fplot Syntax Description Examples Plot Symbolic Expression Plot symbolic expression or function fplot(f) fplot(f,[xmin xmax])

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1 fplot Plot symbolic expression or function Syntax fplot(f) fplot(f,[xmin xmax]) fplot(xt,yt) fplot(xt,yt,[tmin tmax]) fplot(,linespec) fplot(,name,value) fplot(ax, ) fp = fplot( ) Description fplot(f) plots symbolic input f over the default interval [-5 5]. fplot(f,[xmin xmax]) plots f over the interval [xmin xmax]. fplot(xt,yt) plots xt = x(t) and yt = y(t) over the default range of t, which is [ 5 5]. example example example fplot(xt,yt,[tmin tmax]) plots xt = x(t) and yt = y(t) over the specified range [tmin tmax]. fplot(,linespec) uses LineSpec to set the line style, marker symbol, and line color. fplot(,name,value) specifies line properties using one or more Name,Value pair arguments. Use this option with any of the input argument combinations in the previous syntaxes. Name,Value pair settings apply to all the lines plotted. To set options for individual lines, use the objects returned by fplot. example example fplot(ax, ) plots into the axes specified by ax instead of the current axes gca. fp = fplot( ) returns a function line object or parameterized line object, depending on the type of plot. Use the object to query and modify properties of a specific line. For details, see FunctionLine Properties and ParameterizedFunctionLine Properties. example Examples Plot Symbolic Expression Plot tan(x) over the default range of [-5 5]. fplot shows poles by default. For details, see the ShowPoles argument in Name-Value Pair Arguments. syms x fplot(tan(x))

2 Plot Symbolic Function Plot the symbolic function over the default range [-5 5]. syms f(x) f(x) = cos(x); fplot(f)

3 Plot Parametric Curve Plot the parameteric curve and. syms t x = cos(3*t); y = sin(2*t); fplot(x,y)

4 Specify Plotting Interval Plot over by specifying the plotting interval as the second input to fplot. syms x fplot(sin(x),[-pi/2 pi/2])

5 Plot Multiple Lines on Same Figure You can plot multiple lines either by passing the inputs as a vector or by using hold on to successively plot on the same figure. If you specify LineSpec and Name-Value arguments, they apply to all lines. To set options for individual plots, use the function handles returned by fplot. Divide a figure into two subplots using subplot. On the first subplot, plot and using vector input. On the second subplot, plot and using hold on. syms x subplot(2,1,1) fplot([sin(x) cos(x)]) title('multiple Lines Using Vector Inputs') subplot(2,1,2) fplot(sin(x)) hold on fplot(cos(x)) title('multiple Lines Using hold on Command') hold off Change Line Properties and Display Markers Plot three sine curves with a phase shift between each line. For the first line, use a linewidth of 2. For the second, specify a dashed red line style with circle markers. For the third, specify a cyan, dash-dot line style with asterisk markers. Display the legend. syms x fplot(sin(x+pi/5),'linewidth',2) hold on

6 fplot(sin(x-pi/5),'--or') fplot(sin(x),'-.*c') legend('show','location','best') hold off Control Resolution of Plot Control the resolution of a plot by using the MeshDensity option. Increasing MeshDensity can make smoother, more accurate plots, while decreasing it can increase plotting speed. Divide a figure into two by using subplot. In the first subplot, plot a step function from x = 2.1 to x = The plot's resolution is too low to detect the step function. Fix this issue by increasing MeshDensity to 39 in the second subplot. The plot now detects the step function and shows that by increasing MeshDensity you increased the plot's resolution. syms x stepfn = rectangularpulse(2.1, 2.15, x); subplot(2,1,1) fplot(stepfn); title('default MeshDensity = 23') subplot(2,1,2) fplot(stepfn,'meshdensity',39); title('increased MeshDensity = 39')

7 Modify Plot After Creation Plot sin(x). Specify an output to make fplot return the plot object. syms x h = fplot(sin(x)) h = FunctionLine with properties: Function: [1x1 sym] Color: [ ] LineStyle: '-' LineWidth: Show all properties

8 Change the default blue line to a dashed red line by using dot notation to set properties. Similarly, add 'x' markers and set the marker color to blue. h.linestyle = '--'; h.color = 'r'; h.marker = 'x'; h.markeredgecolor = 'b';

9 Add Title and Axis Labels and Format Ticks For from to, plot. Add a title and axis labels. Create the x-axis ticks by spanning the x-axis limits at intervals of pi/2. Display these ticks by using the XTick property. Create x-axis labels by using arrayfun to apply texlabel to S. Display these labels by using the XTickLabel property. To use LaTeX in plots, see latex. syms x fplot(sin(x),[-2*pi 2*pi]) grid on title('sin(x) from -2\pi to 2\pi') xlabel('x') ylabel('y') ax = gca; S = sym(ax.xlim(1):pi/2:ax.xlim(2)); ax.xtick = double(s); ax.xticklabel = arrayfun(@texlabel,s,'uniformoutput',false);

10 Re-evaluation on Zoom When you zoom into a plot, fplot re-evaluates the plot automatically. This re-evaluation on zoom reveals hidden detail at smaller scales. Plot x^3*sin(1/x) for -2 < x < 2 and < y < Zoom in on the plot using zoom and redraw the plot using drawnow. Because of re-evaluation on zoom, fplot reveals smaller-scale detail. Repeat the zoom 6 times to view smaller-scale details. To play the animation, click the image. syms x fplot(x^3*sin(1/x)); axis([ ]); for i=1:6 zoom(1.7) pause(0.5) end

11 Create Animations Create animations by changing the displayed expression using the Function, XFunction, and YFunction properties and then by using drawnow to update the plot. To export to GIF, see imwrite. By varying the variable i from 0.1 to 3, animate the parametric curve x = it sin(it) y = it cos(it). To play the animation, click the image. syms t fp = fplot(t, t); axis([ ]) for i=0.1:0.05:3 fp.xfunction = i.*t.*sin(i*t); fp.yfunction = i.*t.*cos(i*t); drawnow end

12 Input Arguments collapse all f Expression or function to plot symbolic expression symbolic function Expression or function to plot, specified as a symbolic expression or function. [xmin xmax] Plotting interval for x-coordinates [ 5 5] (default) vector of two numbers Plotting interval for x-coordinates, specified as a vector of two numbers. The default range is [-5 5]. However, if fplot detects a finite number of discontinuities in f, then fplot expands the range to show them. xt Parametric input for x-coordinates symbolic expression symbolic function Parametric input for x-coordinates, specified as a symbolic expression or function. fplot uses symvar to find the parameter. yt Parametric input for y-axis symbolic expression symbolic function Parametric input for y-axis, specified as a symbolic expression or function. fplot uses symvar to find the parameter. [tmin tmax] Range of values of parameter t [ 5 5] (default) vector of two numbers Range of values of parameter t, specified as a vector of two numbers. The default range is [-5 5]. ax Axes object axes object Axes object. If you do not specify an axes object, then fplot uses the current axes gca. LineSpec Line specification character vector string Line specification, specified as a character vector or string with a line style, marker, and color. The elements can appear in any order, and you can omit one or more options. To show only markers with no connecting lines, specify a marker and omit the line style.

13 Example: 'r--o' specifies a red color, a dashed line, and circle markers Line Style Specifier Description - Solid line (default) -- Dashed line : Dotted line -. Dash-dot line Marker Specifier o Description Circle + Plus sign * Asterisk. Point x s d ^ v Cross Square Diamond Upward-pointing triangle Downward-pointing triangle > Right-pointing triangle < Left-pointing triangle p h Color Specifier y m c r g b w k Pentagram Hexagram Description yellow magenta cyan red green blue white black Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. Example: 'Marker','o','MarkerFaceColor','red' The function line properties listed here are only a subset. For a complete list, see FunctionLine Properties. collapse all

14 'MeshDensity' Number of evaluation points 23 (default) number Number of evaluation points, specified as a number. The default is 23. Because fplot uses adaptive evaluation, the actual number of evaluation points is greater. 'ShowPoles' Display asymptotes at poles 'on' (default) 'off' Display asymptotes at poles, specified as 'on' (default) or 'off'. The asymptotes display as gray, dashed vertical lines. fplot displays asymptotes only with the fplot(f) syntax or variants, and not with the fplot(xt,yt) syntax. 'Color' Line color [ ] (default) RGB triplet 'r' 'g' 'b'... Line color, specified as an RGB triplet or one of the color options listed in the table. For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [ ]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values. Option Description Equivalent RGB Triplet 'red' or 'r' Red [1 0 0] 'green' or 'g' Green [0 1 0] 'blue' or 'b' Blue [0 0 1] 'yellow' or 'y' Yellow [1 1 0] 'magenta' or 'm' Magenta [1 0 1] 'cyan' or 'c' Cyan [0 1 1] 'white' or 'w' White [1 1 1] 'black' or 'k' Black [0 0 0] Example: 'blue' Example: [0 0 1] 'LineStyle' Line style '-' (default) '--' ':' '-.' 'none' Line style, specified as one of the line styles listed in this table. Line Style Description Resulting Line '-' '--' Solid line Dashed line

15 Line Style Description Resulting Line ':' '-.' Dotted line Dash-dotted line 'none' No line No line 'LineWidth' Line width 0.5 (default) positive value Line width, specified as a positive value in points. If the line has markers, then the line width also affects the marker edges. Example: 0.75 'Marker' Marker symbol 'none' (default) 'o' '+' '*' '.' 'x' 's' 'd'... Marker symbol, specified as one of the values in this table. By default, a line does not have markers. Add markers at selected points along the line by specifying a marker. Value 'o' '+' '*' '.' 'x' 'square' or 's' 'diamond' or 'd' '^' 'v' '>' '<' 'pentagram' or 'p' 'hexagram' or 'h' 'none' Description Circle Plus sign Asterisk Point Cross Square Diamond Upward-pointing triangle Downward-pointing triangle Right-pointing triangle Left-pointing triangle Five-pointed star (pentagram) Six-pointed star (hexagram) No markers 'MarkerEdgeColor' Marker outline color 'auto' (default) RGB triplet 'r' 'g' 'b'... Marker outline color, specified as 'auto', an RGB triplet, or one of the color options listed in the table. The default value of 'auto' uses the same color as the Color property.

16 For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [ ]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values. Option Description Equivalent RGB Triplet 'red' or 'r' Red [1 0 0] 'green' or 'g' Green [0 1 0] 'blue' or 'b' Blue [0 0 1] 'yellow' or 'y' Yellow [1 1 0] 'magenta' or 'm' Magenta [1 0 1] 'cyan' or 'c' Cyan [0 1 1] 'white' or 'w' White [1 1 1] 'black' or 'k' Black [0 0 0] 'none' No color Not applicable Example: [ ] Example: 'blue' 'MarkerFaceColor' Marker fill color 'none' (default) 'auto' RGB triplet 'r' 'g' 'b'... Marker fill color, specified as 'auto', an RGB triplet, or one of the color options listed in the table. The 'auto' value uses the same color as the MarkerEdgeColor property. For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [ ]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values. Option Description Equivalent RGB Triplet 'red' or 'r' Red [1 0 0] 'green' or 'g' Green [0 1 0] 'blue' or 'b' Blue [0 0 1] 'yellow' or 'y' Yellow [1 1 0] 'magenta' or 'm' Magenta [1 0 1] 'cyan' or 'c' Cyan [0 1 1] 'white' or 'w' White [1 1 1] 'black' or 'k' Black [0 0 0] 'none' No color Not applicable Example: [ ] Example: 'green'

17 'MarkerSize' Marker size 6 (default) positive value Marker size, specified as a positive value in points. Example: 10 Output Arguments collapse all fp One or more function or parameterized line objects scalar vector One or more function or parameterized function line objects, returned as a scalar or a vector. If you use the fplot(f) syntax or a variation of this syntax, then fplot returns function line objects. If you use the fplot(xt,yt) syntax or a variation of this syntax, then fplot returns parameterized line objects. You can use these objects to query and modify properties of a specific line. For a list of properties, see FunctionLine Properties and ParameterizedFunctionLine Properties. Tips If fplot detects a finite number of discontinuities in f, then fplot expands the range to show them. See Also Functions fcontour fimplicit fimplicit3 fmesh fplot3 fsurf Properties FunctionLine Properties ParameterizedFunctionLine Properties Topics Create Plots Introduced in R2016a

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