blocks_to_amat

emg3d.core.blocks_to_amat(amat, bvec, middle, left, rhs, im, nC)

Insert middle, left, and rhs into main arrays amat and bvec.

The banded matrix amat contains the main diagonal and the first five lower off-diagonals. They are stored one column after the other, in a 6*n ndarray.

The complete main matrix amat and the middle and left blocks are given by:

.-0
|X|\   0
0-.-0       left:  middle:  right:
 \|X|\                      (not used)
  0-.-0      0-     .-      0
   \|X|\      \     |X      |\
    0-.-0
 0   \|X|
      0-.

. 1*1, - 4*1, | 1*4, X 4*4, \ 4*4 upper or lower

Both, middle and left, are 5x5 matrices. The corresponding right-hand-side rhs is filled into bvec. The matrices left and middle provided in a single call are horizontally aligned (not vertically). The sorting of amat (banded matrix) and bvec are given by:

 amat (66,)             example: n = 11                   bvec (11,)
 --------------                                                 --
|01            |                    FIRST CALL                  01
|02 07         |                    Only `middle` and `rhs`     02
|03 08 13      |                    are used, not `left`.       03
|04 09 14 19   |                                                04
|05 10 15 20 25|                                                05
 -------------- --------------                                  --
| 0 11 16 21 26|31            |     SUBSEQUENT CALLS            06
|   12 17 22 27|32 37         |     (normal case)               07
|      18 23 28|33 38 43      |     Complete `left`,            08
|         24 29|34 39 44 49   |     `middle` and `rhs`          09
|            30|35 40 45 50 55|     are used.                   10
 -------------- -------------- ---                              --
               | 0 41 46 51 56|61   LAST CALL                   11
               |    0  0  0  0| 0   Only top row of `left`
               |       0  0  0| 0   and the first elements
               |          0  0| 0   of `middle` and `rhs`
               |             0| 0   are used.
                -------------- ---
                              | 0

Single zeros (0) show elements in amat which are 0, hence not used.
Their location in amat can be deduced from their neighbours.

Parameters:

amat : ndarray

Main banded matrix (stored as array) of length 6*n.

bvec : ndarray

Main right-hand-side of length n.

middle : ndarray

Middle block of size 5x5, as ndarray of length 25. Only the diagonal and the lower triangular part are used.

left : ndarray

Left block of size 5x5, as ndarray of length 25. Only the diagonal and the first row are used.

rhs : ndarray

Corresponding right-hand-side of length 5.

im : int

Current minus-index of direction of line relaxation, {ixm, iym, izm}.

nC : int

Total number of cells in direction of line relaxation, {nCx, nCy, nCz}.