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added several applications to the presentation
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‎numpy-tutorial-exercises.ipynb‎

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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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{
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"cell_type": "code",
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## An application: sieve of Eratosthenes"
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"## Fancy indexing ‒ Boolean mask"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"a = np.arange(40).reshape(5, 8)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"a %3 == 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"a[a %3 == 0]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Application: sieve of Eratosthenes"
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]
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},
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{
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"plt.axis('scaled')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Application: π from random numbers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"plt.imshow(imdata, cmap='gray')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Application: π from random numbers"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Create an array of random numbers and determine the fraction of points with distance from the origin smaller than one. Determine an approximation for π."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([-0.56155281, 3.56155281])"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"a = np.arange(4).reshape(2, 2)\n",
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"eigenvalues, eigenvectors = LA.eig(a)\n",
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[-0.87192821, -0.27032301],\n",
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" [ 0.48963374, -0.96276969]])"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"eigenvectors"
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]
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"Determine the eigenvalue larger than one appearing in the Fibonacci problem. Verify the result by calculating the ratio of successive Fibonacci numbers. Do you recognize the result?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Application: Brownian motion"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"1. Simulate several trajectories for a one-dimensional\n",
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"Brownian motion \n",
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"Hint: np.random.choice\n",
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"2. Plot the mean distance from the origin as a function\n",
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"of time\n",
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"3. Plot the variance of the trajectories as a function of\n",
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"time\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Application: identify entry closest to ½"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Create a 2d array containing random numbers and generate a vector containing for each row the entry closest to one-half."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,

‎presentation.tex‎

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\usepackage{beramono}
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\usepackage{fontawesome}
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\usepackage{pifont}
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\usepackage{amsmath}
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\usepackage{rotating}
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\usepackage{listings}
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\usepackage{nicefrac}
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\usepackage{ulem}
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\usepackage{hyperref}
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\end{center}
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\end{frame}
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\begin{frame}{Application: sieve of Eratosthenes}
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\includegraphics[width=\textwidth]{eratosthenes_1}\\[0.3truecm]
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\includegraphics[width=\textwidth]{eratosthenes_2}\\[0.3truecm]
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\includegraphics[width=\textwidth]{eratosthenes_3}\\[0.3truecm]
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\includegraphics[width=\textwidth]{eratosthenes_4}\\[0.3truecm]
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\includegraphics[width=\textwidth]{eratosthenes_5}\\[0.3truecm]
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\includegraphics[width=\textwidth]{eratosthenes_6}
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\end{frame}
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\begin{frame}{Axes}
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\begin{Large}
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\begin{displaymath}
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\end{columns}
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\end{frame}
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\begin{frame}{Application: $\pi$ from random numbers}
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\begin{columns}
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\begin{column}{0.4\textwidth}
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\begin{center}
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\includegraphics[width=0.8\textwidth]{random_pi}
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\end{center}
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\end{column}%
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\begin{column}{0.6\textwidth}
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\begin{enumerate}
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\item Create pairs of random numbers and determine the fraction of pairs which
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has a distance from the origin less than one.
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\item Multiply the result by four to obtain an approximation of $\pi$.
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\end{enumerate}
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\end{column}
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\end{columns}
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\vspace{0.5truecm}
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hint: \texttt{count\_nonzero(a)} counts the number of non-zero values in the array \texttt{a} and
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also works for Boolean arrays. Remember that \texttt{np.info(\dots)} can be helpful.
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\vspace{0.3truecm}
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\begin{center}
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\includegraphics[width=3truecm]{yourturn}
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\end{center}
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\end{frame}
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\begin{frame}{Fibonacci series and linear algebra}
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\begin{center}
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\includegraphics[width=0.7\textwidth]{fibonacci}
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We are looking for the eigenvalue larger than one.
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\end{frame}
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\begin{frame}[fragile]{Linear algebra in NumPy}
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\begin{frame}{Linear algebra in NumPy}
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\texttt{import numpy.linalg as LA}
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\vspace{0.3truecm}
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hint: see also the methods for linear algebra in SciPy
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\end{frame}
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\begin{frame}{Statistics in NumPy}
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\structure{Order statistics}\\
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\small{amin, amax, nanmin, nanmax, ptp, percentile, nanpercentile}\\[0.2truecm]
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\structure{Averages and variances}\\
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\small{median, average, mean, std, var, nanmedian, nanmean, nanstd, nanvar}\\[0.2truecm]
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\structure{Correlating}\\
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\small{corrcoef, correlate, cov}\\[0.2truecm]
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\structure{Histograms}\\
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\small{histogram, histogram2d, histogramdd, bincount, digitize}
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\end{frame}
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\begin{frame}{Application: Brownian motion}
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\begin{center}
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\includegraphics[width=0.8\textwidth]{diffusion}
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\end{center}
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\begin{enumerate}
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\item Simulate several trajectories for a one-dimensional Brownian motion\\
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hint: \texttt{np.random.choice}
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\item Plot the mean distance from the origin as a function of time\\
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\item Plot the variance of the trajectories as a function of time
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\end{enumerate}
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\vspace{0.3truecm}
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\begin{center}
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\includegraphics[width=3truecm]{yourturn}
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\end{center}
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\end{frame}
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\begin{frame}{Sorting, searching, and counting in NumPy}
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\structure{Sorting}\\
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\small{sort, lexsort, argsort, ndarray.sort, msort, sort\_complex, partition,
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argpartition}\\[0.2truecm]
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\structure{Searching}\\
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\small{argmax, nanargmax, argmin, nanargmin, argwhere, nonzero, flatnonzero,
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where, searchsorted, extract}\\[0.2truecm]
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\structure{Counting}\\
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\small{count\_nonzero}
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\end{frame}
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\begin{frame}{Application: identify entry closest to $\nicefrac{1}{2}$}
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\begin{displaymath}
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\begin{pmatrix}
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0.05344164 & \alert{0.37648768} & 0.80691163 & 0.71400815\\
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\alert{0.60825034} & 0.35778938 & 0.37393356 & 0.32615374\\
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0.83118547 & 0.33178711 & 0.21548027 & \alert{0.42209291}
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\end{pmatrix}
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\end{displaymath}
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\begin{displaymath}
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\Downarrow
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\end{displaymath}
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\begin{displaymath}
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\begin{pmatrix}
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\alert{0.37648768}\\ \alert{0.60825034}\\ \alert{0.42209291}
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\end{pmatrix}
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\end{displaymath}
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\vspace{0.3truecm}
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\includegraphics[width=3truecm]{yourturn}\qquad
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\raisebox{0.7truecm}{hint: use \texttt{np.argsort}}
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\end{frame}
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\end{document}

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