2D Plotting with Matlab

Transcription

1 GEEN 1300 Introduction to Engineering Computing Class Meeting #22 Monday, Nov. 9 th Engineering Computing and Problem Solving with Matlab 2-D plotting with Matlab Script files User-defined functions Matlab s built-in solvers Section Test 2 graded, handed back in lab this week grade distribution and solution posted on CULearn Homework #8, VBA project assignment, due this Wednesday Homework #9, posted, due Wednesday, Nov. 18 th CULearn grades will be updated later this week 2D Plotting with Matlab Matlab creates figure windows for plots Plotting commands are in 3 categories: figure window management plot generation plot characteristics Figure window management figure(1) create figure window number 1 if a figure window does not exist, the plot command will create one automatically you create a new figure window to preserve the plots in any existing figure windows 1

2 Figure window management (cont d) break the figure into a 2-by-2 matrix of subplots and select the first subplot, counted by rows subplot(2,2,1) zoom zoom(2) hold on turn on mouseselected zoom zoom the current plot by a factor of 2 keep the existing curves and points on the current plot used for adding information to an existing plot Plot generation plot command used most of the time color codes line styles marker styles plot(1,2, gs ) plot a green square at coordinates x=1, y=2 plot([ ],[1.5 1], k: ) plot a straight line from coordinates (0.5,0.5) to (1.5,1), using a black dotted line style 2

3 Useful supporting functions axis( [ xmin xmax ymin ymax ] ) force the axis scaling to given ranges theta = linspace(0,2*pi,50) create a vector of 50 equally-spaced values from 0 to 2 (if you leave the 50 out, 100 is the default) nearly the same as: theta = 0 : 2*pi/50 : 2*pi freq = logspace(-2,2,100) create a vector of 100 values from 10-2 to 10 2 spaced equally according to the log 10 of the values Customizing plot characteristics grid turn on grid lines xlabel( x ) ylabel( y ) label the x axis label the y axis title( Ralphie V, 11/09/09 ) add a plot title text(2,1, YoBubba! ) add a text annotation at coordinates (2,1) axis equal force the x and y axis ranges to be equal 3

4 Plotting functions and families of functions Plotting data and model curves Form of curve suggests fitting a polynomial, perhaps cubic 4

5 Fitting the model curve 3 2 y x x x Adding the fitted curve to the plot User-defined functions same role as in Excel/VBA create using the Matlab Editor Example: a function to calculate the volume of liquid (V) in a spherical tank, given the depth of the liquid (h) and the radius (R) V R h How would the function be used? V = SphereTank(R,h) V 2 h 3R h 3 5

6 Use the Matlab Editor to create the function and save the function (in a convenient place like D:\) as SphereTank.m Then, use the function from the Matlab Command window We can also use algorithm structure ( if s and loops) in functions and m-scripts. This comes later. Script files like macros in Excel/VBA create a file with a.m extension using the Matlab Editor file contains a set of Matlab commands ( use to save time for oft-repeated commands ) run the M-file script by typing its name Example or Open the Matlab Editor for a new M-file 6

7 Type in the Matlab commands [ attention to the use of the ; to suppress output ] Save file ( in a convenient place, like D:\ ) as setupvdwair.m Use the m-script typing the M-file name typing the M file name causes the commands in the file to run 7

8 Matlab s built-in solvers solve what? not in this course roots of single nonlinear algebraic equations systems of linear algebraic equations systems of nonlinear algebraic equations maximum or minimum of a function optimize a function of several variables integration [ quadrature area under a curve ] ordinary differential equations (APPM 2460) partial differential equations (APPM 4660) to use (most of) these solvers, you have to write a Matlab function (using the Matlab Editor) that evaluates your equation(s) 15 Solving for the root of a nonlinear algebraic equation polynomial? use roots [been there, done that] 4 Good ole example: x f x e 2x 10 find a root of this equation near x = 1 initial estimate for x can also use fsolve 16 8

9 Solving a system of linear equations Ax b x 1 A b left divide in Matlab x = inv(a) * b or, better x = A \ b solution 17 Solving a system of nonlinear equations 2 2 x y 4 0 xy 10 Note: In the function, x(1) takes on the personality of x in the equations, and x(2) represents y. initial estimates for x and y 18 9

10 Maximum or minimum of a function in one variable Find a minimum of f x cos x cosh x 1 in the interval 0 x 5 fminbnd: find a minimum between defined bounds -- can also use fminsearch To find a maximum of g(x), set up to find minimum of g(x) Optimize a function of several variables 2 2 Find a maximum of y 54.36st 0.94s t 12.3s 8.9t in the intervals 0 s 10 and 0 t 10 initial estimates for s and min constraints on s and t Use help fmincon to find out about these arguments

11 5 Numerical integration [ quadrature ~ area under a curve ] 0 cos x cosh x 1 dx 25 f(x)=cos(x)*cosh(x) f(x) negative area x 21 Summary of Solving Functions/Techniques root of a single nonlinear algebraic equation roots of multiple nonlinear algebraic equations solving for the roots of a set of linear algebraic equations finding the minimum (or maximum) of a function in one variable finding the minimum (or maximum) of a function of several variables integrating a known function of a single variable (area under the curve) fzero fsolve left-divide fminbnd (also fminsearch) fmincon (Optimization) quadl (also quad) 11