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mtxm_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

Procedure

```   mtxm_c ( Matrix transpose times matrix, 3x3 )

void mtxm_c ( ConstSpiceDouble    m1  [3][3],
ConstSpiceDouble    m2  [3][3],
SpiceDouble         mout[3][3] )

```

Abstract

```   Multiply the transpose of a 3x3 matrix and a 3x3 matrix.
```

```   None.
```

Keywords

```   MATRIX

```

Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
m1         I   3x3 double precision matrix.
m2         I   3x3 double precision matrix.
mout       O   The produce m1 transpose times m2.
```

Detailed_Input

```   m1          is any 3x3 double precision matrix. Typically,
m1 will be a rotation matrix since then its
transpose is its inverse (but this is not a
requirement).

m2          is any 3x3 double precision matrix.
```

Detailed_Output

```   mout        is a 3x3 double precision matrix. mout is the
product

t
mout = m1  m2

mout may overwrite either m1 or m2.
```

Parameters

```   None.
```

Exceptions

```   Error free.
```

Files

```   None.
```

Particulars

```   The code reflects precisely the following mathematical expression

For each value of the subscripts `i' and `j' from 0 to 2:

2
__
\
mout[i][j] =  /_  m1[k][i] * m2[k][j]
k=0

Note that the reversal of the `k' and `i' subscripts in the left-hand
matrix `m1' is what makes `mout' the product of the TRANSPOSE of `m1'
and not simply of `m1' itself. Also, the intermediate results of
the operation above are buffered in a temporary matrix which is
later moved to the output matrix. Thus `mout' can be actually be
`m1' or `m2' if desired without interfering with the computations.
```

Examples

```   The 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 two 3x3 matrices, multiply the transpose of the first
matrix by the second one.

Example code begins here.

/.
Program mtxm_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          mout   [3][3];

SpiceInt             i;

/.
Define `m1' and `m2'.
./
SpiceDouble          m1     [3][3] = { {1.0,  2.0,  3.0},
{4.0,  5.0,  6.0},
{7.0,  8.0,  9.0} };

SpiceDouble          m2     [3][3] = { { 1.0,  1.0,  0.0},
{-1.0,  1.0,  0.0},
{ 0.0,  0.0,  1.0} };

/.
Multiply the transpose of `m1' by `m2'.
./
mtxm_c ( m1, m2, mout );

printf( "Transpose of M1 times M2:\n" );
for ( i = 0; i < 3; i++ )
{

printf( "%10.3f %9.3f %9.3f\n",
mout[i][0], mout[i][1], mout[i][2] );

}

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Transpose of M1 times M2:
-3.000     5.000     7.000
-3.000     7.000     8.000
-3.000     9.000     9.000
```

Restrictions

```   1)  The user is responsible for checking the magnitudes of the
elements of `m1' and `m2' so that a floating point overflow does
not occur. (In the typical use where `m1' and `m2' are rotation
matrices, this not a risk at all.)
```

Literature_References

```   None.
```

Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
W.M. Owen           (JPL)
E.D. Wright         (JPL)
```

Version

```   -CSPICE Version 1.0.1, 04-JUL-2021 (JDR)

Edited the header to comply with NAIF standard.
Added complete code example based on the existing example.

-CSPICE Version 1.0.0, 16-APR-1999 (EDW) (WMO)
```

Index_Entries

```   matrix_transpose times matrix 3x3_case
```
`Fri Dec 31 18:41:09 2021`