Package {rcosmo}

URL:	https://github.com/frycast/rcosmo
BugReports:	https://github.com/frycast/rcosmo/issues
Title:	Cosmic Microwave Background Data Analysis
Version:	1.1.5
Description:	Tools for handling and analysing spherical data on a HEALPix grid, with applications to cosmic microwave background maps. Supports reading FITS files, converting between spherical and Cartesian coordinates and HEALPix ordering schemes, selecting sky regions, sampling pixels, and visualising maps. Implements empirical covariance, correlation and variogram estimation, covariance model fitting, angular power spectrum estimation, and distributional and entropy-based comparisons of spherical data. The package and its methods are described by Fryer, Li and Olenko (2020) <doi:10.32614/RJ-2020-012>.
Depends:	R (≥ 4.5.0)
License:	GPL-3
Encoding:	UTF-8
Imports:	FITSio (≥ 2.1-0), Rcpp (≥ 0.12.11), mmap (≥ 0.6-17), tibble (≥ 1.4.2), rgl (≥ 0.99.16), cli (≥ 1.0.0), entropy (≥ 1.2.1), geoR (≥ 1.7-5.2.1), nnls (≥ 1.4)
Suggests:	testthat, gsl
LinkingTo:	Rcpp
Config/roxygen2/version:	8.0.0
NeedsCompilation:	yes
Packaged:	2026-10-19 08:14:11 UTC; runner
Author:	Daniel Fryer [aut, cre], Andriy Olenko [aut], Ming Li [aut], Yuguang Wang [aut]
Maintainer:	Daniel Fryer <d.fryer@latrobe.edu.au>
Repository:	CRAN
Date/Publication:	2026-10-28 12:20:02 UTC

Handling and Analysing CMB data

Description

Handling and Analysing Spherical, Healpix and Cosmic Microwave Background data on a HEALPix grid.

Details

The package rcosmo offers various tools for

• Downloading and transforming Cosmic Microwave Background radiation (CMB) and spherical data

• Working with Hierarchical Equal Area isoLatitude Pixelation of a sphere (Healpix)

• Spherical geometry

• Statistical analysis of CMB and spherical data

• Visualisation of Healpix data

Most of rcosmo features were developed for CMB, but it can also be used for other spherical data. It contains tools for transforming spherical data in cartesian and geographic coordinates to the Healpix representation.

Update

Current updates are available through URL: https://github.com/frycast/rcosmo

BugReports

https://github.com/frycast/rcosmo/issues

Author(s)

Daniel Fryer d.fryer@latrobe.edu.au, Andriy Olenko a.olenko@latrobe.edu.au, Ming Li Ming.Li@latrobe.edu.au, Yuguang Wang.

See Also

Useful links:

• https://github.com/frycast/rcosmo

• Report bugs at https://github.com/frycast/rcosmo/issues

CMBDat class

Description

The function CMBDat creates objects of class CMBDat. These are lists containing header information and other metadata as well as an element called data, whose columns may include, for example, the intensity (I), polarisation (Q, U), PMASK and TMASK. It also may contain an mmap object that points to the CMB map data table in the FITS file.

Usage

CMBDat(filename, mmap = FALSE, spix)

Arguments

Value

A list containing header information and other metadata as well as an element called data where: If mmap = FALSE then a data.frame is included, named data, whose columns may include, for example, the intensity (I), polarisation (Q, U), PMASK and TMASK. If mmap = TRUE then a mmap object is returned that points to the CMB map data table in the FITS file.

Examples

filename <- system.file("extdata", "CMB_testmap.fits", package = "rcosmo")
cmbdat <- CMBDat(filename, spix = 1:10)
class(cmbdat)
cmbdat$nside
cmbdat$ordering
head(cmbdat$data)

CMBDataFrame class

Description

The function CMBDataFrame creates objects of class CMBDataFrame. These are a special type of data.frame that carry metadata about, e.g., the HEALPix ordering scheme, coordinate system, and nside parameter.

Usage

CMBDataFrame(
  CMBData,
  coords,
  win,
  include.polar = FALSE,
  include.masks = FALSE,
  spix,
  sample.size,
  nside,
  ordering,
  I,
  ...
)

Arguments

Value

A CMBDataFrame whose row.names attribute contains HEALPix indices.

Examples

## Construct a small synthetic sky map.
df <- CMBDataFrame(nside = 16, I = rnorm(12 * 16 ^ 2),
                   ordering = "nested")

## Take a random sample.
df.sample <- CMBDataFrame(df, sample.size = 80)
plot(df.sample)

## Select pixels by index.
df.subset <- CMBDataFrame(df, spix = c(2,4,6))

## Inspect the map and the selected pixel indices.
summary(df)

pix(df.subset)

CMBWindow class.

Description

The function CMBWindow creates objects of class CMBWindow. It is either a polygon or a disc type.

Usage

CMBWindow(..., r, set.minus = FALSE, assume.convex = FALSE)

Arguments

Details

If r is unspecified then the rows of ... correspond to counter-clockwise ordered vertices defining a spherical polygon lying entirely within one open hemisphere on the unit sphere. Counter-clockwise is understood from the perspective outside the sphere, facing the hemisphere that contains the polygon, looking toward the origin. Note that there must be at least 3 rows (vertices) to define a polygon (we exclude bygones). On the other hand, if r is specified then ... must specify just one row, and this row is taken to be the center of a disc of radius r

Value

A data frame of class CMBWindow containing vertex coordinates for a polygon, or centre coordinates and radius r for a disc. Attributes record the coordinate system, window type and convexity assumption.

Examples

win <- CMBWindow(theta = c(pi/2,pi/2,pi/3, pi/3), phi = c(0,pi/3,pi/3,0))
plot(win)


## Create a disc type window
win1<- CMBWindow(x=0,y=3/5,z=4/5,r=0.8, set.minus =TRUE)
plot(win1)


## Apply a disc type window to CMBDataFrame
cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
window(cmbdf) <- CMBWindow(x=0,y=3/5,z=4/5,r=0.8, set.minus =TRUE)
plot(cmbdf)

HPDataFrame class

Description

HPDataFrames are a type of data.frame designed to carry data located on the unit sphere. Each row of a HPDataFrame is associated with a HEALPix pixel index. The HPDataFrame also holds an attribute called nside which stores the HEALPix Nside parameter (i.e., the resolution of the HEALPix grid that is being used). Unlike CMBDataFrame, HPDataFrames may have repeated pixel indices. They are made this way so that multiple data points falling within a given pixel can be stored in different rows of any given HPDataFrame.

Usage

HPDataFrame(
  ...,
  nside,
  ordering = "nested",
  auto.spix = FALSE,
  spix,
  assumedUniquePix = FALSE,
  delete.duplicates = FALSE,
  save.dots = FALSE,
  save.duplicate.indices = FALSE
)

Arguments

Details

HPDataFrame with auto.spix = TRUE can be used to transform any spherical data (not necessarily CMB) to the Healpix representation, see Example 3 below.

Value

A data frame of class HPDataFrame containing the supplied observations and any coordinate columns. HEALPix pixel indices are stored in the pix attribute; further attributes record nside, ordering and whether indices are assumed unique.

Examples

hp <- HPDataFrame(I = c(1, 2, 3), nside = 1, spix = c(1, 1, 2))
pix(hp)
assumedUniquePix(hp)
coords(hp, new.coords = "cartesian")

## Assign pixels automatically from three distinct locations.
hp.unique <- HPDataFrame(x = c(1, 0, 0), y = c(0, 1, 0), z = c(0, 0, 1),
                         auto.spix = TRUE)
pix(hp.unique)
assumedUniquePix(hp.unique)

Return index of kth ancestor pixel

Description

Gives the pixel at resolution j - k that contains p, where p is specified at resolution j (notice it does not depend on j).

Usage

ancestor(p, k)

Arguments

Value

A numeric vector of nested pixel indices at resolution j-k, identifying the ancestors containing the input pixels.

Examples

 ancestor(4,2)
 ancestor(17,2)

Check compatibleness of CMBDataFrames

Description

Compare attributes to decide if two CMBDataFrames are compatible

Usage

areCompatibleCMBDFs(cmbdf1, cmbdf2, compare.pix = FALSE)

Arguments

Details

If the CMBDataFrames do not have compatible attributes then a message is printed indicating the attributes that do not match. To suppress this use the suppressMessages function

Value

A single logical value, TRUE if both objects have the same nside and ordering, and also the same pixel indices when compare.pix = TRUE; otherwise FALSE. Incompatibilities are reported with a suppressible message.

Examples

a <- CMBDataFrame(nside = 2, ordering = "ring", coords = "cartesian")
b <- CMBDataFrame(nside = 1, ordering = "nested", coords = "spherical")
areCompatibleCMBDFs(a,b)

suppressMessages(areCompatibleCMBDFs(a,b))

Convert objects to CMBDataFrame

Description

Safely converts a data.frame to a CMBDataFrame. The rows of the data.frame are assumed to be in the HEALPix order given by ordering, and at the HEALPix resolution given by nside. Coordinates, if present, are assumed to correspond to HEALPix pixel centers. The coordinates must be named either x,y,z (cartesian) or theta, phi (spherical colatitude and longitude respectively). If df is a HPDataFrame then it is possible that df has attribute healpixCentered = TRUE, in which case as.CMBDataFrame will perform HEALPix centering of coordinates.

Usage

as.CMBDataFrame(df, ordering, nside, spix, drop.coords = FALSE)

Arguments

Value

A CMBDataFrame

Examples

## Example 1: Create df with no coords, then create CMBDataFrames cmbdf and
## df2 with spherical coords

df <- data.frame(I=rnorm(12))
df

cmbdf <- as.CMBDataFrame(df,ordering= "ring", nside=1)
summary(cmbdf)
pix(cmbdf)
coords(cmbdf)

df2 <- coords(cmbdf, new.coords = "spherical")
df2

## Example 2: Create CMBDataFrames for first 10 Healpix centers

df <- data.frame(I=rnorm(10))
df
cmbdf <- as.CMBDataFrame(df,ordering= "ring", nside=2, spix=1:10)
summary(cmbdf)
pix(cmbdf)

Check if a CMBWindow is assumed convex.

Description

Initially any CMBWindow is not assumed convex. The assumedConvex attribute can be change for any CMBWindow.

Usage

assumedConvex(win, assume.convex)

Arguments

Value

A logical value giving the convexity assumption when assume.convex is omitted; otherwise the CMBWindow with its convexity attribute updated.

Examples

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
assumedConvex(win1)
win2 <- assumedConvex(win1, assume.convex = TRUE)
assumedConvex(win2)
assumedConvex(win1) <- TRUE
assumedConvex(win1)

Change the assumedConvex boolean of a CMBWindow

Description

Change the assumedConvex boolean of a CMBWindow

Usage

assumedConvex(win, ...) <- value

Arguments

Value

A CMBWindow with its convexity assumption set to value.

Check if object was assumed to have unique HEALPix indices

Description

The function checks object's attribute assumedUniquePix. The attribute is True if the object was assumed to have rows that correspond to unique HEALPix pixel indices.

Usage

assumedUniquePix(obj)

Arguments

Value

A boolean. This is TRUE if obj is a CMBDataFrame or a HPDataFrame whose rows were assumed to correspond to unique HEALPix pixel indices.

Examples

hp1 <- HPDataFrame(I=rnorm(5), nside = 1, spix = c(1,1,2,2,3))
pix(hp1)
coords(hp1, new.coords = "cartesian")
assumedUniquePix(hp1)

sky <- CMBDataFrame(nside = 32, coords = "cartesian", ordering = "nested")
sky.s <- CMBDataFrame(sky, sample.size = 100)
hpdf <- HPDataFrame(sky.s, auto.spix = TRUE)
assumedUniquePix(hpdf)

Return neighbours of base pixels

Description

The base-resolution comprises twelve pixels. baseNeighbours returns a map from the base pixel index bp to the vector of base pixels that are neighbours of bp, in counterclockwise order of direction: S,SE,E,NE,N,NW,W,SW. The presence of -1 indicates that the corresponding direction is empty.

Usage

baseNeighbours(bp)

Arguments

Value

A numeric vector of eight neighbouring base pixel indices in the order S, SE, E, NE, N, NW, W, SW. Missing neighbours are coded as -1. Returns NULL for an index outside 1 to 12.

Examples

## Return neighbours of base pixel 1
baseNeighbours(1)

## There is no base pixel 14, so baseNeighbours returns NULL
baseNeighbours(14)

Border pattern is resolution independent

Description

Border pattern is resolution independent

Usage

borderPattern(ptype)

Arguments

Value

the output is useful as an index to the output of baseNeighbours. It will return the correct neighbouring base pixel in each direction. The 0 indicates to stay in current BP.

cbind for CMBDataFrames

Description

Add a new column or columns (vector, matrix or data.frame) to a CMBDataFrame. Note that method dispatch occurs on the first argument. So, the CMBDataFrame must be the first argument

Usage

## S3 method for class 'CMBDataFrame'
cbind(..., deparse.level = 1)

Arguments

Details

See the documentation for cbind

Value

A CMBDataFrame containing the combined columns, with HEALPix metadata and pixel indices retained from the single CMBDataFrame input.

Examples

cmbdf <- CMBDataFrame(nside = 1, ordering = "nested", coords = "spherical")
cmbdf2 <- cbind(cmbdf, myData = rep(1, 12))
cmbdf2

Chi-squared statistic for two CMBWindows

Description

This function returns the empirical chi-squared statistic for intensities observations from two CMBWindows of the specified CMBDataFrame. The functions employs the function chi2.empirical and uses histogram counts of intensities for computations.

Usage

chi2CMB(cmbdf, win1, win2, intensities = "I")

Arguments

Value

Estimated Chi-squared statistic for observations in two CMBWindows. For small sample sizes and many zero counts Chi-squared statistic is inefficient.

References

chi2.empirical

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
win2 <- CMBWindow(theta = c(pi/2, pi, pi/2), phi = c(0, 0, pi/2))
chi2CMB(cmbdf, win1, win2)

Return children of a pixel

Description

Gives four pixels at resolution j + 1 that are contained in p, where pis a pixel specified at resolution j (notice it does not depend on j).

Usage

children(p)

Arguments

Value

A numeric vector of four nested pixel indices at resolution j+1, identifying the children of pixel p.

Examples

children(11)

Coordinate conversion generic

Description

Detailed descriptions and and examples can be found in documentation for specific coords functions coords.CMBDataFrame, coords.CMBWindow, coords.HPDataFrame, coords.data.frame

Usage

coords(x, ...)

Arguments

Value

A character string naming the coordinate system when it is queried, or an object of the input class with converted coordinates when a new system is supplied. See the individual methods for supported classes.

See Also

coords.CMBDataFrame coords.CMBWindow coords.HPDataFrame coords.data.frame

Coordinate conversion generic

Description

Detailed descriptions and and examples can be found in documentation for specific coords functions coords.CMBDataFrame, coords.CMBWindow, coords.HPDataFrame, coords.data.frame

Usage

coords(x, ...) <- value

Arguments

Value

An object of the same class as x, with coordinates converted to the requested system.

Assign new coordinate system to a CMBDataFrame

Description

Assign new coordinate system to a CMBDataFrame

Usage

## S3 replacement method for class 'CMBDataFrame'
coords(x, ...) <- value

Arguments

Value

A CMBDataFrame with coordinates converted to the system specified by value.

See Also

coords.CMBDataFrame

Examples

## Create df with no coords, then create df2 with cartesian coords
df <- CMBDataFrame(nside = 16)
df
coords(df)
df2 <- coords(df, new.coords = "cartesian")
coords(df2)
coords(df)

## Change the coords of df directly (to spherical)
coords(df) <- "spherical"
df

Assign new coordinate system to CMBWindow

Description

Assign new coordinate system to CMBWindow

Usage

## S3 replacement method for class 'CMBWindow'
coords(x, ...) <- value

Arguments

Value

A CMBWindow with coordinates converted to the system specified by value.

Assign new coordinate system to a HPDataFrame

Description

Assign new coordinate system to a HPDataFrame

Usage

## S3 replacement method for class 'HPDataFrame'
coords(x, ...) <- value

Arguments

Value

A HPDataFrame with coordinates converted to the system specified by value.

See Also

coords.HPDataFrame

Examples

## Create df with no coords, then create df2 with cartesian coords
df <- HPDataFrame(I = rep(0,12), nside = 1)
df
df2 <- coords(df, new.coords = "cartesian")
df2
df

## Change the coords of df directly (to spherical)
coords(df) <- "spherical"
df

Assign new coordinate system to a data.frame

Description

Assign new coordinate system to a data.frame

Usage

## S3 replacement method for class 'data.frame'
coords(x, ...) <- value

Arguments

Value

A data.frame with coordinates converted to the system specified by value.

See Also

coords.data.frame

Examples

## Create df with no coords, then create df2 with cartesian coords
df <- data.frame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1))
df2 <- coords(df, new.coords = "cartesian")
df2
df

## Change the coords of df directly (to spherical)
coords(df) <- "spherical"
df

Coordinate system from a CMBDataFrame

Description

If new.coords is unspecified then this function returns the coordinate system used in the CMBDataFrame cmbdf. The coordinate system is either "cartesian" or "spherical". If a new coordinate system is specified, using e.g. new.coords = "spherical", then this function instead returns a new CMBDataFrame whose coordinates are of the specified type. The original CMBDataFrame, cmbdf, is unaffected. If you would like to change cmbdf without creating a new variable, then use coords<-.CMBDataFrame (see examples below).

Usage

## S3 method for class 'CMBDataFrame'
coords(x, new.coords, ...)

Arguments

Value

If new.coords is unspecified, then the name of the coordinate system of cmbdf is returned. Otherwise a new CMBDataFrame is returned equivalent to cmbdf but having the desired change of coordinates

Examples

## Create df with no coords, then create df2 with cartesian coords
df <- CMBDataFrame(nside = 16)
df
coords(df)
df2 <- coords(df, new.coords = "cartesian")
coords(df2)


## Change the coords of df directly (to spherical)
coords(df) <- "spherical"
coords(df)

Coordinate system from a CMBWindow

Description

This function returns the coordinate system used in a CMBWindow. The coordinate system is either "cartesian" or "spherical"

Usage

## S3 method for class 'CMBWindow'
coords(x, new.coords, ...)

Arguments

Details

If a new coordinate system is specified, using e.g. new.coords = "spherical", the coordinate system of the CMBWindow will be converted

Value

If new.coords is unspecified, then the name of the coordinate system of win is returned. Otherwise a new CMBWindow is returned equivalent to win but having the desired change of coordinates

Examples

## Create win with sperical coords, then change it to win1 with cartesian coords
win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
coords(win)
win1 <- coords(win, new.coords = "cartesian")
coords(win1)

## Change back to spherical coordinates

coords(win1) <- "spherical"
coords(win1)

Coordinate system from a HPDataFrame

Description

Add or change coordinates in a HPDataFrame. This does not affect the argument object hpdf. Instead it returns a new HPDataFrame with the desired coordinates. To change hpdf directly see coords<-.HPDataFrame.

Usage

## S3 method for class 'HPDataFrame'
coords(x, new.coords, healpixCentered = FALSE, ...)

Arguments

Details

If columns exist labelled x,y,z (cartesian) or theta, phi (colatitude and longitude respectively), then these will be treated as the coordinates of hpdf and converted accordingly. If columns x,y,z or theta,phi are not present then the healpix pixel indices as given by pix(hpdf) are used for assigning coordinates.

Value

A HPDataFrame with columns x,y,z (cartesian) or theta, phi (colatitude and longitude respectively)

Examples

df <- HPDataFrame(I = rep(0,12), nside = 1)
coords(df, new.coords = "cartesian")
# Notice that df is unchanged
df

# Instead, change df directly
coords(df) <- "spherical"

## specify cartesian coordinates then convert to spherical
hp1 <- HPDataFrame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1),
                   nside = 1, auto.spix = TRUE)
hp1 <- coords(hp1, new.coords = "spherical")

## Instead, ignore/drop existing coordinates and use HEALPix only
hp2 <- HPDataFrame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1),
                   nside = 1, auto.spix = TRUE)
hp2 <- coords(hp1, new.coords = "spherical", healpixCentered = TRUE)

Create a new data.frame with a given coordinate system

Description

This does not affect the original object unless new coordinate system is directly assigned.

Usage

## S3 method for class 'data.frame'
coords(x, new.coords, ...)

Arguments

Value

A new data.frame whose coordinates are as specified by new.coords

Examples

## Create df with no coords, then create df2 with spherical coords
df <- data.frame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1))
df

df2 <- coords(df, new.coords = "spherical")
df2


## The function coords does not affect the original object.
## To change the coords assign a new value ("spherical or "cartesian")

coords(df, new.coords = "spherical")
df
coords(df) <- "spherical"
df

Sample correlation function

Description

This function provides an empirical correlation function for data in a CMBDataFrame or data.frame. It assumes that data are from a stationary spherical random field and the correlation depends only on a geodesic distance between locations. Output is a binned correlation.

Usage

corrCMB(
  cmbdf,
  num.bins = 10,
  sample.size,
  max.dist = pi,
  breaks,
  equiareal = TRUE,
  calc.max.dist = FALSE
)

Arguments

Value

#' An object of the class CMBCorrelation that is a modification of variog from the package geoR with variogram values replaced by correlation.

The attribute "breaks" contains the break points used to create bins. The result has num.bins + 1 values since the first value at distance 0 is not counted as a bin.

u

a vector with distances.

v

a vector with estimated correlation values at distances given in u.

n

number of pairs in each bin

sd

standard deviation of the values in each bin

bins.lim

limits defining the interval spanned by each bin

ind.bin

a logical vector indicating whether the number of pairs in each bin is greater or equal to the value in the argument pairs.min

var.mark

variance of the data

beta.ols

parameters of the mean part of the model fitted by ordinary least squares

output.type

echoes the option argument

max.dist

maximum distance between pairs allowed in the correlation calculations

n.data

number of data

direction

direction for which the correlation was computed

call

the function call

References

geoR package,variog, variogramCMB, covCMB

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
corcmb <- corrCMB(cmbdf, max.dist = pi/2, num.bins = 6)
corcmb

Sample covariance function

Description

This function provides an empirical covariance function for data in a CMBDataFrame or data.frame. It assumes that data are from a stationary spherical random field and the covariance depends only on a geodesic distance between locations. Output is a binned covariance.

Usage

covCMB(
  cmbdf,
  num.bins = 10,
  sample.size,
  max.dist = pi,
  breaks,
  equiareal = TRUE,
  calc.max.dist = FALSE
)

Arguments

Value

An object of the class CMBCovariance that is a modification of variog from the package geoR with variogram values replaced by covariances.

The attribute "breaks" contains the break points used to create bins. The result has num.bins + 1 values since the first value, the sample variance, is not counted as a bin.

u

a vector with distances.

v

a vector with estimated covariance values at distances given in u.

n

number of pairs in each bin

sd

standard deviation of the values in each bin

bins.lim

limits defining the interval spanned by each bin

ind.bin

a logical vector indicating whether the number of pairs in each bin is greater or equal to the value in the argument pairs.min

var.mark

variance of the data

beta.ols

parameters of the mean part of the model fitted by ordinary least squares

output.type

echoes the option argument

max.dist

maximum distance between pairs allowed in the covariance calculations

n.data

number of data

direction

direction for which the covariance was computed

call

the function call

References

geoR package, variog, variogramCMB, corrCMB

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
Cov <- covCMB(cmbdf, max.dist = pi/2, num.bins = 6)
Cov

Covariance estimate via power spectra

Description

This function provides a covariance estimate using the values of the estimated power spectra.

Usage

covPwSp(PowerSpectra, Ns)

Arguments

Value

A data frame which first column is 1-d grid starting at -1+1/Ns and finishing at 1 with the step 2/Ns. The second column is the values of estimated covariances on this grid.

References

Formula (2.1) in Baran A., Terdik G. Power spectrum estimation of spherical random fields based on covariances. Annales Mathematicae et Informaticae 44 (2015) pp. 15–22.

Power Spectra data are from Planck Legacy Archive https://www.cosmos.esa.int/web/planck/pla

Examples

if (requireNamespace("gsl", quietly = TRUE)) {
  spectrum <- data.frame(l = 1:5, power = exp(-(1:5)))
  Cov_est <- covPwSp(spectrum, Ns = 100)
  plot(acos(Cov_est$t), Cov_est$Estimated_Cov, type = "l",
       xlab = "Angular distance", ylab = "Estimated covariance")
}

Computes values of covariance functions

Description

This function computes the covariances given the separation distance of locations. Options for different covariance functions on spheres are available. The function extends the function cov.spatial for additional covariance models on spheres.

Usage

covmodelCMB(
  obj,
  cov.model = "matern",
  cov.pars = stop("no cov.pars argument provided"),
  kappa = 0.5
)

Arguments

Details

The function returns the value of the covariance C(h) at the distance h. The covariance function has the form

C(h) = sigma^2 * rho(h/phi).

The parameters of the covariance are positive numbers sigma^2, phi and kappa.

Expressions for the correlation functions which are not included in the package geoR:

askey

rho(h/phi) = (1 - h/phi)^{kappa}, if h < phi;

0, otherwise.

c2wendland

rho(h/phi) = (1 + kappa * h/phi) * (1 - h/phi)^{kappa}, if h < phi;

0, otherwise.

c4wendland

rho(h/phi) = (1 + kappa * h/phi + (kappa^2 - 1) * (h/phi)^2 / 3) * (1 - h/phi)^{kappa}, if h < phi;

0, otherwise.

sinepower

rho(h/phi) = 1 - (sin(h/(2 phi))) ^{kappa}

multiquadric

C(h) = (1 - phi) ^{(2 * kappa)} / (1 + phi^2 - 2 * phi * cos(h))^{kappa}, 0<phi<1

Additional information can be found in the section Details in cov.spatial.

Value

Values of a covariance function for the given distances.

References

geoR package, cov.spatial

T. Gneiting. Strictly and non-strictly positive definite functions on spheres. Bernoulli 19 (2013), no. 4, 1327-1349.

Examples

## Compute Askey variogram at x = pi/4

1 - covmodelCMB(pi/4, cov.pars = c(1, pi), kappa = 3, cov.model = "askey" )

## Plot of the Askey covariance function

v1.f <- function(x, ...) {covmodelCMB(x, ...)}
curve( v1.f(x, cov.pars = c(1, 0.03), kappa = 3, cov.model = "askey"),
from = 0, to = 0.1, xlab = "distance", ylab = expression(cov(h)), lty = 2,
main = "covariance")

Plot HEALPix pixel boundaries

Description

Plot the HEALPix pixel boundaries at nside

Usage

displayPixelBoundaries(
  nside,
  eps = pi/90,
  col = "gray",
  lwd = 1,
  ordering,
  incl.labels = 1:(12 * nside^2),
  nums.col = col,
  nums.size = 1,
  font = 2,
  depth_test = "always",
  ...
)

Arguments

Value

Produces a plot of the HEALPix pixel boundaries.

Examples

displayPixelBoundaries(1, eps = pi/90, col = "red")
displayPixelBoundaries(2, eps = pi/90, col = "green")

Display the pixels and grandchildren

Description

Display the pixels spix at resolution j by colouring in the grandchildren of spix at resolution plot.j

Usage

displayPixels(
  boundary.j,
  j,
  plot.j = 5,
  spix,
  boundary.col = "gray",
  boundary.lwd = 1,
  incl.labels = 1:(12 * 4^boundary.j),
  col = "blue",
  size = 3
)

Arguments

Value

No meaningful return value; called for its side effect of drawing pixels and optional boundaries in the current rgl scene.

Examples

## Example 1

## Plot base pixels 1,2,3 by colouring their grandchildren at resolution
## 5 (by default). No pixel boundaries.
displayPixels(j=0, spix=c(1,2,3))

## Plot base pixels 1,2,3 display and their boundaries (boundary.j=0)
displayPixels(0,0, spix=c(1,2,3))

## Plot base pixels 1,2,3 by colouring their grandchildren at resolution 2
displayPixels(0,0, plot.j = 2, spix=c(1,2,3))

## Example 2

demoNeighbours <- function(p,j) {
  neighbours(p, j)
  displayPixels(boundary.j = j, j = j, plot.j = 5,
                spix = neighbours(p, j),
                boundary.col = "gray",
                boundary.lwd = 1,
                incl.labels = neighbours(p, j),
                col = "blue",
                size = 3)
  rcosmo::displayPixelBoundaries(nside = 1, col = "blue", lwd = 3)
}

demoNeighbours(1,2)

Download CMB Maps from Planck Public Data Release.

Description

The function downloadCMBMap downloads CMB maps from https://irsa.ipac.caltech.edu/data/Planck/release_2/all-sky-maps/matrix_cmb.html.

Usage

downloadCMBMap(foreground = "smica", nside = 1024, destfile, release = 2)

Arguments

Details

CMB maps have been produced by the COMMANDER, NILC, SEVEM, and SMICA pipelines, respectively.

For each pipeline, the intensity maps are provided at Nside = 2048, at 5 arcmin resolution, and the polarization maps are provided at Nside = 1024 at 10 arcmin resolution.

Value

The integer status code from utils::download.file, returned invisibly (0 indicates success). The FITS map is saved to destfile and can be read with CMBDataFrame.

References

Planck Public Data Release 2 Maps https://irsa.ipac.caltech.edu/data/Planck/release_2/all-sky-maps/matrix_cmb.html

Other fits maps can also be downloaded using the general command download.file.

Examples

## Requires internet access and downloads a large FITS file.
if (interactive()) {
  dest <- tempfile(fileext = ".fits")
  downloadCMBMap(foreground = "smica", nside = 1024, destfile = dest)
  sky <- CMBDataFrame(dest, spix = 1:10)
  unlink(dest)
}

Download CMB Power Spectra from Planck Legacy Archive.

Description

The function downloadCMBPS downloads CMB power spectra components from https://www.cosmos.esa.int/web/planck/pla.

Usage

downloadCMBPS(link = 1, destfile, save = TRUE)

Arguments

Details

link = 1: Best-fit LCDM CMB power spectra from the baseline Planck TT, TE, EE+lowE+lensing (2 <= ell <= 2508).

link = 2: Baseline high-ell Planck TT power spectra (2 <= ell <= 2508).

link = 3: Baseline high-ell Planck EE power spectra (2 <= ell <= 1996).

link = 4: Baseline high-ell Planck TE power spectra (2 <= ell <= 1996).

link = 5: Low-ell Planck EB power spectra (2 <= ell <= 29).

link = 6: Low-ell Planck BB power spectra (2 <= ell <= 29).

Value

A data frame returned invisibly, containing multipoles in column L and the selected power spectrum and uncertainty columns described above. When save = TRUE, it is also written to destfile.

References

Planck Legacy Archive https://www.cosmos.esa.int/web/planck/pla

Examples

## Requires internet access.
if (interactive()) {
  dest <- tempfile(fileext = ".txt")
  spectrum <- downloadCMBPS(link = 6, destfile = dest)
  unlink(dest)
  spectrum <- downloadCMBPS(link = 1, save = FALSE)
  plot(spectrum$L, spectrum$TT, type = "l")
}

CMB Entropy

Description

This function returns an estimated entropy for the specified CMBDataFrame column intensities and CMBWindow region. The functions employs the function entropy and uses histogram counts of intensities for computations. All arguments of the standard entropy can be used.

Usage

entropyCMB(cmbdf, win, intensities = "I", method)

Arguments

Value

Estimated Shannon entropy for observations in CMBWindow

References

entropy

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
entropyCMB(cmbdf, win1)

Threshold exceedance probability

Description

This function returns an estimated exceedance probability for the specified CMBDataFrame column intensities, threshold level alpha and CMBWindow region.

Usage

exprob(cmbdf, win, alpha, intensities = "I")

Arguments

Value

Estimated threshold exceedance probability

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
exprob(cmbdf, win1, alpha = mean(cmbdf$I))

Extreme values

Description

This function returns n largest extreme values for the specified CMBDataFrame column intensities and CMBWindow region.

Usage

extrCMB(cmbdf, win, n, intensities = "I")

Arguments

Value

A CMBDataFrame with n largest extreme values

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
extremes <- extrCMB(cmbdf, win1, 5)
extremes

Sample Renyi function

Description

This function computes values of the sample Renyi function. Returns the estimated values of T(q) for q taking values on a grid. For large data sets could be rather time consuming.

Usage

fRen(
  cmbdf,
  q.min = 1.01,
  q.max = 10,
  N = 20,
  k.box = log2(nside(cmbdf)) - 3,
  intensities = "I"
)

Arguments

Value

Data frame which first column is the sampling grid seq(q.min, q.max, length.out = N) of q values. Another column consists of values of the sample Renyi function T(q) computed on the grid using the k.boxth level dyadic decomposition of the unit ball.

References

(1) Leonenko, N., and Shieh, N. 2013. Rényi function for multifractal random fields. Fractals 21, Article No. 1350009.

(2) http://mathworld.wolfram.com/RenyiEntropy.html

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
Tq <- fRen(cmbdf, N = 5, k.box = 1)
plot(Tq$q, Tq$tq, xlab = "q", ylab = "Renyi function")

First Minkowski functional

Description

This function returns an area of the spherical region where measured values are above of the specified threshold level alpha.

Usage

fmf(cmbdf, alpha, intensities = "I")

Arguments

Value

The area of the exceedance region

References

Leonenko N., Olenko A. (2014) Sojourn measures of Student and Fisher-Snedecor random fields. Bernoulli, 20:1454-1483.

Examples

n <- 64
cmbdf <- CMBDataFrame(nside=n, I = rnorm(12*n^2),
                      coords = "cartesian",
                      ordering = "nested")
fmf(cmbdf, 0, 4)
fmf(cmbdf, 2, 4)

win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
cmbdf.win <- window(cmbdf, new.window = win)
fmf(cmbdf.win, 0, 4)

Convert geographic to spherical coordinates

Description

Convert latitude (lat) and longitude (lon) to spherical coordinates (theta, phi) with theta in [0,pi] and phi in [0,2*pi). All values lat, lon, theta, phi are assumed to be in radians.

Usage

geo2sph(...)

Arguments

Value

A data.frame with columns theta and phi.

Examples

geo <- data.frame( lat = c(0, pi/3, pi/2), lon = c(0, pi/3, pi))
geo
sph <- geo2sph(geo)
sph

Angle between two spherical directions

Description

Get an angle between two directions defined by arcs on the unit sphere

Usage

geoAngle(p1)

Arguments

Value

Let p1[1,], p1[2,], and p1[3,] denote the rows of p1. Then the returned object is an angle in radians beween two arcs determined by #'the pairs #'of spherical points (p1[1,], p1[2,]) and (p1[2,], p1[3,]) respectively.

Examples

  p1 <- data.frame(diag(3))
  p1
  colnames(p1) <- c("x", "y", "z")
  geoAngle(p1)

  geo <- data.frame( lat = c(30, 0, 20), lon = c(30, 60, 10))*(pi/180)
  geo
  p2 <- geo2sph(geo)
  p2
  geoAngle(p2)

geoArea generic

Description

Detailed descriptions and and examples can be found in documentation for specific geoArea functions geoArea.CMBDataFrame, geoArea.HPDataFrame, geoArea.CMBWindow

Usage

geoArea(x)

Arguments

Value

A numeric scalar giving the area covered by the object on the unit sphere, in steradians.

See Also

geoArea.CMBDataFrame geoArea.HPDataFrame geoArea.CMBWindow

Geodesic area covered by a CMBDataFrame

Description

Gives the surface on the unit sphere that is encompassed by all pixels in cmbdf

Usage

## S3 method for class 'CMBDataFrame'
geoArea(x)

Arguments

Value

The sum of the areas of all pixels (rows) in x.

Examples

## At low resolution, a few data points can
## occupy a large pixel area, e.g.:

cmbdf <- CMBDataFrame(nside = 1, spix = c(1,2,3))
pix(cmbdf)

## The total number of Healpix points at nside=1 equals 12. As cmbdf has 3 Healpix
## it occupies pi = 1/4*(surface area of unit sphere)

geoArea(cmbdf)
plot(cmbdf, size = 5, hp.boundaries = 1)

Geodesic area of a CMBWindow

Description

Geodesic area of a CMBWindow

Usage

## S3 method for class 'CMBWindow'
geoArea(x)

Arguments

Value

The spherical area inside the CMBWindow x.

Examples

## A window that covers 1/8 of the unit sphere is constructed and its area is
## pi/2 = 1/8*(surface area of unit sphere)

win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
geoArea(win)

Geodesic area covered by a HPDataFrame

Description

Gives the surface on the unit sphere that is encompassed by all pixels in x.

Usage

## S3 method for class 'HPDataFrame'
geoArea(x)

Arguments

Value

The sum of the areas of all pixels (rows) in x.

Examples

## Generate random I for HPDataFrame
hp1 <- HPDataFrame(I=rnorm(5), nside = 1, spix = c(1,1,2,2,3))
pix(hp1)

## The total number of Healpix points at nside=1 equals 12. As hp1 has five
## I values at 3 Healpix points, then the occupied area is
## pi = 1/4*(surface area of unit sphere)

geoArea(hp1)
plot(hp1, size = 5, hp.boundaries = 1)

Geodesic distance on the unit sphere

Description

Get geodesic distance between points on the unit sphere

Usage

geoDist(p1, p2, include.names = FALSE)

Arguments

Value

Let n denote the number of rows of p1 and let m denote the number of rows of p2. Then the returned object is an n by m matrix whose entry in position ij is the geodesic distance from the ith row of p1 to the jth row of p2.

Examples

p1 <- data.frame(diag(3))
colnames(p1) <- c("x", "y", "z")
p1
p2 <- data.frame(x=c(1,0), y=c(0,3/5), z=c(0,4/5))
p2
geoDist(p1, p2, include.names = FALSE)

Get the FITS headers from a CMBDataFrame

Description

Get the FITS headers from a CMBDataFrame

Usage

header(cmbdf)

Arguments

Value

The FITS headers belonging to the FITS file from which cmbdf data was imported

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
header(cmbdf)

Check if object is assumed to have HEALPix centered coordinates

Description

The function checks object's attribute healpixCentered. The attribute is TRUE if the object was assumed to have rows that correspond to unique HEALPix pixel indices.

Usage

healpixCentered(obj)

Arguments

Value

A boolean. This is TRUE if obj is a CMBDataFrame or a HPDataFrame whose coordinates were assumed to correspond to HEALPix pixel center locations.

Examples

hp1 <- HPDataFrame(I=rnorm(5), nside = 1, spix = c(1,1,2,2,3))
pix(hp1)
coords(hp1, new.coords = "cartesian")
healpixCentered(hp1)

sky <- CMBDataFrame(nside = 32, coords = "cartesian", ordering = "nested")
sky.s <- CMBDataFrame(sky, sample.size = 100)
hpdf <- HPDataFrame(sky.s, auto.spix = TRUE)
healpixCentered(hpdf)

Computes pixel's index using its subindex within base resolution

Description

Find the pixel index p of a given pixel with index ibp in base pixel bp.

Usage

ibp2p(ibp, bp, j)

Arguments

Value

A numeric vector of full-sky nested pixel indices at resolution j, combining the within-base indices and base pixel indices.

Examples

ibp2p(1, 1, 2)
ibp2p(1, 2, 2)

Check if an object is of class CMBDat

Description

Check if an object is of class CMBDat

Usage

is.CMBDat(cmbdf)

Arguments

Value

TRUE if cmbdf is a CMBDat object, otherwise FALSE

Examples

filename <- system.file("extdata", "CMB_testmap.fits", package = "rcosmo")
cmbdat <- CMBDat(filename, spix = 1:10)
is.CMBDat(cmbdat)

Check if an object is of class CMBDataFrame

Description

Check if an object is of class CMBDataFrame

Usage

is.CMBDataFrame(cmbdf)

Arguments

Value

TRUE if cmbdf is a CMBDataFrame, otherwise FALSE

Examples

df <- CMBDataFrame(nside = 16)
is.CMBDataFrame(df)
df2 <- coords(df, new.coords = "cartesian")
is.CMBDataFrame(df2)

Check if an object is a CMBWindow

Description

Check if an object is a CMBWindow

Usage

is.CMBWindow(win)

Arguments

Value

TRUE or FALSE depending if win is a CMBWindow

Examples

win <- CMBWindow(x=0,y=3/5,z=4/5,r=0.8, set.minus = TRUE)
is.CMBWindow(win)

Check if an object is of class HPDataFrame

Description

Check if an object is of class HPDataFrame

Usage

is.HPDataFrame(hpdf)

Arguments

Value

TRUE if hpdf is a HPDataFrame, otherwise FALSE

Examples

df <- CMBDataFrame(nside = 16)
is.HPDataFrame(df)

df <- HPDataFrame(I = rep(0,12), nside = 1)
is.HPDataFrame(df)

Calculate Jacobi polynomial values

Description

Calculate Jacobi polynomial values of degree L at given point T in [-1,1].

Usage

jacobiPol(a, b, L, t)

Arguments

Value

Jacobi polynomial values

Source

https://dlmf.nist.gov/18.9

Examples

jacobiPol(0,0,5,0)
jacobiPol(2,-5,2,-1)
jacobiPol(1,2,4,0.5)

Adds lines of fitted variograms to variogram plots

Description

This function adds a line with the variogram model fitted by the function variofitCMB to a current variogram plot. The function modifies lines.variomodel.variofit from the package geoR for additional covariance models on spheres.

Usage

linesCMB(x, max.dist, scaled = FALSE, ...)

Arguments

Details

The function adds a line with fitted variogram model to a plot. It is used to compare empirical variograms against fitted models returned by variofitCMB.

Available models are: "matern", "exponential", "spherical", "powered.exponential", "cauchy", "gencauchy", "pure.nugget", "askey", "c2wendland", "c4wendland", "sinepower", "multiquadric".

Value

A line with a fitted variogram model is added to a plot.

References

geoR package, lines.variomodel.variofit, covmodelCMB, variofitCMB

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
varcmb <- variogramCMB(cmbdf, max.dist = pi/2, num.bins = 6)
ols <- variofitCMB(varcmb, ini.cov.pars = c(1, 0.5),
                   cov.model = "matern", weights = "equal", messages = FALSE)
plot(varcmb)
linesCMB(ols, lty = 2)

Get the maximum geodesic distance between points

Description

Get the maximum geodesic distance either between all points in a data.frame pairwise, or between all points in a data.frame and one target point.

Usage

maxDist(df, point)

Arguments

Value

If point is specified: the longest geodesic distance from point to the points specified by the rows of df. If point is not specified: the longest geodesic distance pairwise between points in df.

Examples

## Using a CMBDataFrame with HEALPix coordinates only
cmbdf <- CMBDataFrame(nside = 1, spix = c(1,5,12), ordering = "ring")
plot(cmbdf, hp.boundaries = 1, col = "blue", size = 5)
p <- c(0,0,1)
maxDist(cmbdf, p) # no need to have coordinates

## Using a HPDataFrame with HEALPix coordinates only
hp <- HPDataFrame(nside = 1, I = rep(0,3), spix = c(1,5,12) )
maxDist(hp, p) # notice no need to have coordinates

## Using a data.frame with cartesian coordinates
coords(hp) <- "cartesian"
df <- data.frame(x = hp$x, y = hp$y, z = hp$z)
maxDist(df, p)

## Using a data.frame with spherical coordinates
coords(hp) <- "spherical"
df <- data.frame(theta = hp$theta, phi = hp$phi)
maxDist(df, p)

## max distance between points in cmdf
maxDist(cmbdf)

Get the maximum distance between all points in a CMBWindow

Description

Get the maximum distance between all points in a CMBWindow

Usage

maxWindowDist(x)

Arguments

Value

The maximum distance between window's points.

Examples

## win is a equilateral spherical triangle which sides are pi/2
win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
maxWindowDist(win)

Get the minimum geodesic distance between points

Description

Get the minimum geodesic distance either between all points in a data.frame pairwise, or between all points in a data.frame and one target point.

Usage

minDist(df, point)

Arguments

Value

If point is specified: the shortest distance from point to the points specified by the rows of df. If point is not specified: the shortest distance pairwise between points in df.

Examples

## Using a CMBDataFrame with HEALPix coordinates only
cmbdf <- CMBDataFrame(nside = 1, spix = c(1,5,12), ordering = "ring")
plot(cmbdf, hp.boundaries = 1, col = "blue", size = 5)
p <- c(0,0,1)
minDist(cmbdf, p) # no need to have coordinates

## Using a HPDataFrame with HEALPix coordinates only
hp <- HPDataFrame(nside = 1, I = rep(0,3), spix = c(1,5,12) )
minDist(hp, p) # notice no need to have coordinates

## Using a data.frame with cartesian coordinates
coords(hp) <- "cartesian"
df <- data.frame(x = hp$x, y = hp$y, z = hp$z)
minDist(df, p)

## Using a data.frame with spherical coordinates
coords(hp) <- "spherical"
df <- data.frame(theta = hp$theta, phi = hp$phi)
minDist(df, p)

## min distance between points in cmdf
minDist(cmbdf)

minDist2nside

Description

Get an nside such that all points belong to different pixels, when the minimum distance between the points is dist.

Usage

minDist2nside(dist, factor = 3/4)

Arguments

Details

We treat pixels as circles. From the total surface area of a unit sphere and the radius of a circle with area 4*pi/(12*nside^2), we derive a sufficiently large nside to achieve the desired separation. We aim for (circular) pixels with (default) radius dist*3/4.

Value

A numeric value (a power of two) giving the HEALPix nside selected by the circular-pixel approximation described above.

Return neighbouring pixels

Description

Return the neighbouring pixels to a given pixel p that is specified at resolution j, in the nested order.

Usage

neighbours(p, j)

Arguments

Value

A numeric vector of neighbouring pixel indices in nested order at resolution j; directions without a neighbour are omitted. For j > 0, the vector also includes p itself. For a vector of input pixels, a list of these vectors is returned.

Examples

## Return the neighbouring pixels for base pixel 1
neighbours(1, 0)

## Plot the neighbouring pixels for base pixel 1
demoNeighbours <- function(p,j) {
  neighbours(p, j)
  displayPixels(boundary.j = j, j = j, plot.j = j+3,
                spix = neighbours(p, j),
                boundary.col = "gray",
                boundary.lwd = 1,
                incl.labels = neighbours(p, j),
                col = "blue",
                size = 3)
  rcosmo::displayPixelBoundaries(nside = 1, col = "blue", lwd = 3)
}

demoNeighbours(1,2)
demoNeighbours(1,0)

Convert nest to ring ordering

Description

Convert from "nested" to "ring" ordering

nest2ring computes the HEALPix pixel index in the "ring" ordering scheme from the pixel index in the "nested" ordering scheme.

Usage

nest2ring(nside, pix)

Arguments

Value

the output is the corresponding set of pixel in the ring ordering scheme.

Examples

# compute HEALPix indices in the ring ordering scheme
nside <- 8
pix <-c(1,2,23)
nest2ring(nside,pix)

Finds the closest pixel center to a point

Description

Finds the closest HEALPix pixel center to a given target point, specified in Cartesian coordinates, using an efficient nested search algorithm. HEALPix indices are all assumed to be in the "nested" ordering scheme.

Usage

nestSearch(target, nside, index.only = FALSE, save.dots = FALSE)

Arguments

Value

if index.only = TRUE then the output will be a HEALPix index. If index.only FALSE then the output is the list containing the HEALPix index and Cartesian coordinate vector of the HEALPix point closest to target at resolution nside.

Examples

## Find the closest HEALPix pixel center at resolution j=2 for
## the point (0.6,0.8,0)

point <- c(0.6,0.8,0)
j <- 2
cpoint <- nestSearch(point, nside = 2^j)

## Plot the closest pixel center in blue and the point (0.6,0.8,0) in red
displayPixels(j, j, plot.j=j, spix=c(cpoint$pix),
              size=5, incl.labels =FALSE)
rgl::plot3d(point[1], point[2], point[3],
            col="red", size = 5, add = TRUE)


## Repeat the above for 4 points in a data.frame
points <- data.frame(x = c(1,0,0,0.6),
                     y = c(0,1,0,0.8),
                     z = c(0,0,1,0))
points
j <- 2
cpoints <- nestSearch(points, nside = 2^j)

## Plot the closest pixel center in blue and the point (0.6,0.8,0) in red
displayPixels(j, j, plot.j=j, spix=c(cpoints$pix),
              size=5, incl.labels =FALSE)
rgl::plot3d(points[,1], points[,2], points[,3],
            col="red", size = 5, add = TRUE)

nestSearch_step

Description

This function is intended for use only with nestSearch.

Usage

nestSearch_step(target, j2, pix.j1)

Arguments

Value

A vector containing the HEALPix pixel index, pix, of the closest HEALPix pixel center to the target point, target, at resolution j2, and its neighbours.

nside generic

Description

Detailed descriptions and and examples can be found in documentation for specific nside functions nside.CMBDataFrame, nside.HPDataFrame

Usage

nside(x)

Arguments

Value

A numeric scalar giving the HEALPix nside parameter. The corresponding full-sky grid contains 12*nside^2 pixels.

See Also

nside.CMBDataFrame nside.HPDataFrame

HEALPix Nside parameter from a CMBDataFrame

Description

This function returns the HEALPix Nside parameter of a CMBDataFrame

Usage

## S3 method for class 'CMBDataFrame'
nside(x)

Arguments

Value

The HEALPix Nside parameter.

Examples

df <- CMBDataFrame(nside = 16)
nside(df)

HEALPix Nside parameter from a HPDataFrame

Description

This function returns the HEALPix Nside parameter of a HPDataFrame

Usage

## S3 method for class 'HPDataFrame'
nside(x)

Arguments

Value

The HEALPix Nside parameter.

Examples

df <- HPDataFrame(I = rep(0,12), nside = 1)
nside(df)

numeric2col

Description

Map numeric values to a colour map

Usage

numeric2col(
  num,
  colmap = grDevices::terrain.colors(100),
  breaks.length = length(colmap)
)

Arguments

Value

A character vector of colours, one for each element of num, selected from colmap according to the discretised numeric values.

Examples

ns <- 16
sky <- CMBDataFrame(I = rnorm(12*ns^2), nside = ns)
plot(sky, col = numeric2col(sky$I))

a version of onBPBoundary to use with neighbours

Description

a version of onBPBoundary to use with neighbours

Usage

onBPBoundary(se, so, j)

Arguments

Value

An integer boundary code: 0 for an interior pixel, or 1 to 8 for S, SE, E, NE, N, NW, W and SW respectively.

ordering generic

Description

Detailed descriptions and and examples can be found in documentation for specific ordering functions ordering.CMBDataFrame, ordering.HPDataFrame

Usage

ordering(x, ...)

Arguments

Value

A character string, "nested" or "ring", when queried, or an object of the input class reordered to the requested scheme.

See Also

ordering.CMBDataFrame ordering.HPDataFrame

ordering generic

Description

Detailed descriptions and and examples can be found in documentation for specific ordering functions ordering.CMBDataFrame, ordering.HPDataFrame

Usage

ordering(x, ...) <- value

Arguments

Value

An object of the same class as x, with rows reordered to the requested HEALPix ordering.

See Also

ordering.CMBDataFrame ordering.HPDataFrame

Assign a new ordering scheme to a CMBDataFrame

Description

Assign a new ordering scheme to a CMBDataFrame

Usage

## S3 replacement method for class 'CMBDataFrame'
ordering(x, ...) <- value

Arguments

Value

A CMBDataFrame with rows and pixel indices reordered according to value.

See Also

ordering.CMBDataFrame

Examples

cmbdf <- CMBDataFrame(n = 1, ordering = "ring")
ordering(cmbdf) <- "nested"
ordering(cmbdf)

Assign new ordering scheme to HPDataFrame

Description

Assign new ordering scheme to HPDataFrame

Usage

## S3 replacement method for class 'HPDataFrame'
ordering(x, ...) <- value

Arguments

Value

A HPDataFrame with rows and pixel indices reordered according to value.

HEALPix ordering scheme from a CMBDataFrame

Description

This function returns the HEALPix ordering scheme from a CMBDataFrame. The ordering scheme is either "ring" or "nested".

Usage

## S3 method for class 'CMBDataFrame'
ordering(x, new.ordering, ...)

Arguments

Details

If a new ordering is specified, using e.g. new.ordering = "ring", the ordering scheme of the CMBDataFrame will be converted.

Value

The name of the HEALPix ordering scheme that is used in the CMBDataFrame x.

Examples

df <- CMBDataFrame(nside = 1, ordering = "nested")
ordering(df)
df1 <- ordering(df, new.ordering = "ring")
ordering(df1)

HEALPix ordering scheme from a HPDataFrame

Description

This function returns the HEALPix ordering scheme from a HPDataFrame. The ordering scheme is either "ring" or "nested". If a new ordering is specified, using e.g. new.ordering = "ring", the ordering scheme of the HPDataFrame will be converted.

Usage

## S3 method for class 'HPDataFrame'
ordering(x, new.ordering, ...)

Arguments

Value

The name of the HEALPix ordering scheme that is used in the HPDataFrame x, or a new HPDataFrame with the desired new.ordering

Examples

df <- HPDataFrame(I = rep(0,12), nside = 1, ordering = "nested")
ordering(df)
df1 <- ordering(df, new.ordering = "ring")
ordering(df1)

Return base pixel to which pixel belongs

Description

The base pixel to which pixel p belongs at resolution j

Usage

p2bp(p, j)

Arguments

Value

A numeric vector of base pixel indices from 1 to 12, identifying the base pixel containing each input pixel.

Examples

p2bp(5, 0)
p2bp(5, 1)

Return pixel index within its base pixel

Description

Convert a pixel index p to its index within the base pixel to which p belongs

Usage

p2ibp(p, j)

Arguments

Value

A numeric vector giving the nested index of each input pixel within its base pixel at resolution j.

Examples

p2ibp(6, 0)
p2ibp(6, 1)

Return index of parent pixel

Description

Gives the pixel at resolution j - 1 that contains p, where p is specified at resolution j (notice it does not depend on j).

Usage

parent(p)

Arguments

Value

A numeric vector of nested pixel indices at resolution j-1, identifying the parent containing each input pixel.

Examples

 parent(4)
 parent(5)

pix generic

Description

Detailed descriptions and and examples can be found in documentation for specific pix functions pix.CMBDataFrame, pix.HPDataFrame

Usage

pix(x, ...)

Arguments

Value

A numeric vector of HEALPix pixel indices when queried, or an object of the input class with updated pixel indices when new indices are supplied.

See Also

pix.CMBDataFrame pix.HPDataFrame

pix generic

Description

Detailed descriptions and and examples can be found in documentation for specific pix functions pix.CMBDataFrame, pix.HPDataFrame

Usage

pix(x, ...) <- value

Arguments

Value

An object of the same class as x, with updated HEALPix pixel indices.

See Also

pix.CMBDataFrame pix.HPDataFrame

Assign new pixel indices to a CMBDataFrame

Description

Assign new pixel indices to a CMBDataFrame

Usage

## S3 replacement method for class 'CMBDataFrame'
pix(x, ...) <- value

Arguments

Value

A CMBDataFrame with its HEALPix pixel indices replaced by value.

HEALPix pixel indices from CMBDataFrame

Description

If new.pix is unspecified then this function returns the vector of HEALPix pixel indices from a CMBDataFrame. If new.pix is specified then this function returns a new CMBDataFrame with the same number of rows as cmbdf, but with pix attribute new.pix. Thus, new.pix must have length equal to nrow(cmbdf).

Usage

## S3 method for class 'CMBDataFrame'
pix(x, new.pix, ...)

Arguments

Value

The vector of HEALPix pixel indices or, if new.pix is specified, a new CMBDataFrame.

Examples

df <- CMBDataFrame(nside = 16, sample.size = 10, ordering = "nested")
pix(df)

HEALPix pixel indices from HPDataFrame

Description

If new.pix is unspecified then this function returns the vector of HEALPix pixel indices from a HPDataFrame. If new.pix is specified then this function returns a new HPDataFrame with the same number of rows as x, but with pix attribute new.pix. Thus, new.pix must have length equal to nrow(x).

Usage

## S3 method for class 'HPDataFrame'
pix(x, new.pix, ...)

Arguments

Value

The vector of HEALPix pixel indices (integers) or, if new.pix is specified, a new HPDataFrame.

Examples

df <- HPDataFrame(I = rep(0,12), nside = 1)
pix(df)

Convert pixel indices to cartesian/spherical coordinates

Description

Convert HEALPix pixel indices to cartesian or spherical coordinates

Usage

pix2coords(nside, coords = "cartesian", ordering = "nested", spix)

Arguments

Value

a data.frame with columns 'x', 'y', 'z' (cartesian) or 'theta', 'phi' (spherical)

Examples

pix2coords(nside=1, spix=c(2,5))
pix2coords(nside=1,  coords = "spherical", spix=c(2,5))

Area of a HEALPix pixel

Description

Get the area of a single HEALPix pixel

Usage

pixelArea(nsideObject)

Arguments

Value

the area of a single HEALPix pixel at the nside resolution of nsideObject

Examples

df1 <- CMBDataFrame(nside = 64,
                    coords = "cartesian",
                    ordering = "nested")
pixelArea(df1)

Find high resolution pixels falling in a lower resolution window

Description

Find all pixels in a higher resolution that fall within the specified pixel area at a lower resolution. All pixels are assumed to be in nested ordering.

Usage

pixelWindow(j1, j2, pix.j1)

Arguments

Value

All pixels in resolution j2 that fall within the pixel pix.j1 specified at resolution j1

Examples

pixelWindow(3, 3, 2)
pixelWindow(3, 4, 2)
pixelWindow(3, 5, 2)

Plot sample CMBCorrelation

Description

Plots sample (empirical) correlation function. Uses plot.variogram from geoR package.

Usage

## S3 method for class 'CMBCorrelation'
plot(x, ...)

Arguments

Value

Produces a plot with the sample correlation function.

References

geoR package, corrCMB, variog, plot.variogram

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
corcmb <- corrCMB(cmbdf, max.dist = pi/2, num.bins = 6)
plot(corcmb)

Plot sample CMBCovariance

Description

Plots sample (empirical) covariance function. Uses plot.variogram from geoR package.

Usage

## S3 method for class 'CMBCovariance'
plot(x, ...)

Arguments

Value

Produces a plot with the sample covariance function.

#'@references geoR package, covCMB, variog, plot.variogram

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
Cov <- covCMB(cmbdf, max.dist = pi/2, num.bins = 6)
plot(Cov)

Plot CMB Data

Description

This function produces a plot from a CMBDataFrame.

Usage

## S3 method for class 'CMBDataFrame'
plot(
  x,
  intensities = "I",
  add = FALSE,
  sample.size,
  type = "p",
  size = 1,
  box = FALSE,
  axes = FALSE,
  aspect = FALSE,
  col,
  back.col = "black",
  labels,
  hp.boundaries = 0,
  hpb.col = "gray",
  depth_test = "less",
  lab_depth_test = "always",
  ...
)

Arguments

Value

A plot of the CMB data

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
plot(cmbdf)

Visualise a CMBWindow

Description

Visualise a CMBWindow

Usage

## S3 method for class 'CMBWindow'
plot(
  x,
  add = TRUE,
  type = "l",
  col = "red",
  size = 2,
  box = FALSE,
  axes = FALSE,
  aspect = FALSE,
  back.col,
  depth_test = "always",
  ...
)

Arguments

Value

No meaningful return value; called for its side effect of drawing the window in the current rgl scene.

Examples

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
win2 <- CMBWindow(theta = c(2*pi/3,3*pi/4,3*pi/4, 2*pi/3), phi = c(pi/4,pi/4,pi/3,pi/3))
plot(win1)
plot(win2)

Plot HPDataFrame

Description

This function produces a plot from a HPDataFrame. If columns x,y,z (cartesian) or theta,phi (colatitude and longitude respectively) are present in x, then these will be used as coordinates for plotting. Otherwise, the HEALPix indices as in pix(x) will be used. If HEALPix indices are used and multiple rows correspond to a single pixel index, then beware that values may be obfuscated in the plot, and all locations are pixel centers.

Usage

## S3 method for class 'HPDataFrame'
plot(
  x,
  intensities = "I",
  add = FALSE,
  sample.size,
  type = "p",
  size = 1,
  box = FALSE,
  axes = FALSE,
  aspect = FALSE,
  col = "blue",
  back.col = "black",
  labels,
  hp.boundaries = 0,
  hpb.col = "gray",
  depth_test = "less",
  lab_depth_test = "always",
  ...
)

Arguments

Value

A plot of the data locations according to coordinate columns or HEALPix index

Examples

hpdf <- HPDataFrame(I = rep(0,12), nside = 1)
plot(hpdf, size = 5, col = "yellow", back.col = "black",
     hp.boundaries = 1)

Plot sample variogram

Description

Plots sample (empirical) variogram. Uses plot.variogram from geoR package. See plot.variogram for usage and arguments.

Value

Produces a plot with the sample variogram.

References

geoR package, variogramCMB, variog, plot.variogram

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
varcmb <- variogramCMB(cmbdf, max.dist = pi/2, num.bins = 6)
plot(varcmb)

Plot angular scatterplots and means

Description

For specified measurements from CMBDataFrame this function produces scatterplots and binned means versus theta and phi angles.

Usage

plotAngDis(cmbdf, intensities = "I")

Arguments

Value

2x2 plot. The first row shows scatterplots. The second row gives barplots of the corresponding means computed over bins. The first column corresponds to the values of theta and the second one is for psi.

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
plotAngDis(cmbdf)

Plot theoretical CMBCovariance

Description

Plots theoretical covariance functions from the list defined in covmodelCMB

Usage

plotcovmodelCMB(
  cov.model = "matern",
  sigmasq = 1,
  phi = pi,
  kappa = 0.5,
  from = 0,
  to = pi,
  ...
)

Arguments

Value

Produces a plot with the theoretical covariance function.

References

covmodelCMB

Examples

plotcovmodelCMB("matern", sigmasq = 5)
plotcovmodelCMB("askey", phi = pi/4, to  = pi/2, kappa = 4)

Plot theoretical variogram

Description

Plots theoretical variogram functions from the list defined in covmodelCMB

Usage

plotvariogram(
  cov.model = "matern",
  sigmasq = 1,
  phi = pi,
  kappa = 0.5,
  from = 0,
  to = pi,
  ...
)

Arguments

Value

Produces a plot with the theoretical variogram.

References

covmodelCMB

Examples

plotvariogram("matern", sigmasq = 5)
plotvariogram("askey", phi = pi/4, to  = pi/2, kappa = 4)

Practical range for covariance function

Description

This function computes the practical range for covariance functions on spheres. The function extends practicalRange from the package geoR to additional covariance models on spheres.

Usage

practicalRangeCMB(cov.model, phi, kappa = 0.5, correlation = 0.05, ...)

Arguments

Details

The practical(effective) range for a covariance function is the distance at which a covariance function first time reaches the specified value correlation. For covariance functions on spheres the practical range does not exceed pi, the distance beyond which a covariance function is not defined. For the covariance functions "spherical", "askey", "c2wendland", "c4wendland" their practical ranges are equal to lengths of their support.

Value

Value of the practical range for the covariance function specified in covmodelCMB

References

geoR package, practicalRange, covmodelCMB

Examples

practicalRangeCMB(cov.model = "sinepower", phi = 0.1,  kappa = 0.5)
practicalRangeCMB(cov.model = "askey", phi = 0.1,  kappa = 0.5)

Print CMBDataFrame

Description

This function neatly prints the contents of a CMBDataFrame.

Usage

## S3 method for class 'CMBDataFrame'
print(x, ...)

Arguments

Value

Prints contents of the CMB data frame to the console.

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
print(cmbdf)

Print a HPDataFrame

Description

This function neatly prints the contents of a HPDataFrame.

Usage

## S3 method for class 'HPDataFrame'
print(x, ...)

Arguments

Value

Prints contents of the HPDataFrame to the console.

Examples

df <- HPDataFrame(I = rep(0,12), nside = 1, ordering = "nested")
print(df)
df

Print a summary of a CMBDataFrame

Description

Print a summary of a CMBDataFrame

Usage

## S3 method for class 'summary.CMBDataFrame'
print(x, ...)

Arguments

Value

The input summary.CMBDataFrame object, returned invisibly. Called for its side effect of printing the summary.

Print a summary of a CMBWindow

Description

Print a summary of a CMBWindow

Usage

## S3 method for class 'summary.CMBWindow'
print(x, ...)

Arguments

Value

The input summary.CMBWindow object, returned invisibly. Called for its side effect of printing the summary.

Print a summary of a HPDataFrame

Description

Print a summary of a HPDataFrame

Usage

## S3 method for class 'summary.HPDataFrame'
print(x, ...)

Arguments

Value

The input summary.HPDataFrame object, returned invisibly. Called for its side effect of printing the summary.

Power spectra estimate via correlation

Description

This function provides an angular power spectra estimate using the values of the sample correlations. The approach is based on Lawson-Hanson algorithm for non-negative least squares.

Usage

pwSpCorr(corcmb, lmax = 20 * length(corcmb$u))

Arguments

Value

A data frame which first column is 1-d grid of l values from 0 to lmax. The second column is estimated angular power spectra components on this grid.

References

Formula (2.1) in Baran A., Terdik G. Power spectrum estimation of spherical random fields based on covariances. Annales Mathematicae et Informaticae 44 (2015) pp. 15–22.

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
corcmb <- corrCMB(cmbdf, max.dist = pi, num.bins = 8)
pw <- pwSpCorr(corcmb, lmax = 10)
pw

Normal QQ plot for CMBWindow

Description

This function is a modification of standard qqnorm functions to work with CMBWindow regions.

Usage

qqnormWin(cmbdf, win, intensities = "I")

Arguments

Details

qqnormWin returns a normal QQ plot of for the specified CMBDataFrame column intensities and CMBWindow region. The function automatically adds a line of a “theoretical” normal quantile-quantile plot.

Value

A list with quantile components x and y and a normal QQ plot with QQ line

References

qqnorm, qqplot, qqplotWin

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
qqnormWin(cmbdf, win1)

Quantile-Quantile plots for CMBWindows

Description

This function is a modification of standard qqplot functions to work with CMBWindow regions.

Usage

qqplotWin(cmbdf, win1, win2, intensities = "I")

Arguments

Details

qqplotWin produces a QQ plot of quantiles of observations in two CMBWindows against each other for the specified CMBDataFrame column intensities. The function automatically adds a diagonal line.

Value

A list with quantile components x and y and a QQ plot with a diagonal line

References

qqnormWin, qqnorm, qqplot

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
win2 <- CMBWindow(theta = c(pi/2, pi, pi/2), phi = c(0, 0, pi/2))
qqplotWin(cmbdf, win1, win2)

q-statistic

Description

This function returns an estimated q-statistic for the specified column intensities in a CMBDataFrame and the list of CMBWindows.

Usage

qstat(cmbdf, listwin, intensities = "I")

Arguments

Details

The q-statistics is used to measure spatial stratified heterogeneity and takes values in [0, 1]. It gives the percent of the variance of intensities explained by the stratification. 0 corresponds to no spatial stratified heterogeneity, 1 to perfect spatial stratified heterogeneity.

Value

Estimated q-statistics for observations in a list of CMBWindows

References

Wang, J.F, Zhang, T.L, Fu, B.J. (2016). A measure of spatial stratified heterogeneity. Ecological Indicators. 67: 250–256.

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
win1 <- CMBWindow(theta = c(0, pi/2, pi/2), phi = c(0, 0, pi/2))
win2 <- CMBWindow(theta = c(pi/2, pi, pi/2), phi = c(0, 0, pi/2))
qstat(cmbdf, list(win1, win2))

rbind for CMBDataFrames

Description

Add a new row or rows to a CMBDataFrame. All arguments passed to ... must be CMBDataFrames. If the CMBDataFrame arguments have overlapping pixel indices then all but one of the non-unique rows will be deleted unless unsafe = TRUE. If unsafe = TRUE then a HPDataFrame will be returned instead of a CMBDataFrame.

Usage

## S3 method for class 'CMBDataFrame'
rbind(..., deparse.level = 1, unsafe = FALSE)

Arguments

Value

A CMBDataFrame containing the combined rows and windows, with overlapping pixel indices deduplicated. If unsafe = TRUE, returns an HPDataFrame retaining duplicate pixels instead. All inputs must have matching nside and ordering.

See Also

See the documentation for rbind

Examples

df <- CMBDataFrame(nside = 1, I = 1:12)

df.123 <- CMBDataFrame(df, spix = c(1,2,3))
df.123
df.234 <- CMBDataFrame(df, spix = c(2,3,4))
df.234

df.1234 <- rbind(df.123, df.234)
df.1234
class(df.1234) # A CMBDataFrame
pix(df.1234)

df.123234 <- rbind(df.123, df.234, unsafe = TRUE)
df.123234
class(df.123234) # A HPDataFrame
pix(df.123234)

Get the arcmin resolution from a CMBDataFrame

Description

Get the arcmin resolution from a CMBDataFrame

Usage

resolution(cmbdf)

Arguments

Value

The arcmin resolution as specified by the FITS file where the data was sourced

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
resolution(cmbdf)

Convert ring to nest ordering.

Description

ring2nest converts HEALPix pixel indices in the 'ring' ordering scheme to HEALPix pixel indices in the 'nested' ordering scheme.

Usage

ring2nest(nside, pix)

Arguments

Value

the output is a vector of HEALPix pixel indices in the 'nested' ordering scheme.

Examples

## Convert (1,2,23) from ring to nest at nside = 8
nside <- 8
pix <-c(1,2,23)
ring2nest(nside,pix)

Take a simple random sample from a CMBDataFrame

Description

This function returns a CMBDataFrame which size equals to sample.size, whose rows comprise a simple random sample of the rows from the input CMBDataFrame.

Usage

sampleCMB(cmbdf, sample.size)

Arguments

Value

A CMBDataFrame which size equals to sample.size, whose rows comprise a simple random sample of the rows from the input CMBDataFrame.

Examples

df <- CMBDataFrame(nside = 16, I = rnorm(12 * 16 ^ 2), ordering = "nested")
df.sample <- sampleCMB(df, sample.size = 100)
df.sample

separatingNside

Description

separatingNside

Usage

separatingNside(df)

Arguments

Value

An nside (power of 2) such that all points in df will belong to unique pixels.

Examples

sky <- CMBDataFrame(nside = 16, coords = "cartesian", ordering = "nested")
separatingNside(sky)

Return siblings of pixel

Description

The siblings of pixel p are defined as the children of the parent of p. Note this is resolution independent.

Usage

siblings(p)

Arguments

Value

An integer vector of four nested pixel indices sharing the same parent as p, including p itself.

Examples

siblings(11)
siblings(12)

Compute spherical harmonic values at given points on the sphere.

Description

The function sphericalHarmonics computes the spherical harmonic values for the given 3D Cartesian coordinates.

Usage

sphericalHarmonics(L, m, xyz)

Arguments

Value

values of spherical harmonics

References

See https://en.wikipedia.org/wiki/Table_of_spherical_harmonics

It uses equation (7) in Hesse, K., Sloan, I. H., & Womersley, R. S. (2010). Numerical integration on the sphere. In Handbook of Geomathematics (pp. 1185-1219). Springer Berlin Heidelberg,

but instead of the order k=1,...,2L+1 in the book we use m=k-L-1.

Examples

## Calculate spherical harmonic value at
## the point (0,1,0) with L=5, m=2
point<-data.frame(x=0,y=1,z=0)
sphericalHarmonics(5,2,point)

## Calculate spherical harmonic values at
## the point (1,0,0), (0,1,0), (0,0,1) with L=5, m=2
points<-data.frame(diag(3))
sphericalHarmonics(5,2,points)

subWindow

Description

Restricts a CMBDataFrame, CMBDat object, or data.frame to a CMBWindow region. A single CMBWindow or a list of CMBWindows can be passed to the win argument.

Usage

subWindow(cmbdf, win, intersect = TRUE, in.pixels, in.pixels.res = 0)

Arguments

Details

Windows that are tagged with set.minus (see CMBWindow) are treated differently from other windows.

If the argument is a list of CMBWindows, then interiors of all windows whose winType does not include "minus" are united (let A be their union) and exteriors of all windows whose winType does include "minus" are intersected, (let B be their intersection). Then, provided that intersect = TRUE (the default), the returned CMBDataFrame will be the points of cmbdf in the the intersection of A and B. Otherwise, if intersect = FALSE, the returned CMBDataFrame consists of the points of cmbdf in the union of A and B.

Note that if A (resp. B) is empty then the returned CMBDataFrame will be the points of cmbdf in B (resp. A).

Value

a CMBDataFrame, HPDataFrame, or just a data.frame, which is restricted to the region of the sky specified by win

Summarise a CMBDataFrame

Description

This function produces a summary from a CMBDataFrame.

Usage

## S3 method for class 'CMBDataFrame'
summary(object, intensities = "I", ...)

Arguments

Value

A summary includes window's type and area, total area covered by observations, and main statistics for intensity values

Examples

ns <- 16
df <- CMBDataFrame(I = rnorm(12*ns^2), nside = ns,
                   ordering = "nested")

win1 <- CMBWindow(x=0,y=3/5,z=4/5,r=0.8)
df.sample1 <- window(df, new.window = win1)
summary(df)

Summarise a CMBWindow

Description

This function produces a summary from a CMBWindow

Usage

## S3 method for class 'CMBWindow'
summary(object, ...)

Arguments

Value

A summary includes window's type and area

Examples

win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
summary(win)

win1<- CMBWindow(x=0,y=3/5,z=4/5,r=0.8, set.minus = TRUE)
summary(win1)

Summarise a HPDataFrame

Description

This function produces a summary from a HPDataFrame.

Usage

## S3 method for class 'HPDataFrame'
summary(object, intensities = "I", ...)

Arguments

Value

A summary includes window's type and area, total area covered by observations, and main statistics for intensity values

Examples

ns <- 2
hpdf <- HPDataFrame(I = rnorm(12*ns^2), nside = 2,
                    ordering = "nested")
win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
hpdf.win <- window(hpdf, new.window = win)
summary(hpdf.win)

Triangulate a polygonal CMBWindow

Description

Triangulate a polygonal CMBWindow

Usage

triangulate(win)

Arguments

Value

a list of CMBWindow polygons or minus.polygons, each having 3 vertices and representing a triangle. If winType of win does not include "minus" then these triangles have pairwise disjoint interiors and their union is equal to the original polygon, win. Otherwise, if winType of win does include "minus" the triangles are the same as for the non-minus type above, but have "minus" types.

Examples

## Example 1

win <- CMBWindow(theta = c(2*pi/3,3*pi/4,3*pi/4, 2*pi/3),
                 phi = c(pi/4,pi/4,pi/3,pi/3))
win
plot(win)
win1 <- triangulate(win)
win1
summary(win1[[1]])
plot(win1[[1]], add= FALSE, col="green")
plot(win1[[2]], col="blue")

## Example 2: triangilation minus-type polygon

win <- CMBWindow(theta = c(pi/5,pi/3,pi/4, pi/3, pi/5),
                 phi = c(pi/5,pi/5, pi/4 ,pi/3,pi/3), set.minus =TRUE)
win
plot(win)
summary(win)
win1 <- triangulate(win)
win1
plot(win1[[1]], add= FALSE, col="green")
plot(win1[[2]], col="blue")
plot(win1[[3]], col="yellow")
summary(win1[[1]])
summary(win1[[2]])
summary(win1[[3]])

Estimates parameters of variograms

Description

This function estimates variogram parameters by fitting a parametric model from covmodelCMB to a sample variogram. The function extends variofit from the package geoR to additional covariance models on spheres.

Usage

variofitCMB(
  vario,
  ini.cov.pars,
  cov.model,
  fix.nugget = FALSE,
  nugget = 0,
  fix.kappa = TRUE,
  kappa = 0.5,
  simul.number = NULL,
  max.dist = vario$max.dist,
  weights,
  minimisation.function,
  limits = geoR::pars.limits(),
  messages,
  ...
)

Arguments

Details

The parameter values of a variogram function from covmodelCMB are found by numerical optimization using one of the functions: optim, nlm and nls.

The function extends variofit from the package geoR to additional variogram models on spheres. Available models are: "matern", "exponential", "spherical", "powered.exponential", "cauchy", "gencauchy", "pure.nugget", "askey", "c2wendland", "c4wendland", "sinepower", "multiquadric".

Additionally it rescales an empirical variogram to the range [0,1] before numerical optimisation and then transforms all obtained results to the original scale. If ini.cov.pars are not provided then the 5x5 grid (seq(0,max(vario$v),l=5), seq(0,vario$max.dist,l=5)) of initial values of sigma^2 and phi is used.

Value

An object of the class variomodel and variofit, see variofit

References

geoR package, variofit, covmodelCMB

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
varcmb <- variogramCMB(cmbdf, max.dist = pi/2, num.bins = 6)
ols <- variofitCMB(varcmb, ini.cov.pars = c(1, 0.5),
                   cov.model = "matern", weights = "equal", messages = FALSE)
ols

Sample variogram

Description

This function provides an empirical variogram for data in a CMBDataFrame or data.frame. It assumes that data are from a stationary spherical random field and the covariance depends only on a geodesic distance between locations. Output is a binned variogram.

Usage

variogramCMB(
  cmbdf,
  num.bins = 10,
  sample.size,
  max.dist = pi,
  breaks,
  equiareal = TRUE,
  calc.max.dist = FALSE
)

Arguments

Value

An object of class variog specified in the package geoR.

The attribute "breaks" contains the break points used to create bins. The result has num.bins + 1 values since the first value at distance 0 is not counted as a bin.

u

a vector with distances.

v

a vector with estimated variogram values at distances given in u.

n

number of pairs in each bin

sd

standard deviation of the values in each bin

bins.lim

limits defining the interval spanned by each bin

ind.bin

a logical vector indicating whether the number of pairs in each bin is greater or equal to the value in the argument pairs.min

var.mark

variance of the data

beta.ols

parameters of the mean part of the model fitted by ordinary least squares

output.type

echoes the option argument

max.dist

maximum distance between pairs allowed in the variogram calculations

n.data

number of data

direction

direction for which the variogram was computed

call

the function call

References

geoR package, variog, covCMB, corrCMB

Examples

set.seed(1)
cmbdf <- CMBDataFrame(nside = 8, I = rnorm(12 * 8^2), ordering = "nested")
varcmb <- variogramCMB(cmbdf, max.dist = pi/2, num.bins = 6)
varcmb

Get/change winType

Description

Get/change the winType (polygon or disk) of a CMBWindow. If new.type is missing then the winType of win is returned. Otherwise, a new window is returned with winType equal to new.type. If you want to change the winType of win directly, then use winType<-, see the examples below.

Usage

winType(win, new.type)

Arguments

Value

If new.type is missing then the winType of win is returned. Otherwise a new window is returned with winType equal to new.type

Examples

win <- CMBWindow(theta = c(pi/2,pi/2,pi/3, pi/3), phi = c(0,pi/3,pi/3,0))
winType(win)

win1 <- CMBWindow(x=0,y=3/5,z=4/5,r=0.8)
winType(win1)
cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian",
                      ordering = "nested")
cmbdf.win1 <- window(cmbdf, new.window = win1)
plot(cmbdf.win1)


winType(win1) <- "minus.disc"
winType(win1)
cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian",
                      ordering = "nested")
cmbdf.win1 <- window(cmbdf, new.window = win1)
plot(cmbdf.win1)

Assign new winType to a CMBWindow

Description

Assign new winType to a CMBWindow

Usage

winType(win, ...) <- value

Arguments

Value

A CMBWindow with its window type set to value.

See Also

winType

Examples

win <- CMBWindow(x = 1, y = 0, z = 0, r = 0.5, set.minus = TRUE)
winType(win)
winType(win) <- "disc"
winType(win)

window generic

Description

Detailed descriptions and and examples can be found in documentation for specific window functions window.CMBDataFrame, window.HPDataFrame, window.data.frame

Usage

window(x, ...)

Arguments

Value

The stored window (a CMBWindow, a list of windows, or NULL for full sky) when queried, or an object of the input class restricted to the requested sky region. See the individual methods.

See Also

window.CMBDataFrame window.HPDataFrame window.data.frame

window generic

Description

Detailed descriptions and and examples can be found in documentation for specific window functions window.CMBDataFrame, window.HPDataFrame, window.data.frame

Usage

window(x, ...) <- value

Arguments

Value

An object of the same class as x, with observations restricted to the specified window.

See Also

window.CMBDataFrame window.HPDataFrame window.data.frame

Assign a new CMBWindow to a CMBDataFrame

Description

Assign a new CMBWindow to a CMBDataFrame

Usage

## S3 replacement method for class 'CMBDataFrame'
window(x, ...) <- value

Arguments

Value

A CMBDataFrame restricted to the window specified by value.

Get a sub window from a CMBDat object

Description

This function returns a data.frame containing the data in x restricted to the CMBWindow new.window

Usage

## S3 method for class 'CMBDat'
window(x, new.window, intersect = TRUE, ...)

Arguments

Details

Windows that are tagged with set.minus (see CMBWindow) are treated differently from other windows.

If the argument is a list of CMBWindows, then interious of all windows whose winType does not include "minus" are united (let A be their union) and exteriors of all windows whose winType does include "minus" are intersected, (let B be their intersection). Then, provided that intersect = TRUE (the default), the returned data.frame will be the points of cmbdat$data in the the intersection of A and B. Otherwise, if intersect = FALSE, the returned data.frame consists of the points of x$data in the union of A and B.

Note that if A (resp. B) is empty then the returned data.frame will be the points of x in B (resp. A).

Value

A CMBDataFrame containing the data in x restricted to the CMBWindow new.window

Examples

filename <- system.file("extdata", "CMB_testmap.fits", package = "rcosmo")
cmbdat <- CMBDat(filename)
win <- CMBWindow(x = 0, y = 0, z = 1, r = pi/2)
cmbdat.win <- window(cmbdat, new.window = win)
class(cmbdat.win)

Get a sub window from CMBDataFrame

Description

When new.window or in.pixels is unspecified this function returns the CMBWindow attribute of a CMBDataFrame. The return value is NULL if the window is full sky. When new.window is specified this function instead returns a new CMBDataFrame whose CMBWindow attribute is new.window

Usage

## S3 method for class 'CMBDataFrame'
window(x, new.window, intersect = TRUE, in.pixels, in.pixels.res = 0, ...)

Arguments

Details

Windows that are tagged with set.minus (see CMBWindow) are treated differently from other windows.

If the argument new.window is a list of CMBWindows, then interious of all windows whose winType does not include "minus" are united (let A be their union) and exteriors of all windows whose winType does include "minus" are intersected, (let B be their intersection). Then, provided that intersect = TRUE (the default), the returned CMBDataFrame will be the points of cmbdf in the the intersection of A and B. Otherwise, if intersect = FALSE, the returned CMBDataFrame consists of the points of x in the union of A and B.

Note that if A (resp. B) is empty then the returned CMBDataFrame will be the points of x in B (resp. A).

Value

The window attribute of x or, if new.window/in.pixels is specified, a new CMBDataFrame.

Examples

## Example 1: Create a new CMBDataFrame with a window

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian",
                      ordering = "nested")
win <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
cmbdf.win <- window(cmbdf, new.window = win)
plot(cmbdf.win)
window(cmbdf.win)

## Example 2: Change the window of an existing CMBDataFrame

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
window(cmbdf) <- win2 <- CMBWindow(theta = c(pi/6,pi/3,pi/3, pi/6),
                                   phi = c(0,0,pi/6,pi/6))
plot(cmbdf)

## Example 3: union of windows

## Create 2 windows
win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
win2 <- CMBWindow(theta = c(2*pi/3,3*pi/4,3*pi/4, 2*pi/3),
                            phi = c(pi/4,pi/4,pi/3,pi/3))
plot(win1)
plot(win2)

## Create CMBDataFrame with points in the union of win1 and win2

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
cmbdf.win <- window(cmbdf, new.window = list(win1, win2), intersect = FALSE)
plot(cmbdf.win)

## Example 4: intersection of windows

## Create 2 windows
win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
win2 <- CMBWindow(theta = c(pi/4,pi/3,pi/3, pi/4),
                  phi = c(pi/4,pi/4,pi/3,pi/3))
plot(win1)
plot(win2)

## Create CMBDataFrame with points in the intersection of win1 and win2

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
cmbdf.win1 <- window(cmbdf, new.window = win1)
cmbdf.win12 <- window(cmbdf.win1, new.window = win2)
plot(cmbdf.win12)
plot(win1)
plot(win2)


## Example 5: intersection of windows with "minus" type

## Create 2 windows with "minus" type
win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2),
                  set.minus =TRUE)
win2 <- CMBWindow(theta = c(pi/4,pi/3,pi/3, pi/4),
                  phi = c(pi/4,pi/4,pi/3,pi/3),
                  set.minus =TRUE)
plot(win1)
plot(win2)

## Create CMBDataFrame with points in the intersection of win1 and win2

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
cmbdf.win <- window(cmbdf, new.window = list(win1, win2))
plot(cmbdf.win)


## Example 6: intersection of windows with different types

##Create 2 windows, one with "minus" type

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
win2 <- CMBWindow(theta = c(pi/4,pi/3,pi/3, pi/4),
                  phi = c(pi/4,pi/4,pi/3,pi/3),
                  set.minus =TRUE)
plot(win1)
plot(win2)

## Create CMBDataFrame with points in the intersection of win1 and win2

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
cmbdf.win <- window(cmbdf, new.window = list(win1, win2), intersect = TRUE)
plot(cmbdf.win)

## Example 7: union of windows with different types

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2), set.minus =TRUE)
win2 <- CMBWindow(theta = c(pi/4,pi/3,pi/3, pi/4), phi = c(pi/4,pi/4,pi/3,pi/3))
plot(win1)
plot(win2)

## Create CMBDataFrame with points in the union of win1 and win2

cmbdf <- CMBDataFrame(nside = 64, coords = "cartesian", ordering = "nested")
cmbdf.win <- window(cmbdf, new.window = list(win1, win2), intersect = FALSE)
plot(cmbdf.win)

Get a sub window from a HPDataFrame

Description

This function returns a HPDataFrame containing the data in hpdf restricted to the CMBWindow new.window. If the HPDataFrame has columns x,y,z or theta, phi then these will be used to determine locations with priority over the HEALPix indices in pix(hpdf) unless healpixCentered = TRUE is given. Note that if healpixCentered = TRUE then columns x,y,z or theta, phi will be discarded and replaced with pixel center locations.

Usage

## S3 method for class 'HPDataFrame'
window(x, new.window, intersect = TRUE, healpixCentered = FALSE, ...)

Arguments

Details

Windows that are tagged with set.minus (see CMBWindow) are treated differently from other windows.

If the argument is a list of CMBWindows, then interiors of all windows whose winType does not include "minus" are united (let A be their union) and exteriors of all windows whose winType does include "minus" are intersected, (let B be their intersection). Then, provided that intersect = TRUE (the default), the returned data.frame will be the points of df in the the intersection of A and B. Otherwise, if intersect = FALSE, the returned data.frame consists of the points of df in the union of A and B.

Note that if A (resp. B) is empty then the returned data.frame will be the points of df in B (resp. A).

Value

A HPDataFrame containing the data in x restricted to the CMBWindow new.window. Or, if new.window is unspecified, then the window attribute of x is returned instead (and may be NULL).

Examples

ns <- 16
hpdf <- HPDataFrame(nside = ns, I = 1:(12*ns^2))
hpdf

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))
plot(hpdf); plot(win1)

hpdf.win <- window(hpdf, new.window = win1)
plot(hpdf.win, col = "yellow", size = 4, add = TRUE)
attributes(hpdf.win)
window(hpdf.win)
hpdf.win

Get a sub window from a data.frame

Description

This function returns a data.frame containing the data in x restricted to the CMBWindow new.window

Usage

## S3 method for class 'data.frame'
window(x, new.window, intersect = TRUE, ...)

Arguments

Details

Windows that are tagged with set.minus (see CMBWindow) are treated differently from other windows.

If the argument is a list of CMBWindows, then interiors of all windows whose winType does not include "minus" are united (let A be their union) and exteriors of all windows whose winType does include "minus" are intersected, (let B be their intersection). Then, provided that intersect = TRUE (the default), the returned data.frame will be the points of x in the the intersection of A and B. Otherwise, if intersect = FALSE, the returned data.frame consists of the points of x in the union of A and B.

Note that if A (resp. B) is empty then the returned data.frame will be the points of x in B (resp. A).

Value

A data.frame containing the data in x restricted to the CMBWindow new.window

Examples

win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2))

cmbdf <- CMBDataFrame(nside = 4)
df2 <- coords(cmbdf, new.coords = "cartesian")
df <- as.data.frame(df2[,1:3])
df
df.win <- window(df, new.window = win1)
df.win