indexing.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# A possibly incomplete Demo of all the combinations of indexing methods\n",
        "... and interesting cases"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np"
      ],
      "outputs": [],
      "execution_count": 3,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
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          "shell.execute_reply": "2021-08-23T16:30:25.859Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1d Array"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array(list(\"ABCDEFHIJKLMNOPQRSTUVWXYZ\"))\n",
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "text/plain": "array(['A', 'B', 'C', 'D', 'E', 'F', 'H', 'I', 'J', 'K', 'L', 'M', 'N',\n       'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'],\n      dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 4,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
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        "execution": {
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### \\[int]"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[9]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": "'K'"
          },
          "metadata": {}
        }
      ],
      "execution_count": 5,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
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        "execution": {
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        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### \\[slice]"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[2::3]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
          "data": {
            "text/plain": "array(['C', 'F', 'J', 'M', 'P', 'S', 'V', 'Y'], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 6,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
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        "execution": {
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      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### \\[array]"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[[1,2,3]]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": "array(['B', 'C', 'D'], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 7,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
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          "transient": {
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2D Array"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array(list(\"ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789\")).reshape(6,6)\n",
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": "array([['A', 'B', 'C', 'D', 'E', 'F'],\n       ['G', 'H', 'I', 'J', 'K', 'L'],\n       ['M', 'N', 'O', 'P', 'Q', 'R'],\n       ['S', 'T', 'U', 'V', 'W', 'X'],\n       ['Y', 'Z', '0', '1', '2', '3'],\n       ['4', '5', '6', '7', '8', '9']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
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          "source_hidden": false,
          "outputs_hidden": false
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          "transient": {
            "deleting": false
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### Field access Indexing \\[int\\]\\[int\\]"
      ],
      "metadata": {
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          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[3][4]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 9,
          "data": {
            "text/plain": "'W'"
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": true,
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          "source_hidden": false,
          "outputs_hidden": false
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        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
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        }
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### Regular Indexing \\[int, int\\]\n",
        "usually you index within one square bracket"
      ],
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            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[3, 4]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": "'W'"
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
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    },
    {
      "cell_type": "markdown",
      "source": [
        "Behind the scenes, the comma causes the indexes to be interpreted as a tuple, so explicitely indexing with tuples also works!"
      ],
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            "deleting": false
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        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[(3, 4)]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 13,
          "data": {
            "text/plain": "'W'"
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### Mixing and matching \\[int, slice], \\[slice, int], \\[int, array], \\[array, int]\n",
        "When one index refers to multiple elements and the other does not, the int dimension gets eaten! You end up with a 1D array of the lenth of the multi-element index"
      ],
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          "transient": {
            "deleting": false
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        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[3, ::2]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": "array(['S', 'U', 'W'], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": true,
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    },
    {
      "cell_type": "code",
      "source": [
        "a[3, [1,2]]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 17,
          "data": {
            "text/plain": "array(['T', 'U'], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": true,
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          "source_hidden": false,
          "outputs_hidden": false
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### \\[slice, slice], \\[slice, array], \\[array, slice]\n",
        "When both indexes refer to multiple elements (and at least one of them is a slice) you get orthogonal indexing. You can think of it as subsetting the original array."
      ],
      "metadata": {
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        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[::2, 1::2]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 18,
          "data": {
            "text/plain": "array([['B', 'D', 'F'],\n       ['N', 'P', 'R'],\n       ['Z', '1', '3']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": true,
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          "source_hidden": false,
          "outputs_hidden": false
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          "transient": {
            "deleting": false
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    },
    {
      "cell_type": "code",
      "source": [
        "a[::2, [1,2,3]]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 19,
          "data": {
            "text/plain": "array([['B', 'C', 'D'],\n       ['N', 'O', 'P'],\n       ['Z', '0', '1']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 19,
      "metadata": {
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    {
      "cell_type": "markdown",
      "source": [
        "### \\[array, array]\n",
        "When both indexes are arrays they act like lookup-coordinates for rows and columns. This is fancy indexing!"
      ],
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            "deleting": false
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      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[[3,3,0],[4,1,5]]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 22,
          "data": {
            "text/plain": "array(['W', 'T', 'F'], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 22,
      "metadata": {
        "collapsed": true,
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          "outputs_hidden": false
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          "transient": {
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        "execution": {
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    },
    {
      "cell_type": "markdown",
      "source": [
        "Actually, orthogonal indexing is a subset of fancy indexing! The returned array size always corresponds to the indexing array size. In the case above we have two 1X3 arrays as indexes. When you index with a row and a column vector instead (see below), they get broadcast together to produce the same result you would get with the slice syntax.\n",
        "\n"
      ],
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        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.ix_([0,2], [1,3,5])"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 20,
          "data": {
            "text/plain": "(array([[0],\n        [2]]),\n array([[1, 3, 5]]))"
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
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        "execution": {
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    },
    {
      "cell_type": "code",
      "source": [
        "# get it to be orthogonal \n",
        "a[np.ix_([0,2], [1,3,5])]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 21,
          "data": {
            "text/plain": "array([['B', 'D', 'F'],\n       ['N', 'P', 'R']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {
        "collapsed": true,
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          "source_hidden": false,
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    {
      "cell_type": "markdown",
      "source": [
        "### \\[mdarray, slice\\]\n",
        "indexing with one multidimensionsional array also basically broadcasts them together to get the final shape"
      ],
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    },
    {
      "cell_type": "code",
      "source": [
        "ix = np.array([[1,2],[1,2]])\n",
        "ix"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 32,
          "data": {
            "text/plain": "array([[1, 2],\n       [1, 2]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 32,
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    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 33,
          "data": {
            "text/plain": "array([['A', 'B', 'C', 'D', 'E', 'F'],\n       ['G', 'H', 'I', 'J', 'K', 'L'],\n       ['M', 'N', 'O', 'P', 'Q', 'R'],\n       ['S', 'T', 'U', 'V', 'W', 'X'],\n       ['Y', 'Z', '0', '1', '2', '3'],\n       ['4', '5', '6', '7', '8', '9']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 33,
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    {
      "cell_type": "code",
      "source": [
        "a[ix,:]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 34,
          "data": {
            "text/plain": "array([[['G', 'H', 'I', 'J', 'K', 'L'],\n        ['M', 'N', 'O', 'P', 'Q', 'R']],\n\n       [['G', 'H', 'I', 'J', 'K', 'L'],\n        ['M', 'N', 'O', 'P', 'Q', 'R']]], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 34,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:50:42.727Z",
          "iopub.execute_input": "2021-08-23T16:50:42.749Z",
          "iopub.status.idle": "2021-08-23T16:50:42.785Z",
          "shell.execute_reply": "2021-08-23T16:50:42.802Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[ix,:].shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 35,
          "data": {
            "text/plain": "(2, 2, 6)"
          },
          "metadata": {}
        }
      ],
      "execution_count": 35,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:50:50.118Z",
          "iopub.execute_input": "2021-08-23T16:50:50.135Z",
          "iopub.status.idle": "2021-08-23T16:50:50.169Z",
          "shell.execute_reply": "2021-08-23T16:50:50.184Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 36,
          "data": {
            "text/plain": "array([['A', 'B', 'C', 'D', 'E', 'F'],\n       ['G', 'H', 'I', 'J', 'K', 'L'],\n       ['M', 'N', 'O', 'P', 'Q', 'R'],\n       ['S', 'T', 'U', 'V', 'W', 'X'],\n       ['Y', 'Z', '0', '1', '2', '3'],\n       ['4', '5', '6', '7', '8', '9']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 36,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:51:37.149Z",
          "iopub.execute_input": "2021-08-23T16:51:37.167Z",
          "iopub.status.idle": "2021-08-23T16:51:37.207Z",
          "shell.execute_reply": "2021-08-23T16:51:37.223Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "below you can see how the broadcasting works explicitely"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.broadcast_arrays([[1],[2]],[2,3]))\n",
        "a[[[1],[2]],[2,3]]"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[array([[1, 1],\n",
            "       [2, 2]]), array([[2, 3],\n",
            "       [2, 3]])]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 39,
          "data": {
            "text/plain": "array([['I', 'J'],\n       ['O', 'P']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 39,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:53:18.178Z",
          "iopub.execute_input": "2021-08-23T16:53:18.196Z",
          "iopub.status.idle": "2021-08-23T16:53:18.237Z",
          "shell.execute_reply": "2021-08-23T16:53:18.252Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.broadcast_arrays([2, 3], [[1],[2]]))\n",
        "a[[2, 3], [[1],[2]]]"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[array([[2, 3],\n",
            "       [2, 3]]), array([[1, 1],\n",
            "       [2, 2]])]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 40,
          "data": {
            "text/plain": "array([['N', 'T'],\n       ['O', 'U']], dtype='<U1')"
          },
          "metadata": {}
        }
      ],
      "execution_count": 40,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:53:18.830Z",
          "iopub.execute_input": "2021-08-23T16:53:18.845Z",
          "iopub.status.idle": "2021-08-23T16:53:18.885Z",
          "shell.execute_reply": "2021-08-23T16:53:18.900Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "the reason why fancy indexing works, is that they are also broadcast together but no changes are made"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.broadcast_arrays([2, 3], [1, 2]))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[array([2, 3]), array([1, 2])]\n"
          ]
        }
      ],
      "execution_count": 41,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:54:49.590Z",
          "iopub.execute_input": "2021-08-23T16:54:49.604Z",
          "iopub.status.idle": "2021-08-23T16:54:49.638Z",
          "shell.execute_reply": "2021-08-23T16:54:49.654Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Boolean Indexing"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.random.randint(0,10,(5,5))\n",
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 43,
          "data": {
            "text/plain": "array([[9, 6, 8, 0, 0],\n       [1, 3, 4, 5, 7],\n       [5, 1, 0, 6, 2],\n       [2, 5, 9, 8, 1],\n       [8, 6, 9, 0, 6]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 43,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:55:07.753Z",
          "iopub.execute_input": "2021-08-23T16:55:07.769Z",
          "iopub.status.idle": "2021-08-23T16:55:07.801Z",
          "shell.execute_reply": "2021-08-23T16:55:07.816Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a<4"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 44,
          "data": {
            "text/plain": "array([[False, False, False,  True,  True],\n       [ True,  True, False, False, False],\n       [False,  True,  True, False,  True],\n       [ True, False, False, False,  True],\n       [False, False, False,  True, False]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 44,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:55:08.700Z",
          "iopub.execute_input": "2021-08-23T16:55:08.717Z",
          "iopub.status.idle": "2021-08-23T16:55:08.756Z",
          "shell.execute_reply": "2021-08-23T16:55:08.772Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[a<4]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 45,
          "data": {
            "text/plain": "array([0, 0, 1, 3, 1, 0, 2, 2, 1, 0])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 45,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:55:16.274Z",
          "iopub.execute_input": "2021-08-23T16:55:16.291Z",
          "iopub.status.idle": "2021-08-23T16:55:16.325Z",
          "shell.execute_reply": "2021-08-23T16:55:16.339Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 3+ D Indexing"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.random.randint(0,10,(3,4,5))\n",
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 47,
          "data": {
            "text/plain": "array([[[4, 4, 4, 5, 6],\n        [6, 8, 1, 0, 0],\n        [0, 0, 6, 9, 2],\n        [1, 3, 3, 6, 8]],\n\n       [[9, 6, 8, 3, 1],\n        [5, 1, 5, 2, 2],\n        [8, 1, 5, 9, 6],\n        [7, 2, 3, 7, 5]],\n\n       [[9, 7, 8, 3, 8],\n        [8, 1, 5, 9, 5],\n        [0, 4, 5, 6, 7],\n        [8, 6, 7, 6, 5]]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 47,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:12.045Z",
          "iopub.execute_input": "2021-08-23T16:56:12.060Z",
          "iopub.status.idle": "2021-08-23T16:56:12.091Z",
          "shell.execute_reply": "2021-08-23T16:56:12.107Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 48,
          "data": {
            "text/plain": "(3, 4, 5)"
          },
          "metadata": {}
        }
      ],
      "execution_count": 48,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:12.334Z",
          "iopub.execute_input": "2021-08-23T16:56:12.350Z",
          "iopub.status.idle": "2021-08-23T16:56:12.385Z",
          "shell.execute_reply": "2021-08-23T16:56:12.400Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### all ints"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[1,2,3]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 49,
          "data": {
            "text/plain": "9"
          },
          "metadata": {}
        }
      ],
      "execution_count": 49,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:13.181Z",
          "iopub.execute_input": "2021-08-23T16:56:13.198Z",
          "iopub.status.idle": "2021-08-23T16:56:13.232Z",
          "shell.execute_reply": "2021-08-23T16:56:13.248Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### all slices"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[::2,::2,::2]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 50,
          "data": {
            "text/plain": "array([[[4, 4, 6],\n        [0, 6, 2]],\n\n       [[9, 8, 8],\n        [0, 5, 7]]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 50,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:28.136Z",
          "iopub.execute_input": "2021-08-23T16:56:28.153Z",
          "iopub.status.idle": "2021-08-23T16:56:28.186Z",
          "shell.execute_reply": "2021-08-23T16:56:28.202Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### arrays/fancy"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[[1,2],[1,2],[1,2]]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 52,
          "data": {
            "text/plain": "array([1, 5])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 52,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:48.976Z",
          "iopub.execute_input": "2021-08-23T16:56:48.995Z",
          "iopub.status.idle": "2021-08-23T16:56:49.030Z",
          "shell.execute_reply": "2021-08-23T16:56:49.046Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 53,
          "data": {
            "text/plain": "array([[[4, 4, 4, 5, 6],\n        [6, 8, 1, 0, 0],\n        [0, 0, 6, 9, 2],\n        [1, 3, 3, 6, 8]],\n\n       [[9, 6, 8, 3, 1],\n        [5, 1, 5, 2, 2],\n        [8, 1, 5, 9, 6],\n        [7, 2, 3, 7, 5]],\n\n       [[9, 7, 8, 3, 8],\n        [8, 1, 5, 9, 5],\n        [0, 4, 5, 6, 7],\n        [8, 6, 7, 6, 5]]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 53,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:56:53.450Z",
          "iopub.execute_input": "2021-08-23T16:56:53.466Z",
          "iopub.status.idle": "2021-08-23T16:56:53.502Z",
          "shell.execute_reply": "2021-08-23T16:56:53.516Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Mixing it up \\[slice, int, array\\]\n",
        "the single dimension gets eaten again"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[:,1,[1,2]])\n",
        "print(a[:,1,[1,2]].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[8 1]\n",
            " [1 5]\n",
            " [1 5]]\n",
            "(3, 2)\n"
          ]
        }
      ],
      "execution_count": 54,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:57:12.063Z",
          "iopub.execute_input": "2021-08-23T16:57:12.083Z",
          "iopub.status.idle": "2021-08-23T16:57:12.188Z",
          "shell.execute_reply": "2021-08-23T16:57:12.206Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[:,[1,2],1])\n",
        "print(a[:,[1,2],1].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[8 0]\n",
            " [1 1]\n",
            " [1 4]]\n",
            "(3, 2)\n"
          ]
        }
      ],
      "execution_count": 55,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:57:13.074Z",
          "iopub.execute_input": "2021-08-23T16:57:13.091Z",
          "iopub.status.idle": "2021-08-23T16:57:13.124Z",
          "shell.execute_reply": "2021-08-23T16:57:13.139Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[1, [1,2], :])\n",
        "print(a[1, [1,2], :].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[5 1 5 2 2]\n",
            " [8 1 5 9 6]]\n",
            "(2, 5)\n"
          ]
        }
      ],
      "execution_count": 56,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T16:57:14.494Z",
          "iopub.execute_input": "2021-08-23T16:57:14.515Z",
          "iopub.status.idle": "2021-08-23T16:57:14.552Z",
          "shell.execute_reply": "2021-08-23T16:57:14.567Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[[1,2], 1, :])\n",
        "print(a[[1,2], 1, :].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 3 7 4 8]\n",
            " [8 8 7 2 5]]\n",
            "(2, 5)\n"
          ]
        }
      ],
      "execution_count": 78,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-07-26T14:03:01.925Z",
          "iopub.execute_input": "2020-07-26T14:03:01.948Z",
          "iopub.status.idle": "2020-07-26T14:03:01.986Z",
          "shell.execute_reply": "2020-07-26T14:03:02.004Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[[1,2], :, 1])\n",
        "print(a[[1,2], :, 1].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[7 3 0 9]\n",
            " [1 8 2 0]]\n",
            "(2, 4)\n"
          ]
        }
      ],
      "execution_count": 79,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-07-26T14:03:27.062Z",
          "iopub.execute_input": "2020-07-26T14:03:27.078Z",
          "iopub.status.idle": "2020-07-26T14:03:27.111Z",
          "shell.execute_reply": "2020-07-26T14:03:27.125Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(a[0, :, [1,2]])\n",
        "print(a[0, :, [1,2]].shape)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 0 9 7]\n",
            " [7 7 8 5]]\n",
            "(2, 4)\n"
          ]
        }
      ],
      "execution_count": 82,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-07-26T14:17:03.774Z",
          "iopub.execute_input": "2020-07-26T14:17:03.791Z",
          "iopub.status.idle": "2020-07-26T14:17:03.827Z",
          "shell.execute_reply": "2020-07-26T14:17:03.843Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "why not 4,2 you might ask?\n",
        "\n",
        "slice in the middle -> slice dimensions always go at the back."
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 57,
          "data": {
            "text/plain": "array([[[4, 4, 4, 5, 6],\n        [6, 8, 1, 0, 0],\n        [0, 0, 6, 9, 2],\n        [1, 3, 3, 6, 8]],\n\n       [[9, 6, 8, 3, 1],\n        [5, 1, 5, 2, 2],\n        [8, 1, 5, 9, 6],\n        [7, 2, 3, 7, 5]],\n\n       [[9, 7, 8, 3, 8],\n        [8, 1, 5, 9, 5],\n        [0, 4, 5, 6, 7],\n        [8, 6, 7, 6, 5]]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 57,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T17:01:17.028Z",
          "iopub.execute_input": "2021-08-23T17:01:17.046Z",
          "iopub.status.idle": "2021-08-23T17:01:17.087Z",
          "shell.execute_reply": "2021-08-23T17:01:17.106Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "i1 = (np.arange(2*3*5) % 3).reshape(2,3,5)\n",
        "i2 = (np.arange(2*3*5) % 5).reshape(2,3,5)"
      ],
      "outputs": [],
      "execution_count": 58,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T17:01:17.561Z",
          "iopub.execute_input": "2021-08-23T17:01:17.578Z",
          "iopub.status.idle": "2021-08-23T17:01:17.605Z",
          "shell.execute_reply": "2021-08-23T17:01:17.621Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.broadcast_arrays(i1, i2)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 59,
          "data": {
            "text/plain": "[array([[[0, 1, 2, 0, 1],\n         [2, 0, 1, 2, 0],\n         [1, 2, 0, 1, 2]],\n \n        [[0, 1, 2, 0, 1],\n         [2, 0, 1, 2, 0],\n         [1, 2, 0, 1, 2]]]),\n array([[[0, 1, 2, 3, 4],\n         [0, 1, 2, 3, 4],\n         [0, 1, 2, 3, 4]],\n \n        [[0, 1, 2, 3, 4],\n         [0, 1, 2, 3, 4],\n         [0, 1, 2, 3, 4]]])]"
          },
          "metadata": {}
        }
      ],
      "execution_count": 59,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T17:01:20.842Z",
          "iopub.execute_input": "2021-08-23T17:01:20.859Z",
          "iopub.status.idle": "2021-08-23T17:01:20.896Z",
          "shell.execute_reply": "2021-08-23T17:01:20.913Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# this should be the shape of our output also\n",
        "np.broadcast(i1, i2).shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 61,
          "data": {
            "text/plain": "(2, 3, 5)"
          },
          "metadata": {}
        }
      ],
      "execution_count": 61,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T17:02:34.123Z",
          "iopub.execute_input": "2021-08-23T17:02:34.143Z",
          "iopub.status.idle": "2021-08-23T17:02:34.178Z",
          "shell.execute_reply": "2021-08-23T17:02:34.195Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "slice dimension moves to the back again"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[i1, : ,i2].shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 62,
          "data": {
            "text/plain": "(2, 3, 5, 4)"
          },
          "metadata": {}
        }
      ],
      "execution_count": 62,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-23T17:02:39.680Z",
          "iopub.execute_input": "2021-08-23T17:02:39.698Z",
          "iopub.status.idle": "2021-08-23T17:02:39.735Z",
          "shell.execute_reply": "2021-08-23T17:02:39.752Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[i1, : ,i2]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 93,
          "data": {
            "text/plain": "array([[[[7, 2, 0, 5],\n         [7, 3, 0, 9],\n         [3, 7, 3, 8],\n         [6, 0, 8, 5],\n         [0, 8, 2, 3]],\n\n        [[5, 8, 7, 0],\n         [0, 0, 9, 7],\n         [5, 7, 0, 1],\n         [3, 2, 2, 8],\n         [9, 0, 5, 7]],\n\n        [[1, 0, 1, 5],\n         [1, 8, 2, 0],\n         [7, 7, 8, 5],\n         [6, 4, 2, 8],\n         [3, 5, 4, 2]]],\n\n\n       [[[7, 2, 0, 5],\n         [7, 3, 0, 9],\n         [3, 7, 3, 8],\n         [6, 0, 8, 5],\n         [0, 8, 2, 3]],\n\n        [[5, 8, 7, 0],\n         [0, 0, 9, 7],\n         [5, 7, 0, 1],\n         [3, 2, 2, 8],\n         [9, 0, 5, 7]],\n\n        [[1, 0, 1, 5],\n         [1, 8, 2, 0],\n         [7, 7, 8, 5],\n         [6, 4, 2, 8],\n         [3, 5, 4, 2]]]])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 93,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-07-26T14:27:09.618Z",
          "iopub.execute_input": "2020-07-26T14:27:09.635Z",
          "iopub.status.idle": "2020-07-26T14:27:09.671Z",
          "shell.execute_reply": "2020-07-26T14:27:09.687Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "EXCEPT, when they dont. If the slice is the first thing, it is taken as the first dimension\n"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a[:, i1 ,i2].shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 63,
          "data": {
            "text/plain": "(3, 2, 3, 5)"
          },
          "metadata": {}
        }
      ],
      "execution_count": 63,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2021-08-24T15:19:49.693Z",
          "iopub.execute_input": "2021-08-24T15:19:49.717Z",
          "iopub.status.idle": "2021-08-24T15:19:49.763Z",
          "shell.execute_reply": "2021-08-24T15:19:49.812Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "outputs": [],
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Resources\n",
        "https://www.youtube.com/watch?v=o0EacbIbf58&t=1680s\n",
        "\n",
        "\n",
        "https://stackoverflow.com/questions/53841497/why-does-numpy-mixed-basic-advanced-indexing-depend-on-slice-adjacency\n",
        "\n",
        "https://stackoverflow.com/questions/46325897/non-adjacent-slicing-of-numpy-multidimensional-array-in-python?noredirect=1&lq=1\n",
        "\n",
        "https://numpy.org/doc/stable/reference/arrays.indexing.html#combining-advanced-and-basic-indexing\n",
        "\n",
        "https://towardsdatascience.com/numpy-indexing-explained-c376abb2440d\n",
        "\n",
        "\n",
        "https://github.com/numpy/numpy/pull/6075"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "scenewalk"
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    "language_info": {
      "name": "python",
      "version": "3.8.0",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "kernelspec": {
      "argv": [
        "/Users/lisa/Documents/virtual_envs/scenewalk/bin/python3",
        "-m",
        "ipykernel_launcher",
        "-f",
        "{connection_file}"
      ],
      "display_name": "scenewalk",
      "language": "python",
      "name": "scenewalk"
    },
    "nteract": {
      "version": "0.28.0"
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  },
  "nbformat": 4,
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