown", "id": "9fb413b6-328d-4aca-a270-4ccfe34c6273", "metadata": {}, "source": [ "1. What is the dtype of the resulting array? What are the minimum and maximum values?" ] }, { "cell_type": "code", "execution_count": null, "id": "8988c9c4-3163-4169-ad47-ee39c025b31d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6be43a32-a3d1-40cc-82d5-8039978901a3", "metadata": {}, "source": [ "2. Display a binary image showing which pixels are greater than half the maximum pixel intensity (127)." ] }, { "cell_type": "code", "execution_count": null, "id": "8e4a13fe-0b4c-4cef-bbb5-4c17ffa8c865", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a967c097-eab3-4abe-ab05-53e71197845d", "metadata": {}, "source": [ "3. What is the average value of pixels that have intensity value above 127?" ] }, { "cell_type": "code", "execution_count": null, "id": "4d801220-fe14-4737-97a5-35de27ea0bb3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "df00432a-1d3e-49da-9d22-1e7eeb50ead8", "metadata": {}, "source": [ "4. Which column of the image has the highest average pixel value?" ] }, { "cell_type": "code", "execution_count": null, "id": "8e90318c-b38c-4b57-b4ba-afeee6bc36fb", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }