LogPlot

LogPlot[f,{x,xmin,xmax}]

generates a log plot of f as a function of x from xmin to xmax.

LogPlot[{f1,f2,},{x,xmin,xmax}]

plots several functions fi.

LogPlot[{,w[fi],},]

plots fi with features defined by the symbolic wrapper w.

LogPlot[,{x}reg]

takes the variable x to be in the geometric region reg.

Details and Options

  • LogPlot is also known as semi-logarithmic or semi-log plot, since it has one linear axis and one logarithmic axis.
  • LogPlot makes exponentials appear as straight lines. It allows very small and very large values to be seen at the same time.
  • LogPlot effectively generates a curve based on Log[f], but with tick marks indicating the values of the underlying function f. It visualizes the set .
  • Gaps are left at any x where the fi evaluate to anything other than positive real numbers or
    Quantity.
  • The limits xmin and xmax can be real numbers or Quantity expressions.
  • The region reg can be any RegionQ object in 1D.
  • LogPlot treats the variable x as local, effectively using Block.
  • LogPlot has attribute HoldAll and evaluates f only after assigning specific numerical values to x.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x.
  • The following wrappers w can be used for the fi:
  • Annotation[fi,label]provide an annotation for the fi
    Button[fi,action]evaluate action when the curve for fi is clicked
    Callout[fi,label]label the function with a callout
    Callout[fi,label,pos]place the callout at relative position pos
    EventHandler[fi,events]define a general event handler for fi
    Hyperlink[fi,uri]make the function a hyperlink
    Labeled[fi,label]label the function
    Labeled[fi,label,pos]place the label at relative position pos
    Legended[fi,label]identify the function in a legend
    PopupWindow[fi,cont]attach a popup window to the function
    StatusArea[fi,label]display in the status area on mouseover
    Style[fi,styles]show the function using the specified styles
    Tooltip[fi,label]attach a tooltip to the function
    Tooltip[fi]use functions as tooltips
  • Wrappers w can be applied at multiple levels:
  • w[fi]wrap the fi
    w[{f1,}]wrap a collection of fi
    w1[w2[]]use nested wrappers
  • Callout, Labeled, and Placed can use the following positions pos:
  • Automaticautomatically placed labels
    Above, Below, Before, Afterpositions around the curve
    xnear the curve at a position x
    Scaled[s]scaled position s along the curve
    {s,Above},{s,Below},relative position at position s along the curve
    {pos,epos}epos in label placed at relative position pos of the curve
  • LogPlot has the same options as Graphics, with the following additions and changes:
  • AspectRatio1/GoldenRatioratio of height to width
    AxesTruewhether to draw axes
    ClippingStyleNonewhat to draw where curves are clipped »
    ColorFunctionAutomatichow to determine the coloring of curves
    ColorFunctionScalingTruewhether to scale arguments to ColorFunction
    PlotLabelNoneoverall label for the plot
    PlotLabelsNonelabels to use for curves
    EvaluationMonitorNoneexpression to evaluate at every function evaluation
    ExclusionsAutomaticpoints in x to exclude
    ExclusionsStyleNonewhat to draw at excluded points
    FillingNonefilling to insert under each curve
    FillingStyleAutomaticstyle to use for filling
    LabelingSizeAutomaticmaximum size of callouts and labels
    MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
    MeshNonehow many mesh points to draw on each curve
    MeshFunctions{#1&}how to determine the placement of mesh points
    MeshShadingNonehow to shade regions between mesh points
    MeshStyleAutomaticthe style for mesh points
    MethodAutomaticthe method to use for refining curves
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotLegendsNonelegends for curves
    PlotPointsAutomaticinitial number of sample points
    PlotRange{Full,Automatic}the range of y or other values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyleAutomaticgraphics directives to specify the style for each curve
    PlotTheme$PlotThemeoverall theme for the plot
    RegionFunction(True&)how to determine whether a point should be included
    TargetUnitsAutomaticunits to display in the plot
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • Possible settings for ClippingStyle are:
  • Automaticuse a dotted line for the clipped portion
    Noneomit the clipped portion of the curve
    styleuse style for the clipped portion
  • Possible settings for PlotLayout that show single curves in multiple plot panels include:
  • "Column"use separate curves in a column of panels
    "Row"use separate curves in a row of panels
    {"Column",k},{"Row",k}use k columns or rows
    {"Column",UpTo[k]},{"Row",UpTo[k]}use at most k columns or rows
  • With the default settings Exclusions->Automatic and ExclusionsStyle->None, LogPlot breaks curves at discontinuities and singularities it detects. Exclusions->None joins across discontinuities and singularities.
  • Exclusions->{x1,x2,} is equivalent to Exclusions->{x==x1,x==x2,}.
  • PlotLegends->"Expressions" uses the fi as the legend text.
  • LogPlot initially evaluates f at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
  • Since only a finite number of sample points are used, it is possible for LogPlot to miss features of f. Increasing the settings for PlotPoints and MaxRecursion will often catch such features.
  • Themes that affect curves include:
  • "ThinLines"thin plot lines
    "MediumLines"medium plot lines
    "ThickLines"thick plot lines
  • The arguments supplied to functions in MeshFunctions and RegionFunction are x, y. Functions in ColorFunction are by default supplied with scaled versions of these arguments.

Examples

open allclose all

Basic Examples  (4)

Plot a function with a logarithmically scaled axis:

Plot several functions:

Label each curve:

Fill between curves:

Scope  (25)

Sampling  (7)

More points are sampled when the function changes quickly:

The plot range is selected automatically:

Ranges where the function becomes negative are excluded:

The curve is split when there are discontinuities in the function:

Use Exclusions->None to draw a connected curve:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Plot over an infinite domain with automatic ticks:

Labeling and Legending  (8)

Label curves with Labeled:

Place the labels relative to the curves:

Label curves with PlotLabels:

Place the label near the curve at an value:

Use a scaled position:

Specify the text position relative to the point:

Label curves automatically with Callout:

Place labels at specific locations:

Include legends for each curve:

Use Legended to provide a legend for a specific curve:

Use Placed to change the legend location:

Presentation  (10)

Multiple curves are automatically colored to be distinct:

Provide explicit styling to different curves:

Create legends from the functions:

Specify labels for legends:

Add labels:

Provide an interactive Tooltip for each curve:

Create filled plots:

Create an overlay mesh:

Style the curve segments between mesh points:

Use a plot theme:

Show multiple curves in a row of separate panels:

Use a column instead of a row:

Use multiple rows or columns:

Options  (81)

ClippingStyle  (4)

Omit clipped regions of the plot:

Show clipped regions with red lines:

Show clipped regions as thick at the bottom, and red at the top:

Show clipped regions as red and thick:

ColorFunction  (6)

Color by scaled coordinate and scaled coordinate, respectively:

Color with a named color scheme:

Color a curve red when its absolute coordinate is above 1:

Fill with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use a color function that is red at powers of 10:

ColorFunctionScaling  (3)

No argument scaling on the left, automatic scaling on the right:

Scaling is done on a linear scale in the original coordinates:

Use a color function that is red at powers of 10:

EvaluationMonitor  (3)

Find the list of values sampled by LogPlot:

Show where LogPlot evaluates the function:

Count how many times the function is evaluated:

Exclusions  (2)

Use automatic methods for computing exclusions, in this case for a piecewise function:

Indicate that no exclusions should be computed:

ExclusionsStyle  (2)

Use dashed lines to indicate the vertical asymptotes:

Use blue points to highlight the exclusions:

Filling  (7)

Use symbolic or explicit values:

Overlapping fills by default combine using opacity:

Fill between curve 1 and the axis:

Fill between curves 1 and 2:

Fill between curves 1 and 2 with a specific style:

Fill between curves 1 and 2; use yellow when 1 is below 2 and green when 1 is above 2:

Fill between curves 1 and with yellow:

FillingStyle  (3)

Use different fill colors:

Fill with opacity 0.5 yellow:

Fill with red below and blue above:

LabelingSize  (4)

Textual labels are shown at their actual sizes:

Image labels are automatically resized:

Specify a maximum size for textual labels:

Specify a maximum size for image labels:

Show image labels at their natural sizes:

MaxRecursion  (2)

The default sampling mesh:

Each level of MaxRecursion will subdivide the initial mesh into a finer mesh:

Mesh  (3)

Show the initial and final sampling meshes:

Use 20 mesh levels evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

MeshFunctions  (4)

Use a mesh evenly spaced in the and directions:

Mesh functions use the unscaled values in the direction:

Use Log to scale the mesh functions in the direction:

Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling the curve:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

MeshStyle  (4)

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big red mesh points in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLabel  (1)

Add an overall label to the plot:

PlotLabels  (5)

Specify text to label curves:

Place the labels above the curves:

Place the labels differently for each curve:

PlotLabels->"Expressions" uses functions as curve labels:

Use callouts to identify the curves:

Use None to not add a label:

PlotLegends  (7)

No legends are used by default:

Create a legend based on the functions:

Create a legend with placeholder text:

Create a legend with specific labels:

PlotLegends picks up PlotStyle values automatically:

Use Placed to position legends:

Place legends inside:

Use LineLegend to modify the appearance of the legend:

PlotPoints  (1)

Use more initial points to get a smoother curve:

PlotRange  (2)

Show the curve over the whole domain:

Show the curve only where it is positive:

PlotStyle  (6)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with MeshShading:

MeshStyle by default uses the same style as PlotStyle:

PlotTheme  (2)

Use a theme with simple ticks and grid lines in a high-contrast color scheme:

Change the color scheme:

RegionFunction  (2)

Show the curve where :

Exclude the region where :

Applications  (3)

Some typical algorithm complexities:

Compute the time-discrete Fourier transform of a sequence:

Log plot of the amplitude spectrum:

The supersonic intensity variation over a plane for a point source:

Properties & Relations  (4)

LogPlot samples more points where it needs to:

LogPlot is a special case of Plot for curves:

Use LogLinearPlot and LogLogPlot for logarithmic plots in the direction:

Use ListLogPlot for data:

Wolfram Research (2007), LogPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LogPlot.html (updated 13).

Text

Wolfram Research (2007), LogPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LogPlot.html (updated 13).

CMS

Wolfram Language. 2007. "LogPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 13. https://reference.wolfram.com/language/ref/LogPlot.html.

APA

Wolfram Language. (2007). LogPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogPlot.html

BibTeX

@misc{reference.wolfram_2021_logplot, author="Wolfram Research", title="{LogPlot}", year="13", howpublished="\url{https://reference.wolfram.com/language/ref/LogPlot.html}", note=[Accessed: 23-May-2022 ]}

BibLaTeX

@online{reference.wolfram_2021_logplot, organization={Wolfram Research}, title={LogPlot}, year={13}, url={https://reference.wolfram.com/language/ref/LogPlot.html}, note=[Accessed: 23-May-2022 ]}