HPL_pipid HPL 2.2 Library Functions February 24, 2016
HPL_pipid Simplify the pivot vector.
computes an array IPID that contains the source and final
destination of matrix rows resulting from the application of N
interchanges as computed by the LU factorization with row partial
pivoting. The array IPID is such that the row of global index IPID(i)
should be mapped onto the row of global index IPID(i+1). Note that we
cannot really know the length of IPID a priori. However, we know that
this array is at least 2*N long, since there are N rows to swap and
broadcast. The length of this array must be smaller than or equal to
4*N, since every row is swapped with at most a single distinct remote
row. The algorithm constructing IPID goes as follows: Let IA be the
global index of the first row to be swapped.
For every row src IA + i with i in [0..N) to be swapped with row dst
such that dst is given by DPIV[i]:
Is row src the destination of a previous row of the current block,
that is, is there k odd such that IPID(k) is equal to src ?
Yes: update this destination with dst. For example, if the
pivot array is (0,2)(1,1)(2,5) ... , then when we swap rows 2 and 5,
we swap in fact row 0 and 5, i.e., row 0 goes to 5 and not 2 as it
was thought so far ...
No : add the pair (src,dst) at the end of IPID; row src has not
been moved yet.
Is row dst different from src the destination of a previous row of
the current block, i.e., is there k odd such that IPID(k) is equal to
Yes: update IPID(k) with src. For example, if the pivot array
is (0,5)(1,1)(2,5) ... , then when we swap rows 2 and 5, we swap in
fact row 2 and 0, i.e., row 0 goes to 2 and not 5 as it was thought
so far ...
No : add the pair (dst,src) at the end of IPID; row dst has not
been moved yet.
Note that when src is equal to dst, the pair (dst,src) should not be
added to IPID in order to avoid duplicated entries in this array.
During the construction of the array IPID, we make sure that the
first N entries are such that IPID(k) with k odd is equal to IA+k/2.
For k in [0..K/2), the row of global index IPID(2*k) should be
mapped onto the row of global index IPID(2*k+1).
PANEL (local input/output) HPL_T_panel *
On entry, PANEL points to the data structure containing the
K (global output) int *
On exit, K specifies the number of entries in IPID. K is at
least 2*N, and at most 4*N.
IPID (global output) int *
On entry, IPID is an array of length 4*N. On exit, the first
K entries of that array contain the src and final destination
resulting from the application of the N interchanges as
specified by DPIV. The pairs (src,dst) are contiguously
stored and sorted so that IPID(2*i+1) is equal to IA+i with i