Compute SSS basis for given conditions. Parameters ---------- exp : dict Must contain the following keys: origin : ndarray, shape (3,) Origin of the multipolar moment space in meters int_order : int Order of the internal m
(exp, all_coils)
| 1657 | |
| 1658 | |
| 1659 | def _sss_basis(exp, all_coils): |
| 1660 | """Compute SSS basis for given conditions. |
| 1661 | |
| 1662 | Parameters |
| 1663 | ---------- |
| 1664 | exp : dict |
| 1665 | Must contain the following keys: |
| 1666 | |
| 1667 | origin : ndarray, shape (3,) |
| 1668 | Origin of the multipolar moment space in meters |
| 1669 | int_order : int |
| 1670 | Order of the internal multipolar moment space |
| 1671 | ext_order : int |
| 1672 | Order of the external multipolar moment space |
| 1673 | |
| 1674 | coils : list |
| 1675 | List of MEG coils. Each should contain coil information dict specifying |
| 1676 | position, normals, weights, number of integration points and channel |
| 1677 | type. All coil geometry must be in the same coordinate frame |
| 1678 | as ``origin`` (``head`` or ``meg``). |
| 1679 | |
| 1680 | Returns |
| 1681 | ------- |
| 1682 | bases : ndarray, shape (n_coils, n_mult_moments) |
| 1683 | Internal and external basis sets as a single ndarray. |
| 1684 | |
| 1685 | Notes |
| 1686 | ----- |
| 1687 | Does not incorporate magnetometer scaling factor or normalize spaces. |
| 1688 | |
| 1689 | Adapted from code provided by Jukka Nenonen. |
| 1690 | """ |
| 1691 | rmags, cosmags, bins, n_coils = all_coils[:4] |
| 1692 | int_order, ext_order = exp["int_order"], exp["ext_order"] |
| 1693 | n_in, n_out = _get_n_moments([int_order, ext_order]) |
| 1694 | rmags = rmags - exp["origin"] |
| 1695 | |
| 1696 | # do the heavy lifting |
| 1697 | max_order = max(int_order, ext_order) |
| 1698 | L = _tabular_legendre(rmags, max_order) |
| 1699 | phi = np.arctan2(rmags[:, 1], rmags[:, 0]) |
| 1700 | r_n = np.sqrt(np.sum(rmags * rmags, axis=1)) |
| 1701 | r_xy = np.sqrt(rmags[:, 0] * rmags[:, 0] + rmags[:, 1] * rmags[:, 1]) |
| 1702 | cos_pol = rmags[:, 2] / r_n # cos(theta); theta 0...pi |
| 1703 | sin_pol = np.sqrt(1.0 - cos_pol * cos_pol) # sin(theta) |
| 1704 | z_only = r_xy <= 1e-16 |
| 1705 | sin_pol_nz = sin_pol.copy() |
| 1706 | sin_pol_nz[z_only] = 1.0 # will be overwritten later |
| 1707 | r_xy[z_only] = 1.0 |
| 1708 | cos_az = rmags[:, 0] / r_xy # cos(phi) |
| 1709 | cos_az[z_only] = 1.0 |
| 1710 | sin_az = rmags[:, 1] / r_xy # sin(phi) |
| 1711 | sin_az[z_only] = 0.0 |
| 1712 | # Appropriate vector spherical harmonics terms |
| 1713 | # JNE 2012-02-08: modified alm -> 2*alm, blm -> -2*blm |
| 1714 | r_nn2 = r_n.copy() |
| 1715 | r_nn1 = 1.0 / (r_n * r_n) |
| 1716 | S_tot = np.empty((n_coils, n_in + n_out), np.float64) |
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