7.1.24. 1dsvdΒΆ

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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 = Dec 16 2015

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