Exercise_Numerical_operations_on_array.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"numerical_operations_on_array.ipynb","version":"0.3.2","provenance":[]},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"}},"cells":[{"metadata":{"id":"jfJQ0s3bswc_","colab_type":"code","colab":{}},"cell_type":"code","source":["import numpy as np"],"execution_count":0,"outputs":[]},{"metadata":{"id":"jhQnKQ2KswdE","colab_type":"text"},"cell_type":"markdown","source":["# Elementwise Operations"]},{"metadata":{"id":"Wtu7cWpiswdF","colab_type":"text"},"cell_type":"markdown","source":["**1. Basic Operations**"]},{"metadata":{"id":"F-67X08fswdG","colab_type":"text"},"cell_type":"markdown","source":["**with scalars**"]},{"metadata":{"id":"dVy44XhoswdI","colab_type":"code","colab":{},"outputId":"6c3aab05-af8d-4591-fbf2-298081a81356"},"cell_type":"code","source":["a = np.array([1, 2, 3, 4]) #create an array\n","\n","a + 1"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([2, 3, 4, 5])"]},"metadata":{"tags":[]},"execution_count":2}]},{"metadata":{"id":"C3xGq800swdO","colab_type":"code","colab":{},"outputId":"edc11eed-3015-45f8-b477-14cbcf6f3590"},"cell_type":"code","source":["a ** 2"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 1,  4,  9, 16])"]},"metadata":{"tags":[]},"execution_count":3}]},{"metadata":{"id":"RUCgn5sWswdS","colab_type":"text"},"cell_type":"markdown","source":["**All arithmetic operates elementwise**"]},{"metadata":{"id":"8PnM4PU7swdT","colab_type":"code","colab":{},"outputId":"dec9c525-340a-480c-859f-252e85b768bc"},"cell_type":"code","source":["b = np.ones(4) + 1\n","\n","a - b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([-1.,  0.,  1.,  2.])"]},"metadata":{"tags":[]},"execution_count":4}]},{"metadata":{"id":"rpXvbqFwswdX","colab_type":"code","colab":{},"outputId":"6e10ebe8-378e-492c-9fe1-6e9dac1b1ae8"},"cell_type":"code","source":["a * b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 2.,  4.,  6.,  8.])"]},"metadata":{"tags":[]},"execution_count":5}]},{"metadata":{"id":"2abVO_V_swdb","colab_type":"code","colab":{},"outputId":"e8e3fd83-507b-40c5-ef18-26f4b11680fb"},"cell_type":"code","source":["# Matrix multiplication\n","\n","c = np.diag([1, 2, 3, 4])\n","\n","print(c * c)\n","print(\"*****************\")\n","print(c.dot(c))"],"execution_count":0,"outputs":[{"output_type":"stream","text":["[[ 1  0  0  0]\n"," [ 0  4  0  0]\n"," [ 0  0  9  0]\n"," [ 0  0  0 16]]\n","*****************\n","[[ 1  0  0  0]\n"," [ 0  4  0  0]\n"," [ 0  0  9  0]\n"," [ 0  0  0 16]]\n"],"name":"stdout"}]},{"metadata":{"id":"WQJuiT1uswdf","colab_type":"text"},"cell_type":"markdown","source":["**comparisions**"]},{"metadata":{"id":"fjeX-CiOswdg","colab_type":"code","colab":{},"outputId":"27e205a5-191a-49db-e6bd-5e8d37136ccd"},"cell_type":"code","source":["a = np.array([1, 2, 3, 4])\n","b = np.array([5, 2, 2, 4])\n","a == b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False,  True, False,  True], dtype=bool)"]},"metadata":{"tags":[]},"execution_count":10}]},{"metadata":{"id":"X8TTJ8A2swdk","colab_type":"code","colab":{},"outputId":"a82a7c0f-aea4-4918-cfe8-364bc0c2c74a"},"cell_type":"code","source":["a > b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False, False,  True, False], dtype=bool)"]},"metadata":{"tags":[]},"execution_count":11}]},{"metadata":{"id":"J6VVph4Qswdp","colab_type":"code","colab":{},"outputId":"2a0d11bc-862a-40b0-e367-7308025a6115"},"cell_type":"code","source":["#array-wise comparisions\n","a = np.array([1, 2, 3, 4])\n","b = np.array([5, 2, 2, 4])\n","c = np.array([1, 2, 3, 4])\n","\n","np.array_equal(a, b)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":12}]},{"metadata":{"id":"4WcN5_dEswds","colab_type":"code","colab":{},"outputId":"17c720d1-8743-407b-c1c3-e8aa2cd06b56"},"cell_type":"code","source":["np.array_equal(a, c)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":13}]},{"metadata":{"id":"9zENvq0Eswdw","colab_type":"text"},"cell_type":"markdown","source":["**Logical Operations**"]},{"metadata":{"id":"1jnb4Oyoswdy","colab_type":"code","colab":{},"outputId":"d846450e-26ec-46bf-e5e9-ee1130f85e0e"},"cell_type":"code","source":["a = np.array([1, 1, 0, 0], dtype=bool)\n","b = np.array([1, 0, 1, 0], dtype=bool)\n","\n","np.logical_or(a, b)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True,  True,  True, False], dtype=bool)"]},"metadata":{"tags":[]},"execution_count":14}]},{"metadata":{"id":"0Y_BIY2sswd4","colab_type":"code","colab":{},"outputId":"45b0f028-2953-4b41-f524-719fd0739263"},"cell_type":"code","source":["np.logical_and(a, b)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True, False, False, False], dtype=bool)"]},"metadata":{"tags":[]},"execution_count":15}]},{"metadata":{"id":"TphCEdOgswd_","colab_type":"text"},"cell_type":"markdown","source":["**Transcendental functions:**"]},{"metadata":{"id":"lRgKTcVYsweA","colab_type":"code","colab":{},"outputId":"9d766b16-8896-4695-f408-2c22a2759eec"},"cell_type":"code","source":["a = np.arange(5)\n","\n","np.sin(a)   "],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"]},"metadata":{"tags":[]},"execution_count":16}]},{"metadata":{"id":"o2WNaZYTsweG","colab_type":"code","colab":{},"outputId":"09a4e071-9149-4cba-b220-977205f9877a"},"cell_type":"code","source":["np.log(a)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["/Users/satishatcha/.virtualenvs/course/lib/python2.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log\n","  \"\"\"Entry point for launching an IPython kernel.\n"],"name":"stderr"},{"output_type":"execute_result","data":{"text/plain":["array([       -inf,  0.        ,  0.69314718,  1.09861229,  1.38629436])"]},"metadata":{"tags":[]},"execution_count":17}]},{"metadata":{"id":"4BqEA2-6sweM","colab_type":"code","colab":{},"outputId":"b07f6045-92eb-4536-cdf0-103316629e69"},"cell_type":"code","source":["np.exp(a)   #evaluates e^x for each element in a given input"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([  1.        ,   2.71828183,   7.3890561 ,  20.08553692,  54.59815003])"]},"metadata":{"tags":[]},"execution_count":18}]},{"metadata":{"id":"ZTCX8P40sweR","colab_type":"text"},"cell_type":"markdown","source":["**Shape Mismatch**"]},{"metadata":{"id":"rEWPomresweR","colab_type":"code","colab":{},"outputId":"45081b7d-d37a-4deb-a19a-8b56650517a6"},"cell_type":"code","source":["a = np.arange(4)\n","\n","a + np.array([1, 2])"],"execution_count":0,"outputs":[{"output_type":"error","ename":"ValueError","evalue":"operands could not be broadcast together with shapes (4,) (2,) ","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)","\u001b[0;32m<ipython-input-19-f4d5ac434765>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m","\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,) (2,) "]}]},{"metadata":{"id":"9pyhkSfQsweW","colab_type":"text"},"cell_type":"markdown","source":["# Basic Reductions"]},{"metadata":{"id":"DHyoVepdsweX","colab_type":"text"},"cell_type":"markdown","source":["**computing sums**"]},{"metadata":{"id":"8Ed2Id_-sweY","colab_type":"code","colab":{},"outputId":"a39f4cc1-d624-4430-daa0-2f5a7d78efb4"},"cell_type":"code","source":["x = np.array([1, 2, 3, 4])\n","np.sum(x)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["10"]},"metadata":{"tags":[]},"execution_count":4}]},{"metadata":{"id":"zRoRIgZqswed","colab_type":"code","colab":{},"outputId":"c16ee400-36c0-4f13-fad0-4245ea0a46e0"},"cell_type":"code","source":["#sum by rows and by columns\n","\n","x = np.array([[1, 1], [2, 2]])\n","x"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[1, 1],\n","       [2, 2]])"]},"metadata":{"tags":[]},"execution_count":5}]},{"metadata":{"id":"_vP6O-E2sweh","colab_type":"code","colab":{},"outputId":"3a2c7f40-3b1a-4741-83d7-adac98635e40"},"cell_type":"code","source":["x.sum(axis=0)   #columns first dimension"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([3, 3])"]},"metadata":{"tags":[]},"execution_count":6}]},{"metadata":{"id":"Tcuz_6SRswel","colab_type":"code","colab":{},"outputId":"63fc6808-10da-4875-8245-816e28f5e570"},"cell_type":"code","source":["x.sum(axis=1)  #rows (second dimension)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([2, 4])"]},"metadata":{"tags":[]},"execution_count":7}]},{"metadata":{"id":"958ZeK7bsweq","colab_type":"text"},"cell_type":"markdown","source":["**Other reductions**"]},{"metadata":{"id":"R5zUDMynswer","colab_type":"code","colab":{},"outputId":"df848993-8198-42ea-e5f1-fe0618e3f271"},"cell_type":"code","source":["x = np.array([1, 3, 2])\n","x.min()"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1"]},"metadata":{"tags":[]},"execution_count":8}]},{"metadata":{"id":"kZtfLNX3swet","colab_type":"code","colab":{},"outputId":"14c1c2bf-ffad-4cff-c761-0f1d88f841b4"},"cell_type":"code","source":["x.max()"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["3"]},"metadata":{"tags":[]},"execution_count":9}]},{"metadata":{"id":"AFmjGkYeswex","colab_type":"code","colab":{},"outputId":"14cfd413-affd-44f9-a84c-1ced1c5ae5a6"},"cell_type":"code","source":["x.argmin()# index of minimum element"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0"]},"metadata":{"tags":[]},"execution_count":10}]},{"metadata":{"id":"jZ1Kne4bswe0","colab_type":"code","colab":{},"outputId":"e4476acf-16fa-44dd-edcb-84a926082b54"},"cell_type":"code","source":["x.argmax()# index of maximum element"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1"]},"metadata":{"tags":[]},"execution_count":11}]},{"metadata":{"id":"HMjQrI2Xswe6","colab_type":"text"},"cell_type":"markdown","source":["**Logical Operations**"]},{"metadata":{"id":"yDdavXNvswe7","colab_type":"code","colab":{},"outputId":"803c8e07-fcdb-4e58-a471-5f7fde649abe"},"cell_type":"code","source":["np.all([True, True, False])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":12}]},{"metadata":{"id":"pWQ5lldeswfA","colab_type":"code","colab":{},"outputId":"898a10f8-6fc1-4780-8d30-10039821f77b"},"cell_type":"code","source":["np.any([True, False, False])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":13}]},{"metadata":{"id":"g7ZIbD4YswfD","colab_type":"code","colab":{},"outputId":"b3e6eb8c-6864-4a3b-97b0-74a4a4efe79c"},"cell_type":"code","source":["#Note: can be used for array comparisions\n","a = np.zeros((50, 50))\n","np.any(a != 0)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":14}]},{"metadata":{"id":"zinI9W8hswfH","colab_type":"code","colab":{},"outputId":"601d26ae-d373-4f22-f313-2452f600107b"},"cell_type":"code","source":["np.all(a == a)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":15}]},{"metadata":{"id":"HuTF_mToswfL","colab_type":"code","colab":{},"outputId":"7363a182-2b8b-4e2c-c6a8-066318e563ed"},"cell_type":"code","source":["a = np.array([1, 2, 3, 2])\n","b = np.array([2, 2, 3, 2])\n","c = np.array([6, 4, 4, 5])\n","((a <= b) & (b <= c)).all()"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":16}]},{"metadata":{"id":"APsZAg7_swfO","colab_type":"text"},"cell_type":"markdown","source":["**Statistics**"]},{"metadata":{"id":"cjoteMjGswfP","colab_type":"code","colab":{},"outputId":"ccc68f0b-c334-4667-f18f-97758bfe32d5"},"cell_type":"code","source":["x = np.array([1, 2, 3, 1])\n","y = np.array([[1, 2, 3], [5, 6, 1]])\n","x.mean()"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1.75"]},"metadata":{"tags":[]},"execution_count":23}]},{"metadata":{"id":"JXWE8ldfswfV","colab_type":"code","colab":{},"outputId":"bf404199-5602-442b-98fd-23ad1e5e26f5"},"cell_type":"code","source":["np.median(x)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1.5"]},"metadata":{"tags":[]},"execution_count":24}]},{"metadata":{"id":"uiBhX8Ktswfj","colab_type":"code","colab":{},"outputId":"b162f7f7-2b25-429d-f5f3-c0592c793aa8"},"cell_type":"code","source":["np.median(y, axis=-1) # last axis"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 2.,  5.])"]},"metadata":{"tags":[]},"execution_count":25}]},{"metadata":{"id":"Cy3p6_0nswfo","colab_type":"code","colab":{},"outputId":"4c5b7639-7e09-47a5-8cd1-e1dfa07325d1"},"cell_type":"code","source":["x.std()          # full population standard dev."],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0.82915619758884995"]},"metadata":{"tags":[]},"execution_count":26}]},{"metadata":{"id":"UmJ61pVXswfu","colab_type":"text"},"cell_type":"markdown","source":["**Example:**"]},{"metadata":{"id":"anUWifpEswfx","colab_type":"text"},"cell_type":"markdown","source":["Data in populations.txt describes the populations of hares and lynxes (and carrots) in northern Canada during 20 years.\n"]},{"metadata":{"collapsed":true,"id":"rnVBTztnswfy","colab_type":"code","colab":{}},"cell_type":"code","source":["#load data into numpy array object\n","data = np.loadtxt('populations.txt')"],"execution_count":0,"outputs":[]},{"metadata":{"id":"P6namKkVswf1","colab_type":"code","colab":{},"outputId":"fd6bc8a1-2b47-4be3-e7a3-a9073a2fdda9"},"cell_type":"code","source":["data"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[  1900.,  30000.,   4000.,  48300.],\n","       [  1901.,  47200.,   6100.,  48200.],\n","       [  1902.,  70200.,   9800.,  41500.],\n","       [  1903.,  77400.,  35200.,  38200.],\n","       [  1904.,  36300.,  59400.,  40600.],\n","       [  1905.,  20600.,  41700.,  39800.],\n","       [  1906.,  18100.,  19000.,  38600.],\n","       [  1907.,  21400.,  13000.,  42300.],\n","       [  1908.,  22000.,   8300.,  44500.],\n","       [  1909.,  25400.,   9100.,  42100.],\n","       [  1910.,  27100.,   7400.,  46000.],\n","       [  1911.,  40300.,   8000.,  46800.],\n","       [  1912.,  57000.,  12300.,  43800.],\n","       [  1913.,  76600.,  19500.,  40900.],\n","       [  1914.,  52300.,  45700.,  39400.],\n","       [  1915.,  19500.,  51100.,  39000.],\n","       [  1916.,  11200.,  29700.,  36700.],\n","       [  1917.,   7600.,  15800.,  41800.],\n","       [  1918.,  14600.,   9700.,  43300.],\n","       [  1919.,  16200.,  10100.,  41300.],\n","       [  1920.,  24700.,   8600.,  47300.]])"]},"metadata":{"tags":[]},"execution_count":18}]},{"metadata":{"id":"QmlBep1Mswf5","colab_type":"code","colab":{},"outputId":"c1b341fc-c8c2-43bd-8b74-522f36336074"},"cell_type":"code","source":["year, hares, lynxes, carrots = data.T #columns to variables\n","print(year)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["[ 1900.  1901.  1902.  1903.  1904.  1905.  1906.  1907.  1908.  1909.\n","  1910.  1911.  1912.  1913.  1914.  1915.  1916.  1917.  1918.  1919.\n","  1920.]\n"],"name":"stdout"}]},{"metadata":{"id":"rK1BKEoyswgD","colab_type":"code","colab":{},"outputId":"39556379-8632-4f4b-bc1a-619afce30f6e"},"cell_type":"code","source":["#The mean population over time\n","populations = data[:, 1:]\n","populations"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 30000.,   4000.,  48300.],\n","       [ 47200.,   6100.,  48200.],\n","       [ 70200.,   9800.,  41500.],\n","       [ 77400.,  35200.,  38200.],\n","       [ 36300.,  59400.,  40600.],\n","       [ 20600.,  41700.,  39800.],\n","       [ 18100.,  19000.,  38600.],\n","       [ 21400.,  13000.,  42300.],\n","       [ 22000.,   8300.,  44500.],\n","       [ 25400.,   9100.,  42100.],\n","       [ 27100.,   7400.,  46000.],\n","       [ 40300.,   8000.,  46800.],\n","       [ 57000.,  12300.,  43800.],\n","       [ 76600.,  19500.,  40900.],\n","       [ 52300.,  45700.,  39400.],\n","       [ 19500.,  51100.,  39000.],\n","       [ 11200.,  29700.,  36700.],\n","       [  7600.,  15800.,  41800.],\n","       [ 14600.,   9700.,  43300.],\n","       [ 16200.,  10100.,  41300.],\n","       [ 24700.,   8600.,  47300.]])"]},"metadata":{"tags":[]},"execution_count":21}]},{"metadata":{"id":"x9fl1SFuswgI","colab_type":"code","colab":{},"outputId":"d35111fd-9329-484f-8d9a-07310f2fbe2d"},"cell_type":"code","source":["#sample standard deviations\n","populations.std(axis=0)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 20897.90645809,  16254.59153691,   3322.50622558])"]},"metadata":{"tags":[]},"execution_count":22}]},{"metadata":{"id":"JuRAVBQZswgT","colab_type":"code","colab":{},"outputId":"dddefc54-8d1b-4b01-990c-dea4068cab56"},"cell_type":"code","source":["#which species has the highest population each year?\n","\n","np.argmax(populations, axis=1)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2])"]},"metadata":{"tags":[]},"execution_count":23}]},{"metadata":{"id":"tU_ZXk-TswgY","colab_type":"text"},"cell_type":"markdown","source":["# Broadcasting"]},{"metadata":{"id":"9YhDQLkMswga","colab_type":"text"},"cell_type":"markdown","source":["Basic operations on numpy arrays (addition, etc.) are elementwise\n","\n","This works on arrays of the same size.\n","    Nevertheless, It’s also possible to do operations on arrays of different sizes if NumPy can transform these arrays     so that they all have the same size: this conversion is called broadcasting.\n","\n","The image below gives an example of broadcasting:"]},{"metadata":{"id":"ikjmauQzswgc","colab_type":"text"},"cell_type":"markdown","source":["![title](broadcasting.png)"]},{"metadata":{"id":"nI5avDtJswgd","colab_type":"code","colab":{},"outputId":"4514d3c2-a38d-4750-d6f3-8a709b40df7f"},"cell_type":"code","source":["a = np.tile(np.arange(0, 40, 10), (3,1))\n","print(a)\n","\n","print(\"*************\")\n","a=a.T\n","print(a)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["[[ 0 10 20 30]\n"," [ 0 10 20 30]\n"," [ 0 10 20 30]]\n","*************\n","[[ 0  0  0]\n"," [10 10 10]\n"," [20 20 20]\n"," [30 30 30]]\n"],"name":"stdout"}]},{"metadata":{"id":"cLIID2BSswgf","colab_type":"code","colab":{},"outputId":"066926e7-77bd-4116-a878-3b885f0fd7a1"},"cell_type":"code","source":["\n","b = np.array([0, 1, 2])\n","b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0, 1, 2])"]},"metadata":{"tags":[]},"execution_count":35}]},{"metadata":{"id":"jQrV3eHlswgh","colab_type":"code","colab":{},"outputId":"a580a35e-ab46-409c-92b6-55dca012c40c"},"cell_type":"code","source":["\n","a + b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 0,  1,  2],\n","       [10, 11, 12],\n","       [20, 21, 22],\n","       [30, 31, 32]])"]},"metadata":{"tags":[]},"execution_count":36}]},{"metadata":{"id":"O46UzhDpswgj","colab_type":"code","colab":{},"outputId":"ca8ff2f1-13e9-4ba9-aaa4-e724236b2436"},"cell_type":"code","source":["a = np.arange(0, 40, 10)\n","a.shape\n"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(4,)"]},"metadata":{"tags":[]},"execution_count":45}]},{"metadata":{"id":"OgkzL1i9swgl","colab_type":"code","colab":{},"outputId":"98ee71d0-ef8e-47c0-af1a-c197cfbec692"},"cell_type":"code","source":["a = a[:, np.newaxis]  # adds a new axis -> 2D array\n","a.shape"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(4, 1)"]},"metadata":{"tags":[]},"execution_count":42}]},{"metadata":{"id":"PQiWxq-6swgq","colab_type":"code","colab":{},"outputId":"b4ef9569-1bc8-4b4b-8a6a-30b75e6bf889"},"cell_type":"code","source":["a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 0],\n","       [10],\n","       [20],\n","       [30]])"]},"metadata":{"tags":[]},"execution_count":43}]},{"metadata":{"id":"tsUMMhVMswgw","colab_type":"code","colab":{},"outputId":"1eccf526-2b25-45b1-a67f-b70ffe346c2d"},"cell_type":"code","source":["a + b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 0,  1,  2],\n","       [10, 11, 12],\n","       [20, 21, 22],\n","       [30, 31, 32]])"]},"metadata":{"tags":[]},"execution_count":58}]},{"metadata":{"id":"j_PyiHoLswgz","colab_type":"text"},"cell_type":"markdown","source":["# Array Shape Manipulation"]},{"metadata":{"id":"k_PleE7Tswgz","colab_type":"text"},"cell_type":"markdown","source":["**Flattening**"]},{"metadata":{"id":"ZCNm05mWswg0","colab_type":"code","colab":{},"outputId":"18403ccc-45db-4e09-8e67-6b268246b278"},"cell_type":"code","source":["a = np.array([[1, 2, 3], [4, 5, 6]])\n","a.ravel() #Return a contiguous flattened array. A 1-D array, containing the elements of the input, is returned. A copy is made only if needed."],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([1, 2, 3, 4, 5, 6])"]},"metadata":{"tags":[]},"execution_count":52}]},{"metadata":{"id":"vDHkkj_Cswg2","colab_type":"code","colab":{},"outputId":"e09bd4e6-d56c-4040-b5a1-dea2b20767fa"},"cell_type":"code","source":["a.T #Transpose"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[1, 4],\n","       [2, 5],\n","       [3, 6]])"]},"metadata":{"tags":[]},"execution_count":53}]},{"metadata":{"id":"OQwnB4jMswg7","colab_type":"code","colab":{},"outputId":"d31964f8-cb74-4547-c2a2-7969288282f6"},"cell_type":"code","source":["a.T.ravel()"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([1, 4, 2, 5, 3, 6])"]},"metadata":{"tags":[]},"execution_count":54}]},{"metadata":{"id":"IfyMcSqWswhA","colab_type":"text"},"cell_type":"markdown","source":["**Reshaping**"]},{"metadata":{"id":"QcaiZZ7mswhA","colab_type":"text"},"cell_type":"markdown","source":["The inverse operation to flattening:"]},{"metadata":{"id":"MA6cntc9swhC","colab_type":"code","colab":{},"outputId":"a4aa22e7-1095-4349-b306-56000f8ae7ee"},"cell_type":"code","source":["print(a.shape)\n","print(a)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["(2, 3)\n","[[1 2 3]\n"," [4 5 6]]\n"],"name":"stdout"}]},{"metadata":{"id":"hhJauR24swhE","colab_type":"code","colab":{},"outputId":"e52e66cf-8c93-4769-909b-82137650ab36"},"cell_type":"code","source":["b = a.ravel()\n","print(b)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["[1 2 3 4 5 6]\n"],"name":"stdout"}]},{"metadata":{"id":"vXbnz73uswhG","colab_type":"code","colab":{},"outputId":"db52a819-25c3-45fd-dfb4-372e72cfb8fe"},"cell_type":"code","source":["b = b.reshape((2, 3))\n","b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[1, 2, 3],\n","       [4, 5, 6]])"]},"metadata":{"tags":[]},"execution_count":57}]},{"metadata":{"id":"TNr-WvUzswhI","colab_type":"code","colab":{},"outputId":"13a740fd-c250-4a21-fa13-3a2cd8fce06f"},"cell_type":"code","source":["b[0, 0] = 100\n","a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[100,   2,   3],\n","       [  4,   5,   6]])"]},"metadata":{"tags":[]},"execution_count":59}]},{"metadata":{"id":"_Y5EeOeJswhL","colab_type":"text"},"cell_type":"markdown","source":["**Note and       Beware: reshape may also return a copy!:**"]},{"metadata":{"id":"tf1F72vHswhL","colab_type":"code","colab":{},"outputId":"0726a4b2-566e-4628-cc19-8b894cb40c18"},"cell_type":"code","source":["a = np.zeros((3, 2))\n","b = a.T.reshape(3*2)\n","b[0] = 50\n","a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 0.,  0.],\n","       [ 0.,  0.],\n","       [ 0.,  0.]])"]},"metadata":{"tags":[]},"execution_count":60}]},{"metadata":{"id":"4pnFgWaTswhO","colab_type":"text"},"cell_type":"markdown","source":["**Adding a Dimension**"]},{"metadata":{"id":"b3x7GDphswhP","colab_type":"text"},"cell_type":"markdown","source":["Indexing with the np.newaxis object allows us to add an axis to an array"]},{"metadata":{"id":"zWZFOfB0swhP","colab_type":"text"},"cell_type":"markdown","source":["newaxis is used to increase the dimension of the existing array by one more dimension, when used once. Thus,\n","\n","1D array will become 2D array\n","\n","2D array will become 3D array\n","\n","3D array will become 4D array and so on"]},{"metadata":{"id":"DuHUdNLoswhP","colab_type":"code","colab":{},"outputId":"40fb60a7-c44c-41fa-9be8-09ec5468c6a7"},"cell_type":"code","source":["z = np.array([1, 2, 3])\n","z"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([1, 2, 3])"]},"metadata":{"tags":[]},"execution_count":61}]},{"metadata":{"id":"f48pj0JMswhT","colab_type":"code","colab":{},"outputId":"546f6836-b251-4812-f7b2-cf0461d13178"},"cell_type":"code","source":["z[:, np.newaxis]"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[1],\n","       [2],\n","       [3]])"]},"metadata":{"tags":[]},"execution_count":62}]},{"metadata":{"id":"Wy-2k9NjswhW","colab_type":"text"},"cell_type":"markdown","source":["**Dimension Shuffling**"]},{"metadata":{"id":"MSTSN5IoswhZ","colab_type":"code","colab":{},"outputId":"3c1a1132-68f4-4f3b-bb40-c46ab734643a"},"cell_type":"code","source":["a = np.arange(4*3*2).reshape(4, 3, 2)\n","a.shape"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(4, 3, 2)"]},"metadata":{"tags":[]},"execution_count":63}]},{"metadata":{"id":"-i_qw-2Bswhd","colab_type":"code","colab":{},"outputId":"dd25efea-7155-4b62-efd2-c069cc0f73c1"},"cell_type":"code","source":["a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[[ 0,  1],\n","        [ 2,  3],\n","        [ 4,  5]],\n","\n","       [[ 6,  7],\n","        [ 8,  9],\n","        [10, 11]],\n","\n","       [[12, 13],\n","        [14, 15],\n","        [16, 17]],\n","\n","       [[18, 19],\n","        [20, 21],\n","        [22, 23]]])"]},"metadata":{"tags":[]},"execution_count":77}]},{"metadata":{"id":"sFfdpnwxswhg","colab_type":"code","colab":{},"outputId":"a7f25bdc-c56c-4981-a8ab-ce1627bfd005"},"cell_type":"code","source":["a[0, 2, 1]"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["5"]},"metadata":{"tags":[]},"execution_count":64}]},{"metadata":{"id":"2lFLuLyjswhk","colab_type":"text"},"cell_type":"markdown","source":["**Resizing**"]},{"metadata":{"id":"Yi9xEsTdswhl","colab_type":"code","colab":{},"outputId":"f11c0809-c403-41c9-eaf0-e3f4c90469d8"},"cell_type":"code","source":["a = np.arange(4)\n","a.resize((8,))\n","a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0, 1, 2, 3, 0, 0, 0, 0])"]},"metadata":{"tags":[]},"execution_count":67}]},{"metadata":{"id":"L32_TKH-swhp","colab_type":"text"},"cell_type":"markdown","source":["However, it must not be referred to somewhere else:"]},{"metadata":{"id":"n03o_7jKswhq","colab_type":"code","colab":{},"outputId":"591c6728-d9cd-439f-8287-fce70a25ea2a"},"cell_type":"code","source":["b = a\n","a.resize((4,)) "],"execution_count":0,"outputs":[{"output_type":"error","ename":"ValueError","evalue":"cannot resize an array that references or is referenced\nby another array in this way.  Use the resize function","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)","\u001b[0;32m<ipython-input-68-702766c88583>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m","\u001b[0;31mValueError\u001b[0m: cannot resize an array that references or is referenced\nby another array in this way.  Use the resize function"]}]},{"metadata":{"id":"xm598Xkxswhs","colab_type":"text"},"cell_type":"markdown","source":["**Sorting Data**"]},{"metadata":{"id":"iM9Y-4wfswhs","colab_type":"code","colab":{},"outputId":"417dc55e-8b88-4d3b-c46c-e15aa1f99dcc"},"cell_type":"code","source":["#Sorting along an axis:\n","a = np.array([[5, 4, 6], [2, 3, 2]])\n","b = np.sort(a, axis=1)\n","b"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[4, 5, 6],\n","       [2, 2, 3]])"]},"metadata":{"tags":[]},"execution_count":69}]},{"metadata":{"id":"Z8gWeYynswhw","colab_type":"code","colab":{},"outputId":"51b6c0f4-bc6e-443f-84ce-dccca9039bc3"},"cell_type":"code","source":["#in-place sort\n","a.sort(axis=1)\n","a"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[4, 5, 6],\n","       [2, 2, 3]])"]},"metadata":{"tags":[]},"execution_count":84}]},{"metadata":{"id":"DSSbH76aswh1","colab_type":"code","colab":{},"outputId":"6a5e8098-e5c1-4298-bf36-982d5fa9b9ba"},"cell_type":"code","source":["#sorting with fancy indexing\n","a = np.array([4, 3, 1, 2])\n","j = np.argsort(a)\n","j"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([2, 3, 1, 0])"]},"metadata":{"tags":[]},"execution_count":85}]},{"metadata":{"id":"CtBWBS5Qswh3","colab_type":"code","colab":{},"outputId":"c802fde5-cac6-4495-b3f6-e4c66dbfbb3f"},"cell_type":"code","source":["a[j]"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([1, 2, 3, 4])"]},"metadata":{"tags":[]},"execution_count":86}]}]}