Corrfunc.mocks package¶
Wrapper for all clustering statistic calculations on galaxies in a mock catalog.

Corrfunc.mocks.
DDrppi_mocks
(autocorr, cosmology, nthreads, pimax, binfile, RA1, DEC1, CZ1, weights1=None, RA2=None, DEC2=None, CZ2=None, weights2=None, is_comoving_dist=False, verbose=False, output_rpavg=False, fast_divide_and_NR_steps=0, xbin_refine_factor=2, ybin_refine_factor=2, zbin_refine_factor=1, max_cells_per_dim=100, copy_particles=True, enable_min_sep_opt=True, c_api_timer=False, isa=u'fastest', weight_type=None)[source]¶ Calculate the 2D paircounts corresponding to the projected correlation function, \(\xi(r_p, \pi)\). Pairs which are separated by less than the
rp
bins (specified inbinfile
) in the XY plane, and less thanpimax
in the Zdimension are counted. The input positions are expected to be onsky coordinates. This module is suitable for calculating correlation functions for mock catalogs.If
weights
are provided, the resulting pair counts are weighted. The weighting scheme depends onweight_type
.Returns a numpy structured array containing the pair counts for the specified bins.
Note
that this module only returns pair counts and not the actual correlation function \(\xi(r_p, \pi)\) or \(wp(r_p)\). See the utilities
Corrfunc.utils.convert_3d_counts_to_cf
andCorrfunc.utils.convert_rp_pi_counts_to_wp
for computing \(\xi(r_p, \pi)\) and \(wp(r_p)\) respectively from the pair counts.Parameters:  autocorr (boolean, required) – Boolean flag for auto/crosscorrelation. If autocorr is set to 1, then the second set of particle positions are not required.
 cosmology (integer, required) –
Integer choice for setting cosmology. Valid values are 1>LasDamas cosmology and 2>Planck cosmology. If you need arbitrary cosmology, easiest way is to convert the
CZ
values into comoving distance, based on your preferred cosmology. Setis_comoving_dist=True
, to indicate that the comoving distance conversion has already been done. Choices:
 LasDamas cosmology. \(\Omega_m=0.25\), \(\Omega_\Lambda=0.75\)
 Planck cosmology. \(\Omega_m=0.302\), \(\Omega_\Lambda=0.698\)
To setup a new cosmology, add an entry to the function,
init_cosmology
inROOT/utils/cosmology_params.c
and reinstall the entire package.  nthreads (integer) – The number of OpenMP threads to use. Has no effect if OpenMP was not enabled during library compilation.
 pimax (double) –
A doubleprecision value for the maximum separation along the Zdimension.
Distances along the \(\pi\) direction are binned with unit depth. For instance, if
pimax=40
, then 40 bins will be created along thepi
direction. Only pairs with0 <= dz < pimax
are counted (no equality).  binfile (string or an list/array of floats) –
For string input: filename specifying the
rp
bins forDDrppi_mocks
. The file should contain whitespace separated values of (rpmin, rpmax) for eachrp
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For arraylike input: A sequence of
rp
values that provides the binedges. For example,np.logspace(np.log10(0.1), np.log10(10.0), 15)
is a valid input specifying 14 (logarithmic) bins between 0.1 and 10.0. This array does not need to be sorted.  RA1 (arraylike, real (float/double)) –
The array of Right Ascensions for the first set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
 DEC1 (arraylike, real (float/double)) –
Array of Declinations for the first set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA1.
 CZ1 (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the first set of points. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If is_comoving_dist is set, then
CZ1
is interpreted as the comoving distance, rather than cz.  weights1 (array_like, real (float/double), optional) – A scalar, or an array of weights of shape (n_weights, n_positions) or (n_positions,). weight_type specifies how these weights are used; results are returned in the weightavg field. If only one of weights1 and weights2 is specified, the other will be set to uniform weights.
 RA2 (arraylike, real (float/double)) –
The array of Right Ascensions for the second set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Must be of same precision type as RA1/DEC1/CZ1.
 DEC2 (arraylike, real (float/double)) –
Array of Declinations for the second set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA1/DEC1/CZ1.
 CZ2 (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the second set of points. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If is_comoving_dist is set, then
CZ2
is interpreted as the comoving distance, rather than cz.Must be of same precision type as RA1/DEC1/CZ1.
 weights2 (arraylike, real (float/double), optional) – Same as weights1, but for the second set of positions
 is_comoving_dist (boolean (default false)) – Boolean flag to indicate that
cz
values have already been converted into comoving distances. This flag allows arbitrary cosmologies to be used inCorrfunc
.  verbose (boolean (default false)) – Boolean flag to control output of informational messages
 output_rpavg (boolean (default false)) –
Boolean flag to output the average
rp
for each bin. Code will run slower if you set this flag.If you are calculating in singleprecision,
rpavg
will suffer suffer from numerical loss of precision and can not be trusted. If you need accuraterpavg
values, then pass in double precision arrays for the particle positions.  fast_divide_and_NR_steps (integer (default 0)) – Replaces the division in
AVX
implementation with an approximate reciprocal, followed byfast_divide_and_NR_steps
of NewtonRaphson. Can improve runtime by ~1520% on older computers. Value of 0 uses the standard division operation.  (xyz)bin_refine_factor (integer, default is (2,2,1); typically within [13]) – Controls the refinement on the cell sizes. Can have up to a 20% impact on runtime.
 max_cells_per_dim (integer, default is 100, typical values in [50300]) – Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^3. Only increase if
rpmax
is too small relative to the boxsize (and increasing helps the runtime).  copy_particles (boolean (default True)) –
Boolean flag to make a copy of the particle positions If set to False, the particles will be reordered inplace
New in version 2.3.0.
 enable_min_sep_opt (boolean (default true)) –
Boolean flag to allow optimizations based on min. separation between pairs of cells. Here to allow for comparison studies.
New in version 2.3.0.
 c_api_timer (boolean (default false)) – Boolean flag to measure actual time spent in the C libraries. Here to allow for benchmarking and scaling studies.
 isa (string, caseinsensitive (default
fastest
)) –Controls the runtime dispatch for the instruction set to use. Possible options are: [
fastest
,avx512f
,avx
,sse42
,fallback
]Setting isa to
fastest
will pick the fastest available instruction set on the current computer. However, if you setisa
to, say,avx
andavx
is not available on the computer, then the code will revert to usingfallback
(even thoughsse42
might be available).Unless you are benchmarking the different instruction sets, you should always leave
isa
to the default value. And if you are benchmarking, then the string supplied here gets translated into anenum
for the instruction set defined inutils/defs.h
.  weight_type (string, optional (default None)) – The type of weighting to apply. One of [“pair_product”, None].
Returns:  results (Numpy structured array) – A numpy structured array containing [rpmin, rpmax, rpavg, pimax,
npairs, weightavg] for each radial bin specified in the
binfile
. Ifoutput_ravg
is not set, thenrpavg
will be set to 0.0 for all bins; similarly forweightavg
.npairs
contains the number of pairs in that bin and can be used to compute the actual \(\xi(r_p, \pi)\) or \(wp(rp)\) by combining with (DR, RR) counts.  api_time (float, optional) – Only returned if
c_api_timer
is set.api_time
measures only the time spent within the C library and ignores all python overhead.
Example
>>> from __future__ import print_function >>> import numpy as np >>> from os.path import dirname, abspath, join as pjoin >>> import Corrfunc >>> from Corrfunc.mocks.DDrppi_mocks import DDrppi_mocks >>> import math >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../mocks/tests/", "bins") >>> N = 100000 >>> boxsize = 420.0 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> Y = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> Z = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> weights = np.ones_like(X) >>> CZ = np.sqrt(X*X + Y*Y + Z*Z) >>> inv_cz = 1.0/CZ >>> X *= inv_cz >>> Y *= inv_cz >>> Z *= inv_cz >>> DEC = 90.0  np.arccos(Z)*180.0/math.pi >>> RA = (np.arctan2(Y, X)*180.0/math.pi) + 180.0 >>> autocorr = 1 >>> cosmology = 1 >>> nthreads = 2 >>> pimax = 40.0 >>> results = DDrppi_mocks(autocorr, cosmology, nthreads, ... pimax, binfile, RA, DEC, CZ, ... weights1=weights, weight_type='pair_product', ... output_rpavg=True, is_comoving_dist=True) >>> for r in results[519:]: print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10.1f}" ... " {4:10d} {5:10.6f}".format(r['rmin'], r['rmax'], ... r['rpavg'], r['pimax'], r['npairs'], r['weightavg'])) ... # doctest: +NORMALIZE_WHITESPACE 11.359969 16.852277 14.285169 40.0 104850 1.000000 16.852277 25.000000 21.181246 1.0 274144 1.000000 16.852277 25.000000 21.190844 2.0 272876 1.000000 16.852277 25.000000 21.183321 3.0 272294 1.000000 16.852277 25.000000 21.188486 4.0 272506 1.000000 16.852277 25.000000 21.170832 5.0 272100 1.000000 16.852277 25.000000 21.165379 6.0 271788 1.000000 16.852277 25.000000 21.175246 7.0 270040 1.000000 16.852277 25.000000 21.187417 8.0 269492 1.000000 16.852277 25.000000 21.172066 9.0 269682 1.000000 16.852277 25.000000 21.182460 10.0 268266 1.000000 16.852277 25.000000 21.170594 11.0 268744 1.000000 16.852277 25.000000 21.178608 12.0 266820 1.000000 16.852277 25.000000 21.187184 13.0 266510 1.000000 16.852277 25.000000 21.184937 14.0 265484 1.000000 16.852277 25.000000 21.180184 15.0 265258 1.000000 16.852277 25.000000 21.191504 16.0 262952 1.000000 16.852277 25.000000 21.187746 17.0 262602 1.000000 16.852277 25.000000 21.189778 18.0 260206 1.000000 16.852277 25.000000 21.188882 19.0 259410 1.000000 16.852277 25.000000 21.185684 20.0 256806 1.000000 16.852277 25.000000 21.194036 21.0 255574 1.000000 16.852277 25.000000 21.184115 22.0 255406 1.000000 16.852277 25.000000 21.178255 23.0 252394 1.000000 16.852277 25.000000 21.184644 24.0 252220 1.000000 16.852277 25.000000 21.187020 25.0 251668 1.000000 16.852277 25.000000 21.183827 26.0 249648 1.000000 16.852277 25.000000 21.183121 27.0 247160 1.000000 16.852277 25.000000 21.180872 28.0 246238 1.000000 16.852277 25.000000 21.185251 29.0 246030 1.000000 16.852277 25.000000 21.183488 30.0 242124 1.000000 16.852277 25.000000 21.194538 31.0 242426 1.000000 16.852277 25.000000 21.190702 32.0 239778 1.000000 16.852277 25.000000 21.188985 33.0 239046 1.000000 16.852277 25.000000 21.187092 34.0 237640 1.000000 16.852277 25.000000 21.185515 35.0 236256 1.000000 16.852277 25.000000 21.190278 36.0 233536 1.000000 16.852277 25.000000 21.183240 37.0 233274 1.000000 16.852277 25.000000 21.183796 38.0 231628 1.000000 16.852277 25.000000 21.200668 39.0 230378 1.000000 16.852277 25.000000 21.181153 40.0 229006 1.000000

Corrfunc.mocks.
DDtheta_mocks
(autocorr, nthreads, binfile, RA1, DEC1, weights1=None, RA2=None, DEC2=None, weights2=None, link_in_dec=True, link_in_ra=True, verbose=False, output_thetaavg=False, fast_acos=False, ra_refine_factor=2, dec_refine_factor=2, max_cells_per_dim=100, copy_particles=True, enable_min_sep_opt=True, c_api_timer=False, isa=u'fastest', weight_type=None)[source]¶ Function to compute the angular correlation function for points on the sky (i.e., mock catalogs or observed galaxies).
Returns a numpy structured array containing the pair counts for the specified angular bins.
If
weights
are provided, the resulting pair counts are weighted. The weighting scheme depends onweight_type
.Note
This module only returns pair counts and not the actual correlation function \(\omega(\theta)\). See
Corrfunc.utils.convert_3d_counts_to_cf
for computing \(\omega(\theta)\) from the pair counts returned.Parameters:  autocorr (boolean, required) – Boolean flag for auto/crosscorrelation. If autocorr is set to 1, then the second set of particle positions are not required.
 nthreads (integer) – Number of threads to use.
 binfile (string or an list/array of floats. Units: degrees.) –
For string input: filename specifying the
theta
bins forDDtheta_mocks
. The file should contain whitespace separated values of (thetamin, thetamax) for eachtheta
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For arraylike input: A sequence of
theta
values that provides the binedges. For example,np.logspace(np.log10(0.1), np.log10(10.0), 15)
is a valid input specifying 14 (logarithmic) bins between 0.1 and 10.0 degrees. This array does not need to be sorted.  RA1 (arraylike, real (float/double)) –
The array of Right Ascensions for the first set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
 DEC1 (arraylike, real (float/double)) – Array of Declinations for the first set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0]. Must be of same precision type as RA1.
 weights1 (array_like, real (float/double), optional) – A scalar, or an array of weights of shape (n_weights, n_positions) or (n_positions,). weight_type specifies how these weights are used; results are returned in the weightavg field. If only one of weights1 and weights2 is specified, the other will be set to uniform weights.
 RA2 (arraylike, real (float/double)) – The array of Right Ascensions for the second set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0]. Must be of same precision type as RA1/DEC1.
 DEC2 (arraylike, real (float/double)) – Array of Declinations for the second set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0]. Must be of same precision type as RA1/DEC1.
 weights2 (arraylike, real (float/double), optional) – Same as weights1, but for the second set of positions
 link_in_dec (boolean (default True)) – Boolean flag to create lattice in Declination. Code runs faster with
this option. However, if the angular separations are too small, then
linking in declination might produce incorrect results. When running
for the first time, check your results by comparing with the output
of the code for
link_in_dec=False
andlink_in_ra=False
.  link_in_ra (boolean (default True)) –
Boolean flag to create lattice in Right Ascension. Setting this option implies
link_in_dec=True
. Similar considerations aslink_in_dec
described above.If you disable both
link_in_dec
andlink_in_ra
, then the code reduces to a bruteforce pair counter. No lattices are created at all. For very small angular separations, the bruteforce method might be the most numerically stable method.  verbose (boolean (default false)) – Boolean flag to control output of informational messages
 output_thetaavg (boolean (default false)) –
Boolean flag to output the average
\theta
for each bin. Code will run slower if you set this flag.If you are calculating in singleprecision,
thetaavg
will suffer from numerical loss of precision and can not be trusted. If you need accuratethetaavg
values, then pass in double precision arrays forRA/DEC
.Code will run significantly slower if you enable this option. Use the keyword
fast_acos
if you can tolerate some loss of precision.  fast_acos (boolean (default false)) –
Flag to use numerical approximation for the
arccos
 gives better performance at the expense of some precision. Relevant only ifoutput_thetaavg==True
.Developers: Two versions already coded up in
utils/fast_acos.h
, so you can choose the version you want. There are also notes on how to implement faster (and less accurate) functions, particularly relevant if you know yourtheta
range is limited. If you implement a new version, then you will have to reinstall the entire Corrfunc package.Note: Tests will fail if you run the tests with``fast_acos=True``.
 (radec)_refine_factor (integer, default is (2,2); typically within [15]) –
Controls the refinement on the cell sizes. Can have up to a 20% impact on runtime.
Only two refine factors are to be specified and these correspond to
ra
anddec
(rather, than the usual three of(xyz)bin_refine_factor
for all other correlation functions).  max_cells_per_dim (integer, default is 100, typical values in [50300]) – Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^2. Only increase if
thetamax
is too small relative to the boxsize (and increasing helps the runtime).  copy_particles (boolean (default True)) –
Boolean flag to make a copy of the particle positions If set to False, the particles will be reordered inplace
New in version 2.3.0.
 enable_min_sep_opt (boolean (default true)) –
Boolean flag to allow optimizations based on min. separation between pairs of cells. Here to allow for comparison studies.
New in version 2.3.0.
 c_api_timer (boolean (default false)) – Boolean flag to measure actual time spent in the C libraries. Here to allow for benchmarking and scaling studies.
 isa (string, caseinsensitive (default
fastest
)) –Controls the runtime dispatch for the instruction set to use. Options are: [
fastest
,avx512f
,avx
,sse42
,fallback
]Setting isa to
fastest
will pick the fastest available instruction set on the current computer. However, if you setisa
to, say,avx
andavx
is not available on the computer, then the code will revert to usingfallback
(even thoughsse42
might be available).Unless you are benchmarking the different instruction sets, you should always leave
isa
to the default value. And if you are benchmarking, then the string supplied here gets translated into anenum
for the instruction set defined inutils/defs.h
.  weight_type (string, optional (default None)) – The type of weighting to apply. One of [“pair_product”, None].
Returns:  results (Numpy structured array) – A numpy structured array containing [thetamin, thetamax, thetaavg,
npairs, weightavg] for each angular bin specified in the
binfile
. Ifoutput_thetaavg
is not set thenthetavg
will be set to 0.0 for all bins; similarly forweightavg
.npairs
contains the number of pairs in that bin.  api_time (float, optional) – Only returned if
c_api_timer
is set.api_time
measures only the time spent within the C library and ignores all python overhead.
Example
>>> from __future__ import print_function >>> import numpy as np >>> import time >>> from math import pi >>> from os.path import dirname, abspath, join as pjoin >>> import Corrfunc >>> from Corrfunc.mocks.DDtheta_mocks import DDtheta_mocks >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../mocks/tests/", "angular_bins") >>> N = 100000 >>> nthreads = 4 >>> seed = 42 >>> np.random.seed(seed) >>> RA = np.random.uniform(0.0, 2.0*pi, N)*180.0/pi >>> cos_theta = np.random.uniform(1.0, 1.0, N) >>> DEC = 90.0  np.arccos(cos_theta)*180.0/pi >>> weights = np.ones_like(RA) >>> autocorr = 1 >>> for isa in ['AVX', 'SSE42', 'FALLBACK']: ... for link_in_dec in [False, True]: ... for link_in_ra in [False, True]: ... results = DDtheta_mocks(autocorr, nthreads, binfile, ... RA, DEC, output_thetaavg=True, ... weights1=weights, weight_type='pair_product', ... link_in_dec=link_in_dec, link_in_ra=link_in_ra, ... isa=isa, verbose=True) >>> for r in results: ... print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10d} {4:10.6f}". ... format(r['thetamin'], r['thetamax'], ... r['thetaavg'], r['npairs'], r['weightavg'])) ... # doctest: +NORMALIZE_WHITESPACE 0.010000 0.014125 0.012272 62 1.000000 0.014125 0.019953 0.016978 172 1.000000 0.019953 0.028184 0.024380 298 1.000000 0.028184 0.039811 0.034321 598 1.000000 0.039811 0.056234 0.048535 1164 1.000000 0.056234 0.079433 0.068385 2438 1.000000 0.079433 0.112202 0.096631 4658 1.000000 0.112202 0.158489 0.136834 9414 1.000000 0.158489 0.223872 0.192967 19098 1.000000 0.223872 0.316228 0.272673 37848 1.000000 0.316228 0.446684 0.385344 75520 1.000000 0.446684 0.630957 0.543973 150938 1.000000 0.630957 0.891251 0.768406 301854 1.000000 0.891251 1.258925 1.085273 599896 1.000000 1.258925 1.778279 1.533461 1200238 1.000000 1.778279 2.511886 2.166009 2396338 1.000000 2.511886 3.548134 3.059159 4775162 1.000000 3.548134 5.011872 4.321445 9532582 1.000000 5.011872 7.079458 6.104214 19001930 1.000000 7.079458 10.000000 8.622400 37842502 1.000000

Corrfunc.mocks.
vpf_mocks
(rmax, nbins, nspheres, numpN, threshold_ngb, centers_file, cosmology, RA, DEC, CZ, RAND_RA, RAND_DEC, RAND_CZ, verbose=False, is_comoving_dist=False, xbin_refine_factor=1, ybin_refine_factor=1, zbin_refine_factor=1, max_cells_per_dim=100, copy_particles=True, c_api_timer=False, isa=u'fastest')[source]¶ Function to compute the countsincells on points on the sky. Suitable for mock catalogs and observed galaxies.
Returns a numpy structured array containing the probability of a sphere of radius up to
rmax
containing0numpN1
galaxies.Parameters:  rmax (double) – Maximum radius of the sphere to place on the particles
 nbins (integer) – Number of bins in the countsincells. Radius of first shell is rmax/nbins
 nspheres (integer (>= 0)) – Number of random spheres to place within the particle distribution. For a small number of spheres, the error is larger in the measured pN’s.
 numpN (integer (>= 1)) –
Governs how many unique pN’s are to returned. If
numpN
is set to 1, then only the vpf (p0) is returned. FornumpN=2
, p0 and p1 are returned.More explicitly, the columns in the results look like the following:
numpN Columns in output 1 p0 2 p0 p1 3 p0 p1 p2 4 p0 p1 p2 p3 and so on…
Note:
p0
is the vpf  threshold_ngb (integer) – Minimum number of random points needed in a
rmax
sphere such that it is considered to be entirely within the mock footprint. The commandline version,mocks/vpf/vpf_mocks.c
, assumes that the minimum number of randoms can be at most a 1sigma deviation from the expected random number density.  centers_file (string, filename) –
A file containing random sphere centers. If the file does not exist, then a list of random centers will be written out. In that case, the randoms arrays,
RAND_RA
,RAND_DEC
andRAND_CZ
are used to check that the sphere is entirely within the footprint. If the file does exist but eitherrmax
is too small or there are not enough centers then the file will be overwritten.Note: If the centers file has to be written, the code will take significantly longer to finish. However, subsequent runs can reuse that centers file and will be faster.
 cosmology (integer, required) –
Integer choice for setting cosmology. Valid values are 1>LasDamas cosmology and 2>Planck cosmology. If you need arbitrary cosmology, easiest way is to convert the
CZ
values into comoving distance, based on your preferred cosmology. Setis_comoving_dist=True
, to indicate that the comoving distance conversion has already been done. Choices:
 LasDamas cosmology. \(\Omega_m=0.25\), \(\Omega_\Lambda=0.75\)
 Planck cosmology. \(\Omega_m=0.302\), \(\Omega_\Lambda=0.698\)
To setup a new cosmology, add an entry to the function,
init_cosmology
inROOT/utils/cosmology_params.c
and reinstall the entire package.  RA (arraylike, real (float/double)) –
The array of Right Ascensions for the first set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
 DEC (arraylike, real (float/double)) –
Array of Declinations for the first set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA.
 CZ (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the first set of points. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If
is_comoving_dist
is set, thenCZ
is interpreted as the comoving distance, rather than (Speed Of Light * Redshift).  RAND_RA (arraylike, real (float/double)) –
The array of Right Ascensions for the randoms. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Must be of same precision type as RA/DEC/CZ.
 RAND_DEC (arraylike, real (float/double)) –
Array of Declinations for the randoms. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA/DEC/CZ.
 RAND_CZ (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the randoms. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If
is_comoving_dist
is set, thenCZ2
is interpreted as the comoving distance, rather than(Speed Of Light * Redshift)
. Note: RAND_RA, RAND_DEC and RAND_CZ are only used when the
centers_file
needs to be written out. In that case, the RAND_RA, RAND_DEC, and RAND_CZ are used as random centers.
 verbose (boolean (default false)) – Boolean flag to control output of informational messages
 is_comoving_dist (boolean (default false)) – Boolean flag to indicate that
cz
values have already been converted into comoving distances. This flag allows arbitrary cosmologies to be used inCorrfunc
.  (xyz)bin_refine_factor (integer, default is (1, 1, 1); typically in [12]) –
Controls the refinement on the cell sizes. Higher numbers might have a negative impact on runtime.
Note: Since the counts in spheres calculation is symmetric in all 3 dimensions, the defaults are different from the clustering routines.
 max_cells_per_dim (integer, default is 100, typical values in [50300]) – Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^3. Only increase if
rmax
is too small relative to the boxsize (and increasing helps the runtime).  copy_particles (boolean (default True)) –
Boolean flag to make a copy of the particle positions If set to False, the particles will be reordered inplace
New in version 2.3.0.
 c_api_timer (boolean (default false)) – Boolean flag to measure actual time spent in the C libraries. Here to allow for benchmarking and scaling studies.
 isa (string, caseinsensitive (default
fastest
)) –Controls the runtime dispatch for the instruction set to use. Options are: [
fastest
,avx512f
,avx
,sse42
,fallback
]Setting isa to
fastest
will pick the fastest available instruction set on the current computer. However, if you setisa
to, say,avx
andavx
is not available on the computer, then the code will revert to usingfallback
(even thoughsse42
might be available).Unless you are benchmarking the different instruction sets, you should always leave
isa
to the default value. And if you are benchmarking, then the string supplied here gets translated into anenum
for the instruction set defined inutils/defs.h
.
Returns:  results (Numpy structured array) – A numpy structured array containing [rmax, pN[numpN]] with
nbins
elements. Each row contains the maximum radius of the sphere and thenumpN
elements in thepN
array. Each element of this array contains the probability that a sphere of radiusrmax
contains exactlyN
galaxies. For example, pN[0] (p0, the void probibility function) is the probability that a sphere of radiusrmax
contains 0 galaxies.  api_time (float, optional) – Only returned if
c_api_timer
is set.api_time
measures only the time spent within the C library and ignores all python overhead.
Example
>>> from __future__ import print_function >>> import math >>> from os.path import dirname, abspath, join as pjoin >>> import numpy as np >>> import Corrfunc >>> from Corrfunc.mocks.vpf_mocks import vpf_mocks >>> rmax = 10.0 >>> nbins = 10 >>> numbins_to_print = nbins >>> nspheres = 10000 >>> numpN = 6 >>> threshold_ngb = 1 # does not matter since we have the centers >>> cosmology = 1 # LasDamas cosmology >>> centers_file = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../mocks/tests/data/", ... "Mr19_centers_xyz_forVPF_rmax_10Mpc.txt") >>> N = 1000000 >>> boxsize = 420.0 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> Y = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> Z = np.random.uniform(0.5*boxsize, 0.5*boxsize, N) >>> CZ = np.sqrt(X*X + Y*Y + Z*Z) >>> inv_cz = 1.0/CZ >>> X *= inv_cz >>> Y *= inv_cz >>> Z *= inv_cz >>> DEC = 90.0  np.arccos(Z)*180.0/math.pi >>> RA = (np.arctan2(Y, X)*180.0/math.pi) + 180.0 >>> results = vpf_mocks(rmax, nbins, nspheres, numpN, threshold_ngb, ... centers_file, cosmology, ... RA, DEC, CZ, ... RA, DEC, CZ, ... is_comoving_dist=True) >>> for r in results: ... print("{0:10.1f} ".format(r[0]), end="") ... # doctest: +NORMALIZE_WHITESPACE ... for pn in r[1]: ... print("{0:10.3f} ".format(pn), end="") ... # doctest: +NORMALIZE_WHITESPACE ... print("") # doctest: +NORMALIZE_WHITESPACE 1.0 0.999 0.001 0.000 0.000 0.000 0.000 2.0 0.992 0.007 0.001 0.000 0.000 0.000 3.0 0.982 0.009 0.005 0.002 0.001 0.000 4.0 0.975 0.006 0.006 0.005 0.003 0.003 5.0 0.971 0.004 0.003 0.003 0.004 0.003 6.0 0.967 0.003 0.003 0.001 0.003 0.002 7.0 0.962 0.004 0.002 0.003 0.002 0.001 8.0 0.958 0.004 0.002 0.003 0.001 0.002 9.0 0.953 0.003 0.003 0.002 0.003 0.001 10.0 0.950 0.003 0.002 0.002 0.001 0.002

Corrfunc.mocks.
DDsmu_mocks
(autocorr, cosmology, nthreads, mu_max, nmu_bins, binfile, RA1, DEC1, CZ1, weights1=None, RA2=None, DEC2=None, CZ2=None, weights2=None, is_comoving_dist=False, verbose=False, output_savg=False, fast_divide_and_NR_steps=0, xbin_refine_factor=2, ybin_refine_factor=2, zbin_refine_factor=1, max_cells_per_dim=100, copy_particles=True, enable_min_sep_opt=True, c_api_timer=False, isa=u'fastest', weight_type=None)[source]¶ Calculate the 2D paircounts corresponding to the projected correlation function, \(\xi(s, \mu)\). The pairs are counted in bins of radial separation and cosine of angle to the lineofsight (LOS). The input positions are expected to be onsky coordinates. This module is suitable for calculating correlation functions for mock catalogs.
If
weights
are provided, the resulting pair counts are weighted. The weighting scheme depends onweight_type
.Returns a numpy structured array containing the pair counts for the specified bins.
Note
This module only returns pair counts and not the actual correlation function \(\xi(s, \mu)\). See the utilities
Corrfunc.utils.convert_3d_counts_to_cf
for computing \(\xi(s, \mu)\) from the pair counts.New in version 2.1.0.
Parameters:  autocorr (boolean, required) – Boolean flag for auto/crosscorrelation. If autocorr is set to 1, then the second set of particle positions are not required.
 cosmology (integer, required) –
Integer choice for setting cosmology. Valid values are 1>LasDamas cosmology and 2>Planck cosmology. If you need arbitrary cosmology, easiest way is to convert the
CZ
values into comoving distance, based on your preferred cosmology. Setis_comoving_dist=True
, to indicate that the comoving distance conversion has already been done. Choices:
 LasDamas cosmology. \(\Omega_m=0.25\), \(\Omega_\Lambda=0.75\)
 Planck cosmology. \(\Omega_m=0.302\), \(\Omega_\Lambda=0.698\)
To setup a new cosmology, add an entry to the function,
init_cosmology
inROOT/utils/cosmology_params.c
and reinstall the entire package.  nthreads (integer) – The number of OpenMP threads to use. Has no effect if OpenMP was not enabled during library compilation.
 mu_max (double. Must be in range [0.0, 1.0]) –
A doubleprecision value for the maximum cosine of the angular separation from the line of sight (LOS). Here,
mu
is defined as the angle betweens
andl
. If \(v_1\) and \(v_2\) represent the vectors to each point constituting the pair, then \(s := v_1  v_2\) and \(l := 1/2 (v_1 + v_2)\).Note: Only pairs with \(0 <= \cos(\theta_{LOS}) < \mu_{max}\) are counted (no equality).
 nmu_bins (int) – The number of linear
mu
bins, with the bins ranging from from (0, \(\mu_{max}\))  binfile (string or an list/array of floats) –
For string input: filename specifying the
s
bins forDDsmu_mocks
. The file should contain whitespace separated values of (smin, smax) specifying eachs
bin wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For arraylike input: A sequence of
s
values that provides the binedges. For example,np.logspace(np.log10(0.1), np.log10(10.0), 15)
is a valid input specifying 14 (logarithmic) bins between 0.1 and 10.0. This array does not need to be sorted.  RA1 (arraylike, real (float/double)) –
The array of Right Ascensions for the first set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
 DEC1 (arraylike, real (float/double)) –
Array of Declinations for the first set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA1.
 CZ1 (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the first set of points. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If is_comoving_dist is set, then
CZ1
is interpreted as the comoving distance, rather than cz.  weights1 (array_like, real (float/double), optional) – A scalar, or an array of weights of shape (n_weights, n_positions)
or (n_positions,). weight_type specifies how these weights are used;
results are returned in the weightavg field. If only one of
weights1
orweights2
is specified, the other will be set to uniform weights.  RA2 (arraylike, real (float/double)) –
The array of Right Ascensions for the second set of points. RA’s are expected to be in [0.0, 360.0], but the code will try to fix cases where the RA’s are in [180, 180.0]. For peace of mind, always supply RA’s in [0.0, 360.0].
Must be of same precision type as RA1/DEC1/CZ1.
 DEC2 (arraylike, real (float/double)) –
Array of Declinations for the second set of points. DEC’s are expected to be in the [90.0, 90.0], but the code will try to fix cases where the DEC’s are in [0.0, 180.0]. Again, for peace of mind, always supply DEC’s in [90.0, 90.0].
Must be of same precision type as RA1/DEC1/CZ1.
 CZ2 (arraylike, real (float/double)) –
Array of (Speed Of Light * Redshift) values for the second set of points. Code will try to detect cases where
redshifts
have been passed and multiply the entire array with thespeed of light
.If is_comoving_dist is set, then
CZ2
is interpreted as the comoving distance, rather than cz.Must be of same precision type as RA1/DEC1/CZ1.
 weights2 (arraylike, real (float/double), optional) – Same as weights1, but for the second set of positions
 is_comoving_dist (boolean (default false)) – Boolean flag to indicate that
cz
values have already been converted into comoving distances. This flag allows arbitrary cosmologies to be used inCorrfunc
.  verbose (boolean (default false)) – Boolean flag to control output of informational messages
 output_savg (boolean (default false)) – Boolean flag to output the average
s
for each bin. Code will run slower if you set this flag. Also, note, if you are calculating in singleprecision,savg
will suffer from numerical loss of precision and can not be trusted. If you need accuratesavg
values, then pass in double precision arrays for the particle positions.  fast_divide_and_NR_steps (integer (default 0)) – Replaces the division in
AVX
implementation with an approximate reciprocal, followed byfast_divide_and_NR_steps
of NewtonRaphson. Can improve runtime by ~1520% on older computers. Value of 0 uses the standard division operation.  (xyz)bin_refine_factor (integer, default is (2,2,1); typically within [13]) – Controls the refinement on the cell sizes. Can have up to a 20% impact on runtime.
 max_cells_per_dim (integer, default is 100, typical values in [50300]) – Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^3. Only increase if
rpmax
is too small relative to the boxsize (and increasing helps the runtime).  copy_particles (boolean (default True)) –
Boolean flag to make a copy of the particle positions If set to False, the particles will be reordered inplace
New in version 2.3.0.
 enable_min_sep_opt (boolean (default true)) –
Boolean flag to allow optimizations based on min. separation between pairs of cells. Here to allow for comparison studies.
New in version 2.3.0.
 c_api_timer (boolean (default false)) – Boolean flag to measure actual time spent in the C libraries. Here to allow for benchmarking and scaling studies.
 isa (string, caseinsensitive (default
fastest
)) –Controls the runtime dispatch for the instruction set to use. Options are: [
fastest
,avx512f
,avx
,sse42
,fallback
]Setting isa to
fastest
will pick the fastest available instruction set on the current computer. However, if you setisa
to, say,avx
andavx
is not available on the computer, then the code will revert to usingfallback
(even thoughsse42
might be available).Unless you are benchmarking the different instruction sets, you should always leave
isa
to the default value. And if you are benchmarking, then the string supplied here gets translated into anenum
for the instruction set defined inutils/defs.h
.  weight_type (string, optional (default None)) – The type of weighting to apply. One of [“pair_product”, None].
Returns:  results (Numpy structured array) – A numpy structured array containing [smin, smax, savg, mumax,
npairs, weightavg]. There are a total of
nmu_bins
inmu
for each separation bin specified in thebinfile
, withmumax
being the upper limit of themu
bin. Ifoutput_savg
is not set, thensavg
will be set to 0.0 for all bins; similarly forweightavg
.npairs
contains the number of pairs in that bin and can be used to compute the actual \(\xi(s, \mu)\) by combining with (DR, RR) counts.  api_time (float, optional) – Only returned if
c_api_timer
is set.api_time
measures only the time spent within the C library and ignores all python overhead.