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ME3255F2017/03_Intro to matlab-octave/lecture_03.ipynb

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{
"cells": [
{
"cell_type": "code",
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"metadata": {
"collapsed": true,
"scrolled": true,
"slideshow": {
"slide_type": "skip"
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},
"outputs": [],
"source": [
"%plot --format svg"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"|Question|Answered Right|Answered Wrong|Total \\%|\n",
"|----------------------------------------|---|---|---|\n",
"|Define a cell as C={}; C{1}=1.21; C{2}='Gigawatts'; How do you print '1.21 Gigawatts'?|46|29|61.333333333333%|\n",
"|How do you access the third column of an array assigned to the variable A?|58|17|77.333333333333%|\n",
"|What is the result of the following matlab command \"> a=10; b=20; a=5; c=a+b|71|4|94.666666666667%|\n",
"|What is the result of the following Matlab command \"> 1./[2 2]|57|18|76%|\n",
"|Where would a function be saved that cannot be run in Matlab/Octave?|55|20|73.333333333333%|"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 2 2\n",
"\n"
]
}
],
"source": [
"1*[2 2]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Matlab/Octave basic use"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Matlab environment can be called by:\n",
"\n",
"1. Starting the matlab executable (the gui)\n",
"2. Starting a jupyter notebook with Matlab kernel\n",
"3. Starting matlab with command-line interface (no gui)\n",
"\n",
"Main requirement = matlab kernel (main matlab program) is running and accepting commands\n",
"\n",
"Once started call\n",
"\n",
"1. matlab built-in functions \n",
"2. anything you write in your `MATLABPATH` or \n",
"3. working directory (`pwd`)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Octave's search path contains the following directories:\n",
"\n",
".\n",
"/usr/local/lib/python2.7/dist-packages/octave_kernel\n",
"/home/ryan/Documents/MATLAB\n",
"/usr/lib/x86_64-linux-gnu/octave/4.0.0/site/oct/x86_64-pc-linux-gnu\n",
"/usr/lib/x86_64-linux-gnu/octave/site/oct/api-v50+/x86_64-pc-linux-gnu\n",
"/usr/lib/x86_64-linux-gnu/octave/site/oct/x86_64-pc-linux-gnu\n",
"/usr/share/octave/4.0.0/site/m\n",
"/usr/share/octave/site/api-v50+/m\n",
"/usr/share/octave/site/m\n",
"/usr/share/octave/site/m/startup\n",
"/usr/lib/x86_64-linux-gnu/octave/4.0.0/oct/x86_64-pc-linux-gnu\n",
"/usr/share/octave/4.0.0/m\n",
"/usr/share/octave/4.0.0/m/audio\n",
"/usr/share/octave/4.0.0/m/debian\n",
"/usr/share/octave/4.0.0/m/deprecated\n",
"/usr/share/octave/4.0.0/m/elfun\n",
"/usr/share/octave/4.0.0/m/general\n",
"/usr/share/octave/4.0.0/m/geometry\n",
"/usr/share/octave/4.0.0/m/gui\n",
"/usr/share/octave/4.0.0/m/help\n",
"/usr/share/octave/4.0.0/m/image\n",
"/usr/share/octave/4.0.0/m/io\n",
"/usr/share/octave/4.0.0/m/java\n",
"/usr/share/octave/4.0.0/m/linear-algebra\n",
"/usr/share/octave/4.0.0/m/miscellaneous\n",
"/usr/share/octave/4.0.0/m/optimization\n",
"/usr/share/octave/4.0.0/m/path\n",
"/usr/share/octave/4.0.0/m/pkg\n",
"/usr/share/octave/4.0.0/m/plot\n",
"/usr/share/octave/4.0.0/m/plot/appearance\n",
"/usr/share/octave/4.0.0/m/plot/draw\n",
"/usr/share/octave/4.0.0/m/plot/util\n",
"/usr/share/octave/4.0.0/m/polynomial\n",
"/usr/share/octave/4.0.0/m/prefs\n",
"/usr/share/octave/4.0.0/m/set\n",
"/usr/share/octave/4.0.0/m/signal\n",
"/usr/share/octave/4.0.0/m/sparse\n",
"/usr/share/octave/4.0.0/m/specfun\n",
"/usr/share/octave/4.0.0/m/special-matrix\n",
"/usr/share/octave/4.0.0/m/startup\n",
"/usr/share/octave/4.0.0/m/statistics\n",
"/usr/share/octave/4.0.0/m/statistics/base\n",
"/usr/share/octave/4.0.0/m/statistics/distributions\n",
"/usr/share/octave/4.0.0/m/statistics/models\n",
"/usr/share/octave/4.0.0/m/statistics/tests\n",
"/usr/share/octave/4.0.0/m/strings\n",
"/usr/share/octave/4.0.0/m/testfun\n",
"/usr/share/octave/4.0.0/m/time\n",
"/usr/share/octave/4.0.0/data\n",
"\n"
]
}
],
"source": [
"path"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "slide"
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = /home/ryan/Documents/UConn/ME3255/course_git_S2017/03_Intro to matlab-octave\r\n"
]
}
],
"source": [
"pwd"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Assignments (`=`-operator)\n",
"\n",
"Matlab is interpreted language \n",
"\n",
"each line of code (either saved text file or command-line) is executed as a standalone command\n",
"\n",
"These are reffered to \"scripts\""
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 10\n",
"b = 30\n",
"c = 40\n"
]
}
],
"source": [
"a=10 % line one assigns a to 10\n",
"b=a*3 % line two assigns b to 10 times 3 by calling 'a' from line one\n",
"c=a+b % line three does not assign anything directly, but leaving off the \";\" prints the result\n",
" % ans"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Matlab has a number of \"objects\" that you can assign to variables\n",
"1. arrays (vectors and matrices `[`...`]`) \n",
"3. cells (combination of strings, text, even function calls `{`...`}`)\n",
"2. strings (text `\"`...`\"` )\n",
"3. functions (both built-in, defined or developed)\n",
"4. and more... (classes defined by `classdef` - you can create your own object to help organize data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### 1- Arrays\n",
"\n",
"Default in matlab is that when you assign a value to a variable, it is stored as an array\n",
"\n",
"arrays are N x M x ... values of integers or floating point numbers or complex integers/floating point numbers\n",
"\n",
"Use the parantheses to access values in an array `...(n,m)`"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A =\n",
"\n",
" 1 2 3\n",
" 4 5 6\n",
" 7 8 9\n",
" 10 11 12\n",
"\n",
"size of A is 4 x 3\n"
]
}
],
"source": [
"A = [1 2 3;4,5,6;7,8,9;10,11,12]\n",
"fprintf('size of A is %i x %i\\n',size(A))"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A =\n",
"\n",
" 1 2 3\n",
" 4 5 6\n",
" 7 8 9\n",
" 10 11 12\n",
"\n",
"ans = 7\n",
"ans = 11\n"
]
}
],
"source": [
"A = [1 2 3;4,5,6;7,8,9;10,11,12]\n",
"A(3,1)\n",
"A(8)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 0\r\n"
]
}
],
"source": [
"a=10; % a is 1x1 array where a(1,1)==10\n",
"a(1,1)==1\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 2. Cells \n",
"### combine different size arrays and text\n",
"\n",
"you cannot use math operators 'binary operators'"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" Columns 1 through 8:\n",
"\n",
" 0.00000 0.11111 0.22222 0.33333 0.44444 0.55556 0.66667 0.77778\n",
"\n",
" Columns 9 and 10:\n",
"\n",
" 0.88889 1.00000\n",
"\n"
]
}
],
"source": [
"C={};\n",
"C{1}=linspace(0,1,10);\n",
"C{2}=linspace(0,1,3);\n",
"C{'z'}='holy cow';\n",
"C{1}"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" Columns 1 through 8:\n",
"\n",
" 0.00000 0.22222 0.44444 0.66667 0.88889 1.11111 1.33333 1.55556\n",
"\n",
" Columns 9 and 10:\n",
"\n",
" 1.77778 2.00000\n",
"\n"
]
}
],
"source": [
"C{1}+C{1}"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 3. Strings \n",
"### can be combined and printed"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = computational mechanics rocks!\r\n"
]
}
],
"source": [
"string1 = 'computational'; string2 = 'mechanics';\n",
"[string1, ' ', string2, ' rocks!']"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"use `fprintf` to format strings and numbers for output and `sprintf` to save variables\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"computational mechanics\n",
"\n",
"string = the dog had 4 legs and weighed 30.9 lbs\n"
]
}
],
"source": [
"fprintf([string1,' ',string2,'\\n\\n'])\n",
"string = sprintf('the dog had %i legs and weighed %1.1f lbs',4,30.93)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 4. Functions \n",
"### Some built in Matlab functions \n",
"**(i.e. the reasons to run Matlab)** "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Math operators (=, +, -, /, *, ^)\n",
"\n",
"Matlab assumes all variables are matrices\n",
"\n",
"all operators are matrix operations functions"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 3 3\n",
"\n",
"ans =\n",
"\n",
" 0.50000 0.50000\n",
"\n"
]
}
],
"source": [
"1+[2,2]\n",
"1./[2,2]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Thanks"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Further Examples of Arrays and Functions"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"vectors are either 1xN or Nx1 arrays for row and column"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 100\n",
" 2\n",
" 3\n",
"\n"
]
}
],
"source": [
"v_row = [100, 2,3]; %row vector\n",
"v_column = [1;2;3]; %column vector\n",
"v_row'"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Matrices are MxN arrays\n",
"the `:`-symbol can substitute for a counting"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A =\n",
"\n",
" 1 2 3\n",
" 4 5 6\n",
" 7 8 9\n",
" 10 11 12\n",
"\n",
"ans =\n",
"\n",
" 1\n",
" 4\n",
" 7\n",
" 10\n",
"\n"
]
}
],
"source": [
"A = [1 2 3;4,5,6;7,8,9;10,11,12]\n",
"A(:,1) % the colon assumes you want the first value, 1, counting up by 1 to the last value, 4"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"You can also use every 2nd value or any other integer up to `end` which is the largest value of that row or column of the array"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1 2 3\n",
"\n"
]
}
],
"source": [
"A(1,:) % you can also use `end` "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1\n",
" 4\n",
" 7\n",
" 10\n",
" 2\n",
" 5\n",
" 8\n",
" 11\n",
" 3\n",
" 6\n",
" 9\n",
" 12\n",
"\n"
]
}
],
"source": [
"A(:)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In general, arrays can be any size \n",
"\n",
"take rolling 4 die and determining the sum of the components"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"'mode' is a function from the file /usr/share/octave/4.0.0/m/statistics/base/mode.m\n",
"\n",
" -- Function File: mode (X)\n",
" -- Function File: mode (X, DIM)\n",
" -- Function File: [M, F, C] = mode (...)\n",
" Compute the most frequently occurring value in a dataset (mode).\n",
"\n",
" 'mode' determines the frequency of values along the first\n",
" non-singleton dimension and returns the value with the highest\n",
" frequency. If two, or more, values have the same frequency 'mode'\n",
" returns the smallest.\n",
"\n",
" If the optional argument DIM is given, operate along this\n",
" dimension.\n",
"\n",
" The return variable F is the number of occurrences of the mode in\n",
" the dataset.\n",
"\n",
" The cell array C contains all of the elements with the maximum\n",
" frequency.\n",
"\n",
" See also: mean, median.\n",
"\n",
"Additional help for built-in functions and operators is\n",
"available in the online version of the manual. Use the command\n",
"'doc <topic>' to search the manual index.\n",
"\n",
"Help and information about Octave is also available on the WWW\n",
"at http://www.octave.org and via the help@octave.org\n",
"mailing list.\n"
]
}
],
"source": [
"help mode"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 14\n",
"ans = 3.4170\n",
"ans =\n",
"\n",
"ans(:,:,1) =\n",
"\n",
" 4 5 6 7 8 9\n",
" 5 6 7 8 9 10\n",
" 6 7 8 9 10 11\n",
" 7 8 9 10 11 12\n",
" 8 9 10 11 12 13\n",
" 9 10 11 12 13 14\n",
"\n",
"ans(:,:,2) =\n",
"\n",
" 5 6 7 8 9 10\n",
" 6 7 8 9 10 11\n",
" 7 8 9 10 11 12\n",
" 8 9 10 11 12 13\n",
" 9 10 11 12 13 14\n",
" 10 11 12 13 14 15\n",
"\n",
"ans(:,:,3) =\n",
"\n",
" 6 7 8 9 10 11\n",
" 7 8 9 10 11 12\n",
" 8 9 10 11 12 13\n",
" 9 10 11 12 13 14\n",
" 10 11 12 13 14 15\n",
" 11 12 13 14 15 16\n",
"\n",
"ans(:,:,4) =\n",
"\n",
" 7 8 9 10 11 12\n",
" 8 9 10 11 12 13\n",
" 9 10 11 12 13 14\n",
" 10 11 12 13 14 15\n",
" 11 12 13 14 15 16\n",
" 12 13 14 15 16 17\n",
"\n",
"ans(:,:,5) =\n",
"\n",
" 8 9 10 11 12 13\n",
" 9 10 11 12 13 14\n",
" 10 11 12 13 14 15\n",
" 11 12 13 14 15 16\n",
" 12 13 14 15 16 17\n",
" 13 14 15 16 17 18\n",
"\n",
"ans(:,:,6) =\n",
"\n",
" 9 10 11 12 13 14\n",
" 10 11 12 13 14 15\n",
" 11 12 13 14 15 16\n",
" 12 13 14 15 16 17\n",
" 13 14 15 16 17 18\n",
" 14 15 16 17 18 19\n",
"\n"
]
}
],
"source": [
"mean(A_6666(:))\n",
"std(A_6666(:))\n",
"A_6666(:,:,:,1)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1296 1\n",
"\n"
]
}
],
"source": [
"size(A_6666(:))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## This is helpful to create reports of computed data\n",
"\n",
"the `\\` signifies a special character e.g. `\\n` = newline, `\\t` = tab\n",
"\n",
"to actually print the \"\\\", use `\\\\`"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n\n",
" n\n"
]
}
],
"source": [
"fprintf('n\\n n')"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false,
"scrolled": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 0\r\n"
]
}
],
"source": [
"fid = fopen('file.txt','w');\n",
"string1='Computational';\n",
"string2='Mechanics';\n",
"string='happy semester';\n",
"fprintf(fid,[string1, ' ', string2])\n",
"fprintf(fid,'\\n')\n",
"fprintf(fid,string)\n",
"fprintf(fid,'\\n')\n",
"fprintf(fid,'are you awake?')\n",
"fprintf(fid,'\\n')\n",
"fprintf(fid,'%f is equal to pi',pi)\n",
"fclose(fid)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 20\n"
]
}
],
"source": [
"a=10;\n",
"a+a % add two 1x1 arrays"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 2 4 6\n",
" 8 10 12\n",
" 14 16 18\n",
" 20 22 24\n"
]
}
],
"source": [
"A = [1 2 3;4,5,6;7,8,9;10,11,12];\n",
"A+A % add two 4 x 3 arrays"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 14 32 50 68\n",
" 32 77 122 167\n",
" 50 122 194 266\n",
" 68 167 266 365\n"
]
}
],
"source": [
"A*A'"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1 4 9\n",
" 16 25 36\n",
" 49 64 81\n",
" 100 121 144\n"
]
}
],
"source": [
"A.^2"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1 4 9\n",
" 16 25 36\n",
" 49 64 81\n",
" 100 121 144\n"
]
}
],
"source": [
"A.*A"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[\b> In pymat_eval (line 31)\n",
" In matlabserver (line 24)]\b \n",
"[\bWarning: Rank deficient, rank = 2, tol = 1.696862e-14.]\b \n",
"\n",
"ans =\n",
"\n",
" 1.0000 0 0 -0.0000\n",
" 0.6667 0 0 0.3333\n",
" 0.3333 0 0 0.6667\n",
" 0.0000 0 0 1.0000\n"
]
}
],
"source": [
"A/A"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/ Slash or right matrix divide.\n",
" A/B is the matrix division of B into A, which is roughly the\n",
" same as A*INV(B) , except it is computed in a different way.\n",
" More precisely, A/B = (B'\\A')'. See MLDIVIDE for details.\n",
" \n",
" C = MRDIVIDE(A,B) is called for the syntax 'A / B' when A or B is an\n",
" object.\n",
" \n",
" See also MLDIVIDE, RDIVIDE, LDIVIDE.\n",
"\n",
" Reference page in Doc Center\n",
" doc mrdivide\n",
"\n",
" Other functions named mrdivide\n",
"\n",
" codistributed/mrdivide gf/mrdivide laurpoly/mrdivide\n",
" duration/mrdivide gpuArray/mrdivide StaticModel/mrdivide\n",
" DynamicSystem/mrdivide LagOp/mrdivide timeseries/mrdivide\n",
" fints/mrdivide\n"
]
}
],
"source": [
"help /"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1 1 1\n",
" 1 1 1\n",
" 1 1 1\n",
" 1 1 1\n"
]
}
],
"source": [
"% element-by-element operation with '.'\n",
"A./A"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"But, for 1x1 arrays, these are considered scalars and you get a free-pass"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 10 20 30\n",
" 40 50 60\n",
" 70 80 90\n",
" 100 110 120\n"
]
}
],
"source": [
"a*A % where a=10 and A is 1:12 in a 3 x 4 matrix"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 4.con'd Other built-in functions"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_linear =\n",
"\n",
" Columns 1 through 7\n",
"\n",
" 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000\n",
"\n",
" Columns 8 through 11\n",
"\n",
" 0.7000 0.8000 0.9000 1.0000\n"
]
}
],
"source": [
"t_linear=linspace(0,1,11)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t_log =\n",
"\n",
" 1 10 100\n"
]
}
],
"source": [
"t_log = logspace(0,2,3) % log interval from 10^0 to 10^2 split into 3 values"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"LOGSPACE Logarithmically spaced vector.\n",
" LOGSPACE(X1, X2) generates a row vector of 50 logarithmically\n",
" equally spaced points between decades 10^X1 and 10^X2. If X2\n",
" is pi, then the points are between 10^X1 and pi.\n",
" \n",
" LOGSPACE(X1, X2, N) generates N points.\n",
" For N = 1, LOGSPACE returns 10^X2.\n",
" \n",
" Class support for inputs X1,X2:\n",
" float: double, single\n",
" \n",
" See also LINSPACE, COLON.\n",
"\n",
" Reference page in Doc Center\n",
" doc logspace\n",
"\n",
" Other functions named logspace\n",
"\n",
" codistributed.logspace distributed.logspace\n",
" codistributor1d/logspace gpuArray/logspace\n",
" codistributor2dbc/logspace\n"
]
}
],
"source": [
"help logspace"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 4.con'd scripts, functions or classes (to define objects)\n",
"\n",
"When using the GUI, your command history is saved, \n",
"\n",
"Best practice: save your work either as a script or a function or combination of both\n",
"\n",
"Creating a default graph script:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"set(0, 'defaultAxesFontSize', 16)\n",
"set(0,'defaultTextFontSize',14)\n",
"set(0,'defaultLineLineWidth',3)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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8EZtWVN4g63ocaWQm3CbGZmdnE0Kam5uZ1hIAgF3CluSWxy2QunfvTjPp5MmTcXFx1dXV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\n3hbsG94hAQAAL6CFBAAAvIBAAgAAXvj/u/Oe9/l6M9wAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(t_linear,t_linear.^2)\n",
"xlabel('time (s)')\n",
"ylabel('displacement (m)')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Graphics can be produced with a number of functions\n",
"\n",
"2-D plots, 3-D plots, contour plots, 3D contour plots ... "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg height=\"420px\" viewBox=\"0 0 560 420\" width=\"560px\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"\n",
"<title>Gnuplot</title>\n",
"<desc>Produced by GNUPLOT 5.0 patchlevel 3 </desc>\n",
"\n",
"<g id=\"gnuplot_canvas\">\n",
"\n",
"<rect fill=\"none\" height=\"420\" width=\"560\" x=\"0\" y=\"0\"/>\n",
"<defs>\n",
"\n",
"\t<circle id=\"gpDot\" r=\"0.5\" stroke-width=\"0.5\"/>\n",
"\t<path d=\"M-1,0 h2 M0,-1 v2\" id=\"gpPt0\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<path d=\"M-1,-1 L1,1 M1,-1 L-1,1\" id=\"gpPt1\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<path d=\"M-1,0 L1,0 M0,-1 L0,1 M-1,-1 L1,1 M-1,1 L1,-1\" id=\"gpPt2\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<rect height=\"2\" id=\"gpPt3\" stroke=\"currentColor\" stroke-width=\"0.333\" width=\"2\" x=\"-1\" y=\"-1\"/>\n",
"\t<rect fill=\"currentColor\" height=\"2\" id=\"gpPt4\" stroke=\"currentColor\" stroke-width=\"0.333\" width=\"2\" x=\"-1\" y=\"-1\"/>\n",
"\t<circle cx=\"0\" cy=\"0\" id=\"gpPt5\" r=\"1\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<use fill=\"currentColor\" id=\"gpPt6\" stroke=\"none\" xlink:href=\"#gpPt5\"/>\n",
"\t<path d=\"M0,-1.33 L-1.33,0.67 L1.33,0.67 z\" id=\"gpPt7\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<use fill=\"currentColor\" id=\"gpPt8\" stroke=\"none\" xlink:href=\"#gpPt7\"/>\n",
"\t<use id=\"gpPt9\" stroke=\"currentColor\" transform=\"rotate(180)\" xlink:href=\"#gpPt7\"/>\n",
"\t<use fill=\"currentColor\" id=\"gpPt10\" stroke=\"none\" xlink:href=\"#gpPt9\"/>\n",
"\t<use id=\"gpPt11\" stroke=\"currentColor\" transform=\"rotate(45)\" xlink:href=\"#gpPt3\"/>\n",
"\t<use fill=\"currentColor\" id=\"gpPt12\" stroke=\"none\" xlink:href=\"#gpPt11\"/>\n",
"\t<path d=\"M0,1.330 L1.265,0.411 L0.782,-1.067 L-0.782,-1.076 L-1.265,0.411 z\" id=\"gpPt13\" stroke=\"currentColor\" stroke-width=\"0.333\"/>\n",
"\t<use fill=\"currentColor\" id=\"gpPt14\" stroke=\"none\" xlink:href=\"#gpPt13\"/>\n",
"\t<filter filterUnits=\"objectBoundingBox\" height=\"1\" id=\"textbox\" width=\"1\" x=\"0\" y=\"0\">\n",
"\t <feFlood flood-color=\"white\" flood-opacity=\"1\" result=\"bgnd\"/>\n",
"\t <feComposite in=\"SourceGraphic\" in2=\"bgnd\" operator=\"atop\"/>\n",
"\t</filter>\n",
"\t<filter filterUnits=\"objectBoundingBox\" height=\"1\" id=\"greybox\" width=\"1\" x=\"0\" y=\"0\">\n",
"\t <feFlood flood-color=\"lightgrey\" flood-opacity=\"1\" result=\"grey\"/>\n",
"\t <feComposite in=\"SourceGraphic\" in2=\"grey\" operator=\"atop\"/>\n",
"\t</filter>\n",
"</defs>\n",
"<g color=\"white\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n",
"\t<g shape-rendering=\"crispEdges\" stroke=\"none\">\n",
"\t\t<polygon fill=\"rgb(255, 255, 255)\" points=\"36.4,396.0 543.0,396.0 543.0,11.4 36.4,11.4 \"/>\n",
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],
"source": [
"setdefaults;\n",
"plot(data(:,1),cumsum(data(:,3))/1e6,data(:,1),cumsum(data(:,8))/1e6)\n",
"xlabel('year')\n",
"ylabel('trillions of btus')\n",
"legend('residential totals','transportation totals','Location','Northwest')"
]
},
{
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},
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}
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"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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