Table of contents
CSPICE_INVORT constructs the inverse of a 3x3 matrix with orthogonal
columns and non-zero column norms using a numerically stable algorithm.
The rows of the output matrix are the columns of the input matrix divided
by the length squared of the corresponding columns.
Given:
m a 3x3 matrix.
[3,3] = size(m); double = class(m)
the call:
[mit] = cspice_invort( m )
returns:
mit the matrix obtained by transposing `m' and dividing the rows
by squares of their norms.
[3,3] = size(mit); double = class(mit)
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Given a double precision 3x3 matrix with mutually orthogonal
rows of arbitrary length, compute its inverse. Check that the
original matrix times the computed inverse produces the
identity matrix.
Example code begins here.
function invort_ex1()
%
% Define a matrix to invert.
%
m = [ [0.0, -1.0, 0.0]', [0.5, 0.0, 0.0]', [0.0, 0.0, 1.0]' ]';
fprintf( 'Original Matrix:\n' )
for i=1:3
fprintf( '%16.7f %15.7f %15.7f\n', m(i,1), m(i,2), m(i,3) )
end
%
% Invert the matrix, then output.
%
[mout] = cspice_invort( m );
fprintf( ' \n' )
fprintf( 'Inverse Matrix:\n' )
for i=1:3
fprintf( '%16.7f %15.7f %15.7f\n', ...
mout(i,1), mout(i,2), mout(i,3) )
end
%
% Check the `m' times `mout' produces the identity matrix.
%
imat = m * mout;
fprintf( ' \n' )
fprintf( 'Original times inverse:\n' )
for i=1:3
fprintf( '%16.7f %15.7f %15.7f\n', ...
imat(i,1), imat(i,2), imat(i,3) )
end
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Original Matrix:
0.0000000 -1.0000000 0.0000000
0.5000000 0.0000000 0.0000000
0.0000000 0.0000000 1.0000000
Inverse Matrix:
0.0000000 2.0000000 0.0000000
-1.0000000 0.0000000 0.0000000
0.0000000 0.0000000 1.0000000
Original times inverse:
1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
Suppose that m is the matrix
.- -.
| A*u B*v C*w |
| 1 1 1 |
| |
| A*u B*v C*w |
| 2 2 2 |
| |
| A*u B*v C*w |
| 3 3 3 |
`- -'
where the vectors (u , u , u ), (v , v , v ), and (w , w , w )
1 2 3 1 2 3 1 2 3
are unit vectors. This routine produces the matrix:
.- -.
| a*u a*u a*u |
| 1 2 3 |
| |
| b*v b*v b*v |
| 1 2 3 |
| |
| c*w c*w c*w |
| 1 2 3 |
`- -'
where a = 1/A, b = 1/B, and c = 1/C.
1) If any of the columns of `m' have zero length, the error
SPICE(ZEROLENGTHCOLUMN) is signaled by a routine in the call
tree of this routine.
2) If any column is too short to allow computation of the
reciprocal of its length without causing a floating point
overflow, the error SPICE(COLUMNTOOSMALL) is signaled by a
routine in the call tree of this routine.
3) If the input argument `m' is undefined, an error is signaled
by the Matlab error handling system.
4) If the input argument `m' is not of the expected type, or it
does not have the expected dimensions and size, an error is
signaled by the Mice interface.
None.
None.
MICE.REQ
None.
J. Diaz del Rio (ODC Space)
S.C. Krening (JPL)
E.D. Wright (JPL)
-Mice Version 1.1.0, 01-NOV-2021 (EDW) (JDR)
Updated the header to comply with NAIF standard. Added
complete code example to -Examples section. Extended -Abstract
section.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections, and
completed -Particulars section.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.0, 14-NOV-2013 (EDW) (SCK)
Transpose a matrix and invert the lengths of the rows
Invert a pseudo orthogonal matrix
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