loglog

Log-log scale plot

• 

Syntax

loglog(X,Y)

loglog(X,Y,LineSpec)

loglog(X1,Y1,...,Xn,Yn)

loglog(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn)

loglog(Y)

loglog(Y,LineSpec)

loglog(tbl,xvar,yvar)

loglog(tbl,yvar)

loglog(ax,___)

loglog(___,Name,Value)

p = loglog(___)

Description

Vector and Matrix Data

loglog(X,Y) plots x- and y-coordinates using a base-10 logarithmic scale on the x-axis and the y-axis.

• To plot a set of coordinates connected by line segments, specify X and Y as vectors of the same length.

• To plot multiple sets of coordinates on the same set of axes, specify at least one of X or Y as a matrix.

loglog(X,Y,LineSpec) creates the plot using the specified line style, marker, and color.

loglog(X1,Y1,...,Xn,Yn) plots multiple pairs of x- and y-coordinates on the same set of axes. Use this syntax as an alternative to specifying coordinates as matrices.

loglog(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn) assigns specific line styles, markers, and colors to each x-y pair. You can specify LineSpec for some x-y pairs and omit it for others. For example, loglog(X1,Y1,'o',X2,Y2) specifies markers for the first x-y pair but not for the second pair.

loglog(Y) plots Y against an implicit set of x-coordinates.

• If Y is a vector, the x-coordinates range from 1 to length(Y).

• If Y is a matrix, the plot contains one line for each column in Y. The x-coordinates range from 1 to the number of rows in Y.

If Y contains complex numbers, loglog plots the imaginary part of Y versus the real part of Y. However, if you specify both X and Y, MATLAB^® ignores the imaginary part.

loglog(Y,LineSpec) plots Y using implicit x-coordinates, and specifies the line style, marker, and color.

Table Data

loglog(tbl,xvar,yvar) plots the variables xvar and yvar from the table tbl. To plot one data set, specify one variable for xvar and one variable for yvar. To plot multiple data sets, specify multiple variables for xvar, yvar, or both. If both arguments specify multiple variables, they must specify the same number of variables. (since R2022a)

loglog(tbl,yvar) plots the specified variable from the table against the row indices of the table. Timetables are not supported for this syntax. (since R2022a)

Additional Options

loglog(ax,___) displays the plot in the target axes. Specify the axes as the first argument in any of the previous syntaxes.

loglog(___,Name,Value) specifies Line properties using one or more name-value arguments. The properties apply to all the plotted lines. Specify the name-value arguments after all the arguments in any of the previous syntaxes. For a list of properties, see Line Properties.

p = loglog(___) returns a Line object or an array of Line objects. Use p to modify properties of the plot after creating it. For a list of properties, see Line Properties.

Examples

Plot One Line

Define x as a vector of 50 logarithmically spaced numbers on the interval [${10}^{-1},{10}^2$]. Define y as $2^{\mathit{x}}$. Then plot x and y, and call the grid function to show the grid lines.

x = logspace(-1,2);
y = 2.^x;
loglog(x,y)
grid on

Plot Multiple Lines

Create a vector of x-coordinates and two vectors of y-coordinates. Plot two lines by passing comma-separated x-y pairs to loglog.

x = logspace(-1,2);
y1 = 10.^x;
y2 = 1./10.^x;
loglog(x,y1,x,y2)
grid on

Alternatively, you can create the same plot with one x-y pair by specifying y as a matrix: loglog(x,[y1;y2]).

Specify Axis Labels and Tick Values

Create a set of x- and y-coordinates and display them in a log-log plot.

x = logspace(-1,2,10000);
y = 5 + 3*sin(x);
loglog(x,y)

Call the yticks function to position the y-axis tick values at whole number increments along the y-axis. Then create x- and y-axis labels by calling the xlabel and ylabel functions.

yticks([3 4 5 6 7])
xlabel('x')
ylabel('5 + 3 sin(x)')

Plot Points as Markers Without Lines

Create a set of x- and y-coordinates and display them in a log-log plot. Specify the line style as 's' to display square markers without connecting lines. Specify the marker fill color as the RGB triplet [0 0.447 0.741], which corresponds to a dark shade of blue.

x = logspace(-1,2,20);
y = 10.^x;
loglog(x,y,'s','MarkerFaceColor',[0 0.447 0.741])
grid on

Add a Legend

Create two sets of x- and y-coordinates and display them in a log-log plot. Display a legend in the upper left corner of the plot by calling the legend function and specifying the location as 'northwest'.

x = logspace(-1,2,10000);
y1 = 5 + 3*sin(x/4);
y2 = 5 - 3*sin(x/4);
loglog(x,y1,x,y2,'--')
legend('Signal 1','Signal 2','Location','northwest')

Specify y-Coordinates Only

When you specify only one coordinate vector, loglog plots those coordinates against the values 1:length(y). For example, define y as a vector of 6 values between 0.001 and 100. Create a log-log plot of y.

y = [0.001 0.01 0.1 1 10 100];
loglog(y)
grid on

If you specify y as a matrix, the columns of y are plotted against the values 1:size(y,1). For example, define y as a 5-by-3 matrix and pass it to the loglog function. The resulting plot contains 3 lines, each of which has x-coordinates that range from 1 to 5.

y = [0.0010    0.0100    0.1000
     0.0100    0.1000    1.0000
     0.1000    1.0000   10.0000
     1.0000   10.5000  100.0000
    10.0000  100.0000 1000.0000];

loglog(y)
grid on

Plot Coordinates from a Table

Since R2022a

A convenient way to plot data from a table is to pass the table to the loglog function and specify the variables to plot.

Create a table containing two variables. Then display the first three rows of the table.

Input = logspace(-1,2)';
Output = 10.^Input;
tbl = table(Input,Output);
head(tbl,3)

     Input     Output
    _______    ______

        0.1    1.2589
    0.11514    1.3036
    0.13257     1.357

Plot the Input variable on the x-axis and the Output variable on the y-axis. Return the Line object as p, and turn the axes grid on. Notice that the axis labels match the variable names.

p = loglog(tbl,"Input","Output");
grid on

To modify aspects of the line, set the LineStyle, Color, and Marker properties on the Line object. For example, change the line to a red dotted line with point markers.

p.LineStyle = ":";
p.Color = "red";
p.Marker = ".";

Plot Multiple Table Variables on One Axis

Since R2022a

Create a table containing three variables. Then display the first three rows in the table.

Input = logspace(-1,2)';
Output1 = 10.^Input;
Output2 = 1./10.^Input;
tbl = table(Input,Output1,Output2);
head(tbl,3)

     Input     Output1    Output2
    _______    _______    _______

        0.1    1.2589     0.79433
    0.11514    1.3036     0.76711
    0.13257     1.357     0.73693

Plot the Input variable on the x-axis and the Output1 and Output2 variables on the y-axis. Add a legend. Notice that the legend labels match the variable names.

loglog(tbl,"Input",["Output1" "Output2"])
grid on
legend

Specify Target Axes

Create a tiled chart layout in the 'flow' tile arrangement, so that the axes fill the available space in the layout. Next, call the nexttile function to create an axes object and return it as ax1. Then display a log-log plot by passing ax1 to the loglog function.

tiledlayout('flow')
ax1 = nexttile;
x = logspace(-1,2);
y1 = 10.^x;
loglog(ax1,x,y1)

Repeat the process to create a second axes object and a second log-log plot.

ax2 = nexttile;
y2 = 1./10.^x;
loglog(ax2,x,y2)

Change Line Characteristics After Plotting

Create a log-log plot containing two lines, and return the line objects in the variable lg.

x = logspace(-1,2);
y1 = 10.^x;
y2 = 1./10.^x;
lg = loglog(x,y1,x,y2);

Change the width of the first line to 2, and change the color of the second line to purple.

lg(1).LineWidth = 2;
lg(2).Color = [0.4 0 1];

Input Arguments

X — x-coordinates

scalar | vector | matrix

x-coordinates, specified as a scalar, vector, or matrix. The size and shape of X depends on the shape of your data and the type of plot you want to create. This table describes the most common situations.

Type of Plot	How to Specify Coordinates
Single point	Specify X and Y as scalars and include a marker. For example: loglog(1,2,'o')
One set of points	Specify X and Y as any combination of row or column vectors of the same length. For example: loglog([1 2 3],[4; 5; 6])
Multiple sets of points (using vectors)	Specify consecutive pairs of X and Y vectors. For example: loglog([1 2 3],[4 5 6],[1 2 3],[7 8 9])
Multiple sets of points (using matrices)	If all the sets share the same x- or y-coordinates, specify the shared coordinates as a vector and the other coordinates as a matrix. The length of the vector must match one of the dimensions of the matrix. For example: loglog([1 2 3],[4 5 6; 7 8 9]) If the matrix is square, loglog plots one line for each column in the matrix. Alternatively, specify X and Y as matrices of equal size. In this case, loglog plots each column of Y against the corresponding column of X. For example: loglog([1 2 3; 4 5 6],[7 8 9; 10 11 12])

loglog might exclude coordinates in some cases:

• If the coordinates include positive and negative values, only the positive values are displayed.

• If the coordinates are all negative, all of the values are displayed on a log scale with the appropriate sign.

• Zero values are not displayed.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Y — y-coordinates

scalar | vector | matrix

y-coordinates, specified as a scalar, vector, or matrix. The size and shape of Y depends on the shape of your data and the type of plot you want to create. This table describes the most common situations.

Type of Plot	How to Specify Coordinates
Single point	Specify X and Y as scalars and include a marker. For example: loglog(1,2,'o')
One set of points	Specify X and Y as any combination of row or column vectors of the same length. For example: loglog([1 2 3],[4; 5; 6])
Multiple sets of points (using vectors)	Specify consecutive pairs of X and Y vectors. For example: loglog([1 2 3],[4 5 6],[1 2 3],[7 8 9])
Multiple sets of points (using matrices)	If all the sets share the same x- or y-coordinates, specify the shared coordinates as a vector and the other coordinates as a matrix. The length of the vector must match one of the dimensions of the matrix. For example: loglog([1 2 3],[4 5 6; 7 8 9]) If the matrix is square, loglog plots one line for each column in the matrix. Alternatively, specify X and Y as matrices of equal size. In this case, loglog plots each column of Y against the corresponding column of X. For example: loglog([1 2 3; 4 5 6],[7 8 9; 10 11 12])

loglog might exclude coordinates in some cases:

• If the coordinates include positive and negative values, only the positive values are displayed.

• If the coordinates are all negative, all of the values are displayed on a log scale with the appropriate sign.

• Zero values are not displayed.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

LineSpec — Line style, marker, and color

string scalar | character vector

Line style, marker, and color, specified as a string scalar or character vector containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics (line style, marker, and color). For example, if you omit the line style and specify the marker, then the plot shows only the marker and no line.

Example: "--or" is a red dashed line with circle markers.

Line Style	Description	Resulting Line
"-"	Solid line
"--"	Dashed line
":"	Dotted line
"-."	Dash-dotted line

Marker	Description	Resulting Marker
"o"	Circle
"+"	Plus sign
"*"	Asterisk
"."	Point
"x"	Cross
"_"	Horizontal line
"|"	Vertical line
"square"	Square
"diamond"	Diamond
"^"	Upward-pointing triangle
"v"	Downward-pointing triangle
">"	Right-pointing triangle
"<"	Left-pointing triangle
"pentagram"	Pentagram
"hexagram"	Hexagram

Color Name	Short Name	RGB Triplet	Appearance
"red"	"r"	[1 0 0]
"green"	"g"	[0 1 0]
"blue"	"b"	[0 0 1]
"cyan"	"c"	[0 1 1]
"magenta"	"m"	[1 0 1]
"yellow"	"y"	[1 1 0]
"black"	"k"	[0 0 0]
"white"	"w"	[1 1 1]

tbl — Source table

table | timetable

Source table containing the data to plot, specified as a table or a timetable.

xvar — Table variables containing x-coordinates

character vector | string array | cell array | pattern | numeric scalar or vector | logical vector | vartype()

Table variables containing the x-coordinates, specified using one of the indexing schemes from the table.

Indexing Scheme	Examples
Variable names: A string, character vector, or cell array. A pattern object.	"A" or 'A' — A variable named A ["A","B"] or {'A','B'} — Two variables named A and B "Var"+digitsPattern(1) — Variables named "Var" followed by a single digit
Variable index: An index number that refers to the location of a variable in the table. A vector of numbers. A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing 0 or false values.	3 — The third variable from the table [2 3] — The second and third variables from the table [false false true] — The third variable
Variable type: A vartype subscript that selects variables of a specified type.	vartype("categorical") — All the variables containing categorical values

The table variables you specify can contain any numeric values. However, loglog might exclude negative and zero values from the plot in the same way as it does when you specify X and Y as vectors containing negative or zero values.

If xvar and yvar both specify multiple variables, the number of variables must be the same.

Example: loglog(tbl,["x1","x2"],"y") specifies the table variables named x1 and x2 for the x-coordinates.

Example: loglog(tbl,2,"y") specifies the second variable for the x-coordinates.

Example: loglog(tbl,vartype("numeric"),"y") specifies all numeric variables for the x-coordinates.

yvar — Table variables containing y-coordinates

character vector | string array | cell array | pattern | numeric scalar or vector | logical vector | vartype()

Table variables containing the y-coordinates, specified using one of the indexing schemes from the table.

Indexing Scheme	Examples
Variable names: A string, character vector, or cell array. A pattern object.	"A" or 'A' — A variable named A ["A","B"] or {'A','B'} — Two variables named A and B "Var"+digitsPattern(1) — Variables named "Var" followed by a single digit
Variable index: An index number that refers to the location of a variable in the table. A vector of numbers. A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing 0 or false values.	3 — The third variable from the table [2 3] — The second and third variables from the table [false false true] — The third variable
Variable type: A vartype subscript that selects variables of a specified type.	vartype("categorical") — All the variables containing categorical values

The table variables you specify can contain any numeric values. However, loglog might exclude negative and zero values from the plot in the same way as it does when you specify X and Y as vectors containing negative or zero values.

If xvar and yvar both specify multiple variables, the number of variables must be the same.

Example: loglog(tbl,"x",["y1","y2"]) specifies the table variables named y1 and y2 for the y-coordinates.

Example: loglog(tbl,"x",2) specifies the second variable for the y-coordinates.

Example: loglog(tbl,"x",vartype("numeric")) specifies all numeric variables for the y-coordinates.

ax — Target axes

Axes object

Target axes, specified as an Axes object. If you do not specify the axes and if the current axes is Cartesian, then loglog uses the current axes.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: loglog([1 2],[3 4],'Color','red') specifies a red line for the plot.

Note

The properties listed here are only a subset. For a complete list, see Line Properties.

Color — Color

[0 0.4470 0.7410] (default) | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

Color, specified as an RGB triplet, a hexadecimal color code, a color name, or a short name. The color you specify sets the line color. It also sets the marker edge color when the MarkerEdgeColor property is set to 'auto'.

For a custom color, specify an RGB triplet or a hexadecimal color code.

• 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, [0.4 0.6 0.7].

• A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
"red"	"r"	[1 0 0]	"#FF0000"
"green"	"g"	[0 1 0]	"#00FF00"
"blue"	"b"	[0 0 1]	"#0000FF"
"cyan"	"c"	[0 1 1]	"#00FFFF"
"magenta"	"m"	[1 0 1]	"#FF00FF"
"yellow"	"y"	[1 1 0]	"#FFFF00"
"black"	"k"	[0 0 0]	"#000000"
"white"	"w"	[1 1 1]	"#FFFFFF"
"none"	Not applicable	Not applicable	Not applicable	No color

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	"#0072BD"
[0.8500 0.3250 0.0980]	"#D95319"
[0.9290 0.6940 0.1250]	"#EDB120"
[0.4940 0.1840 0.5560]	"#7E2F8E"
[0.4660 0.6740 0.1880]	"#77AC30"
[0.3010 0.7450 0.9330]	"#4DBEEE"
[0.6350 0.0780 0.1840]	"#A2142F"

LineWidth — Line width

0.5 (default) | positive value

Line width, specified as a positive value in points, where 1 point = 1/72 of an inch. If the line has markers, then the line width also affects the marker edges.

The line width cannot be thinner than the width of a pixel. If you set the line width to a value that is less than the width of a pixel on your system, the line displays as one pixel wide.

MarkerSize — Marker size

6 (default) | positive value

Marker size, specified as a positive value in points, where 1 point = 1/72 of an inch.

MarkerEdgeColor — Marker outline color

"auto" (default) | RGB triplet | hexadecimal color code | "r" | "g" | "b" | ...

Marker outline color, specified as "auto", an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of "auto" uses the same color as the Color property.

For a custom color, specify an RGB triplet or a hexadecimal color code.

• 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, [0.4 0.6 0.7].

• A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
"red"	"r"	[1 0 0]	"#FF0000"
"green"	"g"	[0 1 0]	"#00FF00"
"blue"	"b"	[0 0 1]	"#0000FF"
"cyan"	"c"	[0 1 1]	"#00FFFF"
"magenta"	"m"	[1 0 1]	"#FF00FF"
"yellow"	"y"	[1 1 0]	"#FFFF00"
"black"	"k"	[0 0 0]	"#000000"
"white"	"w"	[1 1 1]	"#FFFFFF"
"none"	Not applicable	Not applicable	Not applicable	No color

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	"#0072BD"
[0.8500 0.3250 0.0980]	"#D95319"
[0.9290 0.6940 0.1250]	"#EDB120"
[0.4940 0.1840 0.5560]	"#7E2F8E"
[0.4660 0.6740 0.1880]	"#77AC30"
[0.3010 0.7450 0.9330]	"#4DBEEE"
[0.6350 0.0780 0.1840]	"#A2142F"

MarkerFaceColor — Marker fill color

"none" (default) | "auto" | RGB triplet | hexadecimal color code | "r" | "g" | "b" | ...

Marker fill color, specified as "auto", an RGB triplet, a hexadecimal color code, a color name, or a short name. The "auto" option uses the same color as the Color property of the parent axes. If you specify "auto" and the axes plot box is invisible, the marker fill color is the color of the figure.

For a custom color, specify an RGB triplet or a hexadecimal color code.

• 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, [0.4 0.6 0.7].

• A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
"red"	"r"	[1 0 0]	"#FF0000"
"green"	"g"	[0 1 0]	"#00FF00"
"blue"	"b"	[0 0 1]	"#0000FF"
"cyan"	"c"	[0 1 1]	"#00FFFF"
"magenta"	"m"	[1 0 1]	"#FF00FF"
"yellow"	"y"	[1 1 0]	"#FFFF00"
"black"	"k"	[0 0 0]	"#000000"
"white"	"w"	[1 1 1]	"#FFFFFF"
"none"	Not applicable	Not applicable	Not applicable	No color

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	"#0072BD"
[0.8500 0.3250 0.0980]	"#D95319"
[0.9290 0.6940 0.1250]	"#EDB120"
[0.4940 0.1840 0.5560]	"#7E2F8E"
[0.4660 0.6740 0.1880]	"#77AC30"
[0.3010 0.7450 0.9330]	"#4DBEEE"
[0.6350 0.0780 0.1840]	"#A2142F"

Tips

• Use NaN or Inf to create breaks in the lines. For example, this code plots a line with a break between y=2 and y=4.

   loglog([1 2 3 4 5],[1 2 NaN 4 5])

• The loglog function uses colors and line styles based on the ColorOrder and LineStyleOrder properties of the axes. loglog cycles through the colors with the first line style. Then, it cycles through the colors again with each additional line style.

  You can change the colors and the line styles after plotting by setting the ColorOrder or LineStyleOrder properties on the axes. You can also call the colororder function to change the color order for all the axes in the figure.

Algorithms

The loglog function plots coordinates on a log scale by setting the XScale and YScale properties of the axes to 'log'. However, if the axes hold state is 'on' before you call loglog, those properties do not change, and the plot might display on a linear or semilog scale.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The loglog function supports GPU array input with these usage notes and limitations:

• This function accepts GPU arrays, but does not run on a GPU.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

• This function operates on distributed arrays, but executes in the client MATLAB.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2022b: Plots created with tables preserve special characters in axis and legend labels

When you pass a table and one or more variable names to the loglog function, the axis and legend labels now display any special characters that are included in the table variable names, such as underscores. Previously, special characters were interpreted as TeX or LaTeX characters.

For example, if you pass a table containing a variable named Sample_Number to the loglog function, the underscore appears in the axis and legend labels. In R2022a and earlier releases, the underscores are interpreted as subscripts.

Release	Label for Table Variable "Sample_Number"
R2022b
R2022a

To display axis and legend labels with TeX or LaTeX formatting, specify the labels manually. For example, after plotting, call the xlabel or legend function with the desired label strings.

xlabel("Sample_Number")
legend(["Sample_Number" "Another_Legend_Label"])

R2022a: Pass tables directly to loglog

Create plots by passing a table to the loglog function followed by the variables you want to plot. When you specify your data as a table, the axis labels and the legend (if present) are automatically labeled using the table variable names.