diff --git a/2_Array_manipulation_routines_Solutions.ipynb b/2_Array_manipulation_routines_Solutions.ipynb
index 49584ee..aa56247 100644
--- a/2_Array_manipulation_routines_Solutions.ipynb
+++ b/2_Array_manipulation_routines_Solutions.ipynb
@@ -1,860 +1,815 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Array manipulation routines"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "import numpy as np"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "'1.11.2'"
- ]
- },
- "execution_count": 2,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "np.__version__"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "collapsed": true
- },
- "source": [
- "Q1. Let x be a ndarray [10, 10, 3] with all elements set to one. Reshape x so that the size of the second dimension equals 150."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1.]\n",
- " [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
- " 1. 1. 1. 1. 1. 1.]]\n"
- ]
- }
- ],
- "source": [
- "x = np.ones([10, 10, 3])\n",
- "out = np.reshape(x, [-1, 150])\n",
- "print out\n",
- "assert np.allclose(out, np.ones([10, 10, 3]).reshape([-1, 150]))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q2. Let x be array [[1, 2, 3], [4, 5, 6]]. Convert it to [1 4 2 5 3 6]."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[1 4 2 5 3 6]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
- "out1 = np.ravel(x, order='F')\n",
- "out2 = x.flatten(order=\"F\")\n",
- "assert np.allclose(out1, out2)\n",
- "print out1\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q3. Let x be array [[1, 2, 3], [4, 5, 6]]. Get the 5th element."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "5\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
- "out1 = x.flat[4]\n",
- "out2 = np.ravel(x)[4]\n",
- "assert np.allclose(out1, out2)\n",
- "print out1\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q4. Let x be an arbitrary 3-D array of shape (3, 4, 5). Permute the dimensions of x such that the new shape will be (4,3,5).\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(4L, 3L, 5L)\n"
- ]
- }
- ],
- "source": [
- "x = np.zeros((3, 4, 5))\n",
- "out1 = np.swapaxes(x, 1, 0)\n",
- "out2 = x.transpose([1, 0, 2])\n",
- "assert out1.shape == out2.shape\n",
- "print out1.shape"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q5. Let x be an arbitrary 2-D array of shape (3, 4). Permute the dimensions of x such that the new shape will be (4,3)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 38,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(4L, 3L)\n"
- ]
- }
- ],
- "source": [
- "x = np.zeros((3, 4))\n",
- "out1 = np.swapaxes(x, 1, 0)\n",
- "out2 = x.transpose()\n",
- "out3 = x.T\n",
- "assert out1.shape == out2.shape == out3.shape\n",
- "print out1.shape"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q5. Let x be an arbitrary 2-D array of shape (3, 4). Insert a nex axis such that the new shape will be (3, 1, 4)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 42,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(3L, 1L, 4L)\n"
- ]
- }
- ],
- "source": [
- "x = np.zeros((3, 4))\n",
- "print np.expand_dims(x, axis=1).shape"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q6. Let x be an arbitrary 3-D array of shape (3, 4, 1). Remove a single-dimensional entries such that the new shape will be (3, 4)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 43,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(3L, 4L)\n"
- ]
- }
- ],
- "source": [
- "x = np.zeros((3, 4, 1))\n",
- "print np.squeeze(x).shape"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q7. Lex x be an array <br/>\n",
- "[[ 1 2 3]<br/>\n",
- "[ 4 5 6].<br/><br/>\n",
- "and y be an array <br/>\n",
- "[[ 7 8 9]<br/>\n",
- "[10 11 12]].<br/>\n",
- "Concatenate x and y so that a new array looks like <br/>[[1, 2, 3, 7, 8, 9], <br/>[4, 5, 6, 10, 11, 12]].\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[ 1 2 3 7 8 9]\n",
- " [ 4 5 6 10 11 12]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
- "y = np.array([[7, 8, 9], [10, 11, 12]])\n",
- "out1 = np.concatenate((x, y), 1)\n",
- "out2 = np.hstack((x, y))\n",
- "assert np.allclose(out1, out2)\n",
- "print out2"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q8. Lex x be an array <br/>\n",
- "[[ 1 2 3]<br/>\n",
- "[ 4 5 6].<br/><br/>\n",
- "and y be an array <br/>\n",
- "[[ 7 8 9]<br/>\n",
- "[10 11 12]].<br/>\n",
- "Concatenate x and y so that a new array looks like <br/>[[ 1 2 3]<br/>\n",
- " [ 4 5 6]<br/>\n",
- " [ 7 8 9]<br/>\n",
- " [10 11 12]]\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 38,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[ 1 2 3]\n",
- " [ 4 5 6]\n",
- " [ 7 8 9]\n",
- " [10 11 12]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
- "y = np.array([[7, 8, 9], [10, 11, 12]])\n",
- "out1 = np.concatenate((x, y), 0)\n",
- "out2 = np.vstack((x, y))\n",
- "assert np.allclose(out1, out2)\n",
- "print out2"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q8. Let x be an array [1 2 3] and y be [4 5 6]. Convert it to [[1, 4], [2, 5], [3, 6]]."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 54,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[1 4]\n",
- " [2 5]\n",
- " [3 6]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array((1,2,3))\n",
- "y = np.array((4,5,6))\n",
- "out1 = np.column_stack((x, y))\n",
- "out2 = np.dstack((x, y))\n",
- "out3 = np.vstack((x, y)).T\n",
- "assert np.allclose(out1, out2)\n",
- "assert np.allclose(out2, out3)\n",
- "print out1\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q9. Let x be an array [[1],[2],[3]] and y be [[4], [5], [6]]. Convert x to [[[1, 4]], [[2, 5]], [[3, 6]]]."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[[1 4]]\n",
- "\n",
- " [[2 5]]\n",
- "\n",
- " [[3 6]]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1],[2],[3]])\n",
- "y = np.array([[4],[5],[6]])\n",
- "out = np.dstack((x, y))\n",
- "print out\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q10. Let x be an array [1, 2, 3, ..., 9]. Split x into 3 arrays, each of which has 4, 2, and 3 elements in the original order."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 62,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[array([1, 2, 3, 4]), array([5, 6]), array([7, 8, 9])]\n"
- ]
- }
- ],
- "source": [
- "x = np.arange(1, 10)\n",
- "print np.split(x, [4, 6])"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q11. Let x be an array<br/>\n",
- "[[[ 0., 1., 2., 3.],<br/>\n",
- " [ 4., 5., 6., 7.]],<br/>\n",
- " \n",
- " [[ 8., 9., 10., 11.],<br/>\n",
- " [ 12., 13., 14., 15.]]].<br/>\n",
- "Split it into two such that the first array looks like<br/>\n",
- "[[[ 0., 1., 2.],<br/>\n",
- " [ 4., 5., 6.]],<br/>\n",
- " \n",
- " [[ 8., 9., 10.],<br/>\n",
- " [ 12., 13., 14.]]].<br/>\n",
- " \n",
- "and the second one look like:<br/>\n",
- " \n",
- "[[[ 3.],<br/>\n",
- " [ 7.]],<br/>\n",
- " \n",
- " [[ 11.],<br/>\n",
- " [ 15.]]].<br/> "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 72,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[array([[[ 0, 1, 2],\n",
- " [ 4, 5, 6]],\n",
- "\n",
- " [[ 8, 9, 10],\n",
- " [12, 13, 14]]]), array([[[ 3],\n",
- " [ 7]],\n",
- "\n",
- " [[11],\n",
- " [15]]])]\n"
- ]
- }
- ],
- "source": [
- "x = np.arange(16).reshape(2, 2, 4)\n",
- "out1 = np.split(x, [3],axis=2)\n",
- "out2 = np.dsplit(x, [3])\n",
- "assert np.allclose(out1[0], out2[0])\n",
- "assert np.allclose(out1[1], out2[1])\n",
- "print out1\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q12. Let x be an array <br />\n",
- "[[ 0., 1., 2., 3.],<br>\n",
- " [ 4., 5., 6., 7.],<br>\n",
- " [ 8., 9., 10., 11.],<br>\n",
- " [ 12., 13., 14., 15.]].<br>\n",
- "Split it into two arrays along the second axis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 74,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[array([[ 0, 1],\n",
- " [ 4, 5],\n",
- " [ 8, 9],\n",
- " [12, 13]]), array([[ 2, 3],\n",
- " [ 6, 7],\n",
- " [10, 11],\n",
- " [14, 15]])]\n"
- ]
- }
- ],
- "source": [
- "x = np.arange(16).reshape((4, 4))\n",
- "out1 = np.hsplit(x, 2)\n",
- "out2 = np.split(x, 2, 1)\n",
- "assert np.allclose(out1[0], out2[0])\n",
- "assert np.allclose(out1[1], out2[1])\n",
- "print out1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q13. Let x be an array <br />\n",
- "[[ 0., 1., 2., 3.],<br>\n",
- " [ 4., 5., 6., 7.],<br>\n",
- " [ 8., 9., 10., 11.],<br>\n",
- " [ 12., 13., 14., 15.]].<br>\n",
- "Split it into two arrays along the first axis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 75,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[array([[0, 1, 2, 3],\n",
- " [4, 5, 6, 7]]), array([[ 8, 9, 10, 11],\n",
- " [12, 13, 14, 15]])]\n"
- ]
- }
- ],
- "source": [
- "x = np.arange(16).reshape((4, 4))\n",
- "out1 = np.vsplit(x, 2)\n",
- "out2 = np.split(x, 2, 0)\n",
- "assert np.allclose(out1[0], out2[0])\n",
- "assert np.allclose(out1[1], out2[1])\n",
- "print out1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q14. Let x be an array [0, 1, 2]. Convert it to <br/>\n",
- "[[0, 1, 2, 0, 1, 2],<br/>\n",
- " [0, 1, 2, 0, 1, 2]]."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 93,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[0 1 2 0 1 2]\n",
- " [0 1 2 0 1 2]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([0, 1, 2])\n",
- "out1 = np.tile(x, [2, 2])\n",
- "out2 = np.resize(x, [2, 6])\n",
- "assert np.allclose(out1, out2)\n",
- "print out1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q15. Let x be an array [0, 1, 2]. Convert it to <br/>\n",
- "[0, 0, 1, 1, 2, 2]."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 83,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[0 0 1 1 2 2]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([0, 1, 2])\n",
- "print np.repeat(x, 2)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q16. Let x be an array [0, 0, 0, 1, 2, 3, 0, 2, 1, 0].<br/>\n",
- "remove the leading the trailing zeros."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 105,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[1 2 3 0 2 1]\n"
- ]
- }
- ],
- "source": [
- "x = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0))\n",
- "out = np.trim_zeros(x)\n",
- "print out"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q17. Let x be an array [2, 2, 1, 5, 4, 5, 1, 2, 3]. Get two arrays of unique elements and their counts.\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 107,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[1 2 3 4 5] [2 3 1 1 2]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([2, 2, 1, 5, 4, 5, 1, 2, 3])\n",
- "u, indices = np.unique(x, return_counts=True)\n",
- "print u, indices"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q18. Lex x be an array <br/>\n",
- "[[ 1 2]<br/>\n",
- " [ 3 4].<br/>\n",
- "Flip x along the second axis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 120,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[2 1]\n",
- " [4 3]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1,2], [3,4]])\n",
- "out1 = np.fliplr(x)\n",
- "out2 = x[:, ::-1]\n",
- "assert np.allclose(out1, out2)\n",
- "print out1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q19. Lex x be an array <br/>\n",
- "[[ 1 2]<br/>\n",
- " [ 3 4].<br/>\n",
- "Flip x along the first axis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 121,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[3 4]\n",
- " [1 2]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1,2], [3,4]])\n",
- "out1 = np.flipud(x)\n",
- "out2 = x[::-1, :]\n",
- "assert np.allclose(out1, out2)\n",
- "print out1"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q20. Lex x be an array <br/>\n",
- "[[ 1 2]<br/>\n",
- " [ 3 4].<br/>\n",
- "Rotate x 90 degrees counter-clockwise."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 122,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[2 4]\n",
- " [1 3]]\n"
- ]
- }
- ],
- "source": [
- "x = np.array([[1,2], [3,4]])\n",
- "out = np.rot90(x)\n",
- "print out"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Q21 Lex x be an array <br/>\n",
- "[[ 1 2 3 4]<br/>\n",
- " [ 5 6 7 8].<br/>\n",
- "Shift elements one step to right along the second axis."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 126,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[4 1 2 3]\n",
- " [8 5 6 7]]\n"
- ]
- }
- ],
- "source": [
- "x = np.arange(1, 9).reshape([2, 4])\n",
- "print np.roll(x, 1, axis=1)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.10"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Array manipulation routines"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'1.11.2'"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.__version__"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Q1. Let x be a ndarray [10, 10, 3] with all elements set to one. Reshape x so that the size of the second dimension equals 150."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1.]\n",
+ " [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
+ " 1. 1. 1. 1. 1. 1.]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.ones([10, 10, 3])\n",
+ "out = np.reshape(x, [-1, 150])\n",
+ "print out\n",
+ "assert np.allclose(out, np.ones([10, 10, 3]).reshape([-1, 150]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q2. Let x be array [[1, 2, 3], [4, 5, 6]]. Convert it to [1 4 2 5 3 6]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 4 2 5 3 6]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
+ "out1 = np.ravel(x, order='F')\n",
+ "out2 = x.flatten(order=\"F\")\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q3. Let x be array [[1, 2, 3], [4, 5, 6]]. Get the 5th element."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "5\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
+ "out1 = x.flat[4]\n",
+ "out2 = np.ravel(x)[4]\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q4. Let x be an arbitrary 3-D array of shape (3, 4, 5). Permute the dimensions of x such that the new shape will be (4,3,5).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(4L, 3L, 5L)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.zeros((3, 4, 5))\n",
+ "out1 = np.swapaxes(x, 1, 0)\n",
+ "out2 = x.transpose([1, 0, 2])\n",
+ "assert out1.shape == out2.shape\n",
+ "print out1.shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q5. Let x be an arbitrary 2-D array of shape (3, 4). Permute the dimensions of x such that the new shape will be (4,3)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(4L, 3L)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.zeros((3, 4))\n",
+ "out1 = np.swapaxes(x, 1, 0)\n",
+ "out2 = x.transpose()\n",
+ "out3 = x.T\n",
+ "assert out1.shape == out2.shape == out3.shape\n",
+ "print out1.shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q5. Let x be an arbitrary 2-D array of shape (3, 4). Insert a nex axis such that the new shape will be (3, 1, 4)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(3L, 1L, 4L)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.zeros((3, 4))\n",
+ "print np.expand_dims(x, axis=1).shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q6. Let x be an arbitrary 3-D array of shape (3, 4, 1). Remove a single-dimensional entries such that the new shape will be (3, 4)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(3L, 4L)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.zeros((3, 4, 1))\n",
+ "print np.squeeze(x).shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q7. Lex x be an array <br/>\n",
+ "[[ 1 2 3]<br/>\n",
+ "[ 4 5 6].<br/><br/>\n",
+ "and y be an array <br/>\n",
+ "[[ 7 8 9]<br/>\n",
+ "[10 11 12]].<br/>\n",
+ "Concatenate x and y so that a new array looks like <br/>[[1, 2, 3, 7, 8, 9], <br/>[4, 5, 6, 10, 11, 12]].\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[ 1 2 3 7 8 9]\n",
+ " [ 4 5 6 10 11 12]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
+ "y = np.array([[7, 8, 9], [10, 11, 12]])\n",
+ "out1 = np.concatenate((x, y), 1)\n",
+ "out2 = np.hstack((x, y))\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q8. Lex x be an array <br/>\n",
+ "[[ 1 2 3]<br/>\n",
+ "[ 4 5 6].<br/><br/>\n",
+ "and y be an array <br/>\n",
+ "[[ 7 8 9]<br/>\n",
+ "[10 11 12]].<br/>\n",
+ "Concatenate x and y so that a new array looks like <br/>[[ 1 2 3]<br/>\n",
+ " [ 4 5 6]<br/>\n",
+ " [ 7 8 9]<br/>\n",
+ " [10 11 12]]\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[ 1 2 3]\n",
+ " [ 4 5 6]\n",
+ " [ 7 8 9]\n",
+ " [10 11 12]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1, 2, 3], [4, 5, 6]])\n",
+ "y = np.array([[7, 8, 9], [10, 11, 12]])\n",
+ "out1 = np.concatenate((x, y), 0)\n",
+ "out2 = np.vstack((x, y))\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q8. Let x be an array [1 2 3] and y be [4 5 6]. Convert it to [[1, 4], [2, 5], [3, 6]]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1, 4],\n",
+ " [2, 5],\n",
+ " [3, 6]])"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x = np.array((1,2,3))\n",
+ "y = np.array((4,5,6))\n",
+ "out1 = np.column_stack((x, y))\n",
+ "out2 = np.squeeze(np.dstack((x, y)))\n",
+ "out3 = np.vstack((x, y)).T\n",
+ "assert np.allclose(out1, out2)\n",
+ "assert np.allclose(out2, out3)\n",
+ "print out1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q9. Let x be an array [[1],[2],[3]] and y be [[4], [5], [6]]. Convert x to [[[1, 4]], [[2, 5]], [[3, 6]]]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[[1 4]]\n",
+ "\n",
+ " [[2 5]]\n",
+ "\n",
+ " [[3 6]]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1],[2],[3]])\n",
+ "y = np.array([[4],[5],[6]])\n",
+ "out = np.dstack((x, y))\n",
+ "print out\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q10. Let x be an array [1, 2, 3, ..., 9]. Split x into 3 arrays, each of which has 4, 2, and 3 elements in the original order."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[array([1, 2, 3, 4]), array([5, 6]), array([7, 8, 9])]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.arange(1, 10)\n",
+ "print np.split(x, [4, 6])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q11. Let x be an array<br/>\n",
+ "[[[ 0., 1., 2., 3.],<br/>\n",
+ " [ 4., 5., 6., 7.]],<br/>\n",
+ " \n",
+ " [[ 8., 9., 10., 11.],<br/>\n",
+ " [ 12., 13., 14., 15.]]].<br/>\n",
+ "Split it into two such that the first array looks like<br/>\n",
+ "[[[ 0., 1., 2.],<br/>\n",
+ " [ 4., 5., 6.]],<br/>\n",
+ " \n",
+ " [[ 8., 9., 10.],<br/>\n",
+ " [ 12., 13., 14.]]].<br/>\n",
+ " \n",
+ "and the second one look like:<br/>\n",
+ " \n",
+ "[[[ 3.],<br/>\n",
+ " [ 7.]],<br/>\n",
+ " \n",
+ " [[ 11.],<br/>\n",
+ " [ 15.]]].<br/> "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[array([[[ 0, 1, 2],\n",
+ " [ 4, 5, 6]],\n",
+ "\n",
+ " [[ 8, 9, 10],\n",
+ " [12, 13, 14]]]), array([[[ 3],\n",
+ " [ 7]],\n",
+ "\n",
+ " [[11],\n",
+ " [15]]])]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.arange(16).reshape(2, 2, 4)\n",
+ "out1 = np.split(x, [3],axis=2)\n",
+ "out2 = np.dsplit(x, [3])\n",
+ "assert np.allclose(out1[0], out2[0])\n",
+ "assert np.allclose(out1[1], out2[1])\n",
+ "print out1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q12. Let x be an array <br />\n",
+ "[[ 0., 1., 2., 3.],<br>\n",
+ " [ 4., 5., 6., 7.],<br>\n",
+ " [ 8., 9., 10., 11.],<br>\n",
+ " [ 12., 13., 14., 15.]].<br>\n",
+ "Split it into two arrays along the second axis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[array([[ 0, 1],\n",
+ " [ 4, 5],\n",
+ " [ 8, 9],\n",
+ " [12, 13]]), array([[ 2, 3],\n",
+ " [ 6, 7],\n",
+ " [10, 11],\n",
+ " [14, 15]])]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.arange(16).reshape((4, 4))\n",
+ "out1 = np.hsplit(x, 2)\n",
+ "out2 = np.split(x, 2, 1)\n",
+ "assert np.allclose(out1[0], out2[0])\n",
+ "assert np.allclose(out1[1], out2[1])\n",
+ "print out1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q13. Let x be an array <br />\n",
+ "[[ 0., 1., 2., 3.],<br>\n",
+ " [ 4., 5., 6., 7.],<br>\n",
+ " [ 8., 9., 10., 11.],<br>\n",
+ " [ 12., 13., 14., 15.]].<br>\n",
+ "Split it into two arrays along the first axis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 75,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[array([[0, 1, 2, 3],\n",
+ " [4, 5, 6, 7]]), array([[ 8, 9, 10, 11],\n",
+ " [12, 13, 14, 15]])]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.arange(16).reshape((4, 4))\n",
+ "out1 = np.vsplit(x, 2)\n",
+ "out2 = np.split(x, 2, 0)\n",
+ "assert np.allclose(out1[0], out2[0])\n",
+ "assert np.allclose(out1[1], out2[1])\n",
+ "print out1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q14. Let x be an array [0, 1, 2]. Convert it to <br/>\n",
+ "[[0, 1, 2, 0, 1, 2],<br/>\n",
+ " [0, 1, 2, 0, 1, 2]]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 93,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[0 1 2 0 1 2]\n",
+ " [0 1 2 0 1 2]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([0, 1, 2])\n",
+ "out1 = np.tile(x, [2, 2])\n",
+ "out2 = np.resize(x, [2, 6])\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q15. Let x be an array [0, 1, 2]. Convert it to <br/>\n",
+ "[0, 0, 1, 1, 2, 2]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 83,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0 0 1 1 2 2]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([0, 1, 2])\n",
+ "print np.repeat(x, 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q16. Let x be an array [0, 0, 0, 1, 2, 3, 0, 2, 1, 0].<br/>\n",
+ "remove the leading the trailing zeros."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 105,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 2 3 0 2 1]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0))\n",
+ "out = np.trim_zeros(x)\n",
+ "print out"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q17. Let x be an array [2, 2, 1, 5, 4, 5, 1, 2, 3]. Get two arrays of unique elements and their counts.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 107,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 2 3 4 5] [2 3 1 1 2]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([2, 2, 1, 5, 4, 5, 1, 2, 3])\n",
+ "u, indices = np.unique(x, return_counts=True)\n",
+ "print u, indices"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q18. Lex x be an array <br/>\n",
+ "[[ 1 2]<br/>\n",
+ " [ 3 4].<br/>\n",
+ "Flip x along the second axis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 120,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[2 1]\n",
+ " [4 3]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1,2], [3,4]])\n",
+ "out1 = np.fliplr(x)\n",
+ "out2 = x[:, ::-1]\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q19. Lex x be an array <br/>\n",
+ "[[ 1 2]<br/>\n",
+ " [ 3 4].<br/>\n",
+ "Flip x along the first axis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 121,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[3 4]\n",
+ " [1 2]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1,2], [3,4]])\n",
+ "out1 = np.flipud(x)\n",
+ "out2 = x[::-1, :]\n",
+ "assert np.allclose(out1, out2)\n",
+ "print out1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q20. Lex x be an array <br/>\n",
+ "[[ 1 2]<br/>\n",
+ " [ 3 4].<br/>\n",
+ "Rotate x 90 degrees counter-clockwise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 122,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[2 4]\n",
+ " [1 3]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.array([[1,2], [3,4]])\n",
+ "out = np.rot90(x)\n",
+ "print out"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Q21 Lex x be an array <br/>\n",
+ "[[ 1 2 3 4]<br/>\n",
+ " [ 5 6 7 8].<br/>\n",
+ "Shift elements one step to right along the second axis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 126,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[4 1 2 3]\n",
+ " [8 5 6 7]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.arange(1, 9).reshape([2, 4])\n",
+ "print np.roll(x, 1, axis=1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "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": "3.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
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