Corrfunc.theory package¶
Wrapper for all clustering statistic calculations on galaxies in a simulation volume.
-
Corrfunc.theory.
DD
(autocorr, nthreads, binfile, X1, Y1, Z1, weights1=None, periodic=True, X2=None, Y2=None, Z2=None, weights2=None, verbose=False, boxsize=0.0, output_ravg=False, 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='fastest', weight_type=None)[source]¶ Calculate the 3-D pair-counts corresponding to the real-space correlation function, \(\xi(r)\).
If
weights
are provided, the mean pair weight is stored in the"weightavg"
field of the results array. The raw pair counts in the"npairs"
field are not weighted. The weighting scheme depends onweight_type
.Note
This module only returns pair counts and not the actual correlation function \(\xi(r)\). See
Corrfunc.utils.convert_3d_counts_to_cf
for computing \(\xi(r)\) from the pair counts returned.- Parameters
autocorr (boolean, required) – Boolean flag for auto/cross-correlation. If autocorr is set to 1, then the second set of particle positions are not required.
nthreads (integer) – The number of OpenMP threads to use. Has no effect if OpenMP was not enabled during library compilation.
binfile (string or an list/array of floats) –
For string input: filename specifying the
r
bins forDD
. The file should contain white-space separated values of (rmin, rmax) for eachr
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For array-like input: A sequence of
r
values that provides the bin-edges. 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.X1/Y1/Z1 (array_like, real (float/double)) – The array of X/Y/Z positions for the first set of points. Calculations are done in the precision of the supplied arrays.
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 theweightavg
field. If only one of weights1 and weights2 is specified, the other will be set to uniform weights.periodic (boolean) – Boolean flag to indicate periodic boundary conditions.
X2/Y2/Z2 (array-like, real (float/double)) – Array of XYZ positions for the second set of points. Must be the same precision as the X1/Y1/Z1 arrays. Only required when
autocorr==0
.weights2 (array-like, real (float/double), optional) – Same as weights1, but for the second set of positions
verbose (boolean (default false)) – Boolean flag to control output of informational messages
boxsize (double) – The side-length of the cube in the cosmological simulation. Present to facilitate exact calculations for periodic wrapping. If boxsize is not supplied, then the wrapping is done based on the maximum difference within each dimension of the X/Y/Z arrays.
output_ravg (boolean (default false)) –
Boolean flag to output the average
r
for each bin. Code will run slower if you set this flag.Note: If you are calculating in single-precision,
ravg
will suffer from numerical loss of precision and can not be trusted. If you need accurateravg
values, then pass in double precision arrays for the particle positions.(xyz)bin_refine_factor (integer, default is (2,2,1); typically within [1-3]) – 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 [50-300]) – 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 re-ordered in-place
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 (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 leaveisa
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 [rmin, rmax, ravg, npairs, weightavg] for each radial bin specified in the
binfile
. Ifoutput_ravg
is not set, thenravg
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 \(\xi(r)\) 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.theory.DD import DD >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../theory/tests/", "bins") >>> N = 10000 >>> boxsize = 420.0 >>> nthreads = 4 >>> autocorr = 1 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> weights = np.ones_like(X) >>> results = DD(autocorr, nthreads, binfile, X, Y, Z, weights1=weights, ... weight_type='pair_product', output_ravg=True) >>> for r in results: print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10d} {4:10.6f}". ... format(r['rmin'], r['rmax'], r['ravg'], ... r['npairs'], r['weightavg'])) 0.167536 0.238755 0.000000 0 0.000000 0.238755 0.340251 0.000000 0 0.000000 0.340251 0.484892 0.000000 0 0.000000 0.484892 0.691021 0.000000 0 0.000000 0.691021 0.984777 0.945372 2 1.000000 0.984777 1.403410 1.340525 10 1.000000 1.403410 2.000000 1.732968 36 1.000000 2.000000 2.850200 2.558878 54 1.000000 2.850200 4.061840 3.564959 208 1.000000 4.061840 5.788530 4.999278 674 1.000000 5.788530 8.249250 7.126673 2154 1.000000 8.249250 11.756000 10.201834 5996 1.000000 11.756000 16.753600 14.517830 17746 1.000000 16.753600 23.875500 20.716017 50252 1.000000
-
Corrfunc.theory.
DDrppi
(autocorr, nthreads, pimax, binfile, X1, Y1, Z1, weights1=None, periodic=True, X2=None, Y2=None, Z2=None, weights2=None, verbose=False, boxsize=0.0, output_rpavg=False, 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='fastest', weight_type=None)[source]¶ Calculate the 3-D pair-counts corresponding to the real-space correlation function, \(\xi(r_p, \pi)\) or \(\wp(r_p)\). Pairs which are separated by less than the
rp
bins (specified inbinfile
) in the X-Y plane, and less thanpimax
in the Z-dimension are counted.If
weights
are provided, the mean pair weight is stored in the"weightavg"
field of the results array. The raw pair counts in the"npairs"
field are not weighted. The weighting scheme depends onweight_type
.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/cross-correlation. If autocorr is set to 1, then the second set of particle positions are not required.
nthreads (integer) – The number of OpenMP threads to use. Has no effect if OpenMP was not enabled during library compilation.
pimax (double) –
A double-precision value for the maximum separation along the Z-dimension.
Distances along the :math:
\pi
direction are binned with unit depth. For instance, ifpimax=40
, then 40 bins will be created along thepi
direction.Note: Only pairs with
0 <= dz < pimax
are counted (no equality).binfile (string or an list/array of floats) –
For string input: filename specifying the
rp
bins forDDrppi
. The file should contain white-space separated values of (rpmin, rpmax) for eachrp
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For array-like input: A sequence of
rp
values that provides the bin-edges. 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.X1/Y1/Z1 (array-like, real (float/double)) – The array of X/Y/Z positions for the first set of points. Calculations are done in the precision of the supplied arrays.
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 theweightavg
field. If only one of weights1 and weights2 is specified, the other will be set to uniform weights.X2/Y2/Z2 (array-like, real (float/double)) – Array of XYZ positions for the second set of points. Must be the same precision as the X1/Y1/Z1 arrays. Only required when
autocorr==0
.weights2 (array-like, real (float/double), optional) – Same as weights1, but for the second set of positions
periodic (boolean) – Boolean flag to indicate periodic boundary conditions.
verbose (boolean (default false)) – Boolean flag to control output of informational messages
boxsize (double) – The side-length of the cube in the cosmological simulation. Present to facilitate exact calculations for periodic wrapping. If boxsize is not supplied, then the wrapping is done based on the maximum difference within each dimension of the X/Y/Z arrays.
output_rpavg (boolean (default false)) –
Boolean flag to output the average
rp
for each bin. Code will run slower if you set this flag.Note: If you are calculating in single-precision,
rpavg
will 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.(xyz)bin_refine_factor (integer, default is (2,2,1); typically within [1-3]) – 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 [50-300]) – 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 re-ordered in-place
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 (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 leaveisa
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_rpavg
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 \(\xi(r_p, \pi)\) 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.theory.DDrppi import DDrppi >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../theory/tests/", "bins") >>> N = 10000 >>> boxsize = 420.0 >>> nthreads = 4 >>> autocorr = 1 >>> pimax = 40.0 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> weights = np.ones_like(X) >>> results = DDrppi(autocorr, nthreads, pimax, binfile, ... X, Y, Z, weights1=weights, weight_type='pair_product', output_rpavg=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'])) ... 11.756000 16.753600 14.379250 40.0 1150 1.000000 16.753600 23.875500 20.449131 1.0 2604 1.000000 16.753600 23.875500 20.604834 2.0 2370 1.000000 16.753600 23.875500 20.523989 3.0 2428 1.000000 16.753600 23.875500 20.475181 4.0 2462 1.000000 16.753600 23.875500 20.458005 5.0 2532 1.000000 16.753600 23.875500 20.537162 6.0 2522 1.000000 16.753600 23.875500 20.443087 7.0 2422 1.000000 16.753600 23.875500 20.474580 8.0 2360 1.000000 16.753600 23.875500 20.420360 9.0 2512 1.000000 16.753600 23.875500 20.478355 10.0 2472 1.000000 16.753600 23.875500 20.485268 11.0 2406 1.000000 16.753600 23.875500 20.372985 12.0 2420 1.000000 16.753600 23.875500 20.647998 13.0 2378 1.000000 16.753600 23.875500 20.556208 14.0 2420 1.000000 16.753600 23.875500 20.527992 15.0 2462 1.000000 16.753600 23.875500 20.581017 16.0 2380 1.000000 16.753600 23.875500 20.491819 17.0 2346 1.000000 16.753600 23.875500 20.534440 18.0 2496 1.000000 16.753600 23.875500 20.529129 19.0 2512 1.000000 16.753600 23.875500 20.501946 20.0 2500 1.000000 16.753600 23.875500 20.513349 21.0 2544 1.000000 16.753600 23.875500 20.471915 22.0 2430 1.000000 16.753600 23.875500 20.450651 23.0 2354 1.000000 16.753600 23.875500 20.550753 24.0 2460 1.000000 16.753600 23.875500 20.540262 25.0 2490 1.000000 16.753600 23.875500 20.559572 26.0 2350 1.000000 16.753600 23.875500 20.534245 27.0 2382 1.000000 16.753600 23.875500 20.511302 28.0 2508 1.000000 16.753600 23.875500 20.491632 29.0 2456 1.000000 16.753600 23.875500 20.592493 30.0 2386 1.000000 16.753600 23.875500 20.506234 31.0 2484 1.000000 16.753600 23.875500 20.482109 32.0 2538 1.000000 16.753600 23.875500 20.518463 33.0 2544 1.000000 16.753600 23.875500 20.482515 34.0 2534 1.000000 16.753600 23.875500 20.503124 35.0 2382 1.000000 16.753600 23.875500 20.471307 36.0 2356 1.000000 16.753600 23.875500 20.384231 37.0 2554 1.000000 16.753600 23.875500 20.454012 38.0 2458 1.000000 16.753600 23.875500 20.585543 39.0 2394 1.000000 16.753600 23.875500 20.504965 40.0 2500 1.000000
-
Corrfunc.theory.
DDsmu
(autocorr, nthreads, binfile, mu_max, nmu_bins, X1, Y1, Z1, weights1=None, periodic=True, X2=None, Y2=None, Z2=None, weights2=None, verbose=False, boxsize=0.0, 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='fastest', weight_type=None, proj_type=None, ncomponents=None, projfn=None)[source]¶ Calculate the 2-D component values (e.g. pair-counts for the tophat basis) corresponding to the redshift-space correlation function, \(\xi(s, \mu)\) Pairs which are separated by less than the
s
bins (specified inbinfile
) in 3-D, and less thans*mu_max
in the Z-dimension are counted.If
weights
are provided, the mean pair weight is stored in the"weightavg"
field of the results array. The raw pair counts in the"npairs"
field are not weighted. The weighting scheme depends onweight_type
.To use the projection capability with suave, set the
proj_type
parameter for the desired basis functions, and setncomponents
andprojfn
accordingly.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/cross-correlation. If autocorr is set to 1, then the second set of particle positions are not required.
nthreads (integer) – The number of OpenMP threads to use. Has no effect if OpenMP was not enabled during library compilation.
binfile (string or an list/array of floats) –
For string input: filename specifying the
s
bins forDDsmu_mocks
. The file should contain white-space 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 array-like input: A sequence of
s
values that provides the bin-edges. 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.mu_max (double. Must be in range (0.0, 1.0]) –
A double-precision value for the maximum cosine of the angular separation from the line of sight (LOS). Here, LOS is taken to be along the Z direction.
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, \(\mu_{max}\))X1/Y1/Z1 (array-like, real (float/double)) – The array of X/Y/Z positions for the first set of points. Calculations are done in the precision of the supplied arrays.
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 theweightavg
field. If only one of weights1 and weights2 is specified, the other will be set to uniform weights.periodic (boolean) – Boolean flag to indicate periodic boundary conditions.
X2/Y2/Z2 (array-like, real (float/double)) – Array of XYZ positions for the second set of points. Must be the same precision as the X1/Y1/Z1 arrays. Only required when
autocorr==0
.weights2 (array-like, real (float/double), optional) – Same as weights1, but for the second set of positions
verbose (boolean (default false)) – Boolean flag to control output of informational messages
boxsize (double) – The side-length of the cube in the cosmological simulation. Present to facilitate exact calculations for periodic wrapping. If boxsize is not supplied, then the wrapping is done based on the maximum difference within each dimension of the X/Y/Z arrays.
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 single-precision,s
will suffer from numerical loss of precision and can not be trusted. If you need accurates
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 Newton-Raphson. Can improve runtime by ~15-20% on older computers. Value of 0 uses the standard division operation.(xyz)bin_refine_factor (integer (default (2,2,1) typical values in [1-3])) – Controls the refinement on the cell sizes. Can have up to a 20% impact on runtime.
max_cells_per_dim (integer (default 100, typical values in [50-300])) – 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 re-ordered in-place
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 (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 leaveisa
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 (str, optional) – The type of pair weighting to apply. Options: “pair_product”, “pair_product_gradient”, None; Default: None.
proj_type (string (default None)) –
Projection method to use; currently supported methods are [‘tophat’, ‘piecewise’, ‘generalr’, ‘gaussian_kernel’, ‘gradient’]. If using ‘gradient’, must set
weight_type="pair_product_gradient"
.New in version suave.
ncomponents (int (default None)) –
Number of basis functions; necessary if projection method
proj_type
is defined.New in version suave.
projfn (string (default None)) –
File path of projection file; necessary for
proj_type='generalr'
.New in version suave.
- Returns
results (A python list) – A python list containing
nmu_bins
of [smin, smax, savg, mu_max, npairs, weightavg] for each spatial bin specified in thebinfile
. There will be a total ofnmu_bins
ranging from [0,mu_max
) per spatial bin. Ifoutput_savg
is not set, thensavg
will be set to 0.0 for all bins; similarly forweight_avg
.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.v_proj (array-like, double, optional) – Only returned if proj_type is not None. The projection vector, an array of length
ncomponents
.t_proj (array-like, double, optional) – Only returned if proj_type is not None. The projection tensor, unrolled in the form of an array with length
ncomponents``*``ncomponents
.
Example
>>> from __future__ import print_function >>> import numpy as np >>> from os.path import dirname, abspath, join as pjoin >>> import Corrfunc >>> from Corrfunc.theory.DDsmu import DDsmu >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../theory/tests/", "bins") >>> N = 10000 >>> boxsize = 420.0 >>> nthreads = 4 >>> autocorr = 1 >>> mu_max = 1.0 >>> seed = 42 >>> nmu_bins = 10 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> weights = np.ones_like(X) >>> results = DDsmu(autocorr, nthreads, binfile, mu_max, nmu_bins, ... X, Y, Z, weights1=weights, weight_type='pair_product', output_savg=True) >>> for r in results[100:]: print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10.1f}" ... " {4:10d} {5:10.6f}".format(r['smin'], r['smax'], ... r['savg'], r['mu_max'], r['npairs'], r['weightavg'])) ... 5.788530 8.249250 7.148213 0.1 230 1.000000 5.788530 8.249250 7.157218 0.2 236 1.000000 5.788530 8.249250 7.165338 0.3 208 1.000000 5.788530 8.249250 7.079905 0.4 252 1.000000 5.788530 8.249250 7.251661 0.5 184 1.000000 5.788530 8.249250 7.118536 0.6 222 1.000000 5.788530 8.249250 7.083466 0.7 238 1.000000 5.788530 8.249250 7.198184 0.8 170 1.000000 5.788530 8.249250 7.127409 0.9 208 1.000000 5.788530 8.249250 6.973090 1.0 206 1.000000 8.249250 11.756000 10.149183 0.1 592 1.000000 8.249250 11.756000 10.213009 0.2 634 1.000000 8.249250 11.756000 10.192220 0.3 532 1.000000 8.249250 11.756000 10.246931 0.4 544 1.000000 8.249250 11.756000 10.102675 0.5 530 1.000000 8.249250 11.756000 10.276180 0.6 644 1.000000 8.249250 11.756000 10.251264 0.7 666 1.000000 8.249250 11.756000 10.138399 0.8 680 1.000000 8.249250 11.756000 10.191916 0.9 566 1.000000 8.249250 11.756000 10.243229 1.0 608 1.000000 11.756000 16.753600 14.552776 0.1 1734 1.000000 11.756000 16.753600 14.579991 0.2 1806 1.000000 11.756000 16.753600 14.599611 0.3 1802 1.000000 11.756000 16.753600 14.471100 0.4 1820 1.000000 11.756000 16.753600 14.480192 0.5 1740 1.000000 11.756000 16.753600 14.493679 0.6 1746 1.000000 11.756000 16.753600 14.547713 0.7 1722 1.000000 11.756000 16.753600 14.465390 0.8 1750 1.000000 11.756000 16.753600 14.547465 0.9 1798 1.000000 11.756000 16.753600 14.440975 1.0 1828 1.000000 16.753600 23.875500 20.720406 0.1 5094 1.000000 16.753600 23.875500 20.735403 0.2 5004 1.000000 16.753600 23.875500 20.721069 0.3 5172 1.000000 16.753600 23.875500 20.723648 0.4 5014 1.000000 16.753600 23.875500 20.650621 0.5 5094 1.000000 16.753600 23.875500 20.688135 0.6 5076 1.000000 16.753600 23.875500 20.735691 0.7 4910 1.000000 16.753600 23.875500 20.714097 0.8 4864 1.000000 16.753600 23.875500 20.751836 0.9 4954 1.000000 16.753600 23.875500 20.721183 1.0 5070 1.000000
-
Corrfunc.theory.
vpf
(rmax, nbins, nspheres, numpN, seed, X, Y, Z, verbose=False, periodic=True, boxsize=0.0, 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='fastest')[source]¶ Function to compute the counts-in-cells on 3-D real-space points.
Returns a numpy structured array containing the probability of a sphere of radius up to
rmax
containing [0, numpN-1] galaxies.- Parameters
rmax (double) – Maximum radius of the sphere to place on the particles
nbins (integer) – Number of bins in the counts-in-cells. 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 vpfseed (unsigned integer) – Random number seed for the underlying GSL random number generator. Used to draw centers of the spheres.
X/Y/Z (arraytype, real (float/double)) –
Particle positions in the 3 axes. Must be within [0, boxsize] and specified in the same units as
rp_bins
and boxsize. All 3 arrays must be of the same floating-point type.Calculations will be done in the same precision as these arrays, i.e., calculations will be in floating point if XYZ are single precision arrays (C float type); or in double-precision if XYZ are double precision arrays (C double type).
verbose (boolean (default false)) – Boolean flag to control output of informational messages
periodic (boolean) – Boolean flag to indicate periodic boundary conditions.
boxsize (double) – The side-length of the cube in the cosmological simulation. Present to facilitate exact calculations for periodic wrapping. If boxsize is not supplied, then the wrapping is done based on the maximum difference within each dimension of the X/Y/Z arrays.
(xyz)bin_refine_factor (integer, default is (1,1,1); typically within [1-3]) –
Controls the refinement on the cell sizes. Can have up to a 20% 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 [50-300]) – 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 re-ordered in-place
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 (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 leaveisa
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 – 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 zero galaxies.if
c_api_timer
is set, then the return value is a tuple containing (results, api_time).api_time
measures only the time spent within the C library and ignores all python overhead.- Return type
Numpy structured array
Example
>>> from __future__ import print_function >>> import numpy as np >>> from Corrfunc.theory.vpf import vpf >>> rmax = 10.0 >>> nbins = 10 >>> nspheres = 10000 >>> numpN = 5 >>> seed = -1 >>> N = 100000 >>> boxsize = 420.0 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> results = vpf(rmax, nbins, nspheres, numpN, seed, X, Y, Z) >>> for r in results: ... print("{0:10.1f} ".format(r[0]), end="") ... ... for pn in r[1]: ... print("{0:10.3f} ".format(pn), end="") ... ... print("") 1.0 0.995 0.005 0.000 0.000 0.000 2.0 0.956 0.044 0.001 0.000 0.000 3.0 0.858 0.130 0.012 0.001 0.000 4.0 0.695 0.252 0.047 0.005 0.001 5.0 0.493 0.347 0.127 0.028 0.005 6.0 0.295 0.362 0.219 0.091 0.026 7.0 0.141 0.285 0.265 0.179 0.085 8.0 0.056 0.159 0.228 0.229 0.161 9.0 0.019 0.066 0.135 0.192 0.192 10.0 0.003 0.019 0.054 0.106 0.150
-
Corrfunc.theory.
wp
(boxsize, pimax, nthreads, binfile, X, Y, Z, weights=None, weight_type=None, verbose=False, output_rpavg=False, 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, c_cell_timer=False, isa='fastest')[source]¶ Function to compute the projected correlation function in a periodic cosmological box. Pairs which are separated by less than the
rp
bins (specified inbinfile
) in the X-Y plane, and less thanpimax
in the Z-dimension are counted.If
weights
are provided, the resulting correlation function is weighted. The weighting scheme depends onweight_type
.Note
Pairs are double-counted. And if
rpmin
is set to 0.0, then all the self-pairs (i’th particle with itself) are added to the first bin => minimum number of pairs in the first bin is the total number of particles.- Parameters
boxsize (double) – A double-precision value for the boxsize of the simulation in same units as the particle positions and the
rp
bins.pimax (double) –
A double-precision value for the maximum separation along the Z-dimension.
Note: Only pairs with
0 <= dz < pimax
are counted (no equality).nthreads (integer) – Number of threads to use.
binfile (string or an list/array of floats) –
For string input: filename specifying the
rp
bins forwp
. The file should contain white-space separated values of (rpmin, rpmax) for eachrp
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For array-like input: A sequence of
rp
values that provides the bin-edges. 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.X/Y/Z (arraytype, real (float/double)) –
Particle positions in the 3 axes. Must be within [0, boxsize] and specified in the same units as
rp_bins
and boxsize. All 3 arrays must be of the same floating-point type.Calculations will be done in the same precision as these arrays, i.e., calculations will be in floating point if XYZ are single precision arrays (C float type); or in double-precision if XYZ are double precision arrays (C double type).
weights (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 theweightavg
field.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.Note: If you are calculating in single-precision,
rpavg
will 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.(xyz)bin_refine_factor (integer, default is (2,2,1); typically within [1-3]) – 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 [50-300]) – 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 re-ordered in-place
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.
c_cell_timer (boolean (default false)) – Boolean flag to measure actual time spent per cell-pair within the C libraries. A very detailed timer that stores information about the number of particles in each cell, the thread id that processed that cell-pair and the amount of time in nano-seconds taken to process that cell pair. This timer can be used to study the instruction set efficiency, and load-balancing of the code.
isa (string (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 leaveisa
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, wp, npairs, weightavg] for each radial specified in the
binfile
. Ifoutput_rpavg
is not set thenrpavg
will be set to 0.0 for all bins; similarly forweightavg
.wp
contains the projected correlation function whilenpairs
contains the number of unique pairs in that bin. If using weights,wp
will be weighted whilenpairs
will not be.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.cell_time (list, optional) – Only returned if
c_cell_timer
is set. Contains detailed stats about each cell-pair visited during pair-counting, viz., number of particles in each of the cells in the pair, 1-D cell-indices for each cell in the pair, time (in nano-seconds) to process the pair and the thread-id for the thread that processed that cell-pair.
Example
>>> from __future__ import print_function >>> import numpy as np >>> from os.path import dirname, abspath, join as pjoin >>> import Corrfunc >>> from Corrfunc.theory.wp import wp >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../theory/tests/", "bins") >>> N = 10000 >>> boxsize = 420.0 >>> pimax = 40.0 >>> nthreads = 4 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> results = wp(boxsize, pimax, nthreads, binfile, X, Y, Z, weights=np.ones_like(X), weight_type='pair_product') >>> for r in results: ... print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10.6f} {4:10d} {5:10.6f}". ... format(r['rmin'], r['rmax'], ... r['rpavg'], r['wp'], r['npairs'], r['weightavg'])) ... 0.167536 0.238755 0.000000 66.717143 18 1.000000 0.238755 0.340251 0.000000 -15.786045 16 1.000000 0.340251 0.484892 0.000000 2.998470 42 1.000000 0.484892 0.691021 0.000000 -15.779885 66 1.000000 0.691021 0.984777 0.000000 -11.966728 142 1.000000 0.984777 1.403410 0.000000 -9.699906 298 1.000000 1.403410 2.000000 0.000000 -11.698771 588 1.000000 2.000000 2.850200 0.000000 3.848375 1466 1.000000 2.850200 4.061840 0.000000 -0.921452 2808 1.000000 4.061840 5.788530 0.000000 0.454851 5802 1.000000 5.788530 8.249250 0.000000 1.428344 11926 1.000000 8.249250 11.756000 0.000000 -1.067885 23478 1.000000 11.756000 16.753600 0.000000 -0.553319 47994 1.000000 16.753600 23.875500 0.000000 -0.086433 98042 1.000000
-
Corrfunc.theory.
xi
(boxsize, nthreads, binfile, X, Y, Z, weights=None, weight_type=None, verbose=False, output_ravg=False, 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='fastest')[source]¶ Function to compute the projected correlation function in a periodic cosmological box. Pairs which are separated by less than the
r
bins (specified inbinfile
) in 3-D real space.If
weights
are provided, the resulting correlation function is weighted. The weighting scheme depends onweight_type
.Note
Pairs are double-counted. And if
rmin
is set to 0.0, then all the self-pairs (i’th particle with itself) are added to the first bin => minimum number of pairs in the first bin is the total number of particles.- Parameters
boxsize (double) – A double-precision value for the boxsize of the simulation in same units as the particle positions and the
r
bins.nthreads (integer) – Number of threads to use.
binfile (string or an list/array of floats) –
For string input: filename specifying the
r
bins forxi
. The file should contain white-space separated values of (rmin, rmax) for eachr
wanted. The bins need to be contiguous and sorted in increasing order (smallest bins come first).For array-like input: A sequence of
r
values that provides the bin-edges. 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.X/Y/Z (arraytype, real (float/double)) –
Particle positions in the 3 axes. Must be within [0, boxsize] and specified in the same units as
rp_bins
and boxsize. All 3 arrays must be of the same floating-point type.Calculations will be done in the same precision as these arrays, i.e., calculations will be in floating point if XYZ are single precision arrays (C float type); or in double-precision if XYZ are double precision arrays (C double type).
weights (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 theweightavg
field.verbose (boolean (default false)) – Boolean flag to control output of informational messages
output_ravg (boolean (default false)) –
Boolean flag to output the average
r
for each bin. Code will run slower if you set this flag.Note: If you are calculating in single-precision,
rpavg
will 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.(xyz)bin_refine_factor (integer, default is (2,2,1); typically within [1-3]) – 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 [50-300]) – 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 re-ordered in-place
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 (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 leaveisa
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 [rmin, rmax, ravg, xi, npairs, weightavg] for each radial specified in the
binfile
. Ifoutput_ravg
is not set thenravg
will be set to 0.0 for all bins; similarly forweightavg
.xi
contains the correlation function whilenpairs
contains the number of pairs in that bin. If using weights,xi
will be weighted whilenpairs
will not be.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.theory.xi import xi >>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)), ... "../theory/tests/", "bins") >>> N = 100000 >>> boxsize = 420.0 >>> nthreads = 4 >>> seed = 42 >>> np.random.seed(seed) >>> X = np.random.uniform(0, boxsize, N) >>> Y = np.random.uniform(0, boxsize, N) >>> Z = np.random.uniform(0, boxsize, N) >>> weights = np.ones_like(X) >>> results = xi(boxsize, nthreads, binfile, X, Y, Z, weights=weights, weight_type='pair_product', output_ravg=True) >>> for r in results: print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10.6f} {4:10d} {5:10.6f}" ... .format(r['rmin'], r['rmax'], ... r['ravg'], r['xi'], r['npairs'], r['weightavg'])) ... 0.167536 0.238755 0.226592 -0.205733 4 1.000000 0.238755 0.340251 0.289277 -0.176729 12 1.000000 0.340251 0.484892 0.426819 -0.051829 40 1.000000 0.484892 0.691021 0.596187 -0.131853 106 1.000000 0.691021 0.984777 0.850100 -0.049207 336 1.000000 0.984777 1.403410 1.225112 0.028543 1052 1.000000 1.403410 2.000000 1.737153 0.011403 2994 1.000000 2.000000 2.850200 2.474588 0.005405 8614 1.000000 2.850200 4.061840 3.532018 -0.014098 24448 1.000000 4.061840 5.788530 5.022241 -0.010784 70996 1.000000 5.788530 8.249250 7.160648 -0.001588 207392 1.000000 8.249250 11.756000 10.207213 -0.000323 601002 1.000000 11.756000 16.753600 14.541171 0.000007 1740084 1.000000 16.753600 23.875500 20.728773 -0.001595 5028058 1.000000