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matrix_array_lib Helpful functions for dealing with arrays of 3x3 matrixes (Nx3x3) $LastChangedBy: aaflores $ $LastChangedDate: 2016-04-29 17:15:55 -0700 (Fri, 29 Apr 2016) $ $LastChangedRevision: 20987 $ $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_3_2/general/cotrans/special/matrix_array_lib.pro $
(See general/cotrans/special/matrix_array_lib.pro)
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
diff_tsize_ok = if set, allows the arrays to have a different number
of elements in time, uses data_cut, which
interpolates the data in v2 to the number of times
given by v1
Outputs(optional):
out:
Returns output in array format, if this argument is present, no tplot variable will be created
Example:
TPLOT;
tcrossp,'tvarname1','tvarname2'
Array:
tcrossp,array_2d_1,array_2d_2,out=array_output
NOTES:
(See general/cotrans/special/tcrossp.pro)
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 general/cotrans/special/tdotp.pro)
Function: tinterpol_mxn
Purpose:
Performs interpolation on tplot variables.
Interpolates xv_tvar to match uz_tvar. Can also interpolate with non-tvar types
and return non-tvar types. (Helpful for interpolating matrices and time-series vectors)
This function works on any n or nxm dimensional vectors. Interpolation always occurs along first dimension(time)
Arguments:
xv_tvar(source) = 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
Can also pass in a struct with the same format as the
data component for a tplot variable:
{x:time_array,y:data_array,v:optional_y_axis_abcissas}
uz_tvar(target) = 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 tplot variable name(optional) defaults to
xv_tvar+'_interp'. If you want vector output, use the keyword "out"
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 = set this keyword to specify linear
interpolation(this is the default behavior)
/QUADRATIC = set this keyword to specify quadratic
interpolation
/SPLINE = set this keyword to specify spline
interpolation
/NEAREST_NEIGHBOR = set this keyowrd to specify repeat
nearest neighbor 'interpolation'
/NO_EXTRAPOLATE = set this keyword to prevent
extrapolation of data values in V passed it's start and
end points
/NAN_EXTRAPOLATE = set this keyword to extrapolate past
the endpoints using NaNs as a fill value
/REPEAT_EXTRAPOLATE = set this keyword to repeat nearest value past the endpoints
/IGNORE_NANS = set this keyword to remove nans in the data before interpolation
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.(ie You can't use this keyword with tplot name-globbing)
CALLING SEQUENCE;
tinterpol_mxn,'tplot_var1','tplot_var2',newname='tplot_var_out'
tinterpol_mxn,'tplot_var1','tplot_var2',/NO_EXTRAPOLATE
tinterpol_mxn,'tplot_var1','tplot_var2',/SPLINE
tinterpol_mxn,'tplot_var1','tplot_var2',out=out_data_struct ;doesn't create tplot variable, instead returns struct
tinterpol_mxn,'tplot_var1',time_array ;This calling method doesn't require second tplot variable
tinterpol_mxn,{x:time_array,y:data_array},'tplot_var2' ;This calling method doesn't require first tplot variable
tinterpol_mxn,{x:time_array,y:data_array,v:y_scale_vals},time_array,out=out_data_struct ; You can mix and match calling types. This calling method doesn't use any tplot variables
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: 2016-10-31 11:32:53 -0700 (Mon, 31 Oct 2016) $
$LastChangedRevision: 22236 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_3_2/general/cotrans/special/tinterpol_mxn.pro $
(See general/cotrans/special/tinterpol_mxn.pro)
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: aaflores $
$LastChangedDate: 2012-01-23 16:21:34 -0800 (Mon, 23 Jan 2012) $
$LastChangedRevision: 9592 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_3_2/general/cotrans/special/tnormalize.pro $
(See general/cotrans/special/tnormalize.pro)
NAME:
ttensor_rotate
PURPOSE:
Wrapper for tvector_rotate, to allow rotation of pressure and
momentum flux tensors defined as ntimes, 6 arrays
CALLING SQEUENCE: (same as tvector_rotate)
Using tplot variables:
ttensor_rotate, 'matrix_var', 'tensor_var' [,newname='out_var']
[,invert=invert] [,suffix=suffix] [,error=error]
[,/vector_skip_nonmonotonic]
[,/matrix_skip_nonmonotonic]
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.
tens_var_in: The name of tplot variable(s) storing a pressure or mf tensor
The y component of the tplot variable's data
struct should be an Nx6 array.
newname(optional): the name of the output variable, defaults to
tens_var_in + '_rot'
Newname should only be used if a single tensor
variable is rotated
suffix: The suffix to be appended to the tplot variable(s)
(Default: '_rot')
error(optional): named variable in which to return the error state
of the computation. 1 = success 0 = failure
NOTES: the program will change the input tensor or tplot variable(s)
to mx3x3 inputs suitable for tvector_rotate and reset at the end
SEE ALSO: tvector_rotate.pro, mva_matrix_make.pro,
fac_matrix_make.pro,rxy_matrix_make
$LastChangedBy: jimm $
$LastChangedDate: 2019-02-05 15:58:04 -0800 (Tue, 05 Feb 2019) $
$LastChangedRevision: 26557 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_3_2/general/cotrans/special/ttensor_rotate.pro $
(See general/cotrans/special/ttensor_rotate.pro)
Procedure:
tvector_rotate
Purpose:
Rotates array data by a set of coordinate
transformation matrices and outputs 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
Assuming that the data array and matrix time-grids match,
this code is the vectorized equivalent to:
for i=0,n_ele-1 do out[i,*]=reform(reform(m[i,*,*])#reform(v[i,*]))
If the target is also an array of matrices then it is equivalent to:
for i=0,n_ele-1 do out[i,*,*] = reform(m[i,*,*]) # reform(v[i,*,*])
If the target is a tensor, KEYWORD_SET = tensor_rotation
then it is equivalent to
for i=0,n_ele-1 do out[i,*,*] = reform(m[i,*,*]) #
reform(v[i,*,*]) # transpose(reform(m[i, *, *]))
Setting the "invert" keyword will produce results that are equivalent to using the '##'
operation in the loop above.
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 array being provided to tvector
rotate to be transformed by those matrices should only be in gsm coordinates.
CALLING SEQUENCE:
Using tplot variables:
tvector_rotate, 'matrix_var', 'vector_var' [,newname='out_var']
[,invert=invert] [,suffix=suffix] [,error=error]
[,/vector_skip_nonmonotonic]
[,/matrix_skip_nonmonotonic]
[,/tensor_rotate]
Using arrays:
tvector_rotate, matrix_array, vector_array, newname=output_array ...
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.
Array or tensor data can be input as well and should be an Mx3x3 array
vec_var_in: The name of a tplot variable storing an array of input vectors.
The tplot variable may also contain matrices.
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.
Array data can also be input and should be an Nx3x3 array.
newname(optional): the name of the output variable, defaults to
vec_var_in + '_rot'
If you use type globbing in the vector variable
If array data is used this variable should be
declared.
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.
tensor_rotate: set if the input is a pressure, or momentum flux
tensor, requiring an extra matrix multiplication
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 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: jimm $
$LastChangedDate: 2019-07-24 12:01:53 -0700 (Wed, 24 Jul 2019) $
$LastChangedRevision: 27496 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_3_2/general/cotrans/special/tvector_rotate.pro $
(See general/cotrans/special/tvector_rotate.pro)