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commit c55c58216e6d1259ab8ed1148f6e8453be16a62a Author: Emily Ruzich <[email protected]> Date: Mon May 16 11:57:46 2011 -0400 fixing manual --- doc/source/manual/analyze.rst | 34 +++++++++++++++++----------------- 1 file changed, 17 insertions(+), 17 deletions(-) diff --git a/doc/source/manual/analyze.rst b/doc/source/manual/analyze.rst index a274485..0ba6485 100755 --- a/doc/source/manual/analyze.rst +++ b/doc/source/manual/analyze.rst @@ -1400,14 +1400,14 @@ whenever they are enabled from the viewer options, see :ref:`CACHGDEA`. Technical description ===================== -Let INLINE_EQUATION be an MEG or an EEG -signal at channel INLINE_EQUATION. This signal -is related to the primary current distribution INLINE_EQUATIONthrough -the lead field INLINE_EQUATION: +Let :math:`x_k` be an MEG or an EEG +signal at channel :math:`k = 1 \dotso N`. This signal +is related to the primary current distribution :math:`J^p(r)` through +the lead field :math:`L_k(r)`: .. math:: x_k = \int_G {L_k(r) \cdot J^p(r)}\,dG\ , -where the integration space INLINE_EQUATION in +where the integration space :math:`G` in our case is a spherical surface. The oblique boldface characters denote three-component locations vectors and vector fields. @@ -1415,14 +1415,14 @@ The inner product of two leadfields is defined as: .. math:: \langle L_j \mid L_k \rangle = \int_G {L_j(r) \cdot L_k(r)}\,dG\ , -These products constitute the Gram matrix INLINE_EQUATION. +These products constitute the Gram matrix :math:`\Gamma_{jk} = \langle L_j \mid L_k \rangle`. The minimum -norm estimate can be expressed as a weighted sum of the lead fields: .. math:: J^* = w^T L\ , -where INLINE_EQUATION is a weight vector -and INLINE_EQUATION is a vector composed of the +where :math:`w` is a weight vector +and :math:`L` is a vector composed of the continuous lead-field functions. The weights are determined by the requirement @@ -1446,35 +1446,35 @@ where .. math:: x^{(p)} = (U^{(p)})^T x \text{ and } \Gamma^{(p)} = (U^{(p)})^T \Gamma\ , -respectively. In the above, the columns of INLINE_EQUATION are -the first *k* left singular vectors of INLINE_EQUATION. +respectively. In the above, the columns of :math:`U^{(p)}` are +the first *k* left singular vectors of :math:`\Gamma`. The weights of the regularized estimate are .. math:: w^{(p)} = V \Lambda^{(p)} U^T x\ , -where INLINE_EQUATION is diagonal with +where :math:`\Lambda^{(p)}` is diagonal with .. math:: \Lambda_{jj}^{(p)} = \Bigg\{ \begin{array}{l} 1/{\lambda_j},j \leq p\\ \text{otherwise} \end{array} -INLINE_EQUATION being the INLINE_EQUATION singular -value of INLINE_EQUATION. The truncation point INLINE_EQUATION is +:math:`\lambda_j` being the :math:`j` th singular +value of :math:`\Gamma`. The truncation point :math:`p` is selected in mne_analyze by specifying -a tolerance INLINE_EQUATION, which is used to -determine INLINE_EQUATION such that +a tolerance :math:`\varepsilon`, which is used to +determine :math:`p` such that .. math:: 1 - \frac{\sum_{j = 1}^p {\lambda_j}}{\sum_{j = 1}^N {\lambda_j}} < \varepsilon The extrapolated and interpolated magnetic field or potential -distribution estimates INLINE_EQUATION in a virtual +distribution estimates :math:`\hat{x'}` in a virtual grid of sensors can be now easily computed from the regularized minimum-norm estimate. With .. math:: \Gamma_{jk}' = \langle L_j' \mid L_k \rangle\ , -where INLINE_EQUATION are the lead fields +where :math:`L_j'` are the lead fields of the virtual sensors, .. math:: \hat{x'} = \Gamma' w^{(k)}\ . -- Alioth's /usr/local/bin/git-commit-notice on /srv/git.debian.org/git/debian-med/python-mne.git _______________________________________________ debian-med-commit mailing list [email protected] http://lists.alioth.debian.org/cgi-bin/mailman/listinfo/debian-med-commit
