# 1dsvd¶

```
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
EXAMPLE:
1dsvd -vmean -vnorm -1Dleft fred.1D'[1..6]' | 1dplot -stdin
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]')
- The pseudo-inverse of [A]
* 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 = May 7 2021 {AFNI_21.1.06:linux_ubuntu_16_64}
```