[med-svn] [python-mne] 254/376: fixing manual
Yaroslav Halchenko
debian at onerussian.com
Fri Nov 27 17:23:02 UTC 2015
This is an automated email from the git hooks/post-receive script.
yoh pushed a commit to annotated tag v0.1
in repository python-mne.
commit f66609fa44f852231a4548e980aab93073d80865
Author: Emily Ruzich <emilyr at nmr.mgh.harvard.edu>
Date: Tue May 17 10:23:12 2011 -0400
fixing manual
---
doc/source/manual/convert.rst | 92 +++++++++++++++++++++----------------------
doc/source/manual/morph.rst | 62 ++++++++++++++---------------
2 files changed, 77 insertions(+), 77 deletions(-)
diff --git a/doc/source/manual/convert.rst b/doc/source/manual/convert.rst
index 33d8189..a3462d6 100755
--- a/doc/source/manual/convert.rst
+++ b/doc/source/manual/convert.rst
@@ -182,7 +182,7 @@ points in centimeters. The first line should contain a single number
which is the number of points listed in the file. Each of the following
lines contains a sequential number of the point, followed by the
three coordinates. mne_ctf_dig2fiff ignores
-any text following the INLINE_EQUATION coordinate
+any text following the :math:`z` coordinate
on each line. If the ``--numfids`` option is specified,
the first three points indicate the three fiducial locations (1
= nasion, 2 = left auricular point, 3 = right auricular point).
@@ -241,18 +241,18 @@ fields originating in the brain. Most often, a compensation matrix
corresponding to a scheme nicknamed *Third-order gradient
compensation* is employed.
-Let us assume that the data contain INLINE_EQUATION MEG
-sensor channels, INLINE_EQUATION reference sensor
-channels, and INLINE_EQUATION other channels.
+Let us assume that the data contain :math:`n_1` MEG
+sensor channels, :math:`n_2` reference sensor
+channels, and :math:`n_3` other channels.
The data from all channels can be concatenated into a single vector
.. math:: x = [x_1^T x_2^T x_3^T]^T\ ,
-where INLINE_EQUATION, INLINE_EQUATION,
-and INLINE_EQUATION are the data vectors corresponding
+where :math:`x_1`, :math:`x_2`,
+and :math:`x_3` are the data vectors corresponding
to the MEG sensor channels, reference sensor channels, and other
channels, respectively. The data before and after compensation,
-denoted here by INLINE_EQUATION and INLINE_EQUATION, respectively,
+denoted here by :math:`x_{(0)}` and :math:`x_{(k)}`, respectively,
are related by
.. math:: x_{(k)} = M_{(k)} x_{(0)}\ ,
@@ -265,8 +265,8 @@ where the composite compensation matrix is
0 & 0 & I_{n_3}
\end{bmatrix}\ .
-In the above, INLINE_EQUATION is a INLINE_EQUATION compensation
-data matrix corresponding to compensation "grade" INLINE_EQUATION.
+In the above, :math:`C_{(k)}` is a :math:`n_1` by :math:`n_2` compensation
+data matrix corresponding to compensation "grade" :math:`k`.
It is easy to see that
.. math:: M_{(k)}^{-1} = \begin{bmatrix}
@@ -275,7 +275,7 @@ It is easy to see that
0 & 0 & I_{n_3}
\end{bmatrix}\ .
-To convert from compensation grade INLINE_EQUATION to INLINE_EQUATION one
+To convert from compensation grade :math:`k` to :math:`p` one
can simply multiply the inverse of one compensate compensation matrix
by another and apply the product to the data:
@@ -411,17 +411,17 @@ The command line options of mne_create_comp_data are:
**\---out <*name*>**
Specifies the output fif file containing the compensation channel weight
- matrix INLINE_EQUATION, see :ref:`BEHDDFBI`.
+ matrix :math:`C_{(k)}`, see :ref:`BEHDDFBI`.
The format of the text-format compensation data file is:
<*number of MEG helmet channels*> <*number of compensation channels included*>
- <*INLINE_EQUATION*> <*INLINE_EQUATION*>INLINE_EQUATION
- <*INLINE_EQUATION*> <*weights*>
- <*INLINE_EQUATION*> <*weights*> INLINE_EQUATION
+ <*cname_1*> <*cname_2*> ...
+ <*name_1*> <*weights*>
+ <*name_2*> <*weights*> ...
-In the above <*INLINE_EQUATION*> denote
-names of MEG helmet channels and <*INLINE_EQUATION*>
+In the above <*name_k*> denote
+names of MEG helmet channels and <*cname_k*>
those of the compensation channels, respectively. If the channel
names contain spaces, they must be surrounded by quotes, for example, ``"MEG 0111"`` .
@@ -478,20 +478,20 @@ of these channels can be afterwards changed with the mne_rename_channels utility
see :ref:`CHDCFEAJ`. In addition, it is possible to synthesize
the digital trigger channel (STI 014) from available analog
trigger channel data, see the ``--stim`` option, below.
-The synthesized trigger channel data value at sample INLINE_EQUATION will
+The synthesized trigger channel data value at sample :math:`k` will
be:
.. math:: s(k) = \sum_{p = 1}^n {t_p(k) 2^{p - 1}}\ ,
-where INLINE_EQUATION are the thresholded
-from the input channel data INLINE_EQUATION:
+where :math:`t_p(k)` are the thresholded
+from the input channel data d_p(k):
.. math:: t_p(k) = \Bigg\{ \begin{array}{l}
0 \text{ if } d_p(k) \leq t\\
1 \text{ if } d_p(k) > t
\end{array}\ .
-The threshold value INLINE_EQUATION can
+The threshold value :math:`t` can
be adjusted with the ``--stimthresh`` option, see below.
mne_kit2fiff accepts
@@ -1340,7 +1340,7 @@ a 4 x 4 coordinate transformation matrix:
\end{bmatrix}
defined so that if the augmented location vectors in the
-dfs file and MRI coordinate systems are denoted by INLINE_EQUATION and INLINE_EQUATION,
+dfs file and MRI coordinate systems are denoted by :math:`r_{dfs} = [x_{dfs} y_{dfs} z_{dfs} 1]^T` and :math:`r_{MRI} = [x_{MRI} y_{MRI} z_{MRI} 1]^T`,
respectively,
.. math:: r_{MRI} = Tr_{dfs}
@@ -1378,10 +1378,10 @@ data as input. The command-line options are:
An MRI volume volume file in mgh or mgz format.
The ``--withdata`` option is implied with this type of
- input. Furthermore, the INLINE_EQUATION transformation,
- the Talairach transformation INLINE_EQUATION from
+ input. Furthermore, the :math:`T_3` transformation,
+ the Talairach transformation :math:`T_4` from
the talairach.xfm file referred to in the MRI volume, and the the
- fixed transforms INLINE_EQUATION and INLINE_EQUATION will
+ fixed transforms :math:`T_-` and :math:`T_+` will
added to the output file. For definition of the coordinate transformations,
see :ref:`CHDEDFIB`.
@@ -1406,7 +1406,7 @@ them into a single fif file. The coordinate transformations used
by MNE software are summarized in Figure 5.1. The output
of mne_collect_transforms may
include all transforms referred to therein except for the sensor
-coordinate system transformations INLINE_EQUATION.
+coordinate system transformations :math:`T_{s_1} \dotso T_{s_n}`.
The command-line options are:
**\---version**
@@ -1419,7 +1419,7 @@ The command-line options are:
**\---meas <*name*>**
- Specifies a measurement data file which provides INLINE_EQUATION.
+ Specifies a measurement data file which provides :math:`T_1`.
A forward solution or an inverse operator file can also be specified
as implied by Table 5.1.
@@ -1427,18 +1427,18 @@ The command-line options are:
Specifies an MRI description or a standalone coordinate transformation
file produced by mne_analyze which
- provides INLINE_EQUATION. If the ``--mgh`` option
+ provides :math:`T_2`. If the ``--mgh`` option
is not present mne_collect_transforms also
- tries to find INLINE_EQUATION, INLINE_EQUATION, INLINE_EQUATION,
- and INLINE_EQUATION from this file.
+ tries to find :math:`T_3`, :math:`T_4`, :math:`T_-`,
+ and :math:`T_+` from this file.
**\---mgh <*name*>**
An MRI volume volume file in mgh or mgz format.
- This file provides INLINE_EQUATION. The transformation INLINE_EQUATION will
+ This file provides :math:`T_3`. The transformation :math:`T_4` will
be read from the talairach.xfm file referred to in the MRI volume.
- The fixed transforms INLINE_EQUATION and INLINE_EQUATIONwill
- be also created.
+ The fixed transforms :math:`T_-` and :math:`T_+` will
+ also be created.
**\---out <*name*>**
@@ -1789,11 +1789,11 @@ The prefix given with the ``--tag`` option is indicated <*tag*> , see :ref:`BEHC
meg_head_trans 4 x 4 The coordinate frame transformation from the MEG device coordinates to the MEG head coordinates
noise_cov nchan x nchan The noise covariance matrix
source_cov nsource The elements of the diagonal source covariance matrix.
- sing nchan The singular values of INLINE_EQUATION with INLINE_EQUATION selected so that INLINE_EQUATION as discussed in :ref:`CHDDHAGE`
- eigen_fields nchan x nchan The rows of this matrix are the left singular vectors of INLINE_EQUATION, i.e., the columns of INLINE_EQUATION, see above.
- eigen_leads nchan x nsource The rows of this matrix are the right singular vectors of INLINE_EQUATION, i.e., the columns of INLINE_EQUATION, see above.
- noise_eigenval nchan In terms of :ref:`CHDDHAGE`, eigenvalues of INLINE_EQUATION, i.e., not scaled with number of averages.
- noise_eigenvec nchan Eigenvectors of the noise covariance matrix. In terms of :ref:`CHDDHAGE`, INLINE_EQUATION.
+ sing nchan The singular values of :math:`A = C_0^{-^1/_2} G R^C = U \Lambda V^T` with :math:`R` selected so that trace :math:`(AA^T)`/trace :math:`(I = 1)` as discussed in :ref:`CHDDHAGE`
+ eigen_fields nchan x nchan The rows of this matrix are the left singular vectors of :math:`A`, i.e., the columns of :math:`U`, see above.
+ eigen_leads nchan x nsource The rows of this matrix are the right singular vectors of :math:`A`, i.e., the columns of :math:`V`, see above.
+ noise_eigenval nchan In terms of :ref:`CHDDHAGE`, eigenvalues of :math:`C_0`, i.e., not scaled with number of averages.
+ noise_eigenvec nchan Eigenvectors of the noise covariance matrix. In terms of :ref:`CHDDHAGE`, :math:`U_C^T`.
data nchan x ntime The measured data. One row contains the data at one time point.
times ntime The time points in the above matrix in seconds
nave 1 Number of averages as listed in the data file.
@@ -2017,12 +2017,12 @@ the following command-line options are:
**\---filtersize <*size*>**
Adjust the length of the FFT to be applied in filtering. The number will
- be rounded up to the next power of two. If the size is INLINE_EQUATION,
- the corresponding length of time is INLINE_EQUATION,
- where INLINE_EQUATION is the sampling frequency
+ be rounded up to the next power of two. If the size is :math:`N`,
+ the corresponding length of time is :math:`^N/_{f_s}`,
+ where :math:`f_s` is the sampling frequency
of your data. The filtering procedure includes overlapping tapers
- of length INLINE_EQUATION so that the total FFT
- length will actually be INLINE_EQUATION. The default
+ of length :math:`^N/_2` so that the total FFT
+ length will actually be :math:`2N`. The default
value is 4096.
**\---highpass <*value/Hz*>**
@@ -2037,7 +2037,7 @@ the following command-line options are:
**\---highpassw <*value/Hz*>**
The width of the transition band of the highpass filter. The default
- is 6 frequency bins, where one bin is INLINE_EQUATION.
+ is 6 frequency bins, where one bin is :math:`^{f_s}/_{(2N)}`.
**\---lowpass <*value/Hz*>**
@@ -2074,9 +2074,9 @@ The binary epoch data file
mne_epochs2mat saves the
epoch data extracted from the raw data file is a simple binary file.
The data are stored as big-endian single-precision floating point
-numbers. Assuming that each of the total of INLINE_EQUATION epochs
-contains INLINE_EQUATION channels and INLINE_EQUATION time
-points, the data INLINE_EQUATION ar e ordered
+numbers. Assuming that each of the total of :math:`p` epochs
+contains :math:`n` channels and :math:`m` time
+points, the data :math:`s_{jkl}` are ordered
as
.. math:: s_{111} \dotso s_{1n1} s_{211} \dotso s_{mn1} \dotso s_{mnp}\ ,
diff --git a/doc/source/manual/morph.rst b/doc/source/manual/morph.rst
index 8a9c29f..25b3c6c 100755
--- a/doc/source/manual/morph.rst
+++ b/doc/source/manual/morph.rst
@@ -29,21 +29,21 @@ maps which can be either computed on demand or precomputed using mne_make_morph_
see :ref:`CHDBBHDH`. The morphing is performed with help
of the registered spherical surfaces (``lh.sphere.reg`` and ``rh.sphere.reg`` )
which must be produced in FreeSurfer .
-A morphing map is a linear mapping froprem cortical surface values
-in subject A (INLINE_EQUATION) to those in another
-subject B (INLINE_EQUATION)
+A morphing map is a linear mapping from cortical surface values
+in subject A (:math:`x^{(A)}`) to those in another
+subject B (:math:`x^{(B)}`)
.. math:: x^{(B)} = M^{(AB)} x^{(A)}\ ,
-where INLINE_EQUATION is a sparse matrix
+where :math:`M^{(AB)}` is a sparse matrix
with at most three nonzero elements on each row. These elements
are determined as follows. First, using the aligned spherical surfaces,
-for each vertex INLINE_EQUATION, find the triangle INLINE_EQUATIONon the
-spherical surface of subject A which contains the location INLINE_EQUATION.
+for each vertex :math:`x_j^{(B)}`, find the triangle :math:`T_j^{(A)}` on the
+spherical surface of subject A which contains the location :math:`x_j^{(B)}`.
Next, find the numbers of the vertices of this triangle and set
-the corresponding elements on the *j*th row of INLINE_EQUATION so that INLINE_EQUATION will
+the corresponding elements on the *j* th row of :math:`M^{(AB)}` so that :math:`x_j^{(B)}` will
be a linear interpolation between the triangle vertex values reflecting
-the location INLINE_EQUATION within the triangle INLINE_EQUATION.
+the location :math:`x_j^{(B)}` within the triangle :math:`T_j^{(A)}`.
It follows from the above definition that in general
@@ -75,31 +75,31 @@ might be smudging or blurring in
accordance with similar operations in image processing programs.
In MNE software terms, smoothing of the vertex data is an
-iterative procedure, which produces a blurred image INLINE_EQUATIONfrom
-the original sparse image INLINE_EQUATION by applying
+iterative procedure, which produces a blurred image :math:`x^{(N)}` from
+the original sparse image :math:`x^{(0)}` by applying
in each iteration step a sparse blurring matrix:
.. math:: x^{(p)} = S^{(p)} x^{(p - 1)}\ .
-On each row INLINE_EQUATIONof the matrix INLINE_EQUATIONthere
-are INLINE_EQUATION nonzero entries whose values
-equal INLINE_EQUATION. Here INLINE_EQUATION is
-the number of immediate neighbors of vertex INLINE_EQUATION which
-had non-zero values at iteration step INLINE_EQUATION.
-Matrix INLINE_EQUATION thus assigns the average
-of the non-zero neighbors as the new value for vertex INLINE_EQUATION.
+On each row :math:`j` of the matrix :math:`S^{(p)}` there
+are :math:`N_j^{(p - 1)}` nonzero entries whose values
+equal :math:`1/N_j^{(p - 1)}`. Here :math:`N_j^{(p - 1)}` is
+the number of immediate neighbors of vertex :math:`j` which
+had non-zero values at iteration step :math:`p - 1`.
+Matrix :math:`S^{(p)}` thus assigns the average
+of the non-zero neighbors as the new value for vertex :math:`j`.
One important feature of this procedure is that it tends to preserve
the amplitudes while blurring the surface image.
-Once the indices non-zero vertices in INLINE_EQUATION and
-the topology of the triangulation are fixed the matrices INLINE_EQUATION are
+Once the indices non-zero vertices in :math:`x^{(0)}` and
+the topology of the triangulation are fixed the matrices :math:`S^{(p)}` are
fixed and independent of the data. Therefore, it would be in principle
possible to construct a composite blurring matrix
.. math:: S^{(N)} = \prod_{p = 1}^N {S^{(p)}}\ .
However, it turns out to be computationally more effective
-to do blurring with an iteration. The above formula for INLINE_EQUATION also
+to do blurring with an iteration. The above formula for :math:`S^{(N)}` also
shows that the smudging (smoothing) operation is linear.
.. _CHDBBHDH:
@@ -127,7 +127,7 @@ of the form:
where <*A*> and <*B*> are
names of subjects. These files contain the maps for both hemispheres,
-and in both directions, *i.e.*, both INLINE_EQUATION and INLINE_EQUATION, as
+and in both directions, *i.e.*, both :math:`M^{(AB)}` and :math:`M^{(BA)}`, as
defined above. Thus the files <*A*> - <*B*> -``morph.fif`` or <*B*> - <*A*> -``morph.fif`` are
functionally equivalent. The name of the file produced by mne_analyze or mne_make_movie depends
on the role of <*A*> and <*B*> in
@@ -324,11 +324,11 @@ The global phrases are:
added to the first time point selected until this value or the last time
point in one of the input stc files is reached.
-**integ < INLINE_EQUATION/ms*>**
+**integ <:math:`\Delta t` /*ms*>**
Integration time for each frame. Defaults to zero. The integration will
- be performed on sensor data. If the time specified for a frame is INLINE_EQUATION,
- the integration range will be INLINE_EQUATION.
+ be performed on sensor data. If the time specified for a frame is :math:`t_0`,
+ the integration range will be :math:`t_0 - ^{\Delta t}/_2 \leq t \leq t_0 + ^{\Delta t}/_2`.
**stc <*filename*>**
@@ -380,9 +380,9 @@ The contextual phrases are:
Means pow 0.5
The effects of the options can be summarized as follows.
-Suppose that the description file includes INLINE_EQUATION contexts
-and the temporally resampled data are organized in matrices INLINE_EQUATION,
-where INLINE_EQUATION is the subject index, and
+Suppose that the description file includes :math:`P` contexts
+and the temporally resampled data are organized in matrices :math:`S^{(p)}`,
+where :math:`p = 1 \dotso P` is the subject index, and
the rows are the signals at different vertices of the cortical surface.
The average computed by mne_average_estimates is
then:
@@ -397,11 +397,11 @@ and
.. math:: \bar{w_p} = w_p / \sum_{p = 1}^p {|w_p|}\ .
-In the above, INLINE_EQUATION and INLINE_EQUATION are
-the powers and weights assigned to each of the subjects whereas INLINE_EQUATION and INLINE_EQUATION are
+In the above, :math:`\beta_p` and :math:`w_p` are
+the powers and weights assigned to each of the subjects whereas :math:`\beta` and :math:`w` are
the output weight and power value, respectively. The sign is either
-included (INLINE_EQUATION, INLINE_EQUATION)
-or omitted (INLINE_EQUATION, INLINE_EQUATION)
+included (:math:`\alpha_p = 1`, :math:`\alpha = 1`)
+or omitted (:math:`\alpha_p = 2`, :math:`\alpha = 2`)
depending on the presence of abs phrases in the description file.
.. note:: mne_average_estimates requires that the number of vertices in the stc files are the same and that the vertex numbers are identical. This will be the case if the files have been produced in mne_make_movie using the ``--morph`` option.
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