.. _basicPlot: Basic Line Plots ==================================== .. include:: ../replace.txt MathWorks has prepared a lot of documentation and videos on plotting, so some links to their documentation follows. Here is an introductory `video demonstrating line plotting `_. Documentation on `2-D Graph and customize lines `_. Documentation on `2-D and 3-D plots `_. Documentation on the `linespec portion of a plot command `_. MathWork's *MATLAB Fundamentals* course [FUNDAMENTALS]_ has a good introduction to creating plots. .. _plot2D: Basic Plotting Notes -------------------------- The Plot Tool is easy to use, however, using commands and functions allows for easier reproduction of plots and more automation. Use the ``plot(x, y)`` function to plot vector ``y`` against vector ``x``. The number of elements in ``x`` and ``y`` must be the same. If only a single vector is passed to ``plot``, then the index values of the vector are used for the :math:`x`--axis. Use an additional argument to the ``plot`` function specifying a color code to change the color of the data curve. The following command will plot `y` versus `x` in magenta. :: >> plot(x, y, 'm') Some other color codes are: * `'b'` blue * `'g'` green * `'r'` red * `'c'` cyan * `'k'` black Line style codes are used if you want something other than a solid line. The following command will plot `y` versus `x` with a dotted line. :: >> plot(x,y,':') Some other line style codes are: * ``'-'`` solid * ``'--'`` dashed * ``'-.'`` dash-dot You can combine these codes. Generally, the order does not matter, so both of the following commands make a plot using a red dotted line. :: >> plot(x, y, 'r:') >> plot(x, y, ':r') In addition to color and line style, you can specify a marker style. The following command will plot `y` versus `x` using asterisks. :: >> plot(x,y,'*') Some other marker style codes are: * `'.'` points * `'o'` circles * `'x'` crosses * `'+'` plus sign * `'s'` square * `'d'` diamond * `'^'` upward-pointing triangle * `'v'` downward-pointing triangle Did you notice that there is no longer a line? If you specify a marker, the default line style is none. Add a dash (``-``) to the marker style to also plot a line. The ``grid`` command adds or removes a grid to your plot:: >> grid on >> grid off .. index:: grid Annotating Plots ------------------- Labels are added to plots using plot annotation functions such as ``xlabel``, ``ylabel``, and ``title``. The input to these functions must be text. Traditionally, the textual data was entered as a *character array* made with characters and digits inside a pair of ``'apostrophes'`` (single quotation marks). |M| now allows text labels that are the newer *string arrays* made with characters and digits inside a pair of ``"quotation marks"``. The text may be a simple textual constant or be held in a variable. See :ref:`strings` for more information on textual data. :: >> xlabel('Text Label for X-Axis') % a text constant >> ylabel(yAxisName) % a text variable If you need more than one line in an axis label or title, use a cell array created with a pair of curly brackets ``{}``. :: >> title({'first line', 'second line'}) LaTeX markup formatting may be used in the annotations. Thus, ``x^2`` will become :math:`x^2` and ``x_2`` becomes :math:`x_2`. LaTeX markup is a default standard for mathematical equations. You can search the Internet and find good documentation on formatting LaTeX math equations. Other symbols, such as Greek letters, can also be added, such as :math:`\Delta`, :math:`\gamma`, and :math:`\pi`. See `MATLAB LaTeX support of Greek letters and special characters `_. Try the following code to see what happens. :: >> xlabel('\sigma \approx e^{\pi/2}') If you need to use a symbol such as an underscore (``_``) or a backslash (``\``) , then preface it with the escape character ``\``. Thus, to display ``\``, you must type ``\\``. The |M| ``text`` function adds a text annotation to a specified position on the plot. See the |M| documentation for ``text``. :: >> text(3, 5, 'Best result') .. index:: text (plotting) Starting a New Plot --------------------- .. index:: figure You may notice your plot being replaced when you enter a new plot command after making a previous plot. Use the ``figure`` command to keep the previous plot and start over in a new window. Multiple Plots in the Same Figure ---------------------------------- .. index:: subplot Several small plots may be put in a figure. The `subplot(m, n, p)` function accomplishes this by making a grid of :math:`m{\times}n` plots. The variable `p` is the plot number from 1 to :math:`m\,\times\,n`. The plot for the following code is shown in :numref:`fig:subplot`. :: >> x = linspace(-5, 5); >> subplot(2, 2, 1), plot(x, x), title('y = x') >> subplot(2, 2, 2), plot(x, x.^2), title('y = x^2') >> subplot(2, 2, 3), plot(x, x.^3), title('y = x^3') >> subplot(2, 2, 4), plot(x, x.^4), title('y = x^4') .. _fig:subplot: .. figure:: subplot.png :align: center :width: 60% Plots created using subplots. With |M| release R2019b, enhanced subplots were introduced with the ``tiledlayout`` function. As with ``subplot``, a fixed layout grid of tiled plots is simple to create. .. index:: tiledlayout :: >> tiledlayout(2, 2); .. index:: nexttile The ``nexttile`` command is used to advance to the next plot. Several new features were added beyond the capabilities of subplots. * Figures may now have a global ``title``, ``xlabel``, and ``ylabel`` for the set of plots. * The size and spacing between tiles is adjustable. The following commands reduce the spacing between tiles and the padding between the edges of the figure and the grid of tiles. The net effect is to increase the size of the individual plots. :: t = tiledlayout(3, 3); t.TileSpacing = 'compact'; t.Padding = 'compact'; * Specifying the size and location of tiles can create a custom layout. This is done by passing a tile number and an optional range of tiles to be used to ``nexttile``. In the following example, a :math:`3{\times}3` grid of tiles is created. Then 3 plots are added across the first row. Starting at tile 4, the whole second row is filled with the next plot, which spans a :math:`1{\times}3` set of tiles. The third row has a single tile plot and a :math:`1{\times}2` tile plot. This plot, with its simple data, is shown in :numref:`fig:tiles`. :: >> x = linspace(-2,2); >> tiledlayout(3,3) >> nexttile, plot(x,x) >> nexttile, plot(x,x) >> nexttile, plot(x,x) >> nexttile(4, [1 3]), plot(x,x) >> nexttile(7), plot(x,x) >> nexttile(8, [1 2]), plot(x,x) * The layout of the plots may be adjusted with each ``nexttile`` command. This is done with the ``'flow'`` option to ``tiledlayout``. The first plot fills the whole figure. After the second plot, two stacked plots are shown. As each tile is added, the layout of tiles is adjusted to accommodate the new tile. This can make for a nice demonstration showing successive changes to data. Run the code from the ``sawTooth.m`` file to see this. Successive plots show the Fourier series of a sawtooth wave as each new sine wave is added. The user presses the ``Enter`` key when they are ready to see the next plot. The final tiled figure with six plots is shown in :numref:`fig:sawtooth`. .. note:: Sawtooth wave Fourier Series The sawtooth wave is a frequently used periodic waveform used in various electrical circuits including music synthesizers. The Fourier series for a sawtooth wave with amplitude of 1 and period of :math:`L` is given by: .. math:: f(t) = \frac{1}{2} - \frac{1}{\pi} \sum_{n = 1}^{\infty} \frac{1}{n} \sin(2\,\pi\,n\,t/L) .. _fig:tiles: .. figure:: tiles.png :align: center :width: 60% Tiled plots with a custom layout. :: % File: sawTooth.m % Plots of the Fourier series of a sawtooth function % displayed using a tiledlayout. Each time through % the loop, a new plot is added. clear; close all L = 5; N = 200; t = linspace(0, 2*L, N); s = zeros(1, N); figure plt = tiledlayout('flow'); title(plt, 'Sawtooth Fourier Series') for n = 1:6 nexttile s = s + sin(2*pi*n*t/L)/n; f = 0.5 - s/pi; plot(t, f, 'k', 'LineWidth', 2) title(['n = ', num2str(n)]) if n < 6 disp('Press enter for next plot') pause end end .. _fig:sawtooth: .. figure:: sawtooth.png :align: center :width: 60% Final sawtooth plots with six tiles. .. _multiCurvePlot: Multiple Plots on the Same Axis --------------------------------- .. index:: hold on, hold off, plot matrix data Visualizations are often be more informative when multiple data sets are plotted on the same axis. To add new plots onto an existing axis without replacing the previous plot, use the ``hold on`` command. When you are done adding plots, issue the ``hold off`` command. Then, unless a new figure is started, the next plotting command issued will replace what is currently in the figure. Another way to plot multiple data sets onto a single axis is to put the :math:`y`--axes values in a matrix. Each column of the matrix will be a different plot. The following simple examples illustrate both methods. See :numref:`fig:multi-line` for the plot. :: >> x = linspace(0,10); >> Y = zeros(100,3); >> Y(:,1) = x; >> Y(:,2) = 2*x; >> Y(:,3) = 3*x; >> plot(x, Y) :: >> y1 = x; >> y2 = 2*x; >> y3 = 3*x; >> hold on >> plot(x, y1, 'k') >> plot(x, y2, 'k:') >> plot(x, y3, 'k-.') >> hold off >> xlabel('x'), ylabel('y') >> legend('y = x', 'y = 2x', 'y = 3 x', 'Location', 'northwest') >> title('Multi-line Plot') .. _fig:multi-line: .. figure:: multi-line.png :align: center :width: 60% Figure with multiple plots Adding a Plot Legend --------------------- .. index:: plot legend, legend A legend helps identify what data each plot in the graph correspond to. The order of legend labels matters -- the inputs to ``legend`` should be in the same order in which the plots were drawn. :: legend('first label','second label') The ``legend`` function also accepts two optional arguments: the keyword ``'Location'`` and a text description of the location that is given by a compass direction, such as ``'north'`` (top center) or ``'southwest'`` (lower left). The default location for the legend is ``'northeast'`` (top right). :: legend('Trucks','Cars','Location','west') 2-D Plot Types ----------------- |M| supports several types of two dimensional plots. Six types of plots other than basic line plots, which we have used in several examples, are described below. Example code to make these plots is also listed below and :numref:`fig:Plots2D` shows what the plots look like. .. describe:: Scatter Plot ``scatter(x, y)``: Scatter plot with variable marker size and color. Example shown in :numref:`fig:Plots2D` (a). .. index:: scatter plot .. describe:: Bar graph ``bar(x, y)``: Bar graph (vertical and horizontal). Example shown in :numref:`fig:Plots2D` (b). .. index:: bar graph .. describe:: Stem plot ``stem(x, y)``: A discrete sequence plot -- each point is plotted with a marker and a vertical line to the :math:`x`--axis. Example shown in :numref:`fig:Plots2D` (c). .. index:: stem plot .. describe:: Stair step plot ``stairs(x, y)``: The lines on the plot are either horizontal or vertical, resembling the run and rise of stairs. Example shown in :numref:`fig:Plots2D` (d). .. index:: stair step plot .. describe:: Pie chart ``pie([0.4 0.3 0.2 0.1], labels)``: The values of the data are passed as a vector that often sums to 1; otherwise, |M| will calculate the percentages. The labels of the pie slices should be in a cell array. Example shown in :numref:`fig:Plots2D` (e). .. index:: pie chart .. describe:: Filled area plot ``area(x, [y1; y2])``: Plot multiple data sets with the area between the :math:`x`--axis and each data curve shaded a different color. Each data set is a row of a matrix passed as the :math:`y` data. Example shown in :numref:`fig:Plots2D` (f). .. index:: area plot :: % File: Plots2D.m % Some 2-D plotting examples x = linspace(0, 2, 10); y = 5 + x.^2; y2 = 5 + x; plts = tiledlayout(3, 3); plts.TileSpacing = 'compact'; plts.Padding = 'compact'; title(plts, '2-D Plots'); nexttile, scatter(x, y, 'ko'), title('(a) Scatter Plot'); nexttile, bar(x, y, 'k'), title('(b) Bar Chart'); nexttile, stem(x, y, 'k'), title('(c) Stem Plot'); nexttile, stairs(x, y, 'k'), title('(d) Stairs Plot'); labels = {'excellent', 'good', 'fair', 'poor'}; nexttile(5, [2 2]), pie([0.4 0.3 0.2 0.1], labels) title('(e) Pie Chart') newcolors = [0.7 0.7 0.7; 0.2 0.2 0.2]; % make grayscale nexttile(7), area(x, [y2; y]'), title('(f) Area Plot'); colororder(newcolors) .. _fig:Plots2D: .. figure:: Plots2D.png :align: center :width: 60% Common types of 2-D plots other than line plots. Axis Control --------------- .. index:: axis, ylim, xlim, daspect The ``axis`` command returns a 4 element row vector containing the :math:`x`-- and :math:`y`--axis limits. :: >> v = axis v = 10 20 1 5 Use the functions ``xlim`` and ``ylim`` to set the :math:`x`-- and :math:`y`--axis limits. Both functions take a vector of two elements as input. For example, the following command sets the lower :math:`y`--axis limit to 2 and the upper :math:`y`--axis limit to 4. :: >> ylim([2 4]) When the lower or upper range of the data falls between the limits that |M| picked, the data may not fill the :math:`x`--axis. Use the ``axis tight`` command to change the limits based on the range of the data. For plots depicting geometry, we would like the :math:`x`--, :math:`y`--, and :math:`z`--axes to have the same scale. There are two ways to accomplish this. The ``axis`` command has an ``equal`` option that sets the scale of each axis to be the same. We can also set the aspect ratio to be the same for each axis with the ``daspect`` function, which takes a vector with three values, even for 2-D plots. :: >> axis equal % Set the axes scales to be the same >> % % or >> daspect([1 1 1]) % Another way to accomplish the same .. _ticks: Tick Marks and Labels ------------------------- .. index:: tick marks, yticks, xticks, xticklabels, yticklabels |M| generally does a good job of setting the tick marks on a plot. The tick labels are by default the numeric values of the tick marks. We sometimes what to change the labels and locations of the tick marks because certain points on the axis have significance. A good example of this is when plotting equations that use trigonometry functions. The ``xticks`` and ``yticks`` functions take vectors of numeric locations for the tick marks. The ``xticklabels`` and ``yticklabels`` functions take cell arrays of textual data. See :ref:`strings` for more information on cell arrays. The following code illustrates custom tick marks and labels on the :math:`x`--axis. Notice also that the title uses the ``texlabel`` function to format strings with LaTeX to match an equation. The plot is shown in :numref:`fig:plotTicks`. :: x = linspace(pi/4, 5*pi/4); figure, plot(x, 4 - 4*sin(2*x - pi/2)) txt = texlabel('f(x) = 4 - 4*sin(2*x - pi/2)'); title(txt), ylabel('f(x)'), xlabel('x') xticks(linspace(pi/4, 5*pi/4, 5)) xticklabels({'\pi/4', '\pi/2', '3\pi/4','\pi', '5\pi/4'}); axis tight .. _fig:plotTicks: .. figure:: plotTicks.png :align: center :width: 60% Sine wave with TeX formated :math:`x`--axis tick marks and title. .. _fplot: Fplots ----------- |M| includes another 2-D plotting function that comes in handy when working with either function handles, anonymous functions, or symbolic math functions. (see :ref:`function-handles` and :ref:`symbODE`) The plot, annotations, and options are the same as with the ``plot`` function that we have used before. However, instead of passing vectors for the :math:`x` and :math:`y` data, we give ``fplot`` a function and a range of values for the :math:`x`--axis, or accept the default :math:`x`--axis range of -5 to 5. In addition to being convenient when working with function handles or symbolic math functions, ``fplot`` also correctly handles plotting difficulties, such as data discontinuities. A good example of this as shown in :numref:`fig-tanFplot` comes from the trigonometric tangent function. :: >> fplot(@(x) tan(x), [0 2*pi]) .. _fig-tanFplot: .. figure:: tanFplot.png :align: center :width: 60% The ``fplot`` function handles the data discontinuities of the tangent function. .. note:: Now work on :ref:`HomeRunHW`. .. raw:: latex \clearpage