spatstat v1.37-0
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Spatial Point Pattern analysis, model-fitting, simulation, tests
A package for analysing spatial data, mainly Spatial Point Patterns, including multitype/marked points and spatial covariates, in any two-dimensional spatial region. Also supports three-dimensional point patterns, space-time point patterns in any number of dimensions, and point patterns on a linear network.
Contains over 1500 functions for plotting spatial data, exploratory data analysis, model-fitting, simulation, spatial sampling, model diagnostics, and formal inference.
Data types include point patterns, line segment patterns, spatial windows, pixel images, tessellations, and linear networks.
Exploratory methods include quadrat counts, K-functions and their simulation envelopes, nearest neighbour distance and empty space statistics, Fry plots, pair correlation function, kernel smoothed intensity, relative risk estimation with cross-validated bandwidth selection, mark correlation functions, segregation indices, mark dependence diagnostics, and kernel estimates of covariate effects. Formal hypothesis tests of random pattern (chi-squared, Kolmogorov-Smirnov, Diggle-Cressie-Loosmore-Ford, Dao-Genton) and tests for covariate effects (Cox-Berman-Waller-Lawson, Kolmogorov-Smirnov) are also supported.
Parametric models can be fitted to point pattern data using the functions ppm, kppm, slrm similar to glm. Types of models include Poisson, Gibbs, Cox and cluster point processes. Models may involve dependence on covariates, interpoint interaction, cluster formation and dependence on marks. Models are fitted by maximum likelihood, logistic regression, minimum contrast, and composite likelihood methods.
Fitted point process models can be simulated, automatically. Formal hypothesis tests of a fitted model are supported (likelihood ratio test, analysis of deviance, Monte Carlo tests) along with basic tools for model selection (stepwise, AIC). Tools for validating the fitted model include simulation envelopes, residuals, residual plots and Q-Q plots, leverage and influence diagnostics, partial residuals, and added variable plots.
Functions in spatstat
Name | Description | |
Kcross | Multitype K Function (Cross-type) | |
Ldot | Multitype L-function (i-to-any) | |
Ord | Generic Ord Interaction model | |
StraussHard | The Strauss / Hard Core Point Process Model | |
Saturated | Saturated Pairwise Interaction model | |
Kmodel | K Function or Pair Correlation Function of a Point Process Model | |
Smooth.fv | Apply Smoothing to Function Values | |
Extract.fasp | Extract Subset of Function Array | |
Hardcore | The Hard Core Point Process Model | |
boxx | Multi-Dimensional Box | |
Ldot.inhom | Inhomogeneous Multitype L Dot Function | |
bramblecanes | Hutchings' Bramble Canes data | |
affine.tess | Apply Geometrical Transformation To Tessellation | |
Jmulti | Marked J Function | |
Triplets | The Triplet Point Process Model | |
applynbd | Apply Function to Every Neighbourhood in a Point Pattern | |
angles.psp | Orientation Angles of Line Segments | |
as.matrix.im | Convert Pixel Image to Matrix or Array | |
MultiStraussHard | The Multitype/Hard Core Strauss Point Process Model | |
anova.ppm | ANOVA for Fitted Point Process Models | |
Extract.influence.ppm | Extract Subset of Influence Object | |
rmhcontrol | Set Control Parameters for Metropolis-Hastings Algorithm. | |
as.interact | Extract Interaction Structure | |
commonGrid | Determine A Common Spatial Domain And Pixel Resolution | |
AreaInter | The Area Interaction Point Process Model | |
affine.lpp | Apply Geometrical Transformations to Point Pattern on a Linear Network | |
Smooth.ppp | Spatial smoothing of observations at irregular points | |
envelope.envelope | Recompute Envelopes | |
as.data.frame.im | Convert Pixel Image to Data Frame | |
as.hyperframe.ppx | Extract coordinates and marks of multidimensional point pattern | |
PairPiece | The Piecewise Constant Pairwise Interaction Point Process Model | |
as.box3 | Convert Data to Three-Dimensional Box | |
dummify | Convert Data to Numeric Values by Constructing Dummy Variables | |
Extract.owin | Extract Subset of Window | |
by.ppp | Apply a Function to a Point Pattern Broken Down by Factor | |
cauchy.estK | Fit the Neyman-Scott cluster process with Cauchy kernel | |
Lest | L-function | |
Extract.linnet | Extract Subset of Linear Network | |
fasp.object | Function Arrays for Spatial Patterns | |
BadGey | Hybrid Geyer Point Process Model | |
by.im | Apply Function to Image Broken Down by Factor | |
closepairs | Close Pairs of Points | |
dclf.progress | Progress Plot of Test of Spatial Pattern | |
as.fv | Convert Data To Class fv | |
default.dummy | Generate a Default Pattern of Dummy Points | |
bdist.tiles | Distance to Boundary of Window | |
colourmap | Colour Lookup Tables | |
Smooth.msr | Smooth a Signed or Vector-Valued Measure | |
bw.diggle | Cross Validated Bandwidth Selection for Kernel Density | |
convolve.im | Convolution of Pixel Images | |
as.lpp | Convert Data to a Point Pattern on a Linear Network | |
im.apply | Apply Function Pixelwise to List of Images | |
areaGain | Difference of Disc Areas | |
Hest | Spherical Contact Distribution Function | |
Finhom | Inhomogeneous Empty Space Function | |
compatible.fasp | Test Whether Function Arrays Are Compatible | |
Jinhom | Inhomogeneous J-function | |
ellipse | Elliptical Window. | |
OrdThresh | Ord's Interaction model | |
cauchy.estpcf | Fit the Neyman-Scott cluster process with Cauchy kernel | |
Jdot | Multitype J Function (i-to-any) | |
edges | Extract Boundary Edges of a Window. | |
Gfox | Foxall's Distance Functions | |
append.psp | Combine Two Line Segment Patterns | |
eval.fasp | Evaluate Expression Involving Function Arrays | |
area.owin | Area of a Window | |
intensity | Intensity of a Dataset or a Model | |
density.psp | Kernel Smoothing of Line Segment Pattern | |
as.linim | Convert to Pixel Image on Linear Network | |
marks.psp | Marks of a Line Segment Pattern | |
Pairwise | Generic Pairwise Interaction model | |
distfun.lpp | Distance Map on Linear Network | |
bw.scott | Scott's Rule for Bandwidth Selection for Kernel Density | |
as.ppm | Extract Fitted Point Process Model | |
Extract.leverage.ppm | Extract Subset of Leverage Object | |
infline | Infinite Straight Lines | |
Extract.listof | Extract or Replace Subset of a List of Things | |
DiggleGatesStibbard | Diggle-Gates-Stibbard Point Process Model | |
Ginhom | Inhomogeneous Nearest Neighbour Function | |
clickpoly | Interactively Define a Polygon | |
dummy.ppm | Extract Dummy Points Used to Fit a Point Process Model | |
demohyper | Demonstration Example of Hyperframe of Spatial Data | |
finpines | Pine saplings in Finland. | |
coef.slrm | Coefficients of Fitted Spatial Logistic Regression Model | |
crossing.psp | Crossing Points of Two Line Segment Patterns | |
layerplotargs | Extract or Replace the Plot Arguments of a Layered Object | |
edge.Ripley | Ripley's Isotropic Edge Correction | |
crossdist.psp | Pairwise distances between two different line segment patterns | |
data.ppm | Extract Original Data from a Fitted Point Process Model | |
affine.linnet | Apply Geometrical Transformations to a Linear Network | |
Extract.tess | Extract or Replace Subset of Tessellation | |
is.ppm | Test Whether An Object Is A Fitted Point Process Model | |
Tstat | Third order summary statistic | |
Gres | Residual G Function | |
Kinhom | Inhomogeneous K-function | |
disc | Circular Window | |
Kmeasure | Reduced Second Moment Measure | |
nncross | Nearest Neighbours Between Two Patterns | |
cbind.hyperframe | Combine Hyperframes by Rows or by Columns | |
is.owin | Test Whether An Object Is A Window | |
clickppp | Interactively Add Points | |
gauss.hermite | Gauss-Hermite Quadrature Approximation to Expectation for Normal Distribution | |
methods.slrm | Methods for Spatial Logistic Regression Models | |
Gcom | Model Compensator of Nearest Neighbour Function | |
intensity.quadratcount | Intensity Estimates Using Quadrat Counts | |
identify.psp | Identify Segments in a Line Segment Pattern | |
bei | Tropical rain forest trees | |
clarkevans.test | Clark and Evans Test | |
SatPiece | Piecewise Constant Saturated Pairwise Interaction Point Process Model | |
linearpcfdot | Multitype Pair Correlation Function (Dot-type) for Linear Point Pattern | |
harmonise.im | Make Pixel Images Compatible | |
localKinhom | Inhomogeneous Neighbourhood Density Function | |
K3est | K-function of a Three-Dimensional Point Pattern | |
Iest | Estimate the I-function | |
nncross.lpp | Nearest Neighbours on a Linear Network | |
Lcross | Multitype L-function (cross-type) | |
plot.plotppm | Plot a plotppm Object Created by plot.ppm | |
invoke.symbolmap | Plot Data Using Graphics Symbol Map | |
as.mask.psp | Convert Line Segment Pattern to Binary Pixel Mask | |
Kres | Residual K Function | |
add.texture | Fill Plot With Texture | |
bdist.pixels | Distance to Boundary of Window | |
blur | Apply Gaussian Blur to a Pixel Image | |
eem | Exponential Energy Marks | |
anova.mppm | ANOVA for Fitted Multiple Point Process Models | |
areaLoss | Difference of Disc Areas | |
cells | Biological Cells Point Pattern | |
anemones | Beadlet Anemones Data | |
linim | Create Pixel Image on Linear Network | |
markvario | Mark Variogram | |
LambertW | Lambert's W Function | |
Kdot.inhom | Inhomogeneous Multitype K Dot Function | |
lineardisc | Compute Disc of Given Radius in Linear Network | |
clmfires | Castilla-La Mancha Forest Fires | |
Strauss | The Strauss Point Process Model | |
linearpcfcross | Multitype Pair Correlation Function (Cross-type) for Linear Point Pattern | |
dilation | Morphological Dilation | |
fitted.mppm | Fitted Conditional Intensity for Multiple Point Process Model | |
edges2triangles | List Triangles in a Graph | |
affine.im | Apply Affine Transformation To Pixel Image | |
fitin.ppm | Extract the Interaction from a Fitted Point Process Model | |
Kdot | Multitype K Function (i-to-any) | |
kstest.ppm | Kolmogorov-Smirnov Test for Point Pattern or Point Process Model | |
is.marked.ppp | Test Whether A Point Pattern is Marked | |
linearpcfcross.inhom | Inhomogeneous Multitype Pair Correlation Function (Cross-type) for Linear Point Pattern | |
inforder.family | Infinite Order Interaction Family | |
as.owin | Convert Data To Class owin | |
methods.lppm | Methods for Fitted Point Process Models on a Linear Network | |
Jcross | Multitype J Function (i-to-j) | |
Linhom | L-function | |
clickjoin | Interactively join vertices on a plot | |
markconnect | Mark Connection Function | |
linearKinhom | Inhomogeneous Linear K Function | |
Smooth | Spatial smoothing of data | |
Gcross | Multitype Nearest Neighbour Distance Function (i-to-j) | |
lansing | Lansing Woods Point Pattern | |
Extract.quad | Subset of Quadrature Scheme | |
erosion | Morphological Erosion | |
chop.tess | Subdivide a Window or Tessellation using a Set of Lines | |
alltypes | Calculate Summary Statistic for All Types in a Multitype Point Pattern | |
nnwhich | Nearest neighbour | |
Hybrid | Hybrid Interaction Point Process Model | |
lgcp.estpcf | Fit a Log-Gaussian Cox Point Process by Minimum Contrast | |
pairdist.ppx | Pairwise Distances in Any Dimensions | |
coef.ppm | Coefficients of Fitted Point Process Model | |
nncorr | Nearest-Neighbour Correlation Indices of Marked Point Pattern | |
Extract.lpp | Extract Subset of Point Pattern on Linear Network | |
gridcentres | Rectangular grid of points | |
logLik.ppm | Log Likelihood and AIC for Point Process Model | |
copper | Berman-Huntington points and lines data | |
envelope.lpp | Envelope for Point Patterns on Linear Network | |
Extract.im | Extract Subset of Image | |
beginner | Print Introduction For Beginners | |
Kcross.inhom | Inhomogeneous Cross K Function | |
pairdist.psp | Pairwise distances between line segments | |
anova.lppm | ANOVA for Fitted Point Process Models on Linear Network | |
markcorrint | Mark Correlation Integral | |
iplot | Point and Click Interface for Displaying Spatial Data | |
chicago | Chicago Street Crime Data | |
plot.fv | Plot Function Values | |
Kmulti | Marked K-Function | |
Gdot | Multitype Nearest Neighbour Distance Function (i-to-any) | |
discpartarea | Area of Part of Disc | |
predict.mppm | Prediction for Fitted Multiple Point Process Model | |
plot.linim | Plot Pixel Image on Linear Network | |
plot.layered | Layered Plot | |
linearmarkconnect | Mark Connection Function for Multitype Point Pattern on Linear Network | |
heather | Diggle's Heather Data | |
imcov | Spatial Covariance of a Pixel Image | |
bronzefilter | Bronze gradient filter data | |
as.psp | Convert Data To Class psp | |
lurking | Lurking variable plot | |
rpoispp3 | Generate Poisson Point Pattern in Three Dimensions | |
linearpcfinhom | Inhomogeneous Linear Pair Correlation Function | |
distmap.ppp | Distance Map of Point Pattern | |
ganglia | Beta Ganglion Cells in Cat Retina, Old Version | |
Extract.hyperframe | Extract or Replace Subset of Hyperframe | |
compatible | Test Whether Objects Are Compatible | |
pcfdot.inhom | Inhomogeneous Multitype Pair Correlation Function (Type-i-To-Any-Type) | |
convexhull.xy | Convex Hull of Points | |
Extract.splitppp | Extract or Replace Sub-Patterns | |
as.function.fv | Convert Function Value Table to Function | |
diameter.boxx | Geometrical Calculations for Multi-Dimensional Box | |
quad.ppm | Extract Quadrature Scheme Used to Fit a Point Process Model | |
deltametric | Delta Metric | |
intensity.ppm | Intensity of Fitted Point Process Model | |
quasirandom | Quasirandom Patterns | |
is.marked.ppm | Test Whether A Point Process Model is Marked | |
integral.msr | Integral of a Measure | |
endpoints.psp | Endpoints of Line Segment Pattern | |
model.matrix.ppm | Extract Design Matrix from Point Process Model | |
clarkevans | Clark and Evans Aggregation Index | |
coef.mppm | Coefficients of Point Process Model Fitted to Multiple Point Patterns | |
crossdist.lpp | Pairwise distances between two point patterns on a linear network | |
letterR | Window in Shape of Letter R | |
as.data.frame.hyperframe | Coerce Hyperframe to Data Frame | |
mean.im | Maximum, Minimum, Mean, Median, Range or Sum of Pixel Values in an Image | |
japanesepines | Japanese Pines Point Pattern | |
model.images | Compute Images of Constructed Covariates | |
Jest | Estimate the J-function | |
formula.fv | Extract or Change the Plot Formula for a Function Value Table | |
Kmodel.ppm | K Function or Pair Correlation Function of Gibbs Point Process model | |
plot.ppp | plot a Spatial Point Pattern | |
clickbox | Interactively Define a Rectangle | |
bdist.points | Distance to Boundary of Window | |
Kscaled | Locally Scaled K-function | |
plot.linnet | Plot a linear network | |
complement.owin | Take Complement of a Window | |
as.im | Convert to Pixel Image | |
dclf.test | Diggle-Cressie-Loosmore-Ford and Maximum Absolute Deviation Tests | |
lohboot | Bootstrap Confidence Bands for Summary Function | |
concatxy | Concatenate x,y Coordinate Vectors | |
exactMPLEstrauss | Exact Maximum Pseudolikelihood Estimate for Stationary Strauss Process | |
nnfun | Nearest Neighbour Index Map as a Function | |
is.rectangle | Determine Type of Window | |
psp.object | Class of Line Segment Patterns | |
centroid.owin | Centroid of a window | |
rknn | Theoretical Distribution of Nearest Neighbour Distance | |
as.polygonal | Convert a Window to a Polygonal Window | |
delaunay | Delaunay Triangulation of Point Pattern | |
ewcdf | Weighted Empirical Cumulative Distribution Function | |
plot.mppm | plot a Fitted Multiple Point Process Model | |
gordon | People in Gordon Square | |
interp.im | Interpolate a Pixel Image | |
is.lpp | Test Whether An Object Is A Point Pattern on a Linear Network | |
split.im | Divide Image Into Sub-images | |
residuals.ppm | Residuals for Fitted Point Process Model | |
is.multitype.ppm | Test Whether A Point Process Model is Multitype | |
rStrauss | Perfect Simulation of the Strauss Process | |
lpp | Create Point Pattern on Linear Network | |
corners | Corners of a rectangle | |
profilepl | Profile Maximum Pseudolikelihood | |
crossdist.ppp | Pairwise distances between two different point patterns | |
as.ppp | Convert Data To Class ppp | |
Smoothfun.ppp | Smooth Interpolation of Marks as a Spatial Function | |
Concom | The Connected Component Process Model | |
default.rmhcontrol | Set Default Control Parameters for Metropolis-Hastings Algorithm. | |
duplicated.ppp | Determine Duplicated Points in a Spatial Point Pattern | |
is.stationary | Recognise Stationary and Poisson Point Process Models | |
adaptive.density | Intensity Estimate of Point Pattern Using Tessellation | |
nncross.pp3 | Nearest Neighbours Between Two Patterns in 3D | |
psstA | Pseudoscore Diagnostic For Fitted Model against Area-Interaction Alternative | |
nnwhich.ppx | Nearest Neighbours in Any Dimensions | |
gorillas | Gorilla Nesting Sites | |
LennardJones | The Lennard-Jones Potential | |
multiplicity.ppp | Count Multiplicity of Duplicate Points | |
methods.rho2hat | Methods for Intensity Functions of Two Spatial Covariates | |
miplot | Morishita Index Plot | |
as.rectangle | Window Frame | |
intersect.tess | Intersection of Two Tessellations | |
unmark | Remove Marks | |
residuals.mppm | Residuals for Point Process Model Fitted to Multiple Point Patterns | |
rmhmodel.default | Build Point Process Model for Metropolis-Hastings Simulation. | |
quadratcount | Quadrat counting for a point pattern | |
transect.im | Pixel Values Along a Transect | |
psst | Pseudoscore Diagnostic For Fitted Model against General Alternative | |
convexhull | Convex Hull | |
F3est | Empty Space Function of a Three-Dimensional Point Pattern | |
boundingbox | Bounding Box of a Window, Image, or Point Pattern | |
scalardilate | Apply Scalar Dilation | |
chorley | Chorley-Ribble Cancer Data | |
pixelquad | Quadrature Scheme Based on Pixel Grid | |
rhohat | Smoothing Estimate of Covariate Transformation | |
Fest | Estimate the empty space function F | |
interp.colourmap | Interpolate smoothly between specified colours | |
nearestsegment | Find Line Segment Nearest to Each Point | |
compareFit | Residual Diagnostics for Multiple Fitted Models | |
rshift | Random Shift | |
methods.pp3 | Methods for three-dimensional point patterns | |
leverage.ppm | Leverage Measure for Spatial Point Process Model | |
plot.listof | Plot a List of Things | |
incircle | Find Largest Circle Inside Window | |
edge.Trans | Translation Edge Correction | |
spruces | Spruces Point Pattern | |
reach | Interaction Distance of a Point Process | |
is.convex | Test Whether a Window is Convex | |
demopat | Artificial Data Point Pattern | |
km.rs | Kaplan-Meier and Reduced Sample Estimator using Histograms | |
objsurf | Objective Function Surface | |
linearK | Linear K Function | |
coords | Extract or Change Coordinates of a Spatial or Spatiotemporal Point Pattern | |
Extract.fv | Extract Subset of Function Values | |
eval.fv | Evaluate Expression Involving Functions | |
formula.ppm | Model Formulae for Gibbs Point Process Models | |
distfun | Distance Map as a Function | |
discretise | Safely Convert Point Pattern Window to Binary Mask | |
connected | Connected components | |
dfbetas.ppm | Parameter influence measure | |
distmap.psp | Distance Map of Line Segment Pattern | |
methods.box3 | Methods for Three-Dimensional Box | |
diameter | Diameter of an Object | |
fitted.slrm | Fitted Probabilities for Spatial Logistic Regression | |
periodify | Make Periodic Copies of a Spatial Pattern | |
nztrees | New Zealand Trees Point Pattern | |
methods.linnet | Methods for Linear Networks | |
osteo | Osteocyte Lacunae Data: Replicated Three-Dimensional Point Patterns | |
bw.ppl | Likelihood Cross Validation Bandwidth Selection for Kernel Density | |
methods.layered | Methods for Layered Objects | |
pairsat.family | Saturated Pairwise Interaction Point Process Family | |
mincontrast | Method of Minimum Contrast | |
rPoissonCluster | Simulate Poisson Cluster Process | |
density.ppp | Kernel Smoothed Intensity of Point Pattern | |
fvnames | Abbreviations for Groups of Columns in Function Value Table | |
psp | Create a Line Segment Pattern | |
gridweights | Compute Quadrature Weights Based on Grid Counts | |
quantile.im | Sample Quantiles of Pixel Image | |
simulate.kppm | Simulate a Fitted Cluster Point Process Model | |
plot.bermantest | Plot Result of Berman Test | |
amacrine | Hughes' Amacrine Cell Data | |
maxnndist | Compute Minimum or Maximum Nearest-Neighbour Distance | |
DiggleGratton | Diggle-Gratton model | |
quadscheme.logi | Generate a Logistic Regression Quadrature Scheme from a Point Pattern | |
identify.ppp | Identify Points in a Point Pattern | |
solutionset | Evaluate Logical Expression Involving Pixel Images and Return Region Where Expression is True | |
residualspaper | Data and Code From JRSS Discussion Paper on Residuals | |
rmh.ppm | Simulate from a Fitted Point Process Model | |
unnormdensity | Weighted kernel smoother | |
plot.ppm | plot a Fitted Point Process Model | |
predict.kppm | Prediction from a Fitted Cluster Point Process Model | |
Extract.msr | Extract Subset of Signed or Vector Measure | |
nsegments | Number of Line Segments in a Line Segment Pattern | |
rthin | Random Thinning | |
flipxy | Exchange X and Y Coordinates | |
closing | Morphological Closing | |
dmixpois | Mixed Poisson Distribution | |
nbfires | Point Patterns of New Brunswick Forest Fires | |
dirichlet.weights | Compute Quadrature Weights Based on Dirichlet Tessellation | |
affine | Apply Affine Transformation | |
run.simplepanel | Run Point-and-Click Interface | |
rgbim | Create Colour-Valued Pixel Image | |
rLGCP | Simulate Log-Gaussian Cox Process | |
methods.rhohat | Methods for Intensity Functions of Spatial Covariate | |
G3est | Nearest Neighbour Distance Distribution Function of a Three-Dimensional Point Pattern | |
marktable | Tabulate Marks in Neighbourhood of Every Point in a Point Pattern | |
ppp | Create a Point Pattern | |
pixelcentres | Extract Pixel Centres as Point Pattern | |
longleaf | Longleaf Pines Point Pattern | |
Extract.ppx | Extract Subset of Multidimensional Point Pattern | |
Gest | Nearest Neighbour Distance Function G | |
pp3 | Three Dimensional Point Pattern | |
methods.boxx | Methods for Multi-Dimensional Box | |
urkiola | Urkiola Woods Point Pattern | |
plot.slrm | Plot a Fitted Spatial Logistic Regression | |
im | Create a Pixel Image Object | |
bw.stoyan | Stoyan's Rule of Thumb for Bandwidth Selection | |
hyperframe | Hyper Data Frame | |
progressreport | Print Progress Reports | |
timed | Record the Computation Time | |
npoints | Number of Points in a Point Pattern | |
default.expand | Default Expansion Rule for Simulation of Model | |
linearpcfdot.inhom | Inhomogeneous Multitype Pair Correlation Function (Dot-type) for Linear Point Pattern | |
pairdist.ppp | Pairwise distances | |
simplenet | Simple Example of Linear Network | |
is.multitype.ppp | Test Whether A Point Pattern is Multitype | |
stratrand | Stratified random point pattern | |
hybrid.family | Hybrid Interaction Family | |
delaunay.distance | Distance on Delaunay Triangulation | |
ripras | Estimate window from points alone | |
rescale.ppp | Convert Point Pattern to Another Unit of Length | |
MultiHard | The Multitype Hard Core Point Process Model | |
methods.funxy | Methods for Spatial Functions | |
is.ppp | Test Whether An Object Is A Point Pattern | |
Kmulti.inhom | Inhomogeneous Marked K-Function | |
istat | Point and Click Interface for Exploratory Analysis of Point Pattern | |
bermantest | Berman's Tests for Point Process Model | |
nnwhich.pp3 | Nearest neighbours in three dimensions | |
Emark | Diagnostics for random marking | |
nnmap | K-th Nearest Point Map | |
rpoispp | Generate Poisson Point Pattern | |
plot.tess | Plot a tessellation | |
opening | Morphological Opening | |
integral.im | Integral of a Pixel Image | |
linearKcross | Multitype K Function (Cross-type) for Linear Point Pattern | |
rMaternI | Simulate Matern Model I | |
Extract.layered | Extract Subset of a Layered Object | |
rmhstart | Determine Initial State for Metropolis-Hastings Simulation. | |
contour.listof | Plot a List of Things | |
npfun | Dummy Function Returns Number of Points | |
bw.relrisk | Cross Validated Bandwidth Selection for Relative Risk Estimation | |
is.empty | Test Whether An Object Is Empty | |
rHardcore | Perfect Simulation of the Hardcore Process | |
raster.x | Cartesian Coordinates for a Pixel Raster | |
logLik.slrm | Loglikelihood of Spatial Logistic Regression | |
psstG | Pseudoscore Diagnostic For Fitted Model against Saturation Alternative | |
expand.owin | Apply Expansion Rule | |
markcorr | Mark Correlation Function | |
idw | Inverse-distance weighted smoothing of observations at irregular points | |
swedishpines | Swedish Pines Point Pattern | |
distmap | Distance Map | |
rQuasi | Generate Quasirandom Point Pattern in Given Window | |
rescue.rectangle | Convert Window Back To Rectangle | |
model.depends | Identify Covariates Involved in each Model Term | |
linearpcf | Linear Pair Correlation Function | |
compatible.im | Test Whether Pixel Images Are Compatible | |
summary.splitppp | Summary of a Split Point Pattern | |
waterstriders | Waterstriders data. Three independent replications of a point pattern formed by insects. | |
plot.fasp | Plot a Function Array | |
nndensity.ppp | Estimate Intensity of Point Pattern Using Nearest Neighbour Distances | |
localpcf | Local pair correlation function | |
fv.object | Function Value Table | |
print.ppp | Print Brief Details of a Point Pattern Dataset | |
layered | Create List of Plotting Layers | |
crossdist | Pairwise distances | |
pcf | Pair Correlation Function | |
plot.scan.test | Plot Result of Scan Test | |
plot.kstest | Plot a Spatial Kolmogorov-Smirnov Test | |
nndist.psp | Nearest neighbour distances between line segments | |
murchison | Murchison gold deposits | |
ponderosa | Ponderosa Pine Tree Point Pattern | |
print.quad | Print a Quadrature Scheme | |
vcov.slrm | Variance-Covariance Matrix for a Fitted Spatial Logistic Regression | |
nndist | Nearest neighbour distances | |
pcfcross.inhom | Inhomogeneous Multitype Pair Correlation Function (Cross-Type) | |
pairdist.default | Pairwise distances | |
kstest.mppm | Kolmogorov-Smirnov Test for Multiple Point Process Model | |
plot.pp3 | Plot a three-dimensional point pattern | |
box3 | Three-Dimensional Box | |
quadrat.test.mppm | Chi-Squared Test for Multiple Point Process Model Based on Quadrat Counts | |
plot.psp | plot a Spatial Line Segment Pattern | |
shift.im | Apply Vector Translation To Pixel Image | |
rMosaicSet | Mosaic Random Set | |
pcf.fv | Pair Correlation Function obtained from K Function | |
hextess | Hexagonal Grid or Tessellation | |
runifpointOnLines | Generate N Uniform Random Points On Line Segments | |
is.hybrid | Test Whether Object is a Hybrid | |
quadrat.test.splitppp | Dispersion Test of CSR for Split Point Pattern Based on Quadrat Counts | |
rotate | Rotate | |
pool | Pool Data | |
summary.ppm | Summarizing a Fitted Point Process Model | |
rescale.owin | Convert Window to Another Unit of Length | |
matclust.estK | Fit the Matern Cluster Point Process by Minimum Contrast | |
dirichlet | Dirichlet Tessellation of Point Pattern | |
pppdist | Distance Between Two Point Patterns | |
compatible.fv | Test Whether Function Objects Are Compatible | |
rpoisppx | Generate Poisson Point Pattern in Any Dimensions | |
spatstat.options | Internal Options in Spatstat Package | |
pyramidal | Pyramidal Neurons in Cingulate Cortex | |
print.psp | Print Brief Details of a Line Segment Pattern Dataset | |
textureplot | Plot Image Using Texture Fill | |
sharpen | Data Sharpening of Point Pattern | |
rshift.psp | Randomly Shift a Line Segment Pattern | |
ippm | Fit Point Process Model Involving Irregular Trend Parameters | |
stieltjes | Compute Integral of Function Against Cumulative Distribution | |
pcf.fasp | Pair Correlation Function obtained from array of K functions | |
rMosaicField | Mosaic Random Field | |
summary.im | Summarizing a Pixel Image | |
affine.owin | Apply Affine Transformation To Window | |
layout.boxes | Generate a Row or Column Arrangement of Rectangles. | |
Kest | K-function | |
simulate.ppm | Simulate a Fitted Gibbs Point Process Model | |
methods.objsurf | Methods for Objective Function Surfaces | |
rDGS | Perfect Simulation of the Diggle-Gates-Stibbard Process | |
varblock | Estimate Variance of Summary Statistic by Subdivision | |
project.ppm | Force Point Process Model to be Valid | |
rotate.owin | Rotate a Window | |
predict.lppm | Predict Point Process Model on Linear Network | |
msr | Signed or Vector-Valued Measure | |
rSSI | Simulate Simple Sequential Inhibition | |
nndist.lpp | Nearest neighbour distances on a linear network | |
spokes | Spokes pattern of dummy points | |
betacells | Beta Ganglion Cells in Cat Retina | |
pairdist | Pairwise distances | |
pairdist.pp3 | Pairwise distances in Three Dimensions | |
ord.family | Ord Interaction Process Family | |
fitted.ppm | Fitted Conditional Intensity for Point Process Model | |
rMatClust | Simulate Matern Cluster Process | |
summary.owin | Summary of a Spatial Window | |
rescale.im | Convert Pixel Image to Another Unit of Length | |
intersect.owin | Intersection, Union or Set Subtraction of Two Windows | |
valid.ppm | Check Whether Point Process Model is Valid | |
rmh | Simulate point patterns using the Metropolis-Hastings algorithm. | |
kppm | Fit Cluster or Cox Point Process Model | |
rotate.psp | Rotate a Line Segment Pattern | |
inside.owin | Test Whether Points Are Inside A Window | |
plot.im | Plot a Pixel Image | |
logLik.mppm | Log Likelihood for Poisson Point Process Model | |
dilated.areas | Areas of Morphological Dilations | |
matchingdist | Distance for a Point Pattern Matching | |
reflect | Reflect In Origin | |
plot.hyperframe | Plot Entries in a Hyperframe | |
rjitter | Random Perturbation of a Point Pattern | |
setcov | Set Covariance of a Window | |
quad.object | Class of Quadrature Schemes | |
texturemap | Texture Map | |
summary.quad | Summarizing a Quadrature Scheme | |
print.im | Print Brief Details of an Image | |
pairdist.lpp | Pairwise shortest-path distances between points on a linear network | |
allstats | Calculate four standard summary functions of a point pattern. | |
simulate.slrm | Simulate a Fitted Spatial Logistic Regression Model | |
pcfmulti | Marked pair correlation function | |
scan.test | Spatial Scan Test | |
unique.ppp | Extract Unique Points from a Spatial Point Pattern | |
tiles | Extract List of Tiles in a Tessellation | |
owin.object | Class owin | |
pixellate.owin | Convert Window to Pixel Image | |
persp.im | Perspective Plot of Pixel Image | |
update.kppm | Update a Fitted Cluster Point Process Model | |
relrisk | Nonparametric Estimate of Spatially-Varying Relative Risk | |
rmhmodel | Define Point Process Model for Metropolis-Hastings Simulation. | |
quadratresample | Resample a Point Pattern by Resampling Quadrats | |
tilenames | Names of Tiles in a Tessellation | |
anova.slrm | Analysis of Deviance for Spatial Logistic Regression Models | |
density.splitppp | Kernel Smoothed Intensity of Split Point Pattern | |
rotate.ppp | Rotate a Point Pattern | |
envelope.pp3 | Simulation Envelopes of Summary Function for 3D Point Pattern | |
pixellate.psp | Convert Line Segment Pattern to Pixel Image | |
rmpoispp | Generate Multitype Poisson Point Pattern | |
diagnose.ppm | Diagnostic Plots for Fitted Point Process Model | |
trim.rectangle | Cut margins from rectangle | |
split.hyperframe | Divide Hyperframe Into Subsets and Reassemble | |
shift.ppp | Apply Vector Translation To Point Pattern | |
levelset | Level Set of a Pixel Image | |
latest.news | Print News About Latest Version of Package | |
subfits | Extract List of Individual Point Process Models | |
runifdisc | Generate N Uniform Random Points in a Disc | |
plot.lpp | Plot Point Pattern on Linear Network | |
rCauchy | Simulate Neyman-Scott Point Process with Cauchy cluster kernel | |
spatstat-package | The Spatstat Package | |
overlap.owin | Compute Area of Overlap | |
rlinegrid | Generate grid of parallel lines with random displacement | |
perimeter | Perimeter Length of Window | |
summary.listof | Summary of a List of Things | |
vcov.ppm | Variance-Covariance Matrix for a Fitted Point Process Model | |
union.quad | Union of Data and Dummy Points | |
flu | Influenza Virus Proteins | |
waka | Trees in Waka national park | |
runifpointx | Generate N Uniform Random Points in Any Dimensions | |
reduced.sample | Reduced Sample Estimator using Histogram Data | |
intensity.lpp | Empirical Intensity of Point Pattern on Linear Network | |
plot.symbolmap | Plot a Graphics Symbol Map | |
fv | Create a Function Value Table | |
nnfun.lpp | Nearest Neighbour Map on Linear Network | |
markstat | Summarise Marks in Every Neighbourhood in a Point Pattern | |
tess | Create a Tessellation | |
vargamma.estpcf | Fit the Neyman-Scott Cluster Point Process with Variance Gamma kernel | |
vcov.mppm | Calculate Variance-Covariance Matrix for Fitted Multiple Point Process Model | |
print.ppm | Print a Fitted Point Process Model | |
is.im | Test Whether An Object Is A Pixel Image | |
ppm | Fit Point Process Model to Data | |
redwood | California Redwoods Point Pattern (Ripley's Subset) | |
scaletointerval | Rescale Data to Lie Between Specified Limits | |
update.symbolmap | Update a Graphics Symbol Map. | |
update.ppm | Update a Fitted Point Process Model | |
rat | Ratio object | |
rNeymanScott | Simulate Neyman-Scott Process | |
qqplot.ppm | Q-Q Plot of Residuals from Fitted Point Process Model | |
Extract.psp | Extract Subset of Line Segment Pattern | |
is.multitype | Test whether Object is Multitype | |
Replace.im | Reset Values in Subset of Image | |
linnet | Create a Linear Network | |
rounding | Detect Numerical Rounding | |
rpoint | Generate N Random Points | |
selfcrossing.psp | Crossing Points in a Line Segment Pattern | |
pixellate | Convert Spatial Object to Pixel Image | |
affine.psp | Apply Affine Transformation To Line Segment Pattern | |
rDiggleGratton | Perfect Simulation of the Diggle-Gratton Process | |
rescale | Convert dataset to another unit of length | |
vcov.kppm | Variance-Covariance Matrix for a Fitted Cluster Point Process Model | |
plot.influence.ppm | Plot Influence Measure | |
distcdf | Distribution Function of Interpoint Distance | |
plot.kppm | Plot a fitted cluster point process | |
runifpoint3 | Generate N Uniform Random Points in Three Dimensions | |
humberside | Humberside Data on Childhood Leukaemia and Lymphoma | |
spatstat-deprecated | Deprecated spatstat functions | |
volume | Volume of an Object | |
runiflpp | Uniform Random Points on a Linear Network | |
tile.areas | Compute Areas of Tiles in a Tessellation | |
tweak.colourmap | Change Colour Values in a Colour Map | |
quantile.ewcdf | Quantiles of Weighted Empirical Cumulative Distribution Function | |
rmpoint | Generate N Random Multitype Points | |
kaplan.meier | Kaplan-Meier Estimator using Histogram Data | |
methods.linfun | Methods for Functions on Linear Network | |
rpoisppOnLines | Generate Poisson Point Pattern on Line Segments | |
summary.psp | Summary of a Line Segment Pattern Dataset | |
summary.ppp | Summary of a Point Pattern Dataset | |
rmhexpand | Specify Simulation Window or Expansion Rule | |
thomas.estpcf | Fit the Thomas Point Process by Minimum Contrast | |
sessionLibs | Print Names and Version Numbers of Libraries Loaded | |
plot.envelope | Plot a Simulation Envelope | |
update.rmhcontrol | Update Control Parameters of Metropolis-Hastings Algorithm | |
vertices | Vertices of a Window | |
localK | Neighbourhood density function | |
rpoisline | Generate Poisson Random Line Process | |
pointsOnLines | Place Points Evenly Along Specified Lines | |
predict.ppm | Prediction from a Fitted Point Process Model | |
rsyst | Simulate systematic random point pattern | |
triplet.family | Triplet Interaction Family | |
rshift.splitppp | Randomly Shift a List of Point Patterns | |
simba | Simulated data from a two-group experiment with replication within each group. | |
pcfcross | Multitype pair correlation function (cross-type) | |
lppm | Fit Point Process Model to Point Pattern on Linear Network | |
rmh.default | Simulate Point Process Models using the Metropolis-Hastings Algorithm. | |
rlabel | Random Re-Labelling of Point Pattern | |
nnmark | Mark of Nearest Neighbour | |
eval.im | Evaluate Expression Involving Pixel Images | |
bounding.box.xy | Convex Hull of Points | |
plot.quadrattest | Display the result of a quadrat counting test. | |
midpoints.psp | Midpoints of Line Segment Pattern | |
methods.fii | Methods for Fitted Interactions | |
pcfdot | Multitype pair correlation function (i-to-any) | |
Gmulti | Marked Nearest Neighbour Distance Function | |
MultiStrauss | The Multitype Strauss Point Process Model | |
will.expand | Test Expansion Rule | |
as.hyperframe | Convert Data to Hyperframe | |
bind.fv | Combine Function Value Tables | |
diameter.box3 | Geometrical Calculations for Three-Dimensional Box | |
bw.frac | Bandwidth Selection Based on Window Geometry | |
cut.im | Convert Pixel Image from Numeric to Factor | |
connected.ppp | Connected components of a point pattern | |
hyytiala | Scots pines and other trees at Hyytiala | |
lengths.psp | Lengths of Line Segments | |
intensity.ppp | Empirical Intensity of Point Pattern | |
pcfinhom | Inhomogeneous Pair Correlation Function | |
lut | Lookup Tables | |
linearmarkequal | Mark Connection Function for Multitype Point Pattern on Linear Network | |
linearKdot | Multitype K Function (Dot-type) for Linear Point Pattern | |
owin | Create a Window | |
im.object | Class of Images | |
matclust.estpcf | Fit the Matern Cluster Point Process by Minimum Contrast Using Pair Correlation | |
parres | Partial Residuals for Point Process Model | |
pcf.ppp | Pair Correlation Function of Point Pattern | |
nndist.ppx | Nearest Neighbour Distances in Any Dimensions | |
plot.leverage.ppm | Plot Leverage Function | |
plot.colourmap | Plot a Colour Map | |
methods.ppx | Methods for Multidimensional Space-Time Point Patterns | |
reload.or.compute | Compute Unless Previously Saved | |
simplify.owin | Approximate a Polygon by a Simpler Polygon | |
mucosa | Cells in Gastric Mucosa | |
project2segment | Move Point To Nearest Line | |
spatstat-internal | Internal spatstat functions | |
pairwise.family | Pairwise Interaction Process Family | |
sumouter | Compute Quadratic Forms | |
is.marked | Test Whether Marks Are Present | |
diameter.owin | Diameter of a Window | |
Fiksel | The Fiksel Interaction | |
Kmodel.kppm | K Function or Pair Correlation Function of Cluster Model or Cox model | |
zapsmall.im | Rounding of Pixel Values | |
circumradius | Circumradius and Diameter of a Linear Network | |
as.tess | Convert Data To Tessellation | |
deriv.fv | Calculate Derivative of Function Values | |
Kcom | Model Compensator of K Function | |
collapse.fv | Collapse Several Function Tables into One | |
hist.im | Histogram of Pixel Values in an Image | |
harmonic | Basis for Harmonic Functions | |
methods.units | Methods for Units | |
envelope | Simulation Envelopes of Summary Function | |
nearest.raster.point | Find Pixel Nearest to a Given Point | |
methods.kppm | Methods for Cluster Point Process Models | |
pppmatching.object | Class of Point Matchings | |
quadrats | Divide Region into Quadrats | |
pool.fasp | Pool Data from Several Function Arrays | |
rshift.ppp | Randomly Shift a Point Pattern | |
rpoislpp | Poisson Point Process on a Linear Network | |
rmhmodel.list | Define Point Process Model for Metropolis-Hastings Simulation. | |
rescale.psp | Convert Line Segment Pattern to Another Unit of Length | |
affine.ppp | Apply Affine Transformation To Point Pattern | |
shift | Apply Vector Translation | |
shift.psp | Apply Vector Translation To Line Segment Pattern | |
linearKcross.inhom | Inhomogeneous multitype K Function (Cross-type) for Linear Point Pattern | |
whist | Weighted Histogram | |
symbolmap | Graphics Symbol Map | |
predict.slrm | Predicted or Fitted Values from Spatial Logistic Regression | |
rcellnumber | Generate Random Numbers of Points for Cell Process | |
paracou | Kimboto trees at Paracou, French Guiana | |
plot.lppm | Plot a Fitted Point Process Model on a Linear Network | |
nndist.pp3 | Nearest neighbour distances in three dimensions | |
mppm | Fit Point Process Model to Several Point Patterns | |
crossdist.pp3 | Pairwise distances between two different three-dimensional point patterns | |
pool.quadrattest | Pool Several Quadrat Tests | |
model.matrix.slrm | Extract Design Matrix from Spatial Logistic Regression Model | |
plot.quad | Plot a Spatial Quadrature Scheme | |
pppmatching | Create a Point Matching | |
rMaternII | Simulate Matern Model II | |
pool.rat | Pool Data from Several Ratio Objects | |
round.ppp | Apply Numerical Rounding to Spatial Coordinates | |
quadscheme | Generate a Quadrature Scheme from a Point Pattern | |
rcell | Simulate Baddeley-Silverman Cell Process | |
rVarGamma | Simulate Neyman-Scott Point Process with Variance Gamma cluster kernel | |
shift.owin | Apply Vector Translation To Window | |
lgcp.estK | Fit a Log-Gaussian Cox Point Process by Minimum Contrast | |
methods.lpp | Methods for Point Patterns on a Linear Network | |
unitname | Name for Unit of Length | |
superimpose | Superimpose Several Geometric Patterns | |
marks | Marks of a Point Pattern | |
Geyer | Geyer's Saturation Point Process Model | |
rotate.im | Rotate a Pixel Image | |
as.data.frame.psp | Coerce Line Segment Pattern to a Data Frame | |
addvar | Added Variable Plot for Point Process Model | |
bw.smoothppp | Cross Validated Bandwidth Selection for Spatial Smoothing | |
clip.infline | Intersect Infinite Straight Lines with a Window | |
beachcolours | Create Colour Scheme for a Range of Numbers | |
eval.linim | Evaluate Expression Involving Pixel Images on Linear Network | |
crossdist.default | Pairwise distances between two different sets of points | |
effectfun | Compute Fitted Effect of a Spatial Covariate in a Point Process Model | |
hamster | Aherne's hamster tumour data | |
Softcore | The Soft Core Point Process Model | |
model.frame.ppm | Extract the Variables in a Point Process Model | |
crossdist.ppx | Pairwise Distances Between Two Different Multi-Dimensional Point Patterns | |
plot.owin | Plot a Spatial Window | |
pcf3est | Pair Correlation Function of a Three-Dimensional Point Pattern | |
plot.msr | Plot a Signed or Vector-Valued Measure | |
plot.splitppp | Plot a List of Point Patterns | |
plot.texturemap | Plot a Texture Map | |
quadrat.test | Dispersion Test for Spatial Point Pattern Based on Quadrat Counts | |
ppm.object | Class of Fitted Point Process Models | |
pairs.im | Scatterplot Matrix for Pixel Images | |
rpoislinetess | Poisson Line Tessellation | |
simplepanel | Simple Point-and-Click Interface Panels | |
simdat | Simulated Point Pattern | |
slrm | Spatial Logistic Regression | |
is.subset.owin | Determine Whether One Window is Contained In Another | |
vargamma.estK | Fit the Neyman-Scott Cluster Point Process with Variance Gamma kernel | |
thomas.estK | Fit the Thomas Point Process by Minimum Contrast | |
Extract.ppp | Extract or Replace Subset of Point Pattern | |
scanLRTS | Likelihood Ratio Test Statistic for Scan Test | |
with.hyperframe | Evaluate an Expression in Each Row of a Hyperframe | |
Lcross.inhom | Inhomogeneous Cross Type L Function | |
Kest.fft | K-function using FFT | |
as.matrix.owin | Convert Pixel Image to Matrix | |
border | Border Region of a Window | |
colourtools | Convert and Compare Colours in Different Formats | |
ants | Harkness-Isham ants' nests data | |
cut.ppp | Classify Points in a Point Pattern | |
distmap.owin | Distance Map of Window | |
Poisson | Poisson Point Process Model | |
contour.im | Contour plot of pixel image | |
as.mask | Pixel Image Approximation of a Window | |
with.fv | Evaluate an Expression in a Function Table | |
influence.ppm | Influence Measure for Spatial Point Process Model | |
eroded.areas | Areas of Morphological Erosions | |
clusterset | Allard-Fraley Estimator of Cluster Feature | |
linfun | Function on a Linear Network | |
pool.envelope | Pool Data from Several Envelopes | |
linearKdot.inhom | Inhomogeneous multitype K Function (Dot-type) for Linear Point Pattern | |
fryplot | Fry Plot of Point Pattern | |
as.data.frame.ppp | Coerce Point Pattern to a Data Frame | |
pixellate.ppp | Convert Point Pattern to Pixel Image | |
ppm.ppp | Fit Point Process Model to Point Pattern Data | |
plot.quadratcount | Plot Quadrat Counts | |
nnclean | Nearest Neighbour Clutter Removal | |
ppp.object | Class of Point Patterns | |
nnwhich.lpp | Identify Nearest Neighbours on a Linear Network | |
rGaussPoisson | Simulate Gauss-Poisson Process | |
rStraussHard | Perfect Simulation of the Strauss-Hardcore Process | |
runifpoint | Generate N Uniform Random Points | |
rmhmodel.ppm | Interpret Fitted Model for Metropolis-Hastings Simulation. | |
shapley | Galaxies in the Shapley Supercluster | |
redwoodfull | California Redwoods Point Pattern (Entire Dataset) | |
split.ppx | Divide Multidimensional Point Pattern into Sub-patterns | |
rho2hat | Smoothed Relative Density of Pairs of Covariate Values | |
edges2vees | List Dihedral Triples in a Graph | |
funxy | Spatial Function Class | |
suffstat | Sufficient Statistic of Point Process Model | |
scanpp | Read Point Pattern From Data File | |
rThomas | Simulate Thomas Process | |
print.owin | Print Brief Details of a Spatial Window | |
square | Square Window | |
sidelengths.owin | Side Lengths of Enclosing Rectangle of a Window | |
rstrat | Simulate Stratified Random Point Pattern | |
split.ppp | Divide Point Pattern into Sub-patterns | |
ppx | Multidimensional Space-Time Point Pattern | |
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Details
Nickname | Model Prisoner |
Date | 2014-05-09 |
License | GPL (>= 2) |
URL | http://www.spatstat.org |
LazyData | true |
NeedsCompilation | yes |
ByteCompile | true |
Packaged | 2014-05-09 02:56:49 UTC; adrian |
Repository | CRAN |
Date/Publication | 2014-05-09 11:24:31 |
imports | abind , deldir (>= 0.0-21) , mgcv , polyclip (>= 1.3-0) , tensor |
depends | base (>= 3.0.2) , graphics , grDevices , R (>= 3.0.2) , stats , utils |
suggests | gsl , locfit , maptools , RandomFields (>= 3.0.0) , rpanel , scatterplot3d , sm , spatial , tkrplot |
Contributors | Rolf Turner, Adrian Baddeley, Ege Rubak |
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