Usage: 1dsvd [options] 1Dfile 1Dfile ... - Computes SVD of the matrix formed by the 1D file(s). - Output appears on stdout; to save it, use ‘>’ redirection.
OPTIONS:
-one = Make 1st vector be all 1’s.
-vmean = Remove mean from each vector (can’t be used with -one).
- -vnorm = Make L2-norm of each vector = 1 before SVD.
- The above 2 options mirror those in 3dpc.
-cond = Only print condition number (ratio of extremes)
- -sing = Only print singular values
To compare the singular values from 1dsvd with those from 3dDeconvolve you must use the -vnorm option with 1dsvd. For example, try
- 3dDeconvolve -nodata 200 1 -polort 5 -num_stimts 1
-stim_times 1 ‘1D: 30 130’ ‘BLOCK(50,1)’ -singvals
1dsvd -sing -vnorm nodata.xmat.1D
-sort = Sort singular values (descending) [the default]
-nosort = Don’t bother to sort the singular values
-asort = Sort singular values (ascending)
- -1Dleft = Only output left eigenvectors, in a .1D format
- This might be useful for reducing the number of columns in a design matrix. The singular values are printed at the top of each vector column, as a ‘#...’ comment line.
- -nev n = If -1Dleft is used, ‘-nev’ specifies to output only
the first ‘n’ eigenvectors, rather than all of them. * If you are a tricky person, such as Souheil, you can
put a ‘%’ after the value, and then you are saying keep eigenvectors until at least n% of the sum of singular values is accounted for. In this usage, ‘n’ must be a number less than 100; for example, to reduce a matrix down to a smaller set of columns that capture most of its column space, try something like
1dsvd -1Dleft -nev 99% Xorig.1D > X99.1D
NOTES: * Call the input n X m matrix [A] (n rows, m columns). The SVD
is the factorization [A] = [U] [S] [V]’ (‘=transpose), where - [U] is an n x m matrix (whose columns are the ‘Left vectors’) - [S] is a diagonal m x m matrix (the ‘singular values’) - [V] is an m x m matrix (whose columns are the ‘Right vectors’)
The default output of the program is - An echo of the input [A] - The [U] matrix, each column headed by its singular value - The [V] matrix, each column headed by its singular value
(please note that [V] is output, not [V]’)
This program was written simply for some testing purposes, but is distributed with AFNI because it might be useful-ish.
Recall that you can transpose a .1D file on input by putting an escaped ‘ character after the filename. For example,
1dsvd fred.1D’
You can use this feature to get around the fact that there is no ‘-1Dright’ option. If you understand.
For more information on the SVD, you can start at http://en.wikipedia.org/wiki/Singular_value_decomposition
Author: Zhark the Algebraical (Linear).
++ Compile date = Dec 16 2015