analysis package - Provides modules to analyse results from cosmomodels runs.
pyflation.analysis.adiabatic - Tools to calculate the spectra of adiabatic perturbations
Return the cross correlation of scalar perturbations P_{I,J}
For multifield systems the full crossterm matrix is returned which has shape nfields*nfields.
Parameters : | modes : array_like
axis : integer
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Returns : | Pphi_matrix : array_like, dtype: float64
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Return the modes of the scalar perturbations P_{I,J}.
This is a helper function which wraps the full calculation in Pphi_matrix and requires only the model as an argument. Provided for compatibility with previous versions.
Parameters : | m : Cosmomodels instance
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Returns : | Pphi_modes : array_like, dtype: float64
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Return the spectrum of (first order) curvature perturbations P_R1 for a model m.
For a multifield model this is given by:
where and are the mode matrix elements.
This is the unscaled version which is related to the scaled version by .
This function is a wrapper function which only requires the model as a parameter. The full calculation is done in the Pr_spectrum function in the pyflation.analysis.adiabatic module.
Parameters : | m : Cosmomodels instance
tix : integer, optional
kix : integer, optional
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Returns : | Pr : array_like, dtype: float64
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Return the spectrum of (first order) curvature perturbations P_R1 for each k, given the first order perturbation modes.
For a multifield model this is given by:
where and are the mode matrix elements.
This is the unscaled version which is related to the scaled version by .
Parameters : | phidot : array_like
modes : array_like
axis : integer
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Returns : | Pr : array_like, dtype: float64
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Return the spectrum of (first order) curvature perturbations P_R1 for each k.
For a multifield model this is given by:
where and are the mode matrix elements.
This is the unscaled version which is related to the scaled version by .
Parameters : | phidot : array_like
Pphi_modes : array_like
axis : integer
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Returns : | Pr : array_like, dtype: float64
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Return the spectrum of (first order) curvature perturbations P_zeta for each k.
For a multifield model this is given by:
This is the unscaled version P_zeta which is related to the scaled version by .
Parameters : | m : Cosmomodels instance
tix : integer, optional
kix : integer, optional
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Returns : | Pzeta : array_like, dtype: float64
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Return the spectrum of (first order) curvature perturbations P_zeta for each k.
For a multifield model this is given by:
This is the unscaled version P_zeta which is related to the scaled version by .
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | Pzeta_spectrum : array_like, dtype: float64
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Find horizon crossing for all ks
Parameters : | m : Cosmomodels instance
factor : float
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Returns : | hcross : array
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Return the value of n_s
Parameters : | sPr : array_like
k : array_like
kix : integer
running : boolean, optional
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Returns : | n_s : float
alpha_s : float, present only if running = True
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Return the spectrum of (first order) curvature perturbations for each timestep and k mode.
This is the scaled power spectrum which is related to the unscaled version by .
Parameters : | m : Cosmomodels instance
tix : integer, optional
kix : integer, optional
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Returns : | calPr : array_like
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Return the spectrum of scaled (first order) curvature perturbations for each timestep and k mode.
This is the scaled power spectrum which is related to the unscaled version by .
Parameters : | m : Cosmomodels instance
tix : integer, optional
kix : integer, optional
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Returns : | scaled_Pzeta : array_like
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pyflation.analysis.nonadiabatic - Module to calculate relative pressure perturbations.
Derivative of pressure of the background fields
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
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Returns : | Pdotalpha : array
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Notes
All the arguments should have the same number of dimensions. Vphi and phidot should be arrays of the same size, but H should have a dimension of size 1 corresponding to the “field” dimension of the other variables.
Return the alternate spectrum of (first order) isocurvature perturbations P_S for each k. This is only available for a two field model and is given by:
where
This is the unscaled version which is related to the scaled version by .
Parameters : | phidot : array_like
Pphi_modes : array_like
axis : integer
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Returns : | Pr : array_like, dtype: float64
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Isocurvature perturbation S of the fields given as quantum mode functions.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | result : array
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Power spectrum of the isocurvature perturbation S.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | Sspectrum : array
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Matrix of the first order perturbed pressure of the field components.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | result : array_like
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Perturbed non-adiabatic pressure of the fields given as quantum mode functions.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Power spectrum of the full perturbed non-adiabatic pressure.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | deltaPnadspectrum : array
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Perturbed relative pressure of the fields given as quantum mode functions.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | result : array
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Power spectrum of the full perturbed relative pressure.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | deltaPrelspectrum : array
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Power spectrum of the full perturbed relative pressure.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | deltaPspectrum : array
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Matrix of the first order perturbed energy densities of the field components.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | result : array_like
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Power spectrum of the perturbed energy density.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
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Returns : | deltarhospectrum : array
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Get the spectrum of delta Prel from a model instance.
Parameters : | m : Cosmomodels model instance
tix : integer
kix : integer
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Returns : | spectrum : array
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Combined derivative in e-fold time of the pressure of the fields.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
axis : integer, optional
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Returns : | fullPdot : array
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Combined derivative in e-fold time of the energy density of the field.
Parameters : | phidot : array_like
H : array_like
axis : integer, optional
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Returns : | fullrhodot : array
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Derivative in e-fold time of the energy densities of the individual fields.
Parameters : | phidot : array_like
H : array_like
Both arrays should have the same number of dimensions, but H should have a : dimension of size 1 corresponding to the field dimension of phidot. : |
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Returns : | rhodots : array
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Return the scaled alternate spectrum of (first order) isocurvature perturbations for each k. This is only available for a two field model and is given by:
This is the scaled version which is related to the unscaled version by .
Parameters : | phidot : array_like
Pphi_modes : array_like
axis : integer
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Returns : | Pr : array_like, dtype: float64
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Return the spectrum of isocurvature perturbations for each timestep and k mode.
This is the scaled power spectrum which is related to the unscaled version by .
Parameters : | m : Cosmomodels instance
tix : integer, optional
kix : integer, optional
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Returns : | scaled_S : array_like
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Power spectrum of S scaled with k^3/(2*pi^2)
Assumes that k dimension is last.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
k : array
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Returns : | scaled_S_spectrum : array
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Power spectrum of delta P scaled with k^3/(2*pi^2)
Assumes that k dimension is last.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
k : array
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Returns : | scaled_dP_spectrum : array
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Power spectrum of delta Pnad scaled with k^3/(2*pi^2)
Assumes that k dimension is last.
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
modes : array_like
modesdot : array_like
axis : integer
k : array
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Returns : | scaled_dPnad_spectrum : array
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Return the value of the slope of the k-scaled spectrum of S
Parameters : | scaled_S : array_like
k : array_like
kix : integer
running : boolean, optional
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Returns : | spec_S : float
running_S : float, present only if running = True
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Sound speeds of the background fields
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
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Returns : | calphasq : array
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Notes
All the arguments should have the same number of dimensions. Vphi and phidot should be arrays of the same size, but H should have a dimension of size 1 corresponding to the “field” dimension of the other variables.
Total sound speed of the fluids
Parameters : | Vphi : array_like
phidot : array_like
H : array_like
axis : integer
All the arguments should have the same number of dimensions. Vphi and phidot : should be arrays of the same size, but H should have a dimension of size 1 : corresponding to the “field” dimension of the other variables. : |
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Returns : | csq : array_like
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pyflation.analysis.utilities - Helper module for analysis package
Get the component variables of delta Prel from a model instance.
Parameters : | m: Cosmomodels model instance :
tix: integer :
kix: integer :
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Returns : | Tuple containing: : Vphi: array_like :
phidot: array_like :
H: array_like :
modes: array_like :
modesdot: array_like :
axis: integer :
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Return variables with the correct shapes for calculation.
Parameters : | Vphi: array_like :
phidot: array_like :
H: array_like :
modes: array_like :
modesdot: array_like :
axis: integer :
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Returns : | result: tuple :
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Flatten the mode matrix given into nfield^2 long vector.
Parameters : | modematrix: array :
nfields: integer :
ix1: integer, optional :
ix2: integer, optional :
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Returns : | mreshaped: array :
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Helper function to reshape flat nfield^2 long y variable into nfield*nfield mode matrix. Returns a view of the y array (changes will be reflected in underlying array).
Parameters : | y: array :
nfields: integer :
ix: integer :
ixslice: index slice, optional :
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Returns : | result: view of y array with shape nfield*nfield structure : |
Return the k scaling for power spectrum calculations.
Parameters : | k: array :
kix: integer, optional :
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Returns : | kscaling: array :
Note for a single variable (not a spectrum) you may want the square root : of this result. : |
Calculate spectrum of input.
Spectrum = Sum_I modes_I * modes_I.conjugate, where sum over I is on the dimension denoted by axis
Parameters : | modes_I: array_like :
axis: integer :
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Returns : | spectrum: array_like, float :
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Return the value of spectral index (and running) of y at k[kix]
Parameters : | y: array_like :
k: array_like :
kix: integer :
running: boolean, optional :
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Returns : | spec_index: float :
alpha: float, present only if running = True :
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