def _fwd_bem_multi_solution(solids, gamma, nps):
"""Do multi surface solution
* Invert I - solids/(2*M_PI)
* Take deflation into account
* The matrix is destroyed after inversion
* This is the general multilayer case
"""
pi2 = 1.0 / (2 * np.pi)
n_tot = np.sum(nps)
assert solids.shape == (n_tot, n_tot)
nsurf = len(nps)
defl = 1.0 / n_tot
# Modify the matrix
offsets = np.cumsum(np.concatenate(([0], nps)))
for si_1 in range(nsurf):
for si_2 in range(nsurf):
mult = pi2 if gamma is None else pi2 * gamma[si_1, si_2]
slice_j = slice(offsets[si_1], offsets[si_1 + 1])
slice_k = slice(offsets[si_2], offsets[si_2 + 1])
solids[slice_j, slice_k] = defl - solids[slice_j, slice_k] * mult
solids += np.eye(n_tot)
return linalg.inv(solids, overwrite_a=True)
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