diff --git a/HW2/README.md b/HW2/README.md new file mode 100644 index 0000000..f74173b --- /dev/null +++ b/HW2/README.md @@ -0,0 +1,36 @@ +# Homework #2 +## due 2/3/17 + +1. Now that you have created your own repository, 'homework_1', that has a README.md file. +Create a new file in this repository called `setdefaults.m`. This file is a matlab/octave +script that will set default plotting parameters. In this file, add the following lines: + + ```matlab + set(0, 'defaultAxesFontSize', 16) + set(0,'defaultTextFontSize',14) + set(0,'defaultLineLineWidth',3) + ``` + + Commit the changes to your repository. + + ![projectile(v_mag,theta) predicts the height of the projectile based upon initial +velocity and position, as see in the Figure](projectile.png) + +2. Clone your 'homework_1' repository to your own computer. Now, we want to create a +function that uses kinematic formulas to predict the path of a projectile. The dimensions +are taken from official dart board dimensions +[darts](http://dartbrokers.com/dartboard-height.html). Create a function, +`projectile.m` that will calculate the location of an object with an initial velocity. The +function inputs are v_mag (initial speed), theta (initial angle). The output is the height +of the object 2.37 m from its starting position. Assume g=9.81 m/s^2 and its initial +height is 1.72 m. + + ```matlab + >> h=projectile(v_mag,theta) + + h= 1 + ``` + + In addition to the output of `h`-height at 2.37 m-plot the path of the object from its + initial position to its position at 2.37 m away from the start. *Note: use your + `setdefaults.m` to set the plot defaults before outputting the result.* diff --git a/HW2/projectile.png b/HW2/projectile.png new file mode 100644 index 0000000..f544224 Binary files /dev/null and b/HW2/projectile.png differ diff --git a/HW2/projectile.svg b/HW2/projectile.svg new file mode 100644 index 0000000..bb33043 --- /dev/null +++ b/HW2/projectile.svg @@ -0,0 +1,331 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + 2.37 m + + + + v_mag + theta + + h + + 1.72 m + + diff --git a/README.md b/README.md index ca1565e..8059993 100644 --- a/README.md +++ b/README.md @@ -22,14 +22,21 @@ matlab/octave functions and programming best practices. **Office hours**: Mon 2:30-4:30pm and Thur 11am-1pm in Engineering II room 315 ## Teaching Assistants: -- Graduate: **TBD** -- Office hours: 2 hours / week in office **TBD** +- Graduate: Peiyu Zhang +- Office hours: Friday 9:00-11:00am in Engineering II room 315 +## Course Information **Prerequisite:** CE 3110, MATH 2410Q **Textbook:** Chapra, Steven, *Applied Numerical Methods with MATLAB for Engineers and Scientists* 3rd edition. +**Tools used:** [Matlab](https://www.mathworks.com/products/matlab.html), +[Octave](https://www.gnu.org/software/octave/) , [Github](https://github.com). + +**Recommended tools:** Github Desktop, git, Atom (text editor), Vim (text editor), +Jupiter notebook (with matlab or octave kernel) + ## Grading | Item | Percent | Requirement | diff --git a/lecture_03/file.txt b/lecture_03/file.txt new file mode 100644 index 0000000..0fb2c92 --- /dev/null +++ b/lecture_03/file.txt @@ -0,0 +1,5 @@ +computational mechanics +the dog had 4 legs and weighed 10.0 lbs +are you awake?computational mechanics +the dog had 4 legs and weighed 10.0 lbs +are you awake? \ No newline at end of file diff --git a/lecture_03/lecture_03.ipynb b/lecture_03/lecture_03.ipynb new file mode 100644 index 0000000..e205d15 --- /dev/null +++ b/lecture_03/lecture_03.ipynb @@ -0,0 +1,6077 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Matlab basic use\n", + "## 1- the environment, path and working directory" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matlab environment can be called by:\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", + "The main requirement is that matlab kernel (main matlab program) is running and accepting commands\n", + "\n", + "When you start, you can call matlab built-in functions or anything you write that is in your `MATLABPATH` or working directory (`pwd`)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MATLABPATH\n", + "\n", + "\t/usr/local/lib/python2.7/dist-packages/matlab_kernel/toolbox\n", + "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab\n", + "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/usrprog\n", + "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util\n", + "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2\n", + "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json\n", + 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}, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + "/home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_03\n" + ] + } + ], + "source": [ + "pwd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "path" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Assignments (`=`-operator)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matlab is interpreted language so 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": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 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", + "a+b % line three does not assign anything directly, but leaving off the \";\" prints the result\n", + " % ans" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matlab has a number of \"objects\" that you can assign to variables\n", + "1. arrays (vectors and matrices `[`...`]`) \n", + "2. strings (text `\"`...`\"` )\n", + "3. cells (combination of strings, text, even function calls `{`...`}`)\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": {}, + "source": [ + "### 1- Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1\n" + ] + } + ], + "source": [ + "a=10; % a is 1x1 array where a(1,1)==10\n", + "a(1,1)==10\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[0;31mIndex exceeds matrix dimensions.\n", + "\u001b[0m" + ] + } + ], + "source": [ + "a(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "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", + "\n", + "ans =\n", + "\n", + " 7\n", + "\n", + "\n", + "ans =\n", + "\n", + " 5\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))\n", + "A(3,1)\n", + "A(6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "vectors are either 1xN or Nx1 arrays for row and column" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v_row =\n", + "\n", + " 1 2 3\n", + "\n", + "\n", + "v_column =\n", + "\n", + " 1\n", + " 2\n", + " 3\n" + ] + } + ], + "source": [ + "v_row = [1,2,3] %row vector\n", + "v_column = [1;2;3] %column vector\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matrices are MxN arrays\n", + "the `:`-symbol can substitute for a counting" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1 2 3\n" + ] + } + ], + "source": [ + "A(1,:) % the colon assumes you want the first value, 1, counting up by 1 to the last value, 4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "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": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1\n", + " 7\n" + ] + } + ], + "source": [ + "A(1:2:end,1) % you can also use `end` " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "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" + ] + } + ], + "source": [ + "A(:)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "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": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "A_6666 = zeros(6,6,6,6); %make a 6 x 6 x 6 x 6 array (1296 different values)\n", + "for i=1:6\n", + " for j=1:6\n", + " for k=1:6\n", + " for l=1:6\n", + " A_6666(i,j,k,l)=i+j+k+l; % each value is the sum of the indices\n", + " end\n", + " end\n", + " end\n", + "end\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 14\n", + "\n", + "\n", + "ans =\n", + "\n", + " 3.4170\n" + ] + } + ], + "source": [ + "mean(A_6666(:))\n", + "std(A_6666(:))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 12\n" + ] + } + ], + "source": [ + "A_6666(1,4,2,5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cells combine different size arrays and text\n", + "### but, you cannot use math operators 'binary operators'" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "C={};\n", + "C{1}=linspace(0,1,10);\n", + "C{2}=linspace(0,1,3);\n", + "C{'z'}='holy cow';" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 3.5185\n" + ] + } + ], + "source": [ + "C{1}*C{1}'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Strings can be combined and printed" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + "computational mechanics\n" + ] + } + ], + "source": [ + "string1 = 'computational'; string2 = 'mechanics';\n", + "[string1, ' ', string2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "use `fprintf` to format strings and numbers for output and `sprintf` to save variables\n" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "computational mechanics\n", + "\n", + "\n", + "string =\n", + "\n", + "the dog had 4 legs and weighed 10.0 lbs\n" + ] + } + ], + "source": [ + "fprintf([string1,' ',string2,'\\n\\n'])\n", + "string = sprintf('the dog had %i legs and weighed %1.1f lbs',4,10.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the `\\` signifies a special character e.g. `\\n` = newline, `\\t` = tab\n", + "\n", + "to actually print the \"\\\", use `\\\\`" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\\n" + ] + } + ], + "source": [ + "fprintf('\\\\')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## This is helpful to create reports of computed data" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 23\n", + "\n", + "\n", + "ans =\n", + "\n", + " 1\n", + "\n", + "\n", + "ans =\n", + "\n", + " 39\n", + "\n", + "\n", + "ans =\n", + "\n", + " 1\n", + "\n", + "\n", + "ans =\n", + "\n", + " 14\n" + ] + } + ], + "source": [ + "%fid = fopen('file.txt','w');\n", + "fprintf(fid,[string1, ' ', string2])\n", + "fprintf(fid,'\\n')\n", + "fprintf(fid,string)\n", + "fprintf(fid,'\\n')\n", + "fprintf(fid,'are you awake?')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Math operators (=, +, -, /, *, ^)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because matlab assumes all variables are matrices, then all operators are matrix operations" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 20\r\n" + ] + } + ], + "source": [ + "a+a % add two 1x1 arrays" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "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", + "\n" + ] + } + ], + "source": [ + "A+A % add two 4 x 3 arrays" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "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": 39, + "metadata": { + "collapsed": false + }, + "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": 40, + "metadata": { + "collapsed": false + }, + "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": 44, + "metadata": { + "collapsed": false + }, + "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": 45, + "metadata": { + "collapsed": false + }, + "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": "markdown", + "metadata": {}, + "source": [ + "To accomplish one-by-one operations, need to include a `.`" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "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", + "\n" + ] + } + ], + "source": [ + "A./A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But, for 1x1 arrays, these are considered scalars and you get a free-pass" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "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", + "\n" + ] + } + ], + "source": [ + "a*A % where a=10 and A is 1:12 in a 3 x 4 matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some built in Matlab functions (e.g. the reasons to run Matlab)" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "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": 46, + "metadata": { + "collapsed": false + }, + "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": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'logspace' is a function from the file /usr/share/octave/4.0.0/m/general/logspace.m\n", + "\n", + " -- Function File: logspace (A, B)\n", + " -- Function File: logspace (A, B, N)\n", + " -- Function File: logspace (A, pi, N)\n", + " Return a row vector with N elements logarithmically spaced from\n", + " 10^A to 10^B.\n", + "\n", + " If N is unspecified it defaults to 50.\n", + "\n", + " If B is equal to pi, the points are between 10^A and pi, _not_ 10^A\n", + " and 10^pi, in order to be compatible with the corresponding MATLAB\n", + " function.\n", + "\n", + " Also for compatibility with MATLAB, return the second argument B if\n", + " fewer than two values are requested.\n", + "\n", + " See also: linspace.\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 ' 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 logspace" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%myscript" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When using the GUI, your command history is saved, but it is better to 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": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "set(0, 'defaultAxesFontSize', 16)\n", + "set(0,'defaultTextFontSize',14)\n", + "set(0,'defaultLineLineWidth',3)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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IsrIy41QFAGB+mMzbxFi8GCsSiWJjYwkhfn5+hYWFpaWlUVFR9vb27u7uGsfd8Xi88+fP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\ncAICCQAAOAGBBAAAnPD/AHltgbQ+BHrdAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(t_linear,t_linear.^2)\n", + "xlabel('time (s)')\n", + "ylabel('displacement (m)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#EOL" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Graphics can be produced with a number of functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2-D plots, 3-D plots, contour plots, 3D contour plots ... " + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Z =\n", + "\n", + " Columns 1 through 8:\n", + "\n", + " 0.00000 0.17100 0.28800 0.35700 0.38400 0.37500 0.33600 0.27300\n", + " -0.17100 0.00000 0.12240 0.20160 0.24300 0.25200 0.23400 0.19440\n", + " -0.28800 -0.12240 0.00000 0.08400 0.13440 0.15600 0.15360 0.13200\n", + " -0.35700 -0.20160 -0.08400 0.00000 0.05460 0.08400 0.09240 0.08400\n", + " -0.38400 -0.24300 -0.13440 -0.05460 0.00000 0.03300 0.04800 0.04860\n", + " -0.37500 -0.25200 -0.15600 -0.08400 -0.03300 0.00000 0.01800 0.02400\n", + " -0.33600 -0.23400 -0.15360 -0.09240 -0.04800 -0.01800 0.00000 0.00840\n", + " -0.27300 -0.19440 -0.13200 -0.08400 -0.04860 -0.02400 -0.00840 0.00000\n", + " -0.19200 -0.13860 -0.09600 -0.06300 -0.03840 -0.02100 -0.00960 -0.00300\n", + " -0.09900 -0.07200 -0.05040 -0.03360 -0.02100 -0.01200 -0.00600 -0.00240\n", + " 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000\n", + " 0.09900 0.07200 0.05040 0.03360 0.02100 0.01200 0.00600 0.00240\n", + " 0.19200 0.13860 0.09600 0.06300 0.03840 0.02100 0.00960 0.00300\n", + " 0.27300 0.19440 0.13200 0.08400 0.04860 0.02400 0.00840 -0.00000\n", + " 0.33600 0.23400 0.15360 0.09240 0.04800 0.01800 -0.00000 -0.00840\n", + " 0.37500 0.25200 0.15600 0.08400 0.03300 0.00000 -0.01800 -0.02400\n", + " 0.38400 0.24300 0.13440 0.05460 -0.00000 -0.03300 -0.04800 -0.04860\n", + " 0.35700 0.20160 0.08400 -0.00000 -0.05460 -0.08400 -0.09240 -0.08400\n", + " 0.28800 0.12240 0.00000 -0.08400 -0.13440 -0.15600 -0.15360 -0.13200\n", + " 0.17100 -0.00000 -0.12240 -0.20160 -0.24300 -0.25200 -0.23400 -0.19440\n", + " 0.00000 -0.17100 -0.28800 -0.35700 -0.38400 -0.37500 -0.33600 -0.27300\n", + "\n", + " Columns 9 through 16:\n", + "\n", + " 0.19200 0.09900 0.00000 -0.09900 -0.19200 -0.27300 -0.33600 -0.37500\n", + " 0.13860 0.07200 0.00000 -0.07200 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environment can be called by: +1. Starting the matlab executable (the gui) +2. Starting a jupyter notebook with Matlab kernel +3. Starting matlab with command-line interface (no gui) + +The main requirement is that matlab kernel (main matlab program) is running and accepting commands + +When you start, you can call matlab built-in functions or anything you write that is in your `MATLABPATH` or working directory (`pwd`) + + +```matlab +path +``` + + MATLABPATH + + /usr/local/lib/python2.7/dist-packages/matlab_kernel/toolbox + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/usrprog + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2 + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json/java + /usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/test + /home/ryan/Documents/MATLAB + /usr/local/MATLAB/R2016a/toolbox/matlab/strfun + /usr/local/MATLAB/R2016a/toolbox/matlab/datatypes + /usr/local/MATLAB/R2016a/toolbox/matlab/elfun + /usr/local/MATLAB/R2016a/toolbox/matlab/ops + /usr/local/MATLAB/R2016a/toolbox/matlab/timefun + /usr/local/MATLAB/R2016a/toolbox/matlab/elmat + /usr/local/MATLAB/R2016a/toolbox/matlab/datafun + /usr/local/MATLAB/R2016a/toolbox/matlab/iofun + /usr/local/MATLAB/R2016a/toolbox/matlab/mvm + /usr/local/MATLAB/R2016a/toolbox/matlab/randfun + /usr/local/MATLAB/R2016a/toolbox/matlab/funfun + /usr/local/MATLAB/R2016a/toolbox/matlab/general + /usr/local/MATLAB/R2016a/toolbox/matlab/polyfun + /usr/local/MATLAB/R2016a/toolbox/matlab/matfun + /usr/local/MATLAB/R2016a/toolbox/matlab/lang + /usr/local/MATLAB/R2016a/toolbox/matlab/specfun + /usr/local/MATLAB/R2016a/toolbox/matlab/sparfun + /usr/local/MATLAB/R2016a/toolbox/matlab/images + /usr/local/MATLAB/R2016a/toolbox/matlab/testframework/performance + /usr/local/MATLAB/R2016a/toolbox/matlab/testframework/parallel + /usr/local/MATLAB/R2016a/toolbox/matlab/optimfun + /usr/local/MATLAB/R2016a/toolbox/matlab/testframework/ext + /usr/local/MATLAB/R2016a/toolbox/matlab/guide + /usr/local/MATLAB/R2016a/toolbox/matlab/testframework/measurement + /usr/local/MATLAB/R2016a/toolbox/matlab/icons + /usr/local/MATLAB/R2016a/toolbox/matlab/demos + /usr/local/MATLAB/R2016a/toolbox/matlab/helptools + /usr/local/MATLAB/R2016a/toolbox/matlab/winfun + /usr/local/MATLAB/R2016a/toolbox/matlab/winfun/NET + /usr/local/MATLAB/R2016a/toolbox/matlab/datamanager + /usr/local/MATLAB/R2016a/toolbox/matlab/verctrl + /usr/local/MATLAB/R2016a/toolbox/matlab/graph2d + /usr/local/MATLAB/R2016a/toolbox/matlab/graph3d + /usr/local/MATLAB/R2016a/toolbox/matlab/graphics + /usr/local/MATLAB/R2016a/toolbox/matlab/graphics/obsolete + /usr/local/MATLAB/R2016a/toolbox/matlab/plottools + /usr/local/MATLAB/R2016a/toolbox/matlab/scribe + /usr/local/MATLAB/R2016a/toolbox/matlab/scribe/obsolete + /usr/local/MATLAB/R2016a/toolbox/matlab/specgraph 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/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntransfer + /usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnweight + /usr/local/MATLAB/R2016a/toolbox/nnet/nnguis + /usr/local/MATLAB/R2016a/toolbox/nnet/nnobsolete + /usr/local/MATLAB/R2016a/toolbox/nnet/nnutils + /usr/local/MATLAB/R2016a/toolbox/matlab/addons_product + /usr/local/MATLAB/R2016a/toolbox/shared/tracking/trackinglib + /usr/local/MATLAB/R2016a/toolbox/shared/simulink/sysarch/sysarch + /usr/local/MATLAB/R2016a/toolbox/shared/slreportgen/reportexplorer + /usr/local/MATLAB/R2016a/toolbox/coder/embeddedcoder_templates + /usr/local/MATLAB/R2016a/toolbox/coder/wizard + /usr/local/MATLAB/R2016a/toolbox/physmod/sm/core/m + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros/helpers + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs/helpers + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore/helpers + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink + /usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink/helpers + /usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine + /usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/numerics + /usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/options + /usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/optim + /usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/blocks + /usr/local/MATLAB/R2016a/toolbox/dsp/filterdesign + /usr/local/MATLAB/R2016a/toolbox/finance/findemos + /usr/local/MATLAB/R2016a/toolbox/physmod/powersys/facts/facts + + + +```matlab +pwd +``` + + ans = + + /home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_03 + + + +path + +## Assignments (`=`-operator) + +Matlab is interpreted language so each line of code (either saved text file or command-line) is executed as a standalone command + +These are reffered to "scripts" + + +```matlab +a=10; % line one assigns a to 10 +b=a*3; % line two assigns b to 10 times 3 by calling 'a' from line one +a+b % line three does not assign anything directly, but leaving off the ";" prints the result + % ans +``` + + ans = + + 40 + + +Matlab has a number of "objects" that you can assign to variables +1. arrays (vectors and matrices `[`...`]`) +2. strings (text `"`...`"` ) +3. cells (combination of strings, text, even function calls `{`...`}`) +3. functions (both built-in, defined or developed) +4. and more... (classes defined by `classdef` - you can create your own object to help organize data) + +### 1- Arrays + +Default in matlab is that when you assign a value to a variable, it is stored as an array + +arrays are N x M x ... values of integers or floating point numbers or complex integers/floating point numbers + +Use the parantheses to access values in an array `...(n,m)` + + +```matlab +a=10; % a is 1x1 array where a(1,1)==10 +a(1,1)==10 + +``` + + ans = + + 1 + + + +```matlab +a(2) +``` + + Index exceeds matrix dimensions. +  + + +```matlab +A = [1 2 3;4,5,6;7,8,9;10,11,12] +fprintf('size of A is %i x %i\n',size(A)) +A(3,1) +A(6) +``` + + A = + + 1 2 3 + 4 5 6 + 7 8 9 + 10 11 12 + + size of A is 4 x 3 + + ans = + + 7 + + + ans = + + 5 + + +vectors are either 1xN or Nx1 arrays for row and column + + +```matlab +v_row = [1,2,3] %row vector +v_column = [1;2;3] %column vector + +``` + + v_row = + + 1 2 3 + + + v_column = + + 1 + 2 + 3 + + +Matrices are MxN arrays +the `:`-symbol can substitute for a counting + + +```matlab +A(1,:) % the colon assumes you want the first value, 1, counting up by 1 to the last value, 4 +``` + + ans = + + 1 2 3 + + +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 + + +```matlab +A(1:2:end,1) % you can also use `end` +``` + + ans = + + 1 + 7 + + + +```matlab +A(:) +``` + + ans = + + 1 + 4 + 7 + 10 + 2 + 5 + 8 + 11 + 3 + 6 + 9 + 12 + + +In general, arrays can be any size + +take rolling 4 die and determining the sum of the components + + +```matlab +A_6666 = zeros(6,6,6,6); %make a 6 x 6 x 6 x 6 array (1296 different values) +for i=1:6 + for j=1:6 + for k=1:6 + for l=1:6 + A_6666(i,j,k,l)=i+j+k+l; % each value is the sum of the indices + end + end + end +end + +``` + + +```matlab +mean(A_6666(:)) +std(A_6666(:)) +``` + + ans = + + 14 + + + ans = + + 3.4170 + + + +```matlab +A_6666(1,4,2,5) +``` + + ans = + + 12 + + +## Cells combine different size arrays and text +### but, you cannot use math operators 'binary operators' + + +```matlab +C={}; +C{1}=linspace(0,1,10); +C{2}=linspace(0,1,3); +C{'z'}='holy cow'; +``` + + +```matlab +C{1}*C{1}' +``` + + ans = + + 3.5185 + + +## Strings can be combined and printed + + +```matlab +string1 = 'computational'; string2 = 'mechanics'; +[string1, ' ', string2] +``` + + ans = + + computational mechanics + + +use `fprintf` to format strings and numbers for output and `sprintf` to save variables + + + +```matlab +fprintf([string1,' ',string2,'\n\n']) +string = sprintf('the dog had %i legs and weighed %1.1f lbs',4,10.0) +``` + + computational mechanics + + + string = + + the dog had 4 legs and weighed 10.0 lbs + + +the `\` signifies a special character e.g. `\n` = newline, `\t` = tab + +to actually print the "\", use `\\` + + +```matlab +fprintf('\\') +``` + + \ + + +## This is helpful to create reports of computed data + + +```matlab +%fid = fopen('file.txt','w'); +fprintf(fid,[string1, ' ', string2]) +fprintf(fid,'\n') +fprintf(fid,string) +fprintf(fid,'\n') +fprintf(fid,'are you awake?') +``` + + ans = + + 23 + + + ans = + + 1 + + + ans = + + 39 + + + ans = + + 1 + + + ans = + + 14 + + +## Math operators (=, +, -, /, *, ^) + +Because matlab assumes all variables are matrices, then all operators are matrix operations + + +```matlab +a+a % add two 1x1 arrays +``` + + ans = 20 + + + +```matlab +A+A % add two 4 x 3 arrays +``` + + ans = + + 2 4 6 + 8 10 12 + 14 16 18 + 20 22 24 + + + + +```matlab +A*A' +``` + + ans = + + 14 32 50 68 + 32 77 122 167 + 50 122 194 266 + 68 167 266 365 + + + +```matlab +A.^2 +``` + + ans = + + 1 4 9 + 16 25 36 + 49 64 81 + 100 121 144 + + + +```matlab +A.*A +``` + + ans = + + 1 4 9 + 16 25 36 + 49 64 81 + 100 121 144 + + + +```matlab +A/A +``` + + [> In pymat_eval (line 31) + In matlabserver (line 24)] + [Warning: Rank deficient, rank = 2, tol = 1.696862e-14.] + + ans = + + 1.0000 0 0 -0.0000 + 0.6667 0 0 0.3333 + 0.3333 0 0 0.6667 + 0.0000 0 0 1.0000 + + + +```matlab +help / +``` + + / Slash or right matrix divide. + A/B is the matrix division of B into A, which is roughly the + same as A*INV(B) , except it is computed in a different way. + More precisely, A/B = (B'\A')'. See MLDIVIDE for details. + + C = MRDIVIDE(A,B) is called for the syntax 'A / B' when A or B is an + object. + + See also MLDIVIDE, RDIVIDE, LDIVIDE. + + Reference page in Doc Center + doc mrdivide + + Other functions named mrdivide + + codistributed/mrdivide gf/mrdivide laurpoly/mrdivide + duration/mrdivide gpuArray/mrdivide StaticModel/mrdivide + DynamicSystem/mrdivide LagOp/mrdivide timeseries/mrdivide + fints/mrdivide + + +To accomplish one-by-one operations, need to include a `.` + + +```matlab +A./A +``` + + ans = + + 1 1 1 + 1 1 1 + 1 1 1 + 1 1 1 + + + +But, for 1x1 arrays, these are considered scalars and you get a free-pass + + +```matlab +a*A % where a=10 and A is 1:12 in a 3 x 4 matrix +``` + + ans = + + 10 20 30 + 40 50 60 + 70 80 90 + 100 110 120 + + + +Some built in Matlab functions (e.g. the reasons to run Matlab) + + +```matlab +t_linear=linspace(0,1,11) +``` + + t_linear = + + Columns 1 through 7 + + 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 + + Columns 8 through 11 + + 0.7000 0.8000 0.9000 1.0000 + + + +```matlab +t_log = logspace(0,2,3) % log interval from 10^0 to 10^2 split into 3 values +``` + + t_log = + + 1 10 100 + + + +```matlab +help logspace +``` + + 'logspace' is a function from the file /usr/share/octave/4.0.0/m/general/logspace.m + + -- Function File: logspace (A, B) + -- Function File: logspace (A, B, N) + -- Function File: logspace (A, pi, N) + Return a row vector with N elements logarithmically spaced from + 10^A to 10^B. + + If N is unspecified it defaults to 50. + + If B is equal to pi, the points are between 10^A and pi, _not_ 10^A + and 10^pi, in order to be compatible with the corresponding MATLAB + function. + + Also for compatibility with MATLAB, return the second argument B if + fewer than two values are requested. + + See also: linspace. + + Additional help for built-in functions and operators is + available in the online version of the manual. Use the command + 'doc ' to search the manual index. + + Help and information about Octave is also available on the WWW + at http://www.octave.org and via the help@octave.org + mailing list. + + +## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects) + + +```matlab +%myscript +``` + + +```matlab +%plot --format svg +``` + +When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both + +Creating a default graph script: + + +```matlab +set(0, 'defaultAxesFontSize', 16) +set(0,'defaultTextFontSize',14) +set(0,'defaultLineLineWidth',3) +``` + + +```matlab +plot(t_linear,t_linear.^2) +xlabel('time (s)') +ylabel('displacement (m)') +``` + + +![png](output_58_0.png) + + +#EOL + +## Graphics can be produced with a number of functions + +2-D plots, 3-D plots, contour plots, 3D contour plots ... + + +```matlab +x=linspace(-1,1,21); y=linspace(-1,1,21); +[X,Y]=meshgrid(x,y); +Z=(X.*Y.^3-X.^3.*Y) +``` + + Z = + + Columns 1 through 8: + + 0.00000 0.17100 0.28800 0.35700 0.38400 0.37500 0.33600 0.27300 + -0.17100 0.00000 0.12240 0.20160 0.24300 0.25200 0.23400 0.19440 + -0.28800 -0.12240 0.00000 0.08400 0.13440 0.15600 0.15360 0.13200 + -0.35700 -0.20160 -0.08400 0.00000 0.05460 0.08400 0.09240 0.08400 + -0.38400 -0.24300 -0.13440 -0.05460 0.00000 0.03300 0.04800 0.04860 + -0.37500 -0.25200 -0.15600 -0.08400 -0.03300 0.00000 0.01800 0.02400 + -0.33600 -0.23400 -0.15360 -0.09240 -0.04800 -0.01800 0.00000 0.00840 + -0.27300 -0.19440 -0.13200 -0.08400 -0.04860 -0.02400 -0.00840 0.00000 + -0.19200 -0.13860 -0.09600 -0.06300 -0.03840 -0.02100 -0.00960 -0.00300 + -0.09900 -0.07200 -0.05040 -0.03360 -0.02100 -0.01200 -0.00600 -0.00240 + 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 + 0.09900 0.07200 0.05040 0.03360 0.02100 0.01200 0.00600 0.00240 + 0.19200 0.13860 0.09600 0.06300 0.03840 0.02100 0.00960 0.00300 + 0.27300 0.19440 0.13200 0.08400 0.04860 0.02400 0.00840 -0.00000 + 0.33600 0.23400 0.15360 0.09240 0.04800 0.01800 -0.00000 -0.00840 + 0.37500 0.25200 0.15600 0.08400 0.03300 0.00000 -0.01800 -0.02400 + 0.38400 0.24300 0.13440 0.05460 -0.00000 -0.03300 -0.04800 -0.04860 + 0.35700 0.20160 0.08400 -0.00000 -0.05460 -0.08400 -0.09240 -0.08400 + 0.28800 0.12240 0.00000 -0.08400 -0.13440 -0.15600 -0.15360 -0.13200 + 0.17100 -0.00000 -0.12240 -0.20160 -0.24300 -0.25200 -0.23400 -0.19440 + 0.00000 -0.17100 -0.28800 -0.35700 -0.38400 -0.37500 -0.33600 -0.27300 + + Columns 9 through 16: + + 0.19200 0.09900 0.00000 -0.09900 -0.19200 -0.27300 -0.33600 -0.37500 + 0.13860 0.07200 0.00000 -0.07200 -0.13860 -0.19440 -0.23400 -0.25200 + 0.09600 0.05040 0.00000 -0.05040 -0.09600 -0.13200 -0.15360 -0.15600 + 0.06300 0.03360 0.00000 -0.03360 -0.06300 -0.08400 -0.09240 -0.08400 + 0.03840 0.02100 0.00000 -0.02100 -0.03840 -0.04860 -0.04800 -0.03300 + 0.02100 0.01200 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0.23400 0.25200 + -0.19200 -0.09900 0.00000 0.09900 0.19200 0.27300 0.33600 0.37500 + + Columns 17 through 21: + + -0.38400 -0.35700 -0.28800 -0.17100 0.00000 + -0.24300 -0.20160 -0.12240 0.00000 0.17100 + -0.13440 -0.08400 0.00000 0.12240 0.28800 + -0.05460 0.00000 0.08400 0.20160 0.35700 + 0.00000 0.05460 0.13440 0.24300 0.38400 + 0.03300 0.08400 0.15600 0.25200 0.37500 + 0.04800 0.09240 0.15360 0.23400 0.33600 + 0.04860 0.08400 0.13200 0.19440 0.27300 + 0.03840 0.06300 0.09600 0.13860 0.19200 + 0.02100 0.03360 0.05040 0.07200 0.09900 + 0.00000 0.00000 0.00000 0.00000 0.00000 + -0.02100 -0.03360 -0.05040 -0.07200 -0.09900 + -0.03840 -0.06300 -0.09600 -0.13860 -0.19200 + -0.04860 -0.08400 -0.13200 -0.19440 -0.27300 + -0.04800 -0.09240 -0.15360 -0.23400 -0.33600 + -0.03300 -0.08400 -0.15600 -0.25200 -0.37500 + 0.00000 -0.05460 -0.13440 -0.24300 -0.38400 + 0.05460 0.00000 -0.08400 -0.20160 -0.35700 + 0.13440 0.08400 0.00000 -0.12240 -0.28800 + 0.24300 0.20160 0.12240 0.00000 -0.17100 + 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move a car that is stuck in the snow? And what would be the approximate cost to do so + +$m_{frog}$=22.7 g (https://en.wikipedia.org/wiki/Common_frog) + +$v_{frog}$=17 kph = 4.72 m/s (http://purelyfacts.com/question/14/is-a-toad-faster-than-a-frog?DDA=113&DDB=40) + +$m_{car}$=1000 kg (reasonable guess) + +conservation of momentum: + +$mv_{1} +mv_{2} = mv_{1}'+mv_{2}' = m_{total}v_{2}'$ + + +```matlab +number_of_frogs = 1; +v2=0; +while v2 < 1 % 1 m/s + m_frogs=number_of_frogs*22.7e-3; + number_of_frogs=number_of_frogs+1; + p1=(m_frogs)*4.72; % momentum 1 + v2=p1/(m_frogs+1000); % p2=p1, so v2=p1/m_total +end +number_of_frogs + +``` + + number_of_frogs = + + 11844 + + + +```matlab +%myscript +``` + + +```matlab +%plot --format svg +``` + +When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both + +Creating a default graph script: `setdefaults.m` + +```matlab +set(0, 'defaultAxesFontSize', 16) +set(0,'defaultTextFontSize',14) +set(0,'defaultLineLineWidth',3) +``` + + +```matlab +set(0, 'defaultAxesFontSize', 16) +set(0,'defaultTextFontSize',14) +set(0,'defaultLineLineWidth',3) +``` + + +```matlab +t_linear=linspace(0,10,100); +plot(t_linear,t_linear.^2) +xlabel('time (s)') +ylabel('displacement (m)') +``` + + +![png](lecture_4_files/lecture_4_7_0.png) + + +#EOL + +## Graphics can be produced with a number of functions + +2-D plots, 3-D plots, contour plots, 3D contour plots ... + + +```matlab +x=linspace(-1,1,21); y=linspace(-1,1,21); +[X,Y]=meshgrid(x,y); +Z=(X.*Y.^3-X.^3.*Y) +``` + + Z = + + Columns 1 through 7 + + 0 0.1710 0.2880 0.3570 0.3840 0.3750 0.3360 + -0.1710 0 0.1224 0.2016 0.2430 0.2520 0.2340 + -0.2880 -0.1224 0 0.0840 0.1344 0.1560 0.1536 + -0.3570 -0.2016 -0.0840 0 0.0546 0.0840 0.0924 + -0.3840 -0.2430 -0.1344 -0.0546 0 0.0330 0.0480 + -0.3750 -0.2520 -0.1560 -0.0840 -0.0330 0 0.0180 + -0.3360 -0.2340 -0.1536 -0.0924 -0.0480 -0.0180 0 + -0.2730 -0.1944 -0.1320 -0.0840 -0.0486 -0.0240 -0.0084 + -0.1920 -0.1386 -0.0960 -0.0630 -0.0384 -0.0210 -0.0096 + -0.0990 -0.0720 -0.0504 -0.0336 -0.0210 -0.0120 -0.0060 + 0 0 0 0 0 0 0 + 0.0990 0.0720 0.0504 0.0336 0.0210 0.0120 0.0060 + 0.1920 0.1386 0.0960 0.0630 0.0384 0.0210 0.0096 + 0.2730 0.1944 0.1320 0.0840 0.0486 0.0240 0.0084 + 0.3360 0.2340 0.1536 0.0924 0.0480 0.0180 0.0000 + 0.3750 0.2520 0.1560 0.0840 0.0330 0 -0.0180 + 0.3840 0.2430 0.1344 0.0546 -0.0000 -0.0330 -0.0480 + 0.3570 0.2016 0.0840 0 -0.0546 -0.0840 -0.0924 + 0.2880 0.1224 0 -0.0840 -0.1344 -0.1560 -0.1536 + 0.1710 0.0000 -0.1224 -0.2016 -0.2430 -0.2520 -0.2340 + 0 -0.1710 -0.2880 -0.3570 -0.3840 -0.3750 -0.3360 + + Columns 8 through 14 + + 0.2730 0.1920 0.0990 0 -0.0990 -0.1920 -0.2730 + 0.1944 0.1386 0.0720 0 -0.0720 -0.1386 -0.1944 + 0.1320 0.0960 0.0504 0 -0.0504 -0.0960 -0.1320 + 0.0840 0.0630 0.0336 0 -0.0336 -0.0630 -0.0840 + 0.0486 0.0384 0.0210 0 -0.0210 -0.0384 -0.0486 + 0.0240 0.0210 0.0120 0 -0.0120 -0.0210 -0.0240 + 0.0084 0.0096 0.0060 0 -0.0060 -0.0096 -0.0084 + 0 0.0030 0.0024 0 -0.0024 -0.0030 0 + -0.0030 0 0.0006 0 -0.0006 0 0.0030 + -0.0024 -0.0006 0 0 0.0000 0.0006 0.0024 + 0 0 0 0 0 0 0 + 0.0024 0.0006 -0.0000 0 0 -0.0006 -0.0024 + 0.0030 0 -0.0006 0 0.0006 0 -0.0030 + 0 -0.0030 -0.0024 0 0.0024 0.0030 0 + -0.0084 -0.0096 -0.0060 0 0.0060 0.0096 0.0084 + -0.0240 -0.0210 -0.0120 0 0.0120 0.0210 0.0240 + -0.0486 -0.0384 -0.0210 0 0.0210 0.0384 0.0486 + -0.0840 -0.0630 -0.0336 0 0.0336 0.0630 0.0840 + -0.1320 -0.0960 -0.0504 0 0.0504 0.0960 0.1320 + -0.1944 -0.1386 -0.0720 0 0.0720 0.1386 0.1944 + -0.2730 -0.1920 -0.0990 0 0.0990 0.1920 0.2730 + + Columns 15 through 21 + + -0.3360 -0.3750 -0.3840 -0.3570 -0.2880 -0.1710 0 + -0.2340 -0.2520 -0.2430 -0.2016 -0.1224 -0.0000 0.1710 + -0.1536 -0.1560 -0.1344 -0.0840 0 0.1224 0.2880 + -0.0924 -0.0840 -0.0546 0 0.0840 0.2016 0.3570 + -0.0480 -0.0330 0.0000 0.0546 0.1344 0.2430 0.3840 + -0.0180 0 0.0330 0.0840 0.1560 0.2520 0.3750 + -0.0000 0.0180 0.0480 0.0924 0.1536 0.2340 0.3360 + 0.0084 0.0240 0.0486 0.0840 0.1320 0.1944 0.2730 + 0.0096 0.0210 0.0384 0.0630 0.0960 0.1386 0.1920 + 0.0060 0.0120 0.0210 0.0336 0.0504 0.0720 0.0990 + 0 0 0 0 0 0 0 + -0.0060 -0.0120 -0.0210 -0.0336 -0.0504 -0.0720 -0.0990 + -0.0096 -0.0210 -0.0384 -0.0630 -0.0960 -0.1386 -0.1920 + -0.0084 -0.0240 -0.0486 -0.0840 -0.1320 -0.1944 -0.2730 + 0 -0.0180 -0.0480 -0.0924 -0.1536 -0.2340 -0.3360 + 0.0180 0 -0.0330 -0.0840 -0.1560 -0.2520 -0.3750 + 0.0480 0.0330 0 -0.0546 -0.1344 -0.2430 -0.3840 + 0.0924 0.0840 0.0546 0 -0.0840 -0.2016 -0.3570 + 0.1536 0.1560 0.1344 0.0840 0 -0.1224 -0.2880 + 0.2340 0.2520 0.2430 0.2016 0.1224 0 -0.1710 + 0.3360 0.3750 0.3840 0.3570 0.2880 0.1710 0 + + + +```matlab +contour(X,Y,Z) +``` + + +![png](lecture_4_files/lecture_4_12_0.png) + + + +```matlab +mesh(X,Y,Z) +``` + + +![png](lecture_4_files/lecture_4_13_0.png) + + + +```matlab +pcolor(X,Y,Z) +``` + + +![png](lecture_4_files/lecture_4_14_0.png) + + +## Functions + +So far, everything has been executed as a script, or calling a built-in function. Now we begin building our own functions. + +Functions are saved in memory (or better yet) in a folder in your path or current directory + +Example of storing function in memory + +$f(x,y) = (xy^{3}-x^{3}y)$ + + +```matlab +f= @(x,y) (x.*y.^3-x.^3.*y) +``` + + f = + + @(x,y)(x.*y.^3-x.^3.*y) + + + +```matlab +f(0.1,-0.5) +``` + + ans = + + -0.0120 + + +Here we will save a function called `my_function` as `my_function.m` + +```matlab +function [vx,vy] = my_function(x,y,t) + % Help documentation of "my_function" + % This function computes the velocity in the x- and y-directions given + % three vectors of position in x- and y-directions as a function of time + % x = x-position + % y = y-position + % t = time + % output + % vx = velocity in x-direction + % vy = velocity in y-direction + + vx=zeros(length(t),1); + vy=zeros(length(t),1); + + vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t + vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t + + vx(end) = vx(end-1); + vy(end) = vy(end-1); + +end +``` + + +```matlab +help my_function +``` + + Help documentation of "my_function" + This function computes the velocity in the x- and y-directions given + three vectors of position in x- and y-directions as a function of time + x = x-position + y = y-position + t = time + output + vx = velocity in x-direction + vy = velocity in y-direction + + + +```matlab +t=linspace(0,10,100)'; +x=t.^3; % vx = 3*t^2 +y=t.^2/2; % vy = t +[vx,vy]=my_function(x,y,t); +``` + + +```matlab +yyaxis left +plot(t(1:10:end),vx(1:10:end),'o',t,3*t.^2) +ylabel('v_{x}') +yyaxis right +plot(t(1:10:end),vy(1:10:end),'s',t, t) +ylabel('v_{y}') +xlabel('time') +``` + + +![png](lecture_4_files/lecture_4_22_0.png) + + +Now, create a new function that calls 'my_function' called, `my_caller.m` + + +```matlab +help my_caller +``` + + Help documentation of "my_caller" + This function computes the acceleration in the x- and y-directions given + three vectors of position in x- and y-directions as a function of time + x = x-position + y = y-position + t = time + output + ax = velocity in x-direction + ay = velocity in y-direction + + + +```matlab +[ax,ay]=my_caller(x,y,t); +``` + + +```matlab +yyaxis left +plot(t(1:10:end),ax(1:10:end),'o',t,6*t) +ylabel('a_{x}') +yyaxis right +plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t) +ylabel('a_{x}') +xlabel('time') +axis([0,10,0,3]) +``` + + +![png](lecture_4_files/lecture_4_26_0.png) + + + +```matlab +diff_match_dims(x,t) +``` + + Undefined function 'diff_match_dims' for input arguments of type 'double'. +  + + +```matlab + +``` diff --git a/lecture_04/lecture_4.pdf b/lecture_04/lecture_4.pdf new file mode 100644 index 0000000..db18202 Binary files /dev/null and b/lecture_04/lecture_4.pdf differ diff --git a/lecture_04/lecture_4_files/lecture_4_12_0.png b/lecture_04/lecture_4_files/lecture_4_12_0.png new file mode 100644 index 0000000..3d8bd34 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_12_0.png differ diff --git a/lecture_04/lecture_4_files/lecture_4_13_0.png b/lecture_04/lecture_4_files/lecture_4_13_0.png new file mode 100644 index 0000000..fbf56f7 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_13_0.png differ diff --git a/lecture_04/lecture_4_files/lecture_4_14_0.png b/lecture_04/lecture_4_files/lecture_4_14_0.png new file mode 100644 index 0000000..b982415 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_14_0.png differ diff --git a/lecture_04/lecture_4_files/lecture_4_22_0.png b/lecture_04/lecture_4_files/lecture_4_22_0.png new file mode 100644 index 0000000..ed48529 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_22_0.png differ diff --git a/lecture_04/lecture_4_files/lecture_4_26_0.png b/lecture_04/lecture_4_files/lecture_4_26_0.png new file mode 100644 index 0000000..df1b771 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_26_0.png differ diff --git a/lecture_04/lecture_4_files/lecture_4_7_0.png b/lecture_04/lecture_4_files/lecture_4_7_0.png new file mode 100644 index 0000000..1584226 Binary files /dev/null and b/lecture_04/lecture_4_files/lecture_4_7_0.png differ diff --git a/lecture_04/myscript.m b/lecture_04/myscript.m new file mode 100644 index 0000000..4488e0f --- /dev/null +++ b/lecture_04/myscript.m @@ -0,0 +1,11 @@ +f=100; + +for i=1:10 + g=i^2; + if f==g + fprintf('we made it\n') + else + fprintf('not yet\n') + end +end + diff --git a/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb b/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb new file mode 100644 index 0000000..2fd6442 --- /dev/null +++ b/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_05/lecture_05.ipynb b/lecture_05/lecture_05.ipynb new file mode 100644 index 0000000..c04b9f5 --- /dev/null +++ b/lecture_05/lecture_05.ipynb @@ -0,0 +1,208 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Good coding habits\n", + "## naming folders and files" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Stanford file naming best practices](https://library.stanford.edu/research/data-management-services/data-best-practices/best-practices-file-naming)\n", + "\n", + "1. Include information to distinguish file name e.g. project name, objective of function, name/initials, type of data, conditions, version of file, \n", + "2. if using dates, use YYYYMMDD, so the computer organizes by year, then month, then day\n", + "3. avoid special characters e.g. !, #, \\$, ...\n", + "4. avoid using spaces if not necessary, some programs consider a space as a break in code use dashes `-` or underscores `_` or CamelCase" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Commenting your code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Its important to comment your code to mention what a variable's units are, what the function is supposed to do, etc. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "function i=code(j)\n", + " % Example of bad variable names and bad function name\n", + " for w=1:j\n", + " i(w)=w;\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'code' is a command-line function\n", + "\n", + " Example of bad variable names and bad function name\n", + "\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 ' 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 code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choose variable names that describe the variable" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "function count_vector=counting_function(max_value)\n", + " % Good variable names and better help documentation\n", + " % \n", + " % counting function creates a vector from 1 to max_value where each index, i, is \n", + " % stored in each vector spot\n", + " for i=1:max_value\n", + " count_vector(i)=i; % set each element in count_vector to i\n", + " end\n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'counting_function' is a command-line function\n", + "\n", + " Good variable names and better help documentation\n", + " \n", + " counting function creates a vector from 1 to max_value where each index, i, is \n", + " stored in each vector spot\n", + "\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 ' 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 counting_function" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Putting it all together" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Clone your homework_1 to your computer\n", + "2. open Matlab (cli, jupyter or gui)\n", + "3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\\Users\\rcc02007\\Documents\\Github\\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`\n", + "4. You have already created your first script `myscript.m` (if not see lecture_4)\n", + "5. Run `>> my_script.m`\n", + "6. Create a new m-file called nitrogen_pressure.m\n", + "7. Create a function based upon the ideal gas law for nitrogen, Pv=RT\n", + " 1. R=0.2968 kJ/(kg-K)\n", + " 2. inputs to function are v (specific volume m^3/kg), and T, temperature (K)\n", + " 3. output is P, pressure (kPa)\n", + "8. Once the function works, commit the change to the repository (add a message, like 'added file nitrogen_pressure.m'\n", + "9. After file is 'committed', 'push' the changes to your github account\n", + "\n", + "for the command-line git user, this is steps 8 and 9:\n", + "1. `$ git add *`\n", + "2. `$ git commit -m 'added file nitrogen_pressure.m'`\n", + "3. `$ git push -u origin master\n", + " Username for 'https://github.uconn.edu':rcc02007 \n", + " Password for 'https://rcc02007@github.uconn.edu': `\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_05/lecture_05.md b/lecture_05/lecture_05.md new file mode 100644 index 0000000..e0bea24 --- /dev/null +++ b/lecture_05/lecture_05.md @@ -0,0 +1,110 @@ + +# Good coding habits +## naming folders and files + +[Stanford file naming best practices](https://library.stanford.edu/research/data-management-services/data-best-practices/best-practices-file-naming) + +1. Include information to distinguish file name e.g. project name, objective of function, name/initials, type of data, conditions, version of file, +2. if using dates, use YYYYMMDD, so the computer organizes by year, then month, then day +3. avoid special characters e.g. !, #, \$, ... +4. avoid using spaces if not necessary, some programs consider a space as a break in code use dashes `-` or underscores `_` or CamelCase + +## Commenting your code + +Its important to comment your code to mention what a variable's units are, what the function is supposed to do, etc. + + + +```octave +function i=code(j) + % Example of bad variable names and bad function name + for w=1:j + i(w)=w; + end +end +``` + + +```octave +help code +``` + + 'code' is a command-line function + + Example of bad variable names and bad function name + + + Additional help for built-in functions and operators is + available in the online version of the manual. Use the command + 'doc ' to search the manual index. + + Help and information about Octave is also available on the WWW + at http://www.octave.org and via the help@octave.org + mailing list. + + +## Choose variable names that describe the variable + + +```octave +function count_vector=counting_function(max_value) + % Good variable names and better help documentation + % + % counting function creates a vector from 1 to max_value where each index, i, is + % stored in each vector spot + for i=1:max_value + count_vector(i)=i; % set each element in count_vector to i + end +end +``` + + +```octave +help counting_function +``` + + 'counting_function' is a command-line function + + Good variable names and better help documentation + + counting function creates a vector from 1 to max_value where each index, i, is + stored in each vector spot + + + Additional help for built-in functions and operators is + available in the online version of the manual. Use the command + 'doc ' to search the manual index. + + Help and information about Octave is also available on the WWW + at http://www.octave.org and via the help@octave.org + mailing list. + + +## Putting it all together + +1. Clone your homework_1 to your computer +2. open Matlab (cli, jupyter or gui) +3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\Users\rcc02007\Documents\Github\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')` +4. You have already created your first script `myscript.m` (if not see lecture_4) +5. Run `>> my_script.m` +6. Create a new m-file called nitrogen_pressure.m +7. Create a function based upon the ideal gas law for nitrogen, Pv=RT + 1. R=0.2968 kJ/(kg-K) + 2. inputs to function are v (specific volume m^3/kg), and T, temperature (K) + 3. output is P, pressure (kPa) +8. Once the function works, commit the change to the repository (add a message, like 'added file nitrogen_pressure.m' +9. After file is 'committed', 'push' the changes to your github account + +for the command-line git user, this is steps 8 and 9: + +1. `$ git add *` +2. `$ git commit -m 'added file nitrogen_pressure.m'` +3. `$ git push -u origin master + Username for 'https://github.uconn.edu':rcc02007 + ` + + + +```octave + +``` diff --git a/lecture_05/lecture_05.pdf b/lecture_05/lecture_05.pdf new file mode 100644 index 0000000..b125659 Binary files /dev/null and b/lecture_05/lecture_05.pdf differ diff --git a/lecture_05/octave-workspace b/lecture_05/octave-workspace new file mode 100644 index 0000000..1ca4b38 Binary files /dev/null and b/lecture_05/octave-workspace differ