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(___,Name,Value)

loglog(ax,___)

lineobj = loglog(___)

Description

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 the 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) specifies line style, marker, and color.

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

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

lineobj = loglog(___) returns a Line object or an array of Line objects. Use lineobj 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

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

character vector | string

Line style, marker, and color, specified as a character vector or string 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
-	Solid line
--	Dashed line
:	Dotted line
-.	Dash-dot line

Marker	Description
'o'	Circle
'+'	Plus sign
'*'	Asterisk
'.'	Point
'x'	Cross
'_'	Horizontal line
'|'	Vertical line
's'	Square
'd'	Diamond
'^'	Upward-pointing triangle
'v'	Downward-pointing triangle
'>'	Right-pointing triangle
'<'	Left-pointing triangle
'p'	Pentagram
'h'	Hexagram

Color	Description
y	yellow
m	magenta
c	cyan
r	red
g	green
b	blue
w	white
k	black

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 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 quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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 character vector or a string scalar 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. Thus, 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 character vector or a string scalar 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. Thus, 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 character vector or a string scalar 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. Thus, 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™.

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).