Package 'rcosmo'

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)

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))

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)

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)

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)

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)

Description

Gives four pixels at resolution $j + 1$ that are contained in $p$, where $p$is 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)

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)

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)

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)

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 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)

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

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)

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

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

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")

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")
}

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")

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)

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)
}

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")
}

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)

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))

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

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)

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 $k.box$th 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")

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

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)

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)

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 $i$th row of p1 to the $j$th 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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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))

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

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)

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)

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)

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)

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)

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

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)

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))

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)

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)

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)

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)

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)

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)