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Index Page xposeg_c

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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

       xposeg_c ( Transpose a matrix, general )

       void xposeg_c ( const void   * matrix,
                       SpiceInt       nrow,
                       SpiceInt       ncol,
                       void         * xposem )

#### Abstract

       Transpose a matrix of arbitrary size (in place, the matrix
       need not be square).

#### Required_Reading

       None.

#### Keywords

       MATRIX

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       matrix     I   Matrix to be transposed.
       nrow       I   Number of rows of input matrix `matrix'.
       ncol       I   Number of columns of input matrix `matrix'.
       xposem     O   Transposed matrix.

#### Detailed_Input

       matrix      is a matrix to be transposed.

       nrow        is the number of rows of input matrix `matrix'.

       ncol        is the number of columns of input matrix `matrix'.

#### Detailed_Output

       xposem      is the transposed matrix.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  If either `nrow' or `ncol' is less than or equal to zero, no
           action is taken. The routine simply returns.

#### Files

       None.

#### Particulars

       This routine transposes the input matrix and writes the
       result to the matrix `xposem'. This algorithm is performed in
       such a way that the transpose can be performed in place. That
       is, `matrix' and `xposem' can use the same storage area in memory.

       NOTE:  The matrices `matrix' and `xposem' are declared
              one-dimensional for computational purposes only. The
              calling program should declare them as matrix[nrow][ncol]
              and xposem[ncol][nrow].

              This routine works on the assumption that the input and
              output matrices are defined as described above. More
              specifically it assumes that the elements of the matrix
              to be transformed is stored in contiguous memory locations
              as shown here. On output these elements will be
              rearranged in consecutive memory locations as shown.

                 matrix                xposem

                 m[0][0]               m[0][0]
                 m[0][1]               m[1][0]
                 m[0][2]               m[2][0]
                 .                     .
                 .                     .
                 m[0][ncol-1]          .
                 m[1][0]               m[nrow-1][0]
                 m[1][1]               m[0][1]
                 m[1][2]               m[1][1]
                 .                     m[2][1]
                 .                     .
                 m[1][ncol-1]          .
                 .                     .
                                       m[nrow-1][1]
                 .                     .

                 .                     .

                 .                     .
                                       m[0][ncol-1]
                 m[nrow-1][0]          m[1][ncol-1]
                 m[nrow-1][1]          m[2][ncol-1]
                 m[nrow-1][2]          .
                 .                     .
                 .                     .
                 m[nrow-1][ncol-1]     m[nrow-1][ncol-1]

       For those familiar with permutations, this algorithm relies upon the
       fact that the transposition of a matrix, which has been stored as a
       string, is simply the action of a permutation applied to that
       string. Since any permutation can be decomposed as a product of
       disjoint cycles, it is possible to transpose the matrix with only
       one additional storage register. However, once a cycle has been
       computed it is necessary to find the next entry in the string that
       has not been moved by the permutation. For this reason the
       algorithm is slower than would be necessary if the numbers of rows
       and columns were known in advance.

#### Examples

       This routine is primarily useful when attempting to transpose large
       matrices, where inplace transposition is important. For example
       suppose you have the following declarations

          SpiceDouble           matrix [1003][800];

       If the transpose of the matrix is needed, it may not be possible to
       fit a second matrix requiring the same storage into memory. Instead
       declare xposem as below so that no additional memory is allocated.

          SpiceDouble        (* xposem) [1003]  =  matrix;

       To obtain the transpose simply execute

          xposeg_c ( matrix, 1003, 800, xposem );

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       W.L. Taber          (JPL)

#### Version

       -CSPICE Version 1.1.1, 13-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

       -CSPICE Version 1.1.0, 24-JUL-2001 (NJB)

           Changed prototype: input matrix is now type (const void *).
           Implemented interface macro for casting input matrix to const.

       -CSPICE Version 1.0.0, 31-MAY-1999 (NJB) (WLT)

#### Index_Entries

       transpose a matrix general

#### Link to routine xposeg_c source file xposeg_c.c

    Fri Dec 31 18:41:15 2021