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# Directory Listing of Routines

# ssl_general/cotrans/special

- TCROSSP
- TDOTP
- TINTERPOL_MXN
- TNORMALIZE
- TVECTOR_ROTATE

# Routine Descriptions

## TCROSSP

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    PROCEDURE: TCROSSP
    Purpose:
      Vectorized routine to calculate the cross product of two tplot
      variables containing arrays of 3d vectors and storing the result
      in a tplot variable.  Also, can perform vectorized cross product on
      arrays.

    Arguments:
     v1: The name of the tplot variable  or an Nx3 length array storing the first vector in the cross product

     v2: The name of the tplot variable or an Nx3 length array storing the second vector in the
         cross product

     newname(optional): the name of the output tplot variable

     error(optional): named variable in which to return error state of
     the computation.  1 = success 0 = failure

     Outputs(optional):
       out:
         Returns output in array format, if this argument is present, no tplot variable will be created

    NOTES:

(See ssl_general/cotrans/special/tcrossp.pro)

## TDOTP

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    PROCEDURE: TDOTP
    Purpose:
      Vectorized routine to calculate the dot product of two tplot
      variables containing arrays of vectors and storing the results
      in a tplot variable

    Arguments:
     v1: The name of the tplot variable storing the first vector in the dot product
     v2: The name of the tplot variable storing the second vector in the
     dot product

     newname(optional): the name of the output tplot variable

     error(optional): named variable in which to return the error state
     of the computation.  1 = success 0 = failure

    NOTES:

(See ssl_general/cotrans/special/tdotp.pro)

## TINTERPOL_MXN

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    Function: tinterpol_mxn

    Purpose:  Generalized interpolates across a series of vectors(since
    interpol only works on 1-d vectors) This function works on any
    n-dimensional vectors. Basically, this is an element by element
    interpolation across M

     - i. works on tplot variables
         - ii. allows no extrapolation beyond valid data with
              /no_extrapolate keyword"

    Arguments:
                xv_tvar = tplot variable to be interpolated, the y component
                can have any dimesions, can use globbing to interpolate
                many values at once
                uses x component for x abcissa values

                uz_tvar = tplot variable that V will be fit to
                uses x component for u abcissa values.  Can also
                pass in an array of time values rather than a tplot
                variable.

                newname = output variable name(optional) defaults to
                xv_tvar+'_interp'

                suffix = a suffix other than interp you can use,
                particularily useful when using globbing

                overwrite=set this variable if you just want
                the original variable overwritten instead of using
                newname or suffix

                Use only newname or suffix or overwrite. If you combine
                them the naming behavior may be erratic

                /LINEAR = pass this argument to specify linear
                interpolation(this is the default behavior)

                /QUADRATIC = pass this argument to specify quadratic
                interpolation

                /SPLINE = pass this argument to specify spline
                interpolation

                /NO_EXTRAPOLATE = pass this argument to prevent
                extrapolation of data values in V passed it's start and
                end points

                /NAN_EXTRAPOLATE = pass this argument to extrapolate past
                the endpoints using NaNs as a fill value

                ERROR(optional): named variable in which to return the error state
                of the computation.  1 = success 0 = failure

    Outputs(optional):
       out:
         Returns output as a data struct. If this argument is present, no tplot variable will be created
         Note that only one result can be returned through this keyword.

    CALLING SEQUENCE;
               tinterpol_mxn,'tplot_var1','tplot_var2',out_var='tplot_var_out'
               tinterpol_mxn,'tplot_var1','tplot_var2',/NO_EXTRAPOLATE
               tinterpol_mxn,'tplot_var1','tplot_var2',/SPLINE

    Output: an N by D1 by D2 by ... array stored in an output tplot variabel

    Notes:
    Uses a for loop over D1*D2*..., but I'm operating under the assumption that
    D1*D2... << M (D1 * D2 *... is waaaay less than M)

    It uses a little bit of modular arithmatic so this function is
    generalized to any array dimensionality(IDL limits at 8)

    Examples:
     if the input is an array of 3-d vectors(say 1,1,1 and 2,2,2) and we
     want 3 vectors out the output is 1,1,1 1.5 1.5 1.5 2,2,2
     if the input is an array of 3x3 matrices(say all ones and all twos)
     and we want three matrices then output is all 1s all 1.5s all 2s

     $LastChangedBy: pcruce $
     $LastChangedDate: 2009-12-09 14:39:12 -0800 (Wed, 09 Dec 2009) $
     $LastChangedRevision: 6983 $
     $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/ssl_general/trunk/cotrans/special/tinterpol_mxn.pro $

(See ssl_general/cotrans/special/tinterpol_mxn.pro)

## TNORMALIZE

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    PROCEDURE: TNORMALIZE
    Purpose:
      Vectorized routine to normalize all the vectors stored in a tplot
      variable

    Arguments:
     v: The name or number of the tplot variable storing the vectors to be
     normalized, or an array of vectors to be normalized.  NOTE, if the input is
     not a tplot variable, this routine will not generate a tplot variable for output
     newname(optional): The name of the output tplot variable. Defaults
     to v+'_normalized'
     error(optional): Named variable in which to return the error state
     of the computation, 1 = success, 0 = failure
     out(optional):  If set to a named variable, the output will be stored
                  in out, rather than a tplot variable.

    NOTES:

     $LastChangedBy: pcruce $
     $LastChangedDate: 2009-06-23 17:40:09 -0700 (Tue, 23 Jun 2009) $
     $LastChangedRevision: 6314 $
     $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/ssl_general/trunk/cotrans/special/tnormalize.pro $

(See ssl_general/cotrans/special/tnormalize.pro)

## TVECTOR_ROTATE

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    Procedure: tvector_rotate

    Purpose:  rotates a set of vectors by a set of coordinate
              transformation matrices inputs and outputs are tplot
              variables.  This is designed mainly for use with
              fac_matrix_make.pro and minvar_matrix_make, but can be used
              for more general purposes

    Warning:
     The transformation matrices generated by
    fac_matrix_make,thm_fac_matrix_make, and minvar_matrix_make are
    defined relative to a specific coordinate system.  This means that if
    you use vectors in one coordinate system to generate the rotation
    matrices they will only correctly transform data from that coordinate
    system into the functional coordinate system.

      For example if you use
    magnetic field data in gsm to generate Rgeo transformation matrices
    using fac_matrix_make then the vectors being provided to tvector
    rotate to be transformed by those matrices should only be in gsm coordinates.

    Arguments:

     mat_var_in: the name of the tplot variable storing input matrices
     The y component of the tplot variable's data struct should be
     an Mx3x3 array, storing a list of transformation matrices.

     vec_var_in: the name of the tplot variable storing input
    vectors. You can use globbing to rotate several tplot variables
    storing vectors with a single matrix. The y component of the tplot variable's
     data struct should be an Nx3 array.

     newname(optional): the name of the output variable, defaults to
                        vec_var_in + '_rot'
                        If you use type globbing in the vector variable
                        This option will be disabled

     suffix: The suffix to be appended to the tplot variables that the output matrices will be stored in.
             (Default: '_rot')

     error(optional): named variable in which to return the error state
     of the computation.  1 = success 0 = failure

     invert(optional):  If matrix_var naturally transforms vector_var from Coord A to B,
                        (ie Vb = M#Va where # denotes matrix multiplication) then setting
                        this keyword will transform vector_var from Coord B to A( ie Va = M^T#Vb
                        This is done by transposing the input matrices, as it is a property of
                        rotation matrices that M#M^T = I and M^T#M = I(ie M^T = M^-1)

     vector_skip_nonmonotonic(optional): Removes any vector data with non-ascending or repeated
                                timestamps before SLERPing matrices rather than throwing an error.

     matrix_skip_nonmonotonic(optional): Removes any vector data with non-ascending
                                timestamps before SLERPing matrices rather than throwing an error.

    CALLING SEQUENCE:

     tvector_rotate,'matrix_var','vector_var',newname = 'out_var',error=error

     tvector_rotate,'matrix_var','vector_var'

    Notes:
     1.  mat_var_in should store rotation or permutation matrices.
         (ie the columns of any matrix in mat_var_in should form an orthonormal basis)
         tvector_rotate will test and warn if input matrices are inalid.
         Permutation matrices are allowed so that coordinates can be transformed
         from right to left handed systems and vice-versa.  This is verified via the following
         contraints.
         M#M^-1 = I and abs(determ(m)) = 1

     2.  transformation matrices generally only transform from one particular basis
         to another particular basis.  Since tvector_rotate as no way to test that
         vector_var is in the correct basis, you need to be very careful that
         vector_var has the correct coordinate system and representation
         so that it can correctly transform the data.

    3.   If M!=N, then M must be >= 2 (where M,N refer to the dimensions of the
         input variables.)

    4.  Also If the x components of mat_var_in and vec_var_in data structs
        do not match then, the matrices will be interpolated to match the
        cadence of the vector data.  Interpolation is done by turning the
        matrices into quaternions and performing spherical linear
        interpolation.  As noted above this interpolation behavior will
        not be predictable if the matrices do anything other than rotate.

    5.  If the timestamps of mat_var_in are not monotonic(ascending or identical) or
        if the timestamps vec_var_in are not strictly monotonic(always ascending) the
        program will not work correctly in the event that matrix SLERPing is required.
        Set the keywords vector_skip_nonmonotonic or matrix_skip_nonmonotonic to have
        the routine remove the non-monotonic data when generating the output. Alternatively,
        if matrix and vector timestamps match no SLERPing will be required, also fixing
        nonmonotonicities manually will fix the problem.

     SEE ALSO:  mva_matrix_make.pro, fac_matrix_make.pro,rxy_matrix_make

     $LastChangedBy: pcruce $
     $LastChangedDate: 2009-09-16 15:37:17 -0700 (Wed, 16 Sep 2009) $
     $LastChangedRevision: 6742 $
     $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/ssl_general/trunk/cotrans/special/tvector_rotate.pro $

(See ssl_general/cotrans/special/tvector_rotate.pro)