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• See Also
  • ArrayPlot
  • ReliefPlot
  • ListDensityPlot3D
  • ListSliceDensityPlot3D
  • ListContourPlot
  • DensityPlot
  • MatrixPlot
  • Raster
  • ListStreamDensityPlot
  • ListVectorDensityPlot
  • DataReversed
• Related Guides
  • Data Visualization
  • Tabular Visualization
  • Scientific Data Analysis
  • Handling Arrays of Data
  • GPU Computing
  • GPU Computing with NVIDIA
  • GPU Computing with Apple
• Tech Notes
  • Plotting Lists of Data

ListDensityPlot[{{f₁₁,…,f_1n},…,{f_m1,…,f_mn}}]

generates a smooth density plot from an array of values f_ij.

ListDensityPlot[{{x₁,y₁,f₁},…,{x_k,y_k,f_k}}]

generates a density plot with values f_i defined at specified points {x_i,y_i}.

• ListDensityPlot is also known as heat map and intensity plot.
• Regular data {{f₁₁,…,f_1n},…,{f_m1,…,f_mn}} is plotted as a color at the point {x,y} where has value f_ij and c is a color-valued function.
• Irregular data {{x₁,y₁,f₁},…,{x_k,y_k,f_k}} is plotted as a color at the point {x,y} where has value f_i and c is a color-valued function.
• The plot visualizes the set where is a color-valued function and the region is the Cartesian product for regular data and the convex hull of {{x₁,y₁},…,{x_n,y_n}} for irregular data.
• For regular data {{f₁₁,…,f_1n},…,{f_m1,…,f_mn}}, the location for value f_ij is taken to be . Use the option DataRange to override that.
• ListDensityPlot is intended for continuous data; ArrayPlot is intended for discrete data.
• By default, the color scale generates output in which larger values are shown as lighter colors.
• ListDensityPlot[data] can use the following forms and interpretations for data:
• {<|x_keyx₁,y_keyy₁,f_keyf₁|>,…,<|x_keyx_n,y_keyy_n,f_keyf_n|>} irregular triples {x_i,y_i,f_i} {{x₁,y₁},…,{x_n,y_n}}{f₁,…,f_n} irregular triples {x_i,y_i,f_i} Dataset values as a normal array NumericArray values as a normal array QuantityArray magnitudes SparseArray values as a normal array
• ListDensityPlot[Tabular[…]cspec] extracts and plots values from the tabular object using the column specification cspec.
• The following forms of column specifications cspec are allowed for plotting tabular data:
• {col_x,col_y,col_z} plot column z against columns x and y {{col_x1,col_y1,col_z1},{col_x2,col_y2,col_z2},…} plot column z₁ against column x₁ and y₁ , z₂ against x₂ and y₂, etc.
• ListDensityPlot has the same options as Graphics, with the following additions and changes: [List of all options]
• DataRange determines the {x,y} position for value f_ij in the array {{f₁₁,…,f_1n},…,{f_m1,…,f_mn}}. Possible settings include:
• Automatic,All uniform in x from 1 to n and in y from 1 to m {{x_min,x_max},{y_min,y_max}} uniform in x from x_min to x_max and in y from y_min to y_max
• The case ListDensityPlot[{{a₁₁,a₁₂,a₁₃},…}] can be interpreted as both regular and irregular data. With DataRange->Automatic it is interpreted as irregular {{x₁,y₁,f₁},{x₂,y₂,f₂},…} and with DataRangeAll it is interpreted as regular {{f₁₁,…,f_1n},…,{f_m1,…,f_mn}}.
• Possible settings for ScalingFunctions include:
• s_f scale the f-values {s_x,s_y} scale x and y axes {s_x,s_y,s_f} scale x and y axes and f-values
• Each scaling function s_i is either a string "scale" or {g,g^-1}, where g^-1 is the inverse of g.
• For ListDensityPlot[array], Mesh->Full draws a mesh that crosses at the position of each data point.
• The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, f.
• ColorFunction is supplied with a single argument, given by default by the scaled value of f.
• Typical settings for PlotLegends include:
• Possible settings for PlotLayout that show single densities in multiple plot panels include:
• "Column" use separate densities in a column of panels "Row" use separate densities 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
• The setting for VertexColors must be an array or list with the same structure as the array or list of values.
• An explicit setting for VertexColors overrides colors determined from ColorFunction.
• ListDensityPlot returns Graphics[GraphicsComplex[data]].

Use an array of values to define heights for a density:

Give explicit , , coordinates for points in a density:

A larger set of , , samples:

Use a multipanel layout to show multiple datasets at the same time:

Use different interpolations of data:

For regular data consisting of values, the and data ranges are taken to be integer values:

Provide explicit and data ranges by using DataRange:

For irregular data consisting of triples, the and data ranges are inferred from data:

Areas around where the data is nonreal are excluded:

Use MaxPlotPoints to limit the number of points used:

PlotRange is selected automatically:

Use PlotRange to focus in on areas of interest:

Use RegionFunction to restrict the density to a region given by inequalities:

Get tabular data:

Plot a shaded density plot of column f over columns x and y:

Plot multiple sets of columns, arranging the plots in a row:

Include color bar legends for the plot:

Add labels:

Color the density by height:

Include a legend:

Provide overlay meshes:

Provide an interactive Tooltip for the density:

Use a theme with simple ticks and a legend in a bold color scheme:

Use a multipanel layout to show multiple datasets at the same time:

Use a column instead of a row:

By default, ListDensityPlot uses the same width and height:

Use a numerical value to specify the height to width ratio:

AspectRatioAutomatic determines the ratio from the plot ranges:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

By default, ListDensityPlot uses a frame instead of axes:

Use axes instead of a frame:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

Use units as labels:

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

No boundary is used by default:

Use a red boundary around the edges of the surface:

BoundaryStyle applies to holes cut by RegionFunction:

BoundaryStyle applies between Voronoi regions associated with the data:

Clipped regions are not shown by default:

Color clipped regions like the rest of the density:

Use pink to fill the clipped regions:

Use light red where the surface is clipped above and pink below:

Color by scaled coordinate:

Specify gray-level intensity by scaled coordinate:

Named color gradients color in the direction:

Use brightness to correspond to the height or density of a function:

Use the interpolation between two colors to indicate the height or density of a function:

Arrays of height values are displayed against the number of elements in each direction:

Rescale to the sampling space:

Triples are interpreted as , , coordinates:

Force interpretation as arrays of height values:

The dataset is normally interpreted as a list of triples:

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

Densities are normally blended across polygons:

Use zero-order or piecewise constant interpolation:

Use third-order spline interpolation to fit the data:

Interpolation order 0 to 5:

For irregular data, zero-order interpolation gives Voronoi regions for each point:

ListDensityPlot normally uses all the points in the dataset:

Limit the number of points used in each direction:

MaxPlotPoints imposes a regular grid on irregular data:

The grid does not extend beyond the convex hull of the original data:

No mesh is used by default:

Show the initial and final sampling mesh:

The entire mesh for irregular data is a Delaunay triangulation:

Use 5 mesh lines in each direction:

Use 3 mesh lines in the direction and 6 mesh lines in the direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

Use the value as the mesh function, giving a continuously colored contour plot:

Use mesh lines in the and directions:

Show where the real and imaginary parts of a function are constant over the complex plane:

Mesh lines are partially transparent by default:

Use red mesh lines:

Use red mesh lines in the direction and dashed mesh lines in the direction:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Place each density in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

No legend is used, by default:

Include a legend:

Legends automatically use the same colors as the density plot:

Use Placed to change legend placement:

Use BarLegend to customize the legend:

Automatically compute the range and clip extreme portions of it:

Use all points to compute the range:

Use a theme with simple ticks and a legend in a bright color scheme:

Change the color scheme:

Plot over a region in :

The region depends on DataRange:

Regions do not have to be connected:

Use any logical combination of conditions:

By default, plots have linear scales in each direction:

Use a log scale in the direction:

Use a linear scale in the direction that shows smaller numbers at the top:

Use a reciprocal scale in the direction:

Use different scales in the and directions:

Reverse the axis without changing the axis:

Use a scale defined by a function and its inverse:

Positions in Ticks and GridLines are automatically scaled:

PlotRange is automatically scaled:

ListDensityPlot usually colors the density using a color function:

Specify random colors for each vertex:

Plot a probability density function of two variables:

Compare to the empirical density function:

Show the regions closest to a set of points:

Show ozone density around the world:

Use CountryData to add country outlines:

The appearance may depend on the source of the data:

An ×3 matrix is by default interpreted as a list of triples:

Use DataRange->All to force interpretation as a matrix of values:

Or provide an explicit list of data ranges to force interpretation as a matrix of values:

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