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xaesa_ft.py
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#import numpy as np
from numpy import sqrt, zeros, pi, arctan, asarray, arange, delete, sum, multiply, sin, cos
def FT(k, exafs, rmin, rmax, dr):
con = sqrt(2 / pi)
nn = len(k)
rx = zeros(int((rmax - rmin) / dr), float)
exafs_re = zeros(nn, float)
# exafs_im = zeros(nn, float)
# transform_re = zeros(nn, float)
# transform_im = zeros(nn, float)
# fourier_re = zeros(int((rmax - rmin) / dr), float)
# fourier_im = zeros(int((rmax - rmin) / dr), float)
# sn = zeros(nn, float)
# cs = zeros(nn, float)
exafs_re = asarray(exafs, float)
rx = arange(rmin, rmax, dr)
r = rx*2
# dx1 = delete(k,0)
# dx2 = delete(k, len(k)-1)
# dx = dx1 - dx2
dx = k[1:]-k[:-1]
v1 = multiply.outer(r, asarray(k,float))
# eix = exp(1j*v1)
# cos1, sin1 = eix.real, eix.imag
sin1 = sin(v1)
cos1 = cos(v1)
sin1 = sin1*(-1)
# transform_re1 = exafs_re * cos1 - exafs_im * sin1
# transform_im1 = exafs_re * sin1 + exafs_im * cos1
transform_re1 = exafs_re * cos1
transform_im1 = exafs_re * sin1
tre11 = delete(transform_re1, 0, 1)
tre22 = delete(transform_re1, len(transform_re1[0])-1, 1)
tim11 = delete(transform_im1, 0, 1)
tim22 = delete(transform_im1, len(transform_im1[0])-1, 1)
tre111 = (tre11+tre22)/2
tim111 = (tim11+tim22)/2
r11 = sum(dx*tre111, axis=1)
r22 = sum(dx*tim111, axis=1)
fourier_re = r11*con
fourier_im = r22*con
return rx, fourier_re, fourier_im
def BFT(r, fre, fim, kmin, kmax, dk):
print(kmin, kmax, dk)
con = sqrt(2 / pi)
n = int((kmax-kmin)/dk + 1.0)
dk = (kmax-kmin)/(n-1.0)
bftk = []
nn = len(r)
bftr = zeros(n, float)
bfti = zeros(n, float)
#transform_re = zeros(nn, float)
#transform_im = zeros(nn, float)
#sn = zeros(nn, float)
#cs = zeros(nn, float)
bftk = arange(kmin, kmax+dk, dk)
dx1 = delete(r,0)
dx2 = delete(r, len(r)-1)
dx = dx1 - dx2
r5 = bftk * 2
v1 = multiply.outer(r5, asarray(r,float))
sin1 = sin(v1)
cos1 = cos(v1)
transform_re1 = fre * cos1 - fim * sin1
transform_im1 = fre * sin1 + fim * cos1
tre11 = delete(transform_re1, 0, 1)
tre22 = delete(transform_re1, len(transform_re1[0])-1, 1)
tim11 = delete(transform_im1, 0, 1)
tim22 = delete(transform_im1, len(transform_im1[0])-1, 1)
tre111 = (tre11+tre22)/2
tim111 = (tim11+tim22)/2
r11 = sum(dx*tre111, axis=1)
r22 = sum(dx*tim111, axis=1)
bftr = r11*con
bfti = r22*con
return bftk, bftr, bfti
def BFTWindow(r, rmin, rmax, a):
xmin = rmin
xmax = rmax
a1 = a
#wind = np.zeros(len(r))
wind = [0] * len(r)
for i in range(0, len(r)):
if r[i] < rmin:
wind[i] = 0.0
if r[i] > rmax:
wind[i] = 0.0
if r[i] >= rmin and r[i] <= rmax:
if r[i]>=(xmin+a1) and r[i]<=(xmax-a1):
wind[i] = 1.0
if r[i] < (xmin+a1):
wind[i] = 0.5*(1-cos(pi*((r[i]-xmin)/a1)))
if r[i] > (xmax-a1):
wind[i] = 0.5*(1+cos(pi*((r[i]-xmax+a1)/a1)))
return wind
def GETPHASE(yr, yi):
n1 = 0
n2 = 0
i = 0
j = 0
p = 0
#{ Phase calculation }
if(yr[0] < 0.0):
n1=-1
if(yr[0] > 0.0):
n1=1
if( (yr[0] == 0.0) and (yr[1]<0.0) ):
n1=1
if( (yr[0] == 0.0) and (yr[1]>0.0) ):
n1=-1
n2 = n1
p = 0
i = 0
fi = []
for j in range(0, len(yr)):
fi.append(0)
for j in range(0, len(yr)):
if (yr[j] < 0.0):
n1=-1
if (yr[j] > 0.0):
n1=+1;
if (yr[j] == 0.0):
n1=-n1
if (n1 != n2):
p=p+1
n2 = n1
if (yr[j] > yr[i]):
i=j
if (yr[j] != 0.0):
fi[j] = arctan(yi[j]/yr[j])+pi/2 + p*pi
else:
fi[j] = p * pi
if (sin(fi[i]) <= 0.0):
for j in range(0, len(yr)):
fi[j]=fi[j] + pi;
return fi