# Documentation of vectsig

Global Index (all files) (short | long) | Local Index (files in subdir) (short | long)

## Function Synopsis

`[fval, dof1, dof2] = vectsig(c1, c2);`

## Help text

```
[fval, dof1, dof2] = vectsig(c1, c2);

This function returns the F-score (see Tatsuoka, Multivariate
Analysis, 1988, pp 85 - 88).  These can be compared using the
tables in the back of the above mentioned book.  Notice that
c1 and c2 are complex matrices formed like:

c1 = u1 + j*v1

where j = sqrt(-1)

c1 and c2 need not have the same number of time realizations
(columns), but need to have the same number of spatial real-
izations (rows)

Note that dof1 refers to the degrees of freedom in the denominator,
while dof2 refers to the degrees of freedom in the numerator,
when obtaining the F-value.

e.g.:
fsig = finv(0.95, dof2, dof1);

```

## Cross-Reference Information

This function calls

## Listing of function vectsig

```function [fval, dof1, dof2] = vectsig(c1, c2);
[m1, n1] = size(c1);
[m2, n2] = size(c2);
if n1 ~= n2; error('ERROR - number of stations (rows) must be the same'); end;
n = n1;
dif_mean = mean2(c1) - mean2(c2);
c11 = c1 - ones(m1,1) * mean2(c1);
c22 = c2 - ones(m2,1) * mean2(c2);
for i = 1:n;
s1 = [real(c11(:,i)) imag(c11(:,i))]' * [real(c11(:,i)) imag(c11(:,i))];
s2 = [real(c22(:,i)) imag(c22(:,i))]' * [real(c22(:,i)) imag(c22(:,i))];
%
w = s1 + s2;
%
%   Calculate the T statistic, ref. Tatsuoka, p. 86
%
t(i) = [real(dif_mean(i)) imag(dif_mean(i))] * ...
inv(w * ((m1 + m2) / (m1 * m2 * (m1 + m2 - 2)))) * ...
[real(dif_mean(i)) imag(dif_mean(i))]';
end
%
%   Calculate the F statistic, ref. Tatsuoka, p. 86
%

fval = ((m1 + m2 - 3) / (2 * (m1 + m2 - 2))) * t;
dof1 = m1 + m2 -3;
dof2 = 2;

```