The input may also be a 3x3 covariance matrix or 3x3 covariance matrix series. If this is the case, the eigenvalues and eigenvectors of this matrix is calculated. The time series output is then a empty dummy, and the Covariance Matrix output is a copy of the input. Constraining have no effect, and no plots are generated.
Constrain can be one of the following :
0 - standard covariance matrix (see Blue ISSI book, ch 8)
1 - constrained (same as setting constrain == 1) (see Blue ISSI book, ch 8)
2 - use a Siscoe type variance matrix (see Siscoe et al, JGR no 73, 1968)
3 - use a Weimer type variance matrix (see Weimer, JGR, vol 109, dec 2004)
4 - use Mij = < Vi > < Vj > (Weimer for large N. For demonstration only - this gives nonsense)
Use the methods 2,3 with care; Method 4 is for demonstration purposes, and should not be used. Both method 2 and 4 produce ill-posed covariance matrices, and give one or two negative eigenvalues.
If the input is a time series, a hodogram plot is generated. The boundary normal
estimate is marked with green.
Constraining has no effect if the input is a covariance matrix or matrix input. Also, no plot is generated in this case.
2002-05-14 - initial version
2002-08-25 - covariance as output to WL
2004-01-07 - QSAS 2.x version
2004-01-15 - allow matrix input
2005-05-02 - output projection matrix (used for constrain)
2005-08-08 - added possibility to select covariance matrix type
2005-08-19 - corrected minor bug in printout of Bn for matrix type 2
2005-11-09 - removed redundant link with lapack
Siscoe et al, JGR, 1968 : Description of reduced covariance matrix
Weimer, JGR, vol 109, A12, 2004 : Description of Weimer type covariance matrix
Bargatze et al, JGR, A07, vol 110, 2005 : Discussion of Weimers matrix
ISSI book, 'Multi Spacecraft Analysis', chapter 8