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det_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

```   det_c ( Determinant of a double precision 3x3 matrix )

SpiceDouble det_c ( ConstSpiceDouble m1[3][3] )

```

#### Abstract

```   Compute the determinant of a double precision 3x3 matrix.
```

```   None.
```

#### Keywords

```   MATH
MATRIX

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
m1         I   Matrix whose determinant is to be found.

The function returns the value of the determinant found by direct
application of the definition of the determinant.
```

#### Detailed_Input

```   m1          is any double precision, 3x3 matrix.
```

#### Detailed_Output

```   The function returns the value of the determinant found by direct
application of the definition of the determinant.
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   det_c calculates the determinant of `m1' in a single arithmetic
expression which is, effectively, the expansion of `m1' about its
first row. Since the calculation of the determinant involves
the multiplication of numbers whose magnitudes are unrestricted,
there is the possibility of floating point overflow or underflow.
NO error checking or recovery is implemented in this routine.
```

#### 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 a 3x3 double precision matrix, compute its determinant.

Example code begins here.

/.
Program det_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Set `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,  2.0,  3.0},
{0.0,  5.0,  6.0},
{0.0,  0.0,  9.0} };

/.
Display the determinant of `m1' and `m2'.
./
printf( "Determinant of M1: %5.2f\n", det_c ( m1 ) );
printf( "Determinant of M2: %5.2f\n", det_c ( m2 ) );

return ( 0 );
}

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

Determinant of M1:  0.00
Determinant of M2: 45.00
```

#### Restrictions

```   1)  No checking is implemented to determine whether `m1' will cause
overflow or underflow in the process of calculating the
determinant. In most cases, this will not pose a problem.
The user is required to determine if `m1' is suitable matrix
for det_c to operate on.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
W.M. Owen           (JPL)
```

#### Version

```   -CSPICE Version 1.0.1, 02-JUL-2021 (JDR)

```   determinant of a d.p. 3x3_matrix
`Fri Dec 31 18:41:04 2021`