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Procedure: minvar.pro
This program computes the principal variance directions and variances of a
vector quantity (can be 2D or 3D) as well as the associated
eigenvalues. This routine is a simple version
designed to be used by a tplot wrapper with the contrans_var library
Works with trired and triql (IDL's version of Num. Recipies w/ permission)
Input: Vxyz, an (ndim,npoints) array of data(ie 3xN)
Output: eigenVijk, an (ndim,ndim) array containing the principal axes vectors
Maximum variance direction eigenvector, Vi=eigenVijk(*,0)
Intermediate variance direction, Vj=eigenVijk(*,1) (descending order)
Vrot: if set to a name, that name becomes an array of (ndim,npoints)
containing the rotated data in the new coordinate system, ijk.
Vi(maximum direction)=Vrot(0,*)
Vj(intermediate direction)=Vrot(1,*)
Vk(minimum variance direction)=Vrot(2,*)
lambdas2=if set to a name returns the eigenvalues of the
computation
Written by: Vassilis Angelopoulos
$LastChangedBy: lbwilson $
$LastChangedDate: 2016-06-23 12:01:09 -0700 (Thu, 23 Jun 2016) $
$LastChangedRevision: 21356 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/general/cotrans/special/minvar/minvar.pro $
(See general/cotrans/special/minvar/minvar.pro)
Procedure: minvar_matrix_make
Purpose: tplot wrapper for minvar.pro. This routine generates a
matrix or set of matrices from a time series of 3-d vector data that
will transform three dimensional data into a minimum variance
coordinate system. This routine takes a tplot variable that stores 3
dimensional vector data as an argument and produces a tplot variable
storing the transformation matrix or matrices.
The minimum variance coordinate system is taken by generating the covariance
matrix for an interval of data. This matrix is then diagonalized to
identify the eigenvalues and eigenvectors of the covariance matrix.
The eigenvector with the smallest eigenvalue will form the direction
of the z component of the new coordinate system. The eigenvector
with the largest eigenvalue will form the direction of the x
component of the new coordinate system. The third eigenvector will
form the y direction of the coordinate system.
Warning: The resulting transformation matrices will only correctly
transform data from the coordinate system of the input variable to
the minimum variance coordinate system. So if in_var_name is in gse
coordinates then you should only use the output matrices to transform
other data in gse coordinates.
Arguments:
in_var_name: the name of the tplot variable holding the input
data, can be any sort of timeseries 3-d data
tstart(optional): the start time of the data you'd like to
consider for generating the transformation matrix(defaults to
minimum time of in_var timeseries)
tstop(optional): the stop time of the data you'd like to
consider for generating the transformation matrix(defaults to
maximum time of in_var timeseries)
twindow(optional): the size of the window(in seconds) you'd like to
consider when using a moving boxcar average to generate
multiple transformations. (defaults to the entire time series)
tslide(optional): the number of seconds the boxcar should
slide forward after each average.(defaults to twindow/2)
set tslide=0 to cause the program to generate only a single
matrix
newname(optional): the name of the tplot variable in which to
store the transformation matrix(matrices) (defaults to
in_var_name+'_mva_mat'
evname(optional): the name of the tplot variable in which to
store the eigenvalues of the mva matrix(matrices) (defaults to
nowhere, ie if unset doesn't store them
error(optional): named variable that holds the error state of
the computation, 1=success 0 = failure
tminname(optional): name of a tplot variable in which you would
like to store the minimum variance direction vectors this
vector will be represented in the original coordinate system
tmidname(optional): name of a tplot variable in which you would
like to store the intermediate variance direction vectors this
vector will be represented in the original coordinate system
tmaxname(optional): name of a tplot variable in which you would
like to store the minimum variance direction vectors this
vector will be represented in the original coordinate system
SEE ALSO:
minvar.pro
tvector_rotate.pro
thm_crib_mva.pro (THEMIS project)
$LastChangedBy: jwl $
$LastChangedDate: 2021-12-10 11:18:45 -0800 (Fri, 10 Dec 2021) $
$LastChangedRevision: 30461 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/general/cotrans/special/minvar/minvar_matrix_make.pro $
(See general/cotrans/special/minvar/minvar_matrix_make.pro)
Basic tests for minvar.pro Written by Vassilis Angelopolous(vassilis@ssl.berkeley.edu) $LastChangedBy: pcruce $ $LastChangedDate: 2007-10-04 15:40:27 -0700 (Thu, 04 Oct 2007) $ $LastChangedRevision: 1667 $ $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/ssl_general/trunk/cotrans/special/minvar/minvar.pro $
(See general/cotrans/special/minvar/minvar_test.pro)