DATA PLOTTING WITH MATLAB

Transcription

1 DATA PLOTTING WITH MATLAB Prof. Marco Pilotti Dr. Giulia Valerio Giulia Valerio 7Marzo

2 1. WHY MATLAB? WHY MATLAB? Matlab is a high-level programming language that provides a numerical computing environment for algorithms development, data visualization and data analysis The use of Matlab is more appropriate in the following cases: If you have to evaluate large amounts of data that are acquired automatically by means of computers and other technical appliances. If you want to develop general programmed data evaluation routines to be applied to different set of data. The application of these routines is a more efficient way if the evaluation procedure has to be changed over and over again to 'fine-tune' it. Re-calculating the whole data set with the changed procedure is then done in a snap. If you need graphics functions and dedicated statistics functions as well as other interesting features which are not available in other software packages. 2

3 1. WHY MATLAB? At the end of this lesson you will be able to ps_solve/player.html 3

4 2. MATLAB ENVIRONMENT MATLAB ENVIRONMENT THE USER INTERFACE Introduction to Matlab 5. Matlab's help system is an indispensable aid for beginners as well 4. The «Workspace» as experienced is the working users. It makes a memory of Matlab. printed It manual stores unnecessary. the used Here you variables on which can programs also find DEMOS, operate.. the on-line tutorials. Otherwise, see 1. The «Command Window» area is the communication channel between 2. In the the user window and the «Command Matlab program. History» Here, you commands can be entered, 3. The «Current and programs Directory» can output browser results is used and messages. to access the Warnings, computer's find the commands you have entered error file messages system. and There, the you like can are select also shown the current here. In directory the Command for data throughout the current session in the Window, previously storage entered as well as commands the root can directory be repeated for the with editor. command window. the keys <arrow up> and <arrow down>, and then changed and re-executed. 4

5 3. MATLAB FUNDAMENTALS COMMANDS SINGLE COMMANDS in the Command window GROUPS OF COMMANDS in the Matlab editor Introduction to Matlab SCRIPTS You have to type any valid command in the Matlab editor and then save the script as Namefile.m. Back in the Command window, typing Namefile Matlab will execute all the commands written in Nomefile.m Notes: %. to make comments a = 3; without ; shows the variables in the Command window; without doesn t 5

6 4. DATA MANIPULATION PRACTICE Today we will plot some of the data measured by the monitoring station active on Lake Iseo, showing some peculiar aspect of the thermal and hydrodynamic behaviour of this water body 6

7 3. MATLAB FUNDAMENTALS READING AND DEFINING VARIABLES A variable is MATRIX, with elements identified by their position EXTRACT SINGLE ELEMENTS rv1(2) read the second element of the vector m1(2, 3) read the element of the matrix m1 in the 2nd row and 3th column m1(end, 3:4) read the element of the matrix m1 in the last row, 3th and 4th column EXTRACTSINGLE ELEMENTS AND CREATE NEW VAR FUNCTION datenum m2 = m1(2, 3) read back the element of the matrix in the 2nd row and 3th column and assign it to a new variable m2 datenum([aaaa mm dd hh mi ss]) converts a date to a single number [days] that matlab uses to manage time series of data. aaaa is the year, mm is the month, dd is the day, hh is the hour, mi is the minute and ss is the second 7

8 3. MATLAB FUNDAMENTALS READING AND DEFINING VARIABLES 8

9 3. MATLAB FUNDAMENTALS IMPORTING DATA A. Import through the IMPORT WIZAD A1. In the Current folder go to the directory of interest A2. Select the file and right click on Import A3. Specify the Import parameters A4. You will se the data in the Workspace B. Import PROGRAMMATICALLY B1. cd Nomepath B2. new_var = importdata( Nomefile.txt ) new_var = importdata(filename, delimiter, nheaderlines); B3. You will se the new_var in the Workspace Editing >> doc fileformats you will see the help page where to find more about the supported filetypes and how to extract them 9

10 3. MATLAB FUNDAMENTALS A. Saving MANUALLY from the workspace A1. Select with the CNTR-key A2. Right-click on one of the variable and select Save as A3. Specify the folder and the Nomefile.mat B. Saving PROGRAMMATICALLY Save(filename) stores all variables from the current workspace in a MATLAB formatted binary file (MAT-file) called filename Introduction to Matlab save(filename, variables) stores only the specified variables. Matlab FIGURES can be saved into.fig files or exported as.tif.jpg file see Figure File- Export set up 10

11 3. MATLAB FUNDAMENTALS SAVING AND LOADING DATA Matlab DATA can be easily stored into formatted binary.mat files 11

12 3. MATLAB FUNDAMENTALS PRACTICE We want to analyze the hydrodynamic conditions that were observed between 01 and 10 August 2011 in Lake Iseo. Load the data by by following the instructions in the data.m script. Select the directory where you saved the files Import the temperature.txt file and meteo.txt with the data set measured by the floating station. Meteo.txt includes air temperature, wind and radiation data as a function of time. Temperature.txt include the water temperature data measured at 21 depths as a function of time Extract the series of time, windspeed, winddirection, temperature and depth in variables called wspeed, wdir, temp and depth. Keep on the workspace only these last variables and save them as a Iseo.mat file 12

13 2D PLOTTING FUNCTIONS 4. DATA PLOTTING MATLAB FOR DATA PLOTTING VISUALIZING DATA - OVERVIEW 13

14 3D PLOTTING FUNCTIONS 4. DATA PLOTTING VISUALIZING DATA - OVERVIEW 14

15 4. DATA PLOTTING VISUALIZING DATA FIGURE PROPERTIES figure create a figure window clf clear the contents of a figure window close, close all close figure(s) hold on, hold off fixate graph, or release fixation subplot create or address sub-figures Introduction to Matlab set(gcf, 'property', parameter); gcf = get current figure handle Change the properties of a figure window by means of argument pairs, such as: Name, Color, Position, Toolbar, Visible 15

16 4. DATA PLOTTING VISUALIZING DATA PLOT TOOLS plot(x1,y1,...,xn,yn) plots each vector Yn versus vector Xn on the same axes. If one of Yn or Xn is a matrix and the other is a vector, it plots the vector versus the matrix row or column with a matching dimension to the vector. If Xn is a scalar and Yn is a vector, it plots discrete Yn points vertically at Xn. If Xn or Yn are matrices, they must be 2-D and the same size, and the columns of Yn are plotted against the columns of Xn. plot(...,'propertyname',propertyvalue,...) manipulates plot characteristics You can find all the properties at: Among them, the following are particularly useful: LineStyle: the style of the line (standard, dotted, dashed etc.) LineWidth : the width of the line Marker: the style of the data point markers (dot, circle, triangle, star ) Color : the color of the curve 16

17 4. DATA PLOTTING VISUALIZING DATA PLOT TOOLS Example: plot(x1,y1, LineStyle, -, Color,'b','Linewidth',2) = plot(x1,y1, -b,'linewidth',2) 17

18 4. DATA PLOTTING VISUALIZING DATA FIGURE AXES xlabel, ylabel, zlabel label an axis datetick label the axis with a data format (e.g. 01 Jul 2011) grid on, grid off show or hide the grid axis on, axis off show or hide the axes axis([xmin xmax ymin ymax]) set axis limits axis equal impose the same scale for the axis Introduction to Matlab set(gca, 'property', parameter); gca = get current axeshandle Change the properties of an axes (see ) Among them, the following are particularly useful: FontName, FontSize, XLim, Ylim, Xlabel, Ylabel, Xtick, Ytick Example: set(gca, 'Xtick',0:0.5:8,'Ytick',0:0.5:6,'FontName', Arial','FontSize',10); 18

19 4. DATA MANIPULATION PRACTICE Create a figure (Figure1) that shows the temperature profile T(z) measured the beginning and at the end of the period of interest, by following the instructions in the profile.m script. Use two different colors and a solid line with circles. The vertical axis must be limited between 0 and -50m and spaced every 5m and must have z (m) as label. The vertical axis must be limited between 5 and 30m and spaced every 5 C and must have T ( C) as label. Use Arial 10 as font. Add the lagend. Once the figure has been created, modify the dimension of the plot, fix the resolution of the figure as 300 dpi. Save the figures both as Profile.fig and Profile.tif file. 19

20 4. DATA MANIPULATION PRACTICE Create a figure (Figure 2) that shows the meteorological conditions in the period of interest by following the instructions in the meteo.m script. It should include 2 subplots for a) wind speed c) wind direction Plot wind speed with a continuous lines and wind direction with dots. Choose the line and marker sizes, axis label and ticks that you find more suitable to obtain an effective plot. Use the function datetick to label the x axis with a data format Once the figure has been created, modify the dimension of the plot, fix the resolution of the figure as 300 dpi and save the figures both as Meteo.fig and Meteo.tif file. 20

21 4. DATA PLOTTING VISUALIZING DATA 2D PLOTS contour(x,y,z,v) A contour plot displays isolines of matrix Z. contour(x,y,z) draw contour plots of Z using X and Y to determine the x- and y-axis limits. It is possible to specify contour levels in the monotonically increasing vector v. The number of contour levels is equal to length(v). contourf(x,y,z,v) contourf(x,y,z) draws a filled contour plot of matrix Z. colormap(jet) sets the colormap to the matrix according to a certain built-in Matlab colorbar colorbar isplays the current colormap in the current figure caxis([cmin cmax]) sets the color limits to specified minimum and maximum values. Data values less than cmin or greater than cmax map to cmin and cmax, respectively. 21

22 4. DATA PLOTTING VISUALIZING DATA 2D PLOTS quiver(x,y,u,v) Quiver A quiver plot displays velocity vectors as arrows with components (u,v) at the points (x,y). quiver(...,scale) automatically scales the arrows to fit within the grid and then stretches them by the factor scale. streamline(x,y,u,v,startx,starty) Streamline draws streamlines from 2-D vector data. The arrays X, Y, which define the coordinates for U, V, must be monotonic, but do not need to be uniformly spaced. X, Y, must have the same number of elements, as if produced by meshgrid. startx, starty define the starting positions of the streamlines 22

23 4. DATA MANIPULATION PRACTICE Create a figure (Figure 3) that shows the temperature field as a function of time and depth, drawing a contour line every 1 C. Follow the contour.m script as a guide. Depth is in y axis, time is in the x axis and the color refers to the temperature values. The vertical axis must be limited between 0 and 50m and spaced every 5m and must have z (m) as label. The horizontal axis must be limited between 01/08 to 10/08, be spaced every day and have time as label. Use the function datetick to label the x axis with a data format. Add the grid, the title and the colourmap. Once the figure has been created, fix the resolution of the figure as 300 dpi and save the figures both as Meteo.fig and Meteo.tif file. 23

24 4. DATA MANIPULATION LET S PRACTICE Through a numerical model, we set up a simulation of the entrance of Oglio river (Q=50m 3 /s; T = 15 C) in Lake Iseo during the stratified season. The river s plume intrudes at about 10m depth. Accordingly, we have extracted the velocity field (u and v components) at -10m depth. The matrixes in the Inflow_path.mat file include: the x and y coordinates, the u and y components of the velocity and the lake depth z for each point of the grid. Load the data and create a figure (Figure 4) that shows the contour of the water speed (vel) superimposed to the velocity vector field, following the inflow.m script. Choose the scale of the vector that assures a good visibility of the velocity field. Superimpose the streamline traced from the Oglio inlet and zoom the figure in the area around the Oglio inlet. Save the figure 24

25 4. DATA PLOTTING VISUALIZING DATA 3D PLOTS plot3(x1,y1,z1) plot3(x1,y1,z1,...), where X1, Y1, Z1 are vectors or matrices, plots one or more lines in threedimensional space through the points whose coordinates are the elements of X1, Y1, and Z1. quiver3(x,y,z,u,v,w) quiver3(x,y,z,u,v,w) plots vectors with components (u,v,w) at the points (x,y,z). The matrices x,y,z,u,v,w must all be the same size and contain the corresponding position and vector components. surf(x,y,z) Surf(X,Y,Z) uses Z for the color data and surface height. X and Y are vectors or matrices defining the x and y components of a surface. If X and Y are vectors, length(x) = n and length(y) = m, where [m,n] = size(z). 25

26 4. DATA MANIPULATION PRACTICE Use the previous data to create a figure (Figure 5) that shows the bathymetry of lake Iseo superimposed to the Oglio vectors located at -10m depth 26