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Commit b551c379 authored by Cristian Barrera-Hinojosa's avatar Cristian Barrera-Hinojosa
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jupyter notebook for tutorial

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%% Cell type:markdown id: tags:
------------------------------------------
# GRAMSES Tutorial
------------------------------------------
## Introduction
This Jupyter Notebook will (try to) guide you step-by-step through some GRAMSES examples.
## Definitions and conventions
### Metric
In GRAMSES the metric is given in the 3+1 form:
\begin{equation}
{\rm d}s^2 = g_{\mu\nu}{\rm d}x^{\mu}{\rm d}x^{\nu} = -\alpha^2 {\rm d}t^2+\gamma_{ij}\left(\beta^i{\rm d}t+{\rm d}x^i\right)\left(\beta^j{\rm d}t+{\rm d}x^j\right)
\end{equation}
where $\alpha$ is the lapse function, $\beta^i$ the shift vector and $\gamma_{ij}$ the induced metric on the spatial hypersurfaces, which in the constrained formulation adopted by GRAMSES is approximated by a conformally-flat metric, i.e.
\begin{equation}
\gamma_{ij}=\psi^4\delta_{ij}
\end{equation}
with $\psi$ being the conformal factor and $\delta_{ij}$ the Kronecker delta.
### Matter sources
The usual matter source terms defined in the 3+1 formalism are given by the following projections of the energy-momentum tensor:
\begin{align}
\rho &\equiv n_\mu n_\nu T^{\mu\nu}\,,\label{rho-def}\\
S_i&\equiv-\gamma_{i\mu}n_\nu T^{\mu\nu}\,,\label{S_i-def}\\
S_{ij}&\equiv\gamma_{i\mu}\gamma_{j\nu}T^{\mu\nu}\,, \qquad\qquad S=\gamma^{ij}S_{ij}\,.
\end{align}
GRAMSES uses and outputs the following conformal matter source terms:
\begin{align}
s_0({\bf x})&\equiv\sqrt{\gamma}\rho&&\propto{m\alpha{u}^0}\,,\label{eq:s0-cic}\\
s_i({\bf x})&\equiv\sqrt{\gamma}S_i&&\propto m{u}_i\,,\\
s_{ij}({\bf x})&\equiv\sqrt{\gamma}S_{ij}&&\propto m\frac{{u}_i{u}_j}{\alpha{u}^0}\,.\label{eq:s-cic}
\end{align}
In these, ${\bf x}$ is a (discrete) position vector on the cartesian simulation grid and the proportionality symbol in each equation stands for the standard cloud-in-cell (CIC) weights used for the particle-mesh projection. From these we have the following useful relations:
\begin{align}
s_0&=\rho\Gamma\,,\\
s_i&=\frac{\rho}{\Gamma}u_i\,,\label{eq:s_i-rel}\\
s_{ij}&=\frac{\rho}{\Gamma^2}u_iu_j\,, \qquad\implies s=\rho(1-\Gamma^{-2})\,,\\
u_i&=\Gamma^2\frac{s_i}{s_0}\,,
\end{align}
where $\Gamma\equiv\alpha{u}^0=\sqrt{1+\gamma^{ij}u_iu_j}$ is the Lorentz factor.
%% Cell type:markdown id: tags:
# 0. Converting Fortran data to numpy format
The first step is to run the readgrav script provided.
%% Cell type:code id: tags:
``` python
# You can run it from here where the arguments are:
#
# output_000xx/ ncpus ilevelmin
#
# where 2^ilevelmin is the cells number along 1D.
%run -i 'readgrav_gr.py' output_00004/ 4 7
```
%% Cell type:code id: tags:
``` python
# Import python libraries needed
import numpy as np
import matplotlib.pyplot as plt
import math
from matplotlib import gridspec
from matplotlib.colors import LogNorm
import matplotlib.ticker as ticker
from nbodykit.lab import *
# Plots style
font = {'size':14}
plt.rc('font', **font)
plt.rc('font', family='serif')
plt.rc('text', usetex=True)
```
%% Cell type:markdown id: tags:
## Read snapshot in numpy format
%% Cell type:code id: tags:
``` python
# Simulations & snapshot info
a_out = 1.0
box_size = 256. # Mpc/h
grid_size= 128
# load snapshot file in npy format
#grav_raw = np.load('output_00004_B256_PM128/grav_00004_new.out.npy')
grav_raw = np.load('output_00004/grav_00004.out.npy')
grad_b = [grav_raw[:,1],grav_raw[:,2],grav_raw[:,3]]
gr_pot = [grav_raw[:,4],grav_raw[:,5],grav_raw[:,6],grav_raw[:,7],grav_raw[:,8],grav_raw[:,9]]
gr_mat = [grav_raw[:,10],grav_raw[:,11],grav_raw[:,12],grav_raw[:,13],grav_raw[:,14]]
x = grav_raw[:,15]
y = grav_raw[:,16]
z = grav_raw[:,17]
# Conversion from internal code units to physical units -- do not modify!
ctilde = 3*10**3/box_size
norm_B = 1/a_out**2/ctilde
norm_si= 2/(ctilde*box_size)**2/a_out**4
B_x = gr_pot[2] * norm_B
B_y = gr_pot[3] * norm_B
B_z = gr_pot[4] * norm_B
dx_b=grad_b[0] * norm_B
dy_b=grad_b[1] * norm_B
dz_b=grad_b[2] * norm_B
s_x = gr_mat[1] * norm_si
s_y = gr_mat[2] * norm_si
s_z = gr_mat[3] * norm_si
```
%% Cell type:code id: tags:
``` python
# Construct 3D box of fields
xx_box= grid_size*x
yy_box= grid_size*y
zz_box= grid_size*z
x_box = xx_box.astype(int)
y_box = yy_box.astype(int)
z_box = zz_box.astype(int)
# Shift vector components
B_x_box = np.zeros((grid_size,grid_size,grid_size))
B_y_box = np.zeros((grid_size,grid_size,grid_size))
B_z_box = np.zeros((grid_size,grid_size,grid_size))
B_x_box[(x_box,y_box,z_box)] = B_x
B_y_box[(x_box,y_box,z_box)] = B_y
B_z_box[(x_box,y_box,z_box)] = B_z
dx_b_box = np.zeros((grid_size,grid_size,grid_size))
dy_b_box = np.zeros((grid_size,grid_size,grid_size))
dz_b_box = np.zeros((grid_size,grid_size,grid_size))
dx_b_box[(x_box,y_box,z_box)] = dx_b
dy_b_box[(x_box,y_box,z_box)] = dy_b
dz_b_box[(x_box,y_box,z_box)] = dz_b
```
%% Cell type:code id: tags:
``` python
# Matter source terms
s0_box = np.zeros((grid_size,grid_size,grid_size))
s_x_box= np.zeros((grid_size,grid_size,grid_size))
s_y_box= np.zeros((grid_size,grid_size,grid_size))
s_z_box= np.zeros((grid_size,grid_size,grid_size))
s0_box [(x_box,y_box,z_box)]= gr_mat[0]
s_x_box[(x_box,y_box,z_box)]= s_x
s_y_box[(x_box,y_box,z_box)]= s_y
s_z_box[(x_box,y_box,z_box)]= s_z
# Magnitude of vector field
s_i_box = np.sqrt(s_x_box**2+s_y_box**2+s_z_box**2)
```
%% Cell type:markdown id: tags:
# 1. Plot density and momentum maps
%% Cell type:code id: tags:
``` python
# Select a slice of the data
s0_slice = s0_box[:,:,50]
s0_slice+= 1E-10 # Add a small number to visualise in log scale.
s_i_slice = s_i_box[:,:,50]
s_i_slice+= 1E-10 # Add a small number to visualise in log scale.
#Figs
fig= plt.figure(figsize=(10, 6))
gs = gridspec.GridSpec(1,2, wspace=0.5)
ax0 = plt.subplot(gs[0,0])
ax1 = plt.subplot(gs[0,1])
fig_s0 = ax0.imshow(s0_slice , origin='lower', cmap='inferno', aspect='equal',
norm=LogNorm(vmin=2E-1,vmax=1*s0_slice.max()),interpolation='None')
fig_si = ax1.imshow(s_i_slice , origin='lower', cmap='jet', aspect='equal',
norm=LogNorm(vmin=1E-10,vmax=1*s_i_slice.max()),interpolation='None')
#Colorbars
cx1 = fig.add_axes([0.45,0.25,0.02,.5])
cx2 = fig.add_axes([0.92,0.25,0.02,.5])
cb_s0 = plt.colorbar(fig_s0, cax = cx1, orientation='vertical')
cb_si = plt.colorbar(fig_si, cax = cx2, orientation='vertical')
cb_s0.ax.tick_params(labelsize=14, color='k')
cb_si.ax.tick_params(labelsize=14, color='k')
plt.show()
#fig.savefig("2D_map_s0_z-1_dpi_200.pdf",bbox_inches='tight',dpi=200)
plt.close()
```
%% Cell type:markdown id: tags:
## 1.1 Measure $P(k)$ using N-body kit
%% Cell type:code id: tags:
``` python
# Select field to measure
k_fun = 2*np.pi/box_size # fundamental mode of the box
k_Nyq = np.pi*grid_size/box_size # Nyquist mode
sim_field = s0_box
mesh_var = ArrayMesh( sim_field, Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_var = FFTPower( mesh_var, mode='1d', kmin= k_fun )
k_bins= np.array( r_var.power['k'] )
Pk_var= np.array( r_var.power['power'].real )
```
%% Cell type:code id: tags:
``` python
# CAMB z=0 matter P(k)
Pk_lin_z_0 = np.loadtxt('cmc_gauge_matterpower_z_0.dat',usecols=[1],skiprows=0,unpack=True,dtype=np.float32)[0:]
k_lin = np.loadtxt('cmc_gauge_matterpower_z_0.dat',usecols=[0],skiprows=0,unpack=True,dtype=np.float32)[0:]
```
%% Cell type:code id: tags:
``` python
# Plots
font = {'size':14}
plt.rc('font', **font)
plt.rc('font', family='serif')
plt.rc('text', usetex=True)
fig = plt.figure(figsize=(4, 5))
gs = gridspec.GridSpec(2,1, height_ratios=[4,1])
ax0 = plt.subplot(gs[0])
fig_lin= ax0.plot(k_lin,Pk_lin_z_0,'gray' , linewidth=1.0,zorder=-10, label='linear')
fig_Pk = ax0.scatter( k_bins, Pk_var, edgecolors='b', s=20,marker='.',facecolors='b',zorder=-2 )
plt.tick_params(axis='y', direction='in', which='both', labelleft='on', labelright='off', right='on')
plt.tick_params(axis='x', direction='in', which='both', labeltop='off', labelbottom='on', top='on')
ax0.set_ylabel(r'$P(k)$')
ax0.set_xlabel(r'$k$ [$h$ Mpc$^{-1}$]')
ax0.set_xscale('log')
ax0.set_yscale('log')
ax0.set_xlim( [ k_fun, 1.5*k_Nyq ] )
plt.fill_betweenx(np.array([1E-20,1E20]),k_Nyq,20 , alpha=0.2,color='red',interpolate=True)
ax0.set_ylim([1E1, 4E4])
plt.show()
#fig.savefig("Pk_gramses.pdf", bbox_inches='tight')
plt.close()
```
%% Cell type:markdown id: tags:
# 2. Vector potential
The vector mode of the shift vector is given by the linear combination below:
%% Cell type:code id: tags:
``` python
Bv_x = B_x_box -4.*dx_b_box
Bv_y = B_y_box -4.*dy_b_box
Bv_z = B_z_box -4.*dz_b_box
# Magnitude of vector field
Bv_box = np.sqrt(Bv_x**2+Bv_y**2+Bv_z**2)
```
%% Cell type:code id: tags:
``` python
# Select a slice of the data
s0_slice = s0_box[:,:,50]
s0_slice+= 1E-10 # Add a small number to visualise in log scale.
Bv_slice = Bv_box [:,:,50]
#Figs
fig= plt.figure(figsize=(10, 6))
gs = gridspec.GridSpec(1,2, wspace=0.5)
ax0 = plt.subplot(gs[0,0])
ax1 = plt.subplot(gs[0,1])
fig_s0 = ax0.imshow(s0_slice , origin='lower', cmap='inferno', aspect='equal',
norm=LogNorm(vmin=2E-1,vmax=1*s0_slice.max()),interpolation='None')
fig_Bv = ax1.imshow(Bv_slice , origin='lower', cmap='jet', aspect='equal',
norm=LogNorm(vmin=1E-10,vmax=1*Bv_slice.max()),interpolation='bicubic')
#Colorbars
cx1 = fig.add_axes([0.45,0.25,0.02,.5])
cx2 = fig.add_axes([0.92,0.25,0.02,.5])
cb_s0 = plt.colorbar(fig_s0, cax = cx1, orientation='vertical')
cb_Bv = plt.colorbar(fig_Bv, cax = cx2, orientation='vertical')
cb_s0.ax.tick_params(labelsize=14, color='k')
cb_Bv.ax.tick_params(labelsize=14, color='k')
plt.show()
#fig.savefig("2D_map_s0_z-1_dpi_200.pdf",bbox_inches='tight',dpi=200)
plt.close()
```
%% Cell type:markdown id: tags:
## 2.1 Power spectrum
%% Cell type:code id: tags:
``` python
# Measure P(k) from Bv
mesh_B_x = ArrayMesh( Bv_x, Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_B_x_Pk = FFTPower( mesh_B_x, mode='1d', kmin=2*np.pi/box_size )
k_B_x = np.array( r_B_x_Pk.power['k'] )
Pk_B_x= np.array( r_B_x_Pk.power['power'].real )
mesh_B_y = ArrayMesh( Bv_y, Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_B_y_Pk = FFTPower( mesh_B_y, mode='1d', kmin=2*np.pi/box_size )
k_B_y = np.array( r_B_y_Pk.power['k'] )
Pk_B_y= np.array( r_B_y_Pk.power['power'].real )
mesh_B_z = ArrayMesh( Bv_z, Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_B_z_Pk = FFTPower( mesh_B_z, mode='1d', kmin=2*np.pi/box_size )
k_B_z = np.array( r_B_z_Pk.power['k'] )
Pk_B_z= np.array( r_B_z_Pk.power['power'].real )
Pk_Bv = Pk_B_x+Pk_B_y+Pk_B_z
```
%% Cell type:markdown id: tags:
## 2.2 Calculate Curl: $[\nabla\times V]_i=\epsilon_{ijk}\partial_jV_k$
%% Cell type:code id: tags:
``` python
def curl_array(array_x, array_y, array_z, grid_len, box_len):
Vx1_z = np.zeros((grid_size,grid_size,grid_size))
Vx1_y = np.zeros((grid_size,grid_size,grid_size))
Vy1_z = np.zeros((grid_size,grid_size,grid_size))
Vy1_x = np.zeros((grid_size,grid_size,grid_size))
Vz1_y = np.zeros((grid_size,grid_size,grid_size))
Vz1_x = np.zeros((grid_size,grid_size,grid_size))
Vx2_z = np.zeros((grid_size,grid_size,grid_size))
Vx2_y = np.zeros((grid_size,grid_size,grid_size))
Vy2_z = np.zeros((grid_size,grid_size,grid_size))
Vy2_x = np.zeros((grid_size,grid_size,grid_size))
Vz2_y = np.zeros((grid_size,grid_size,grid_size))
Vz2_x = np.zeros((grid_size,grid_size,grid_size))
# Shifted positions & PBC
xbox1 = x_box + 1
xbox2 = x_box - 1
ybox1 = y_box + 1
ybox2 = y_box - 1
zbox1 = z_box + 1
zbox2 = z_box - 1
for i in (range(len(xbox1))):
if(xbox1[i]==grid_len): xbox1[i]=0
if(xbox2[i]==-1): xbox2[i]=grid_len-1
if(ybox1[i]==grid_len): ybox1[i]=0
if(ybox2[i]==-1): ybox2[i]=grid_len-1
if(zbox1[i]==grid_len): zbox1[i]=0
if(zbox2[i]==-1): zbox2[i]=grid_len-1
# Define nodes for FD:
Vx1_z[(x_box,y_box,zbox1)] = array_x
Vx1_y[(x_box,ybox1,z_box)] = array_x
Vy1_z[(x_box,y_box,zbox1)] = array_y
Vy1_x[(xbox1,y_box,z_box)] = array_y
Vz1_y[(x_box,ybox1,z_box)] = array_z
Vz1_x[(xbox1,y_box,z_box)] = array_z
Vx2_z[(x_box,y_box,zbox2)] = array_x
Vx2_y[(x_box,ybox2,z_box)] = array_x
Vy2_z[(x_box,y_box,zbox2)] = array_y
Vy2_x[(xbox2,y_box,z_box)] = array_y
Vz2_y[(x_box,ybox2,z_box)] = array_z
Vz2_x[(xbox2,y_box,z_box)] = array_z
# Calculate FD using shifted arrays
dx = box_len/float(grid_size)
curl_V_x= ((Vz1_y-Vz2_y)-(Vy1_z-Vy2_z))/(2*dx)
curl_V_y= ((Vx1_z-Vx2_z)-(Vz1_x-Vz2_x))/(2*dx)
curl_V_z= ((Vy1_x-Vy2_x)-(Vx1_y-Vx2_y))/(2*dx)
return [curl_V_x,curl_V_y,curl_V_z]
```
%% Cell type:code id: tags:
``` python
curl_B = curl_array(B_x, B_y, B_z, grid_size, box_size )
# curl of momentum field s_i
curl_s = curl_array(s_x, s_y, s_z, grid_size, box_size )
```
%% Cell type:code id: tags:
``` python
# Measure Power spectra of curls
mesh_cB_x = ArrayMesh( curl_B[0], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cB_x_Pk = FFTPower( mesh_cB_x, mode='1d', kmin=2*np.pi/box_size )
k_cB_x = np.array( r_cB_x_Pk.power['k'] )
Pk_cB_x= np.array( r_cB_x_Pk.power['power'].real )
mesh_cB_y = ArrayMesh( curl_B[1], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cB_y_Pk = FFTPower( mesh_cB_y, mode='1d', kmin=2*np.pi/box_size )
k_cB_y = np.array( r_cB_y_Pk.power['k'] )
Pk_cB_y= np.array( r_cB_y_Pk.power['power'].real )
mesh_cB_z = ArrayMesh( curl_B[2], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cB_z_Pk = FFTPower( mesh_cB_z, mode='1d', kmin=2*np.pi/box_size )
k_cB_z = np.array( r_cB_z_Pk.power['k'] )
Pk_cB_z= np.array( r_cB_z_Pk.power['power'].real )
# Spectrum from curl
Pk_cBB = Pk_cB_x+Pk_cB_y+Pk_cB_z
Pk_BB = Pk_cBB/k_cB_x**2
k_cB = k_cB_x
# Curl of density field
mesh_cs_x = ArrayMesh( curl_s[0], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cs_x_Pk = FFTPower( mesh_cs_x, mode='1d', kmin=2*np.pi/box_size )
k_cs_x = np.array( r_cs_x_Pk.power['k'] )
Pk_cs_x= np.array( r_cs_x_Pk.power['power'].real )
mesh_cs_y = ArrayMesh( curl_s[1], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cs_y_Pk = FFTPower( mesh_cs_y, mode='1d', kmin=2*np.pi/box_size )
k_cs_y = np.array( r_cs_y_Pk.power['k'] )
Pk_cs_y= np.array( r_cs_y_Pk.power['power'].real )
mesh_cs_z = ArrayMesh( curl_s[2], Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_cs_z_Pk = FFTPower( mesh_cs_z, mode='1d', kmin=2*np.pi/box_size )
k_cs_z = np.array( r_cs_z_Pk.power['k'] )
Pk_cs_z= np.array( r_cs_z_Pk.power['power'].real )
# Spectrum from curl
Pk_csi= Pk_cs_x+Pk_cs_y+Pk_cs_z
Pk_si = Pk_csi/k_cs_x**2
k_cs = k_cs_x
```
%% Cell type:markdown id: tags:
## Plot all the vector modes $P(k)$
%% Cell type:code id: tags:
``` python
# Plots
font = {'size':14}
plt.rc('font', **font)
plt.rc('font', family='serif')
plt.rc('text', usetex=True)
fig = plt.figure(figsize=(4, 5))
gs = gridspec.GridSpec(2,1, height_ratios=[4,1])
ax0 = plt.subplot(gs[0])
fig_Pk = ax0.scatter( k_B_x, k_B_x**3*Pk_Bv/(2*np.pi**2)
, edgecolors='b', s=20,marker='.',facecolors='b',zorder=-2 )
fig_Pk = ax0.scatter( k_cB , k_cB**3*Pk_BB*1/(2*np.pi**2)
, edgecolors='r', s=20,marker='.',facecolors='r',zorder=-2 )
fig_Pk = ax0.scatter( k_cs , k_cs**3*Pk_si/k_cs**4/(2*np.pi**2)
, edgecolors='gray', s=20,marker='.',facecolors='gray',zorder=-2 )
plt.tick_params(axis='y', direction='in', which='both', labelleft='on', labelright='off', right='on')
plt.tick_params(axis='x', direction='in', which='both', labeltop='off', labelbottom='on', top='on')
ax0.set_ylabel(r'$k^3P(k)/(2\pi^2)$')
ax0.set_xlabel(r'$k$ [$h$ Mpc$^{-1}$]')
ax0.set_xscale('log')
ax0.set_yscale('log')
ax0.set_xlim( [ k_fun, 1.5*k_Nyq ] )
ax0.set_ylim([1E-20, 1E-15])
plt.fill_betweenx(np.array([1E-20,1E-10]),k_Nyq, 20, alpha=0.2,color='red',interpolate=True)
plt.show()
#fig.savefig("Pk_gramses.pdf", bbox_inches='tight')
plt.close()
```
%% Cell type:markdown id: tags:
# 3. Gravitational slip: $\chi=\vert \Phi-\Psi \vert$
%% Cell type:code id: tags:
``` python
# Define nonlinear scalar perturbations
# Conformal factor perturbation
Psi = gr_pot[0]/(a_out*ctilde)**2/2
# Lapse function perturbation
lapse = 1. + gr_pot[1]/(a_out*ctilde)**2/(1. - Psi)
Phi = 0.5*(lapse**2-1.)
# Define gravitational slip
chi = np.abs(Phi - Psi)
# Map to box
chi_box = np.zeros((grid_size,grid_size,grid_size))
chi_box[(x_box,y_box,z_box)] = chi
print(Phi.max(),Phi.min())
print(Psi.max(),Psi.min())
print(chi.max(),chi.min(),np.mean((chi)) )
```
%% Cell type:code id: tags:
``` python
# Select a slice of the data
s0_slice = s0_box[:,:,50]
s0_slice+= 1E-10 # Add a small number to visualise in log scale.
chi_slice= chi_box[:,:,50]
#Figs
fig= plt.figure(figsize=(10, 6))
gs = gridspec.GridSpec(1,2, wspace=0.5)
ax0 = plt.subplot(gs[0,0])
ax1 = plt.subplot(gs[0,1])
fig_s0 = ax0.imshow(s0_slice , origin='lower', cmap='inferno', aspect='equal',
norm=LogNorm(vmin=2E-1,vmax=1*s0_slice.max()),interpolation='None')
fig_chi= ax1.imshow(chi_slice , origin='lower', cmap='jet', aspect='equal',
norm=LogNorm(vmin=1E-7,vmax=1*chi_slice.max()),interpolation='bicubic')
#Colorbars
cx1 = fig.add_axes([0.45,0.25,0.02,.5])
cx2 = fig.add_axes([0.92,0.25,0.02,.5])
cb_s0= plt.colorbar(fig_s0, cax = cx1, orientation='vertical')
cb_Bv = plt.colorbar(fig_chi, cax = cx2, orientation='vertical')
cb_s0.ax.tick_params(labelsize=14, color='k')
cb_Bv.ax.tick_params(labelsize=14, color='k')
plt.show()
#fig.savefig("2D_map_s0_z-1_dpi_200.pdf",bbox_inches='tight',dpi=200)
plt.close()
```
%% Cell type:code id: tags:
``` python
# Measure spectrum
mesh_chi = ArrayMesh( chi_box, Nmesh=grid_size, compensated=False, BoxSize=box_size )
r_chi = FFTPower( mesh_chi, mode='1d', kmin= k_fun )
k_bins= np.array( r_chi.power['k'] )
Pk_chi= np.array( r_chi.power['power'].real )
```
%% Cell type:code id: tags:
``` python
# Plots
font = {'size':14}
plt.rc('font', **font)
plt.rc('font', family='serif')
plt.rc('text', usetex=True)
fig = plt.figure(figsize=(4, 5))
gs = gridspec.GridSpec(2,1, height_ratios=[4,1])
ax0 = plt.subplot(gs[0])
fig_Pk = ax0.scatter( k_bins, Pk_chi, edgecolors='b', s=20,marker='.',facecolors='b',zorder=-2 )
plt.tick_params(axis='y', direction='in', which='both', labelleft='on', labelright='off', right='on')
plt.tick_params(axis='x', direction='in', which='both', labeltop='off', labelbottom='on', top='on')
ax0.set_ylabel(r'$P(k)$')
ax0.set_xlabel(r'$k$ [$h$ Mpc$^{-1}$]')
ax0.set_xscale('log')
ax0.set_yscale('log')
ax0.set_xlim( [ k_fun, 1.5*k_Nyq ] )
plt.fill_betweenx(np.array([1E-15,1E1]),k_Nyq,20 , alpha=0.2,color='red',interpolate=True)
ax0.set_ylim([1E-15, 1E-4])
plt.show()
#fig.savefig("Pk_gramses.pdf", bbox_inches='tight')
plt.close()
```
cmc_gauge_matterpower_z_0.dat 0 → 100644
+ 695
− 0
View file @ b551c379
# k/h P
0.100000E-03 0.495744E+06
0.102020E-03 0.467647E+06
0.104081E-03 0.441188E+06
0.106184E-03 0.416272E+06
0.108329E-03 0.392807E+06
0.110517E-03 0.370708E+06
0.112750E-03 0.349895E+06
0.115027E-03 0.330290E+06
0.117351E-03 0.311824E+06
0.119722E-03 0.294430E+06
0.122140E-03 0.278043E+06
0.124608E-03 0.262604E+06
0.127125E-03 0.248059E+06
0.129693E-03 0.234353E+06
0.132313E-03 0.221438E+06
0.134986E-03 0.209266E+06
0.137713E-03 0.197795E+06
0.140495E-03 0.186983E+06
0.143333E-03 0.176791E+06
0.146228E-03 0.167183E+06
0.149182E-03 0.158125E+06
0.152196E-03 0.149586E+06
0.155271E-03 0.141535E+06
0.158407E-03 0.133944E+06
0.161607E-03 0.126787E+06
0.164872E-03 0.120039E+06
0.168203E-03 0.113675E+06
0.171601E-03 0.107674E+06
0.175067E-03 0.102015E+06
0.178604E-03 0.966773E+05
0.182212E-03 0.916425E+05
0.185893E-03 0.868932E+05
0.189648E-03 0.824126E+05
0.193479E-03 0.781851E+05
0.197388E-03 0.741961E+05
0.201375E-03 0.704318E+05
0.205443E-03 0.668790E+05
0.209594E-03 0.635258E+05
0.213828E-03 0.603607E+05
0.218147E-03 0.573729E+05
0.222554E-03 0.545523E+05
0.227050E-03 0.518893E+05
0.231637E-03 0.493749E+05
0.236316E-03 0.470005E+05
0.241090E-03 0.447582E+05
0.245960E-03 0.426402E+05
0.250929E-03 0.406397E+05
0.255998E-03 0.387497E+05
0.261170E-03 0.369640E+05
0.266446E-03 0.352766E+05
0.271828E-03 0.336820E+05
0.277319E-03 0.321748E+05
0.282922E-03 0.307500E+05
0.288637E-03 0.294031E+05
0.294468E-03 0.281296E+05
0.300417E-03 0.269253E+05
0.306485E-03 0.257865E+05
0.312677E-03 0.247094E+05
0.318993E-03 0.236906E+05
0.325437E-03 0.227268E+05
0.332012E-03 0.218150E+05
0.338719E-03 0.209523E+05
0.345561E-03 0.201360E+05
0.352542E-03 0.193636E+05
0.359664E-03 0.186326E+05
0.366930E-03 0.179408E+05
0.374342E-03 0.172861E+05
0.381904E-03 0.166664E+05
0.389619E-03 0.160800E+05
0.397490E-03 0.155249E+05
0.405520E-03 0.149996E+05
0.413712E-03 0.145022E+05
0.422070E-03 0.140314E+05
0.430596E-03 0.135857E+05
0.439295E-03 0.131637E+05
0.448169E-03 0.127642E+05
0.457222E-03 0.123861E+05
0.466459E-03 0.120281E+05
0.475882E-03 0.116892E+05
0.485496E-03 0.113686E+05
0.495303E-03 0.110652E+05
0.505309E-03 0.107783E+05
0.515517E-03 0.105070E+05
0.525931E-03 0.102506E+05
0.536556E-03 0.100084E+05
0.547395E-03 0.977977E+04
0.558453E-03 0.956402E+04
0.569734E-03 0.936050E+04
0.581244E-03 0.916860E+04
0.592986E-03 0.898774E+04
0.604965E-03 0.881738E+04
0.617186E-03 0.865702E+04
0.629654E-03 0.850620E+04
0.642374E-03 0.836449E+04
0.655350E-03 0.823147E+04
0.668589E-03 0.810679E+04
0.682096E-03 0.799008E+04
0.695875E-03 0.788102E+04
0.709933E-03 0.777932E+04
0.724274E-03 0.768470E+04
0.738906E-03 0.759689E+04
0.753832E-03 0.751566E+04
0.769061E-03 0.744079E+04
0.784597E-03 0.737204E+04
0.800447E-03 0.730915E+04
0.816617E-03 0.725191E+04
0.833114E-03 0.720011E+04
0.849944E-03 0.715355E+04
0.867114E-03 0.711205E+04
0.884631E-03 0.707544E+04
0.902501E-03 0.704356E+04
0.920733E-03 0.701628E+04
0.939333E-03 0.699345E+04
0.958309E-03 0.697494E+04
0.977668E-03 0.696065E+04
0.997418E-03 0.695046E+04
0.101757E-02 0.694427E+04
0.103812E-02 0.694200E+04
0.105910E-02 0.694355E+04
0.108049E-02 0.694884E+04
0.110232E-02 0.695780E+04
0.112459E-02 0.697035E+04
0.114730E-02 0.698641E+04
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0.121825E-02 0.705508E+04
0.124286E-02 0.708460E+04
0.126797E-02 0.711735E+04
0.129358E-02 0.715328E+04
0.131971E-02 0.719235E+04
0.134637E-02 0.723451E+04
0.137357E-02 0.727972E+04
0.140132E-02 0.732793E+04
0.142963E-02 0.737912E+04
0.145851E-02 0.743325E+04
0.148797E-02 0.749027E+04
0.151803E-02 0.755016E+04
0.154870E-02 0.761291E+04
0.157998E-02 0.767849E+04
0.161190E-02 0.774691E+04
0.164446E-02 0.781813E+04
0.167768E-02 0.789216E+04
0.171158E-02 0.796898E+04
0.174615E-02 0.804858E+04
0.178143E-02 0.813094E+04
0.181741E-02 0.821604E+04
0.185413E-02 0.830389E+04
0.189158E-02 0.839445E+04
0.192980E-02 0.848771E+04
0.196878E-02 0.858366E+04
0.200855E-02 0.868228E+04
0.204913E-02 0.878354E+04
0.209052E-02 0.888742E+04
0.213276E-02 0.899391E+04
0.217584E-02 0.910303E+04
0.221979E-02 0.921476E+04
0.226464E-02 0.932911E+04
0.231039E-02 0.944608E+04
0.235706E-02 0.956566E+04
0.240467E-02 0.968785E+04
0.245325E-02 0.981263E+04
0.250281E-02 0.994001E+04
0.255337E-02 0.100700E+05
0.260495E-02 0.102025E+05
0.265758E-02 0.103376E+05
0.271126E-02 0.104752E+05
0.276603E-02 0.106154E+05
0.282191E-02 0.107580E+05
0.287892E-02 0.109031E+05
0.293708E-02 0.110507E+05
0.299641E-02 0.112007E+05
0.305694E-02 0.113531E+05
0.311870E-02 0.115079E+05
0.318170E-02 0.116651E+05
0.324597E-02 0.118247E+05
0.331155E-02 0.119867E+05
0.337844E-02 0.121510E+05
0.344669E-02 0.123176E+05
0.351632E-02 0.124866E+05
0.358735E-02 0.126577E+05
0.365982E-02 0.128311E+05
0.373376E-02 0.130067E+05
0.380918E-02 0.131845E+05
0.388613E-02 0.133643E+05
0.396464E-02 0.135462E+05
0.404473E-02 0.137302E+05
0.412644E-02 0.139161E+05
0.420980E-02 0.141039E+05
0.429484E-02 0.142936E+05
0.438160E-02 0.144852E+05
0.447012E-02 0.146785E+05
0.456042E-02 0.148736E+05
0.465255E-02 0.150704E+05
0.474653E-02 0.152687E+05
0.484242E-02 0.154686E+05
0.494024E-02 0.156699E+05
0.504004E-02 0.158727E+05
0.514186E-02 0.160767E+05
0.524573E-02 0.162820E+05
0.535170E-02 0.164885E+05
0.545981E-02 0.166960E+05
0.557011E-02 0.169045E+05
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0.579743E-02 0.173241E+05
0.591455E-02 0.175350E+05
0.603403E-02 0.177465E+05
0.615592E-02 0.179585E+05
0.628028E-02 0.181708E+05
0.640715E-02 0.183833E+05
0.653658E-02 0.185960E+05
0.666863E-02 0.188087E+05
0.680335E-02 0.190213E+05
0.694078E-02 0.192336E+05
0.708100E-02 0.194455E+05
0.722404E-02 0.196568E+05
0.736998E-02 0.198674E+05
0.751886E-02 0.200772E+05
0.767075E-02 0.202860E+05
0.782571E-02 0.204936E+05
0.798380E-02 0.206998E+05
0.814509E-02 0.209045E+05
0.830963E-02 0.211075E+05
0.847750E-02 0.213086E+05
0.864875E-02 0.215077E+05
0.882347E-02 0.217044E+05
0.900171E-02 0.218987E+05
0.918356E-02 0.220904E+05
0.936908E-02 0.222791E+05
0.955835E-02 0.224647E+05
0.975144E-02 0.226470E+05
0.994843E-02 0.228257E+05
0.101494E-01 0.230007E+05
0.103544E-01 0.231716E+05
0.105636E-01 0.233383E+05
0.107770E-01 0.235005E+05
0.109947E-01 0.236579E+05
0.112168E-01 0.238103E+05
0.114434E-01 0.239574E+05
0.116746E-01 0.240990E+05
0.119104E-01 0.242348E+05
0.121510E-01 0.243645E+05
0.123965E-01 0.244879E+05
0.126469E-01 0.246046E+05
0.129024E-01 0.247145E+05
0.131631E-01 0.248171E+05
0.134290E-01 0.249124E+05
0.137003E-01 0.249999E+05
0.139770E-01 0.250793E+05
0.142594E-01 0.251505E+05
0.145474E-01 0.252131E+05
0.148413E-01 0.252668E+05
0.151411E-01 0.253115E+05
0.154470E-01 0.253467E+05
0.157590E-01 0.253723E+05
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0.164022E-01 0.253935E+05
0.167335E-01 0.253886E+05
0.170716E-01 0.253731E+05
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0.177683E-01 0.253093E+05
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0.204384E-01 0.247242E+05
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0.217022E-01 0.242948E+05
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0.230442E-01 0.237579E+05
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0.395440E-01 0.157482E+05
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