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commit 62e89f5d7f5dc8c51bda9378c7c62b68f839b173 Author: Emily Ruzich <[email protected]> Date: Tue Apr 5 14:45:41 2011 -0400 fixing manual --- doc/source/manual/browse.rst | 38 +++++++++++++++++++------------------- doc/source/manual/cookbook.rst | 13 +++++++------ 2 files changed, 26 insertions(+), 25 deletions(-) diff --git a/doc/source/manual/browse.rst b/doc/source/manual/browse.rst index 4c94d4e..7a1a4e2 100755 --- a/doc/source/manual/browse.rst +++ b/doc/source/manual/browse.rst @@ -2371,13 +2371,13 @@ Without loss of generality we can always decompose any INLINE_EQUATION-channel measurement INLINE_EQUATION into its signal and noise components as -.. math:: 1 + 1 = 2 +.. math:: b(t) = b_s(t) + b_n(t) Further, if we know that INLINE_EQUATION is well characterized by a few field patterns INLINE_EQUATION, we can express the disturbance as -.. math:: 1 + 1 = 2 +.. math:: b_n(t) = Uc_n(t) + e(t)\ , where the columns of INLINE_EQUATION constitute an orthonormal basis for INLINE_EQUATION, INLINE_EQUATION is @@ -2390,11 +2390,11 @@ a small basis set INLINE_EQUATION such that the conditions described above are satisfied. We can now construct the orthogonal complement operator -.. math:: 1 + 1 = 2 +.. math:: P_{\perp} = I - UU^T and apply it to INLINE_EQUATION yielding -.. math:: 1 + 1 = 2 +.. math:: b(t) = P_{\perp}b_s(t)\ , since INLINE_EQUATION. The projection operator INLINE_EQUATION is called the signal-space projection operator and generally provides @@ -2458,16 +2458,16 @@ software employs the average-electrode reference, which means that the average over all electrode signals INLINE_EQUATION is subtracted from each INLINE_EQUATION: -.. math:: 1 + 1 = 2 +.. math:: v_{j}' = v_j - \frac{1}{p} \sum_{k} v_k\ . It is easy to see that the above equation actually corresponds to the projection: -.. math:: 1 + 1 = 2 +.. math:: v' = (I - uu^T)v\ , where -.. math:: 1 + 1 = 2 +.. math:: u = \frac{1}{\sqrt{p}}[1\ ...\ 1]^T\ . .. _CACHAAEG: @@ -2486,11 +2486,11 @@ accepted INLINE_EQUATION samples from all channels to the vectors INLINE_EQUATION. The estimate of the covariance matrix is then computed as: -.. math:: 1 + 1 = 2 +.. math:: \hat{C} = \frac{1}{M - 1} \sum_{j = 1}^M {(s_j - \bar{s})(s_j - \bar{s})}^T where -.. math:: 1 + 1 = 2 +.. math:: \bar{s} = \frac{1}{M} \sum_{j = 1}^M s_j is the average of the signals over all times. Note that no attempt is made to correct for low frequency drifts in the data. @@ -2501,7 +2501,7 @@ applied. For actual computations, it is convenient to rewrite the expression for the covariance matrix as -.. math:: 1 + 1 = 2 +.. math:: \hat{C} = \frac{1}{M - 1} \sum_{j = 1}^M {s_j s_j^T} - \frac{M}{M - 1} \bar{s} \bar{s}^T .. _BABHJDEJ: @@ -2515,7 +2515,7 @@ epoch. Let the vectors -.. math:: 1 + 1 = 2 +.. math:: s_{rpj}\ ,\ p = 1\ ...\ P_r\ ,\ j = 1\ ...\ N_r\ ,\ r = 1\ ...\ R be the samples from all channels in the baseline corrected epochs used to calculate the covariance matrix. In the above, INLINE_EQUATION is @@ -2529,31 +2529,31 @@ correction is applied to the epochs but the means at individual samples are not subtracted. Thus the covariance matrix will be computed as: -.. math:: 1 + 1 = 2 +.. math:: \hat{C} = \frac{1}{N_C} \sum_{r,p,j} {s_{rpj} s_{rpj}^T}\ , where -.. math:: 1 + 1 = 2 +.. math:: N_C = \sum_{r = 1}^R N_r P_r\ . If keepsamplemean is *not* specified, we estimate the covariance matrix as -.. math:: 1 + 1 = 2 +.. math:: \hat{C} = \frac{1}{N_C} \sum_{r = 1}^R \sum_{j = 1}^{N_r} \sum_{p = 1}^{P_r} {(s_{rpj} - \bar{s_{rj}}) ((s_{rpj} - \bar{s_{rj}})^T}\ , where -.. math:: 1 + 1 = 2 +.. math:: \bar{s_{rj}} = \frac{1}{P_r} \sum_{p = 1}^{P_r} s_{rpj} and -.. math:: 1 + 1 = 2 +.. math:: N_C = \sum_{r = 1}^R {N_r (P_r - 1)}\ , which reflects the fact that INLINE_EQUATION means are computed for category INLINE_EQUATION. It is easy to see that the expression for the covariance matrix estimate can be cast into a more convenient form -.. math:: 1 + 1 = 2 +.. math:: \hat{C} = \frac{1}{N_C} \sum_{r,p,j} {s_{rpj} s_{rpj}^T} - \frac{1}{N_C} \sum_r P_r \sum_j {\bar{s_{rj}} \bar{s_rj}^T}/ . Subtraction of the means at individual samples is useful if it can be expected that the evoked response from previous stimulus @@ -2567,11 +2567,11 @@ estimates INLINE_EQUATION with corresponding degrees of freedom INLINE_EQUATION. We can combine these matrices together as -.. math:: 1 + 1 = 2 +.. math:: C = \sum_q {\alpha_q \hat{C}_q}\ , where -.. math:: 1 + 1 = 2 +.. math:: \alpha_q = \frac{N_q}{\sum_q {N_q}}\ . SSP information included with covariance matrices ================================================= diff --git a/doc/source/manual/cookbook.rst b/doc/source/manual/cookbook.rst index 14282a9..2fdad48 100755 --- a/doc/source/manual/cookbook.rst +++ b/doc/source/manual/cookbook.rst @@ -815,14 +815,15 @@ anatomy only, not on the MEG/EEG data to be analyzed. .. note:: The MEG head to MRI transformation matrix specified with the ``--trans`` option should be a text file containing a 4-by-4 matrix: -.. math:: T = \[ +.. math:: \[ + T= \begin{matrix} - R_11 & R_12 & R_13 x_0 \\ - R_13 & R_13 & R_13 y_0 \\ - R_13 & R_13 & R_13 z_0 \\ - 0 & 0 & 0 & 1 \\ + R_{11} & R_{12} & R_{13} x_{0} \\ + R_{13} & R_{13} & R_{13} y_{0} \\ + R_{13} & R_{13} & R_{13} z_{0} \\ + 0 & 0 & 0 & 1 \end{matrix} - \] + \] defined so that if the augmented location vectors in MRI head and MRI coordinate systems are denoted by :math:`r_{head}[x_{head}\ y_{head}\ z_{head}\ 1]` and :math:`r_{MRI}[x_{MRI}\ y_{MRI}\ z_{MRI}\ 1]`, -- 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
