Procedure

     XPOSBL ( Transpose a matrix by blocks    )

     SUBROUTINE XPOSBL ( BMAT, NROW, NCOL, BSIZE, BTMAT )

Abstract

     Transpose the square blocks within a matrix.

Required_Reading

     None.

Keywords

     MATH
     MATRIX
     TRANSFORMATION

Declarations

     IMPLICIT NONE

     INTEGER               NROW
     INTEGER               NCOL
     INTEGER               BSIZE
     DOUBLE PRECISION      BMAT  ( NROW, NCOL )
     DOUBLE PRECISION      BTMAT ( NROW, NCOL )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     BMAT       I   a matrix composed of square block submatrices
     NROW       I   the number of rows in the matrix BMAT
     NCOL       I   the number of columns in the matrix BMAT
     BSIZE      I   the size of the square blocks in BMAT
     BTMAT      O   the result of transposing the blocks of BMAT

Detailed_Input

     NROW     is the number of rows in the input matrix.

     NCOL     is the number of columns in the input matrix.

     BSIZE    is the number of rows and columns in each block
              of the input matrix.

     BMAT     is a block structured matrix. In other words
              it looks like:


                 -                                -
                |      :      :       :     :      |
                |  B   :  B   :   B   :     :  B   |
                |   11 :   12 :    13 : ... :   1C |
                |......:......:.......:     :......|
                |      :      :       :     :      |
                |  B   :  B   :   B   :     :  B   |
                |   21 :   22 :    23 : ... :   2C |
                |......:......:.......:     :......|
                |      .                           |
                |      .                           |
                |      .                           |
                |......................     .......|
                |      :      :       :     :      |
                |  B   :  B   :   B   :     :  B   |
                |   R1 :   R2 :    R3 : ... :   RC |
                |......:......:.......:     :......|
                 -                                -

              where each B   is a square matrix of BSIZE rows and
                          ij
              and columns.

Detailed_Output

     BTMAT    is the matrix obtained from BMAT when each of its
              blocks is transposed. Given the description of
              BMAT above, BTMAT looks like:


                  -                                -
                 |   t  :   t  :    t  :     :   t  |
                 |  B   :  B   :   B   :     :  B   |
                 |   11 :   12 :    13 : ... :   1C |
                 |......:......:.......:     :......|
                 |      :      :       :     :      |
                 |   t  :   t  :    t  :     :   t  |
                 |  B   :  B   :   B   :     :  B   |
                 |   21 :   22 :    23 : ... :   2C |
                 |......:......:.......:     :......|
                 |      .                           |
                 |      .                           |
                 |      .                           |
                 |......................     .......|
                 |      :      :       :     :      |
                 |   t  :   t  :    t  :     :   t  |
                 |  B   :  B   :   B   :     :  B   |
                 |   R1 :   R2 :    R3 : ... :   RC |
                 |......:......:.......:     :......|
                  -                                -

Parameters

     None.

Exceptions

     1)  If the number of rows input is not positive, the error
         SPICE(BADROWCOUNT) is signaled.

     2)  If the number of columns input is not positive, the error
         SPICE(BADCOLUMNCOUNT) is signaled.

     3)  If the block size input is not positive, the error
         SPICE(BADBLOCKSIZE) is signaled.

     4)  If BMAT cannot be partitioned into an integer number of
         blocks, the error SPICE(BLOCKSNOTEVEN) is signaled.

Files

     None.

Particulars

     This routine transposes the blocks of a block structured
     matrix. This operation is valuable, as it is a means
     for computing the inverse of a state transformation matrix
     (see the example below).

Examples

     The following code fragment illustrates how you would convert
     a state relative to earth-fixed coordinates to J2000 coordinates.

     C
     C     We want to state earthfixed coordinates (399) to J2000
     C     coordinates
     C
           BODY = 399
           REF  = 'J2000'

     C
     C     Get the 6 by 6 state transformation matrix from J2000
     C     coordinates to earthfixed coordinates.
     C
           CALL TISBOD ( REF, BODY, ET, TISPM )

     C
     C     The inverse of TISPM can be obtained by transposing the
     C     3 by 3 blocks of the 6 by 6 matrix TISPM.
     C
           CALL XPOSBL ( TISPM, 6, 6, 3, TSPMI )


     C
     C     Now transform the earthfixed state (ESTATE) to the
     C     inertial state (ISTATE).
     C
           CALL MXVG   ( TSPMI, ESTATE, 6, 6, ISTATE )

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 1.1.0, 16-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Updated
        $Exceptions section.

    SPICELIB Version 1.0.2, 22-APR-2010 (NJB)

        Header correction: assertions that the output
        can overwrite the input have been removed.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 05-NOV-1990 (WLT)