From d16475b51a3e8608db006246a5ef57d6a079239e Mon Sep 17 00:00:00 2001 From: "Ryan C. 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100644 05_consistent coding/lecture_05_files/lecture_05_11_0.png delete mode 100644 05_consistent coding/lecture_05_files/lecture_05_25_0.png delete mode 100644 05_consistent coding/q1.png delete mode 100644 05_consistent coding/q2.png diff --git "a/01_Introduction/\340\204\264\001" "b/01_Introduction/\340\204\264\001" deleted file mode 100644 index e69de29..0000000 diff --git "a/01_Introduction/\360\006\336\001" "b/01_Introduction/\360\006\336\001" deleted file mode 100644 index e69de29..0000000 diff --git a/02_Roundoff-Truncation errors/README.md b/02_Roundoff-Truncation errors/README.md deleted file mode 100644 index 12365ce..0000000 --- a/02_Roundoff-Truncation errors/README.md +++ /dev/null @@ -1,174 +0,0 @@ - -# Solution to Form #1 - - -```octave -[1,2,3]*[1;2;3] -``` - - ans = - - 14 - - - - -```octave -[1,2,3]*[1;2;3]=? -``` - - -```octave - -``` - -# The first source of error is roundoff error -## Just storing a number in a computer requires rounding - - -```octave -fprintf('realmax = %1.20e\n',realmax) -fprintf('realmin = %1.20e\n',realmin) -fprintf('maximum relative error = %1.20e\n',eps) - -``` - - realmax = 1.79769313486231570815e+308 - realmin = 2.22507385850720138309e-308 - maximum relative error = 2.22044604925031308085e-16 - - - -```octave -s=1; -for i=1:1000 - s=s+eps/10; -end -s==1 -``` - - ans = 1 - - -# Freefall Model (revisited) -## Octave solution (will run same on Matlab) - -Set default values in Octave for linewidth and text size - - -```octave -%plot --format svg -``` - - -```octave -set (0, "defaultaxesfontname", "Helvetica") -set (0, "defaultaxesfontsize", 18) -set (0, "defaulttextfontname", "Helvetica") -set (0, "defaulttextfontsize", 18) -set (0, "defaultlinelinewidth", 4) -``` - -Define time from 0 to 12 seconds with `N` timesteps -function defined as `freefall` - - -```octave -function [v_analytical,v_terminal,t]=freefall(N) - t=linspace(0,12,N)'; - c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c); - - v_analytical = v_terminal*tanh(g*t/v_terminal); - v_numerical=zeros(length(t),1); - delta_time =diff(t); - for i=1:length(t)-1 - v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i); - end - % Print values near 0,2,4,6,8,10,12 seconds - indices = round(linspace(1,length(t),7)); - fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n') - fprintf('-----------------------------------------------\n') - M=[t(indices),v_analytical(indices),v_numerical(indices)]; - fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)'); - plot(t,v_analytical,'-',t,v_numerical,'o-') -end - -``` - - -```octave -[v_analytical,v_terminal,t]=freefall(120); -``` - - time (s)|vel analytical (m/s)|vel numerical (m/s) - ----------------------------------------------- - 0.0 | 0.00 | 0.00 - 2.0 | 18.76 | 18.82 - 4.0 | 32.64 | 32.80 - 6.1 | 40.79 | 40.97 - 8.0 | 44.80 | 44.94 - 10.0 | 46.84 | 46.93 - 12.0 | 47.77 | 47.82 - - - -![svg](output_13_1.svg) - - -# Types of error -## Freefall is example of "truncation error" -### Truncation error results from approximating exact mathematical procedure - -We approximated the derivative as $\delta v/\delta t\approx\Delta v/\Delta t$ - -Can reduce error by decreasing step size -> $\Delta t$=`delta_time` - -## Another example of truncation error is a Taylor series (or Maclaurin if centered at a=0) - -Taylor series: -$f(x)=f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+\frac{f'''(a)}{3!}(x-a)^{3}+...$ - -We can approximate the next value in a function by adding Taylor series terms: - -|Approximation | formula | -|---|-------------------------| -|$0^{th}$-order | $f(x_{i+1})=f(x_{i})+R_{1}$ | -|$1^{st}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+R_{2}$ | -|$2^{nd}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\frac{f''(x_{i})}{2!}h^{2}+R_{3}$| -|$n^{th}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\frac{f''(x_{i})}{2!}h^{2}+...\frac{f^{(n)}}{n!}h^{n}+R_{n}$| - -Where $R_{n}=\frac{f^{(n+1)}(\xi)}{(n+1)!}h^{n+1}$ is the error associated with truncating the approximation at order $n$. - -The $n^{th}$-order approximation estimates that the unknown function, $f(x)$, is equal to an $n^{th}$-order polynomial. - -In the Freefall example, we estimated the function with a $1^{st}$-order approximation, so - -$v(t_{i+1})=v(t_{i})+v'(t_{i})(t_{i+1}-t_{i})+R_{1}$ - -$v'(t_{i})=\frac{v(t_{i+1})-v(t_{i})}{t_{i+1}-t_{i}}-\frac{R_{1}}{t_{i+1}-t_{i}}$ - -$\frac{R_{1}}{t_{i+1}-t_{i}}=\frac{v''(\xi)}{2!}(t_{i+1}-t_{i})$ - -or the truncation error for a first-order Taylor series approximation is - -$\frac{R_{1}}{t_{i+1}-t_{i}}=O(\Delta t)$ - - -1. digital representation of a number is rarely exact - -2. arithmetic (+,-,/,\*) causes roundoff error - - -```octave -fprintf('%1.20f\n',double(pi)) -fprintf('%1.20f\n',single(pi)) -``` - - 3.14159265358979311600 - 3.14159274101257324219 - - - -```octave - -``` diff --git a/02_Roundoff-Truncation errors/lecture_02.pdf b/02_Roundoff-Truncation errors/lecture_02.pdf deleted file mode 100644 index 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0fb2c92..0000000 --- a/03_Intro to matlab-octave/file.txt +++ /dev/null @@ -1,5 +0,0 @@ -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/03_Intro to matlab-octave/lecture_03.md b/03_Intro to matlab-octave/lecture_03.md deleted file mode 100644 index ce76e7f..0000000 --- a/03_Intro to matlab-octave/lecture_03.md +++ /dev/null @@ -1,1447 +0,0 @@ - -# Matlab basic use -## 1- the environment, path and working directory - -Matlab 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 - 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/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 0.00000 -0.01200 -0.02100 -0.02400 -0.01800 0.00000 - 0.00960 0.00600 0.00000 -0.00600 -0.00960 -0.00840 0.00000 0.01800 - 0.00300 0.00240 0.00000 -0.00240 -0.00300 0.00000 0.00840 0.02400 - 0.00000 0.00060 0.00000 -0.00060 0.00000 0.00300 0.00960 0.02100 - -0.00060 0.00000 0.00000 0.00000 0.00060 0.00240 0.00600 0.01200 - 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 - 0.00060 -0.00000 0.00000 0.00000 -0.00060 -0.00240 -0.00600 -0.01200 - -0.00000 -0.00060 0.00000 0.00060 0.00000 -0.00300 -0.00960 -0.02100 - -0.00300 -0.00240 0.00000 0.00240 0.00300 0.00000 -0.00840 -0.02400 - -0.00960 -0.00600 0.00000 0.00600 0.00960 0.00840 0.00000 -0.01800 - -0.02100 -0.01200 0.00000 0.01200 0.02100 0.02400 0.01800 0.00000 - -0.03840 -0.02100 0.00000 0.02100 0.03840 0.04860 0.04800 0.03300 - -0.06300 -0.03360 0.00000 0.03360 0.06300 0.08400 0.09240 0.08400 - -0.09600 -0.05040 0.00000 0.05040 0.09600 0.13200 0.15360 0.15600 - -0.13860 -0.07200 0.00000 0.07200 0.13860 0.19440 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 - 0.38400 0.35700 0.28800 0.17100 0.00000 - - - - -```matlab -contour(X,Y,Z) -``` - - -![svg](output_63_0.svg) - - - -```matlab -mesh(X,Y,Z) -``` - - -![svg](output_64_0.svg) - - - -```matlab -pcolor(X,Y,Z) -``` - - -![svg](output_65_0.svg) - - -## diff --git a/03_Intro to matlab-octave/output_58_0.png b/03_Intro to matlab-octave/output_58_0.png deleted file mode 100644 index 1737c765d3f41f26bd77bb971b0f5a0e1a064238..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 17421 zcmb`vby!vH*DgBgMTZCok^%zKseq&)Ez(LYK)O^qB&3y8DFqSfkPamTML+}u=|-iy zK|tV)^}fIFoc-;y|M>pc>$=`oS)53LbRc|8qz1zr|CJ8KqA3wJw1*N2X7yez6NR{YXNlXP%A8|HY$ht?ME z_O320diKuNh_EQ1nuQCWu%M6xi;$qCsFr(`#+ zsKm1(Q9PT!EgoP|620ZJs(xbNTrhM(S^e&Jw4{8qaXaaX5oIlnV?q5p zhTnER)D*?U?{A~&P+U*X-6JJzl8to>OpRZ&X;hWjXd;vFI^1^n*6z0PVWG;=*_i__ zbG}W)3k&`XWr;_Spi2}g2+~Z5Vn>jlxVZ30?qg#UBFI&&U|a-A3zCE9rX|M$$6x;E z@N@rz!zmWs%5Ja~ynC0Z!md*=@cp0H=xA!Y;#WA2V=+!acJ{sYSjJk{>5{@i2PY?| 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -1 - - - - - - - - - -0.5 - - - - - - - - - 0 - - - - - - - - - 0.5 - - - - - - - - - 1 - - - - - - - - - -1 - - - - - - - - - -0.5 - - - - - - - - - 0 - - - - - - - - - 0.5 - - - - - - - - - 1 - - - - - - \ No newline at end of file diff --git a/04_intro to m-files/lecture_4.md b/04_intro to m-files/lecture_4.md deleted file mode 100644 index dd549aa..0000000 --- a/04_intro to m-files/lecture_4.md +++ /dev/null @@ -1,339 +0,0 @@ - -## 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) - -Questions from last class: -- I downloaded GitHub to my desktop but I cannot sign into my UConn account like I can online. -- I checked my grades on HuskyCt recently and I received a 0 / 100 for Homework 1. -- It is very hard to tell if what I'm doing on github is right or wrong. -- How often will be using our laptops during the lecture? -- How many frogs would it take to 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/04_intro to m-files/lecture_4.pdf b/04_intro to m-files/lecture_4.pdf deleted file mode 100644 index db182024f65059b9b875cfb18267872e05710ced..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 152101 zcmc$_bySsKv@X06l#mWVKtQ^?8w57pf+*ccDcztTt+aG^NlBM5{TK9LNpCj|z^H;NC*N{{$pCE~b zUJMwKd?DTFAoj}VVQLg%ZXD6;H)30scZ;e}=i 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