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EFT implementation #9

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EFT implementation #9

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113 changes: 112 additions & 1 deletion fastpt/FASTPT.py
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Original file line number Diff line number Diff line change
Expand Up @@ -44,7 +44,7 @@
from scipy.signal import fftconvolve
import scipy.integrate as integrate
from .fastpt_extr import p_window, c_window, pad_left, pad_right
from .matter_power_spt import P_13_reg, Y1_reg_NL, Y2_reg_NL
from .matter_power_spt import P_13_reg, Y1_reg_NL, Y2_reg_NL, J2_integral, J3_integral
from .initialize_params import scalar_stuff, tensor_stuff
from .IA_tt import IA_tt
from .IA_ABD import IA_A, IA_DEE, IA_DBB, P_IA_B
Expand Down Expand Up @@ -172,6 +172,7 @@ def __init__(self, k, nu=None, to_do=None, param_mat=None, low_extrap=None, high
self.OV_do = False
self.kPol_do = False
self.RSD_do = False
self.EFT_do = False

for entry in to_do: # convert to_do list to instructions for FAST-PT initialization
if entry == 'one_loop_dd':
Expand Down Expand Up @@ -223,6 +224,9 @@ def __init__(self, k, nu=None, to_do=None, param_mat=None, low_extrap=None, high
self.RSD_do = True
self.cleft = True
continue
elif entry == 'EFT':
self.EFT_do = True
continue
else:
raise ValueError('FAST-PT does not recognize "' + entry + '" in the to_do list.')

Expand Down Expand Up @@ -305,6 +309,42 @@ def __init__(self, k, nu=None, to_do=None, param_mat=None, low_extrap=None, high
p_mat = tabB[:, [0, 1, 5, 6, 7, 8, 9]]
self.X_RSDB = tensor_stuff(p_mat, self.N, self.m, self.eta_m, self.l, self.tau_l)

if self.EFT_do:
# Computes relevant quantities for all (22) integrals in EFT of IA theory.
nu = -2
p_mat_11 = np.array([[0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 4, 0], [2, -2, 2, 0],
[1, -1, 1, 0], [1, -1, 3, 0], [2, -2, 0, 1]])
p_mat_12 = np.array([[0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 4, 0], [1, -1, 1, 0],
[1, -1, 3, 0], [-1, 1, 1, 0], [-1, 1, 3, 0]
])
p_mat_13 = np.array([[0, 0, 0, 0], [0, 0, 2, 0], [1, -1, 1, 0], [-1, 1, 1, 0]])
p_mat_22 = np.array([[0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 4, 0]])
p_mat_23 = np.array([[0, 0, 0, 0], [0, 0, 2, 0]])
p_mat_24 = np.array([[2, 0, 0, 0], [2, 0, 2, 0], [2, 0, 4, 0], [1, 1, 1, 0],
[1, 1, 3, 0], [1, 1, 5, 0], [0, 2, 0, 0], [0, 2, 2, 0],
[0, 2, 4, 0]])
p_mat_33 = np.array([[0, 0, 0, 0]])
p_mat_34 = np.array([[2, 0, 0, 0], [2, 0, 2, 0], [1, 1, 1, 0,], [1, 1, 3, 0],
[0, 2, 0, 0], [0, 2, 2, 0]])
p_mat_44 = np.array([[4, 0, 0, 0,], [4, 0, 2, 0], [4, 0, 4, 0], [3, 1, 1, 0],
[3, 1, 3, 0], [3, 1, 5, 0], [2, 2, 0, 0], [2, 2, 2, 0],
[2, 2, 4, 0], [2, 2, 6, 0], [1, 3, 1, 0], [1, 3, 3, 0],
[1, 3, 5, 0], [0, 4, 0, 0], [0, 4, 2, 0], [0, 4, 4, 0]])
p_mat_55 = np.array([[4, 0, 0, 0], [4, 0, 2, 0], [4, 0, 4, 0], [2, 2, 0, 0],
[2, 2, 2, 0], [2, 2, 4, 0], [0, 4, 0, 0], [0, 4, 2, 0],
[0, 4, 4, 0]])

self.Jabl_I11 = scalar_stuff(p_mat_11, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I12 = scalar_stuff(p_mat_12, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I13 = scalar_stuff(p_mat_13, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I22 = scalar_stuff(p_mat_22, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I23 = scalar_stuff(p_mat_23, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I24 = scalar_stuff(p_mat_24, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I33 = scalar_stuff(p_mat_33, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I34 = scalar_stuff(p_mat_34, nu, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I44 = scalar_stuff(p_mat_44, -1.6, self.N, self.m, self.eta_m, self.l, self.tau_l)
self.Jabl_I55 = scalar_stuff(p_mat_55, -1.6, self.N, self.m, self.eta_m, self.l, self.tau_l)

### Top-level functions to output final quantities ###
def one_loop_dd(self, P, P_window=None, C_window=None):
nu = -2
Expand Down Expand Up @@ -702,6 +742,77 @@ def presum(x):
# p1loop = interpolate.InterpolatedUnivariateSpline(k,out_1loop) # is this necessary? out_1loop should already be at the correct k spacing
return psmooth(k) + out_1loop + pw(k) * exp(-k ** 2 * Sigma) * (1 + Sigma * k ** 2)

def eft_integrals(self, P, P_window=None, C_window=None):
# Returns the I_nm, J_n integrals based on arXiv:2303.15565. See Eqs. (2.39), (2.40) and
# corresponding kernels in Eqs. (A.1)-(A.3). Power spectra can be obtained using (2.41) and (2.63).

# Coefficients for the (22)-type integrals:
coef_11 = [1219/1470., 671/1029., 32/1715., 1/3., 62/35., 8/35., 1/6.]
coef_12 = [31/105., 94/147., 16/245., 3/10., 1/5., 3/10., 1/5.]
coef_13 = [17/21., 4/21., 1/2., 1/2.]
coef_22 = [1/5., 4/7., 8/35.]
coef_23 = [1/3., 2/3.]
coef_24 = np.sqrt(2/3) * np.array([1/5., 4/7., 8/35., 3*13/35., 37/45,
4/63., 1/5., 4/7., 8/35.])
coef_33 = 1.
coef_34 = np.sqrt(2/3) * np.array([1/3., 2/3., 3*3/5., 1/5., 1/3., 2/3.])
coef_44 = [2/15., 8/21., 16/105., 52/35., 148/135., 16/189., 104/105., 152/63., 676/1155,
8/693., 52/35., 148/135., 16/189., 2/15., 8/21., 16/105.]
coef_55 = [1/30., 1/42., -2/35., -1/15., -1/21., 4/35., 1/30., 1/42., -2/35.]

def get_Inm(P, coef, Jabl, nu, P_window=P_window, C_window=C_window):
# Function to compute the final (22)-integrals:
Ps, mat = self.J_k_scalar(P, Jabl, nu, P_window, C_window)
P_mat = np.multiply(coef, np.transpose(mat))
Inm = np.sum(P_mat, 1)
return Inm, Ps

# Compute the (22)-integrals
I11, Ps = get_Inm(P, coef_11, self.Jabl_I11, -2, C_window)
I12, _ = get_Inm(P, coef_12, self.Jabl_I12, -2, C_window)
I13, _ = get_Inm(P, coef_13, self.Jabl_I13, -2, C_window)
I22, _ = get_Inm(P, coef_22, self.Jabl_I22, -2, C_window)
I23, _ = get_Inm(P, coef_23, self.Jabl_I23, -2, C_window)
I24, _ = get_Inm(P, coef_24, self.Jabl_I24, -2, C_window)
I33, _ = get_Inm(P, coef_33, self.Jabl_I33, -2, C_window)
I34, _ = get_Inm(P, coef_34, self.Jabl_I34, -2, C_window)
I44, _ = get_Inm(P, coef_44, self.Jabl_I44, -1.6, C_window)
I55, _ = get_Inm(P, coef_55, self.Jabl_I55, -1.6, C_window)

I24 /= self.k_old**2
I34 /= self.k_old**2
I44 /= self.k_old**4
I55 /= self.k_old**4

# subtract the low-k limit of the integral:
I22 -= I22[0]
I23 -= I23[0]
I24 -= I24[0]
I33 -= I33[0]
I44 -= I44[0]
I55 -= I55[0]

# Compute the (13)-integrals:
J1 = P_13_reg(self.k_old, Ps)/2
J2 = J2_integral(self.k_old, Ps)
J3 = J3_integral(self.k_old, Ps)

_, I11 = self.EK.PK_original(I11)
_, I12 = self.EK.PK_original(I12)
_, I13 = self.EK.PK_original(I13)
_, I22 = self.EK.PK_original(I22)
_, I23 = self.EK.PK_original(I23)
_, I24 = self.EK.PK_original(I24)
_, I33 = self.EK.PK_original(I33)
_, I34 = self.EK.PK_original(I34)
_, I44 = self.EK.PK_original(I44)
_, I55 = self.EK.PK_original(I55)
_, J1 = self.EK.PK_original(J1)
_, J2 = self.EK.PK_original(J2)
_, J3 = self.EK.PK_original(J3)

return I11, I12, I13, I22, I23, I24, I33, I34, I44, I55, J1, J2, J3

######################################################################################
### functions that use the older version structures. ###
def one_loop(self, P, P_window=None, C_window=None):
Expand Down
67 changes: 67 additions & 0 deletions fastpt/matter_power_spt.py
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Original file line number Diff line number Diff line change
Expand Up @@ -154,3 +154,70 @@ def one_loop(k,P,P_window=None,C_window=None,n_pad=None):
return P1,P22_reg,P13_reg


def J2_integral(k, P):
# calculates the J_2 integral in the EFT of IA
# via a discrete convolution integral

N = k.size
n = np.arange(-N+1, N)
dL = log(k[1])-log(k[0])
s = n*dL

cut = 4
high_s = s[s > cut]
low_s = s[s < -cut]
mid_high_s = s[(s <= cut) & (s > 0)]
mid_low_s = s[(s >= -cut) & (s < 0)]

Z = lambda r: (15/r-55*r-55*r**3+15*r**5 +
(60-15/r**2-90*r**2+60*r**4-15*r**6)*log((r+1)/np.absolute(r-1))/2)
Z_low = lambda r: -128*r+384/7/r-128/21/r**3-128/231/r**5-128/1001/r**7
Z_high = lambda r: -128*r**3+384/7*r**5-128/21*r**7

f_mid_low = Z(exp(-mid_low_s))
f_mid_high = Z(exp(-mid_high_s))
f_high = Z_high(exp(-high_s))
f_low = Z_low(exp(-low_s))

f = np.hstack((f_low, f_mid_low, -80, f_mid_high, f_high))

g = fftconvolve(P, f) * dL
g_k = g[N-1:2*N-1]
P_bar = 1/42*k**3/(2*pi)**2*P*g_k

return P_bar


def J3_integral(k, P):
# calculates the J_3 integral in the EFT of IA
# via a discrete convolution integral

N = k.size
n = np.arange(-N+1, N)
dL = log(k[1])-log(k[0])
s = n*dL

cut = 4
high_s = s[s > cut]
low_s = s[s < -cut]
mid_high_s = s[(s <= cut) & (s > 0)]
mid_low_s = s[(s >= -cut) & (s < 0)]

Z = lambda r: (15/r-10*r+164*r**3-150*r**5+45*r**7+
(15-15/r**2+90*r**2-210*r**4+165*r**6-
45*r**8)*log((r+1)/np.absolute(r-1))/2)
Z_low = lambda r: 256/7*r+256/7/r-256/33/r**3-256/273/r**5-256/1001/r**7
Z_high = lambda r: 256*r**3-2304/7*r**5+3328/21*r**7

f_mid_low = Z(exp(-mid_low_s))
f_mid_high = Z(exp(-mid_high_s))
f_high = Z_high(exp(-high_s))
f_low = Z_low(exp(-low_s))

f = np.hstack((f_low, f_mid_low, 64, f_mid_high, f_high))

g = fftconvolve(P, f) * dL
g_k = g[N-1:2*N-1]
P_bar = 1/168*k**3/(2*pi)**2*P*g_k

return P_bar