# xmat_tool.py¶

```
=============================================================================
xmat_tool.py - a tool for evaluating an AFNI X-matrix
This program gives the user the ability to evaluate a regression matrix
(often referred to as an X-matrix). With an AFNI X-matrix specified via
-load_xmat, optionally along with an MRI time series specified via
-load_1D, this program can display the:
o matrix condition numbers
o correlation matrix
o warnings regarding the correlation matrix
o cosine matrix (normalized XtX)
o warnings regarding the cosine matrix
o beta weights for fit against 1D time series
o fit time series
--------------------------------------------------------------------------
examples:
Note that -no_gui is applied in each example, so that the program
performs any requested actions and terminates, without opening a GUI
(graphical user interface).
0. Basic commands:
xmat_tool.py -help
xmat_tool.py -help_gui
xmat_tool.py -hist
xmat_tool.py -show_valid_opts
xmat_tool.py -test
xmat_tool.py -test_libs
xmat_tool.py -ver
1. Load an X-matrix and display the condition numbers.
xmat_tool.py -no_gui -load_xmat X.xmat.1D -show_conds
2. Load an X-matrix and display correlation and cosine warnings.
xmat_tool.py -no_gui -load_xmat X.xmat.1D \
-show_cormat_warnings -show_cosmat_warnings
3. Load an X-matrix and a 1D time series. Display beta weights for
the best fit to all regressors (specifed as columns 0 to the last).
xmat_tool.py -no_gui -load_xmat X.xmat.1D -load_1D norm.ts.1D \
-choose_cols '0..$' -show_fit_betas
4. Similar to 3, but show the actual fit time series. Also, redirect
the output to save the results in a 1D file.
xmat_tool.py -no_gui -load_xmat X.xmat.1D -load_1D norm.ts.1D \
-choose_cols '0..$' -show_fit_ts > fitts.1D
5. Show many things. Load an X-matrix and time series, and display
conditions and warnings (but setting own cutoff values), as well as
fit betas.
xmat_tool.py -no_gui -load_xmat X.xmat.1D -load_1D norm.ts.1D \
-choose_cols '0..$' \
-show_conds \
-cormat_cutoff 0.3 -cosmat_cutoff 0.25 \
-show_cormat_warnings -show_cosmat_warnings \
-show_fit_betas
6. Script many operations. Load a sequence of X-matrices, and display
condition numbers and warnings for each.
Note that with -chrono, options are applied chronologically.
xmat_tool.py -no_gui -chrono \
-load_xmat X.1.xmat.1D \
-show_conds -show_cormat_warnings -show_cosmat_warnings \
-load_xmat X.2.xmat.1D \
-show_conds -show_cormat_warnings -show_cosmat_warnings \
-load_xmat X.3.xmat.1D \
-show_conds -show_cormat_warnings -show_cosmat_warnings \
-load_1D norm.ts.1D \
-show_fit_betas \
-choose_cols '0..$' \
-show_fit_betas \
-choose_cols '0..26,36..$' \
-show_fit_betas \
-load_xmat X.2.xmat.1D \
-choose_cols '0..$' \
-show_fit_betas
--------------------------------------------------------------------------
basic informational options:
-help : show this help
-help_gui : show the GUI help
-hist : show the module history
-show_valid_opts : show all valid options
-test : run a basic test
(requires X.xmat.1D and norm.022_043_012.1D)
-test_libs : test for required python libraries
-ver : show the version number
------------------------------------------
general options:
-choose_cols 'COLUMN LIST' : select columns to fit against
e.g. -choose_cols '0..$'
e.g. -choose_cols '1..19(3),26,29,40..$'
These columns will be used as the basis for the top condition
number, as well as the regressor columns for fit computations.
The column selection string should not contain spaces, and should
be in the format of AFNI sub-brick selection. Consider these
examples
2..13 : 2,3,4,5,6,7,8,9,10,11,12,13
2..13(3) : 2,5,8,11
3,7,11 : 3,7,11
20..$(4) : 20,24,28,32 (assuming 33 columns, say)
-chrono : apply options chronologically
By default, the general options are applied before the show
options, with the show options being in order.
When the -chrono option is applied, all options are chronological,
allowing the options to be applied as in a script.
For example, a matrix could be loaded, and then a series of fit
betas could be displayed by alternating a sequence of -choose_cols
and -show_fit_betas options.
Consider example 6.
-cormat_cutoff CUTOFF : set min cutoff for cormat warnings
e.g. -cormat_cutoff 0.5
By default, any value in the correlation matrix that is greater
than or equal to 0.4 generates a warning. This option can be used
to override that minumum cutoff.
-cosmat_cutoff CUTOFF : set min cutoff for cosmat warnings
e.g. -cosmat_cutoff 0.5
By default, any value in the cosine matrix that is greater than or
equal to 0.3827 generates a warning. This option can be used to
override that minumum cutoff.
Note a few cosine values, relative to 90 degrees (PI/2):
cos(.50 *PI/2) = .707
cos(.75 *PI/2) = .3827
cos(.875*PI/2) = .195
-cosmat_motion : include motion in cosmat warnings
In the cosine matrix, motion regressors are often pointing in a
direction close to that of either baseline or other motion
regressors. By default, such warnings are not displayed.
Use this option to include all such warnings.
-load_xmat XMAT.xmat.1D : load the AFNI X-matrix
e.g. -load_xmat X.xmat.1D
Load the X-matrix, as the basis for most computations.
-load_1D DATA.1D : load the 1D time series
e.g. -load_1D norm_ts.1D
Load the 1D time series, for which fit betas and a fit time series
can be generated.
-no_gui : do not start the GUI
By default, this program runs a graphical interface. If the user
wishes to perform some actions and terminate without starting the
GUI, this option can be applied.
-verb LEVEL : set the verbose level
Specify how much extra text should be displayed regarding the
internal operations. Valid levels are currently 0..5, with 0
meaning 'quiet', 1 being the default, and 5 being the most verbose.
------------------------------------------
show options:
-show_col_types : display columns by regressor types
Show which columns are considered 'main', 'chosen', 'baseline'
and 'motion'. This would correspond to condition numbers.
-show_conds : display a list of condition numbers
The condition number is the ratio of the largest eigen value to
the smallest. It provides an indication of how sensitive results
of linear regression are to small changes in the data. Condition
numbers will tend to be larger with regressors that are more highly
correlated.
This option requests to display condition numbers for the X-matrix,
restricted to the given sets of columns (regressors):
- all regressors
- chosen regressors (if there are any)
- main regressors (non-baseline, non-motion)
- main + baseline (non-motion)
- main + motion (non-baseline)
- motion + baseline
- baseline
- motion
-show_cormat : show the correlation matrix
Display the entire correlation matrix as text.
For an N-regressor (N columns) matrix, the NxN correlation matrix
has as its i,j entry the Pearson correlation between regressors
i and j. It is computed as the de-meaned, normalized XtX.
Values near +/-1.0 are highly correlated (go up and down together,
or in reverse). A value of 0.0 would mean they are orthogonal.
-show_cormat_warnings : show correlation matrix warnings
Correlations for regressor pairs that are highly correlated
(abs(r) >= 0.4, say) are displayed, unless it is for a motion
regressor with either another motion regressor or a baseline
regressor.
-show_cosmat : show the cosine matrix
Display the entire cosine matrix as text.
This is similar to the correlation matrix, but the values show the
cosines of the angles between pairs of regressor vectors. Values
near 1 mean the regressors are "pointed in the same direction" (in
M-dimensional space). A value of 0 means they are at right angles,
which is to say orthogonal.
-show_cosmat_warnings : show cosine matrix warnings
Cosines for regressor pairs that are pointed similar directions
(abs(cos) >= 0.3827, say) are displayed.
-show_fit_betas : show fit betas
If a 1D time series is specified, beta weights will be displayed as
best fit parameters of the model (X-matrix) to the data (1D time
series). These values are the scalars by which the corresponding
regressors are multiplied, in order to fit the data as closely as
possibly (minimizing the sum of squared errors).
Only chosen columns are fit to the data.
see -choose_cols
-show_fit_ts : show fit time series
Similar to showing beta weights, the actual fit time series can
be displayed with this option. The fit time series is the sum of
each regressor multiplied by its corresponding beta weight.
Only chosen columns are fit to the data.
see -choose_cols
-show_xmat : display general X-matrix information
This will display some general information that is stored in the
.xmat.1D file.
-show_1D : display general 1D information
This will display some general information from the 1D time series
file.
------------------------------------------
GUI (graphical user interface) options:
-gui_plot_xmat_as_one : plot Xmat columns on single axis
-----------------------------------------------------------------------------
R Reynolds October 2008
=============================================================================
```