def nufft_r(om, N, J, K, alpha, beta):
'''
equation (30) of Fessler's paper
'''
M = numpy.size(om) # 1D size
gam = 2.0 * numpy.pi / (K * 1.0)
nufft_offset0 = nufft_offset(om, J, K) # om/gam - nufft_offset , [M,1]
dk = 1.0 * om / gam - nufft_offset0 # om/gam - nufft_offset , [M,1]
arg = outer_sum(-numpy.arange(1, J + 1) * 1.0, dk)
L = numpy.size(alpha) - 1
# print('alpha',alpha)
rr = numpy.zeros((J, M), dtype=numpy.float32)
rr = iterate_l1(L, alpha, arg, beta, K, N, rr)
return (rr, arg)
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