invert_c |
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Procedureinvert_c ( Invert a 3x3 matrix ) void invert_c ( ConstSpiceDouble m [3][3], SpiceDouble mout[3][3] ) AbstractGenerate the inverse of a 3x3 matrix. Required_ReadingNone. KeywordsMATH MATRIX Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m I Matrix to be inverted. mout O Inverted matrix (m)^-1. Detailed_Inputm is an arbitrary 3x3 matrix. The limits on the size of elements of `m' are determined by the process of calculating the cofactors of each element of the matrix. For a 3x3 matrix this amounts to the differencing of two terms, each of which consists of the multiplication of two matrix elements. This multiplication must not exceed the range of double precision numbers or else an overflow error will occur. Detailed_Outputmout is the inverse of `m' and is calculated explicitly using the matrix of cofactors. `mout' is set to be the zero matrix if `m' is singular. `mout' can overwrite `m'. ParametersNone. Exceptions1) No internal checking on the input matrix `m' is performed except on the size of its determinant. Thus it is possible to generate a floating point overflow or underflow in the process of calculating the matrix of cofactors. 2) If the determinant is less than 10**-16, the matrix is deemed to be singular and the output matrix is filled with zeros. FilesNone. ParticularsA temporary matrix is used to compute the result, so the output matrix may overwrite the input matrix. ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Given a double precision 3x3 matrix, compute its inverse. Check that the original matrix times the computed inverse produces the identity matrix. Example code begins here. /. Program invert_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble imat [3][3]; SpiceDouble mout [3][3]; SpiceInt i; /. Define a matrix to invert. ./ SpiceDouble m [3][3] = { {0.0, -1.0, 0.0}, {0.5, 0.0, 0.0}, {0.0, 0.0, 1.0} }; printf( "Original Matrix:\n" ); for ( i = 0; i < 3; i++ ) { printf( "%16.7f %15.7f %15.7f\n", m[i][0], m[i][1], m[i][2] ); } /. Invert the matrix, then output. ./ invert_c ( m, mout ); printf( " \n" ); printf( "Inverse Matrix:\n" ); for ( i = 0; i < 3; i++ ) { printf( "%16.7f %15.7f %15.7f\n", mout[i][0], mout[i][1], mout[i][2] ); } /. Check the `m' times `mout' produces the identity matrix. ./ mxm_c ( m, mout, imat ); printf( " \n" ); printf( "Original times inverse:\n" ); for ( i = 0; i < 3; i++ ) { printf( "%16.7f %15.7f %15.7f\n", imat[i][0], imat[i][1], imat[i][2] ); } return ( 0 ); } When this program was executed on a Mac/Intel/cc/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 Restrictions1) The input matrix must be such that generating the cofactors will not cause a floating point overflow or underflow. The strictness of this condition depends, of course, on the computer installation and the resultant maximum and minimum values of double precision numbers. Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.M. Owen (JPL) Version-CSPICE Version 1.1.0, 06-JUL-2021 (JDR) Changed input argument name "m1" to "m" for consistency with other routines. Updated the header to comply with NAIF standard. Added complete code example. -CSPICE Version 1.0.0, 13-SEP-1999 (NJB) (WMO) Index_Entriesinvert a 3x3_matrix |
Fri Dec 31 18:41:08 2021