SuperSCRAM/variance_demo.py at master · mcdigman/SuperSCRAM · GitHub

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"""demonstration of ability to compute super sample variance term in a geometry"""
from __future__ import division,print_function,absolute_import
from builtins import range
from time import time
import numpy as np
from polygon_geo import PolygonGeo
from cosmopie import CosmoPie
import defaults
from sph_klim import SphBasisK
import matter_power_spectrum as mps

if __name__=='__main__':
    time0 = time()
    camb_params = { 'npoints':1000,
                    'minkh':1.1e-4,
                    'maxkh':1.476511342960e+02,
                    'kmax':1.476511342960e+02,
                    'leave_h':False,
                    'force_sigma8':True,
                    'return_sigma8':False,
                    'accuracy':2
                  }
    print("main: building cosmology")
    power_params = defaults.power_params.copy()
    power_params.camb = camb_params
    cosmo_use = defaults.cosmology.copy()
    cosmo_use['h'] = 0.6774
    cosmo_use['Omegabh2'] = 0.02230
    cosmo_use['mnu'] = 0.06
    cosmo_use['Omegamh2'] = 0.1188
    cosmo_use['OmegaL'] = 0.7
    cosmo_use['de_model'] = 'constant_w'
    cosmo_use['w'] = -0.9
    cosmo_use['ns'] = 0.9667
    cosmo_use['As'] = 2.142e-9
    cosmo_use['OmegaLh2'] = 0.7*0.6774**2
    cosmo_use['Omegakh2'] = 0.
    cosmo_use['LogAs'] = np.log(2.142e-9)
    C = CosmoPie(defaults.cosmology.copy(),p_space='jdem')
    P_lin = mps.MatterPower(C,power_params)
    C.set_power(P_lin)

    #x_cut = 527.
    #l_max = 515
    #x_cut = 360
    #l_max = 340
    x_cut = 150
    l_max = 140
    #x_cut = 30
    #l_max = 30
    #x_cut = 150
    #l_max = 10

    param_use = 7
    do_plot = False
    if param_use==1:
        #matches to  0.918455921357 for l_max=340,x_cut=360, not monotonic
        theta0 = np.pi/2.-np.pi*0.21644180767757945
        theta1 = np.pi/2.+np.pi*0.21644180767757945
        phi0 = 0.
        phi1 = np.pi*0.4328860177816256

        z_coarse = np.array([0.001,0.005])
        z_max = 0.0055
        z_fine = np.arange(0.00001,0.2,0.00001)

        variance_pred1 = 6.94974e-01
        variance_pred2 = 6.47471e-01
    elif param_use==2:
        #matches to 0.984883733033 for l_max=340,x_cut=360, monotonic
        theta0 = np.pi/2.-np.pi*0.005549789940450755
        theta1 = np.pi/2.+np.pi*0.005549789940450755
        phi0 = 0.
        phi1 = np.pi*0.011099641481580144

        z_coarse = np.array([0.9,1.0])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.05

        variance_pred1 = 1.32333e-02
        variance_pred2 = 1.38770e-02
    elif param_use==3:
        #matches to  0.256984236659 for l_max=340,x_cut=360, monotonic but convergence appears poor
        #matches to 0.442356296589 for l_max=515, x_cut=
        theta0 = np.pi/2.-np.pi/1801.87
        theta1 = np.pi/2.+np.pi/1801.87
        phi0 = 0.
        phi1 = np.pi/900.93

        z_coarse = np.array([0.99525,1.0])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.05

        variance_pred1 = 1.18262e+00
        variance_pred2 = 1.18253e+00
    elif param_use==4:
        #matches to 0.982422823102 side 0.985672230237 volume  for l_max=340,x_cut=360, monotonic, convergence looks good
        theta0 = np.pi/2.-np.pi*0.025320951131222628
        theta1 = np.pi/2.+np.pi*0.025320951131222628
        phi0 = 0.
        phi1 = np.pi*0.05064218331592479

        z_coarse = np.array([0.8102,1.0])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.05

        variance_pred1 = 4.91106e-04
        variance_pred2 = 4.89487E-04
    elif param_use==5:
        #20000 deg^2
        #matches to side 1.17896133281 vol 0.914043964767 for l_max=340,x_cut=360, appears converged
        theta0 = np.pi/2.-np.pi*0.48476681987396752
        theta1 = np.pi/2.+np.pi*0.48476681987396752
        phi0 = 0.
        phi1 = np.pi*0.96953902048583762

        z_coarse = np.array([0.9,1.3])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.301

        #by sides
        variance_pred1 = 2.88548E-07
        #by volume
        variance_pred2 = 3.10674E-07
    elif param_use==6:
        #2000 deg^2
        #matches to side 1.17896133281 vol 0.914043964767 for l_max=340,x_cut=360, appears converged
        theta0 = np.pi/2.-np.pi*0.12306206198097261
        theta1 = np.pi/2.+np.pi*0.12306206198097261

        phi0 = 0.
        phi1 = np.pi*0.24612548990671312

        z_coarse = np.array([0.9,1.3])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.301

        #by sides
        variance_pred1 = 5.50604e-06
        #by volume
        variance_pred2 = 4.95809e-06
    elif param_use==7:
        #20000 deg^2
        #matches to side 1.17896133281 vol 0.914043964767 for l_max=340,x_cut=360, appears converged
        theta0 = np.pi/2.-np.pi*0.48476681987396752
        theta1 = np.pi/2.+np.pi*0.48476681987396752
        phi0 = 0.
        phi1 = np.pi*0.96953902048583762

        z_coarse = np.array([0.2,1.3])
        z_fine = np.arange(0.0005,1.,0.0005)
        z_max = 1.301

        #by sides
        variance_pred1 = 1.12606e-07
        #by volume
        variance_pred2 = 1.50551e-07
    thetas = np.array([theta0,theta1,theta1,theta0,theta0])
    phis = np.array([phi0,phi0,phi1,phi1,phi0])
    theta_in = (theta1+theta0)/2.
    phi_in = (phi1+phi0)/2.

    l_sw = np.logspace(np.log(30),np.log(5000),base=np.exp(1.),num=40)

    print("main: building geometries")
    polygon_params = defaults.polygon_params.copy()
    polygon_params['n_double'] = 80
    geo1 = PolygonGeo(z_coarse,thetas,phis,theta_in,phi_in,C,z_fine,l_max,polygon_params)
    print('main: r diffs',np.diff(geo1.rs))
    print('main: theta width',(geo1.rs[1]+geo1.rs[0])/2.*(theta1-theta0))
    #print('main: phi width',(geo1.rs[1]+geo1.rs[0])/2.*(phi1-phi0)*np.sin((theta1+theta0)/2))
    print('main: phi width',(geo1.rs[1]+geo1.rs[0])/2.*(phi1-phi0))
#    geo2 = PolygonGeo(z_coarse,thetas,phis+phi1,theta_in,phi_in+phi1,C,z_fine,l_max,polygon_params)
#    #geo1 = RectGeo(z_coarse,np.array([theta0,theta1]),np.array([phi0,phi1]),C,z_fine)
#    #geo2 = RectGeo(z_coarse,np.array([theta0,theta1]),np.array([phi0,phi1])+phi1,C,z_fine)

    print("main: building basis")
    basis_params = defaults.basis_params.copy()
    basis_params['n_bessel_oversample']*=1
    basis_params['x_grid_size']*=10

    r_max = C.D_comov(z_max)
    k_cut = x_cut/r_max
    k_tests = np.linspace(20./r_max,k_cut,100)
    n_basis = np.zeros(k_tests.size)
    variances = np.zeros(k_tests.size)

    basis = SphBasisK(r_max,C,k_cut,basis_params,l_ceil=l_max)
    for i in range(0,k_tests.size):
        print("r_max,k_cut",r_max,k_tests[i])
        n_basis[i] = np.sum(basis.C_id[:,1]<=k_tests[i])
        variances[i] = basis.get_variance(geo1,k_cut_in=k_tests[i])
        print("main: with k_cut="+str(k_tests[i])+" size="+str(n_basis[i])+" got variance="+str(variances[i]))

    if do_plot:
        import matplotlib.pyplot as plt
        plt.plot(n_basis,variances)
        plt.show()
    print("main: getting variance")
    variance_res = basis.get_variance(geo1)
    time1 = time()
    print("main: finished building in "+str(time1-time0)+"s")

    r_width = np.diff(geo1.rs)[0]
    theta_width = (geo1.rs[1]+geo1.rs[0])/2.*(theta1-theta0)
    phi_width = (geo1.rs[1]+geo1.rs[0])/2.*(phi1-phi0)
    volume = 4./3.*np.pi*(geo1.rs[1]**3-geo1.rs[0]**3)*geo1.angular_area()/(4.*np.pi)
    square_equiv = volume**(1./3.)
    print('main: r diffs',r_width*C.h)
    print('main: theta width',theta_width*C.h)
    #print('main: phi width',(geo1.rs[1]+geo1.rs[0])/2.*(phi1-phi0)*np.sin((theta1+theta0)/2))
    print('main: phi width',phi_width*C.h)
    print('main: square side length',square_equiv*C.h)
    print("main: variance is "+str(variance_res))
    print("main: variance/predicted by sides is "+str(variances[-1]/variance_pred1))
    print("main: variance/predicted by volume is "+str(variances[-1]/variance_pred2))
    #print("main: rate of change of variance is "+str((variances[-1]-variances[-2])/(k_tests[-1]-k_tests[-2])))
    #approx_deriv = np.average((np.diff(variances)/np.diff(n_basis))[-5::])
    approx_deriv = (variances[-1]-variances[-5])/(n_basis[-1]-n_basis[-5])
    estim_change = approx_deriv*n_basis[-1]*2.
    estim_converge = estim_change/variances[-1]
    print("main: estimate variance converged to within an error of"+str(estim_converge*100.)+"%, first approx of true value ~"+str(estim_change+variances[-1]))