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| 2 | 1 | equemene | <HEAD>
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| 3 | 1 | equemene | <TITLE>HPL_pipid HPL 2.0 Library Functions September 10, 2008</TITLE> |
| 4 | 1 | equemene | </HEAD>
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| 8 | 1 | equemene | |
| 9 | 1 | equemene | <H1>Name</H1> |
| 10 | 1 | equemene | <B>HPL_pipid</B> Simplify the pivot vector. |
| 11 | 1 | equemene | |
| 12 | 1 | equemene | <H1>Synopsis</H1> |
| 13 | 1 | equemene | <CODE>#include "hpl.h"</CODE><BR><BR> |
| 14 | 1 | equemene | <CODE>void</CODE> |
| 15 | 1 | equemene | <CODE>HPL_pipid(</CODE> |
| 16 | 1 | equemene | <CODE>HPL_T_panel *</CODE> |
| 17 | 1 | equemene | <CODE>PANEL</CODE>, |
| 18 | 1 | equemene | <CODE>int *</CODE> |
| 19 | 1 | equemene | <CODE>K</CODE>, |
| 20 | 1 | equemene | <CODE>int *</CODE> |
| 21 | 1 | equemene | <CODE>IPID</CODE> |
| 22 | 1 | equemene | <CODE>);</CODE> |
| 23 | 1 | equemene | |
| 24 | 1 | equemene | <H1>Description</H1> |
| 25 | 1 | equemene | <B>HPL_pipid</B> |
| 26 | 1 | equemene | computes an array IPID that contains the source and final |
| 27 | 1 | equemene | destination of matrix rows resulting from the application of N |
| 28 | 1 | equemene | interchanges as computed by the LU factorization with row partial |
| 29 | 1 | equemene | pivoting. The array IPID is such that the row of global index IPID(i) |
| 30 | 1 | equemene | should be mapped onto the row of global index IPID(i+1). Note that we |
| 31 | 1 | equemene | cannot really know the length of IPID a priori. However, we know that |
| 32 | 1 | equemene | this array is at least 2*N long, since there are N rows to swap and |
| 33 | 1 | equemene | broadcast. The length of this array must be smaller than or equal to |
| 34 | 1 | equemene | 4*N, since every row is swapped with at most a single distinct remote |
| 35 | 1 | equemene | row. The algorithm constructing IPID goes as follows: Let IA be the |
| 36 | 1 | equemene | global index of the first row to be swapped. |
| 37 | 1 | equemene | |
| 38 | 1 | equemene | For every row src IA + i with i in [0..N) to be swapped with row dst |
| 39 | 1 | equemene | such that dst is given by DPIV[i]: |
| 40 | 1 | equemene | |
| 41 | 1 | equemene | Is row src the destination of a previous row of the current block, |
| 42 | 1 | equemene | that is, is there k odd such that IPID(k) is equal to src ? |
| 43 | 1 | equemene | Yes: update this destination with dst. For example, if the |
| 44 | 1 | equemene | pivot array is (0,2)(1,1)(2,5) ... , then when we swap rows 2 and 5, |
| 45 | 1 | equemene | we swap in fact row 0 and 5, i.e., row 0 goes to 5 and not 2 as it |
| 46 | 1 | equemene | was thought so far ... |
| 47 | 1 | equemene | No : add the pair (src,dst) at the end of IPID; row src has not |
| 48 | 1 | equemene | been moved yet. |
| 49 | 1 | equemene | |
| 50 | 1 | equemene | Is row dst different from src the destination of a previous row of |
| 51 | 1 | equemene | the current block, i.e., is there k odd such that IPID(k) is equal to |
| 52 | 1 | equemene | dst ? |
| 53 | 1 | equemene | Yes: update IPID(k) with src. For example, if the pivot array |
| 54 | 1 | equemene | is (0,5)(1,1)(2,5) ... , then when we swap rows 2 and 5, we swap in |
| 55 | 1 | equemene | fact row 2 and 0, i.e., row 0 goes to 2 and not 5 as it was thought |
| 56 | 1 | equemene | so far ... |
| 57 | 1 | equemene | No : add the pair (dst,src) at the end of IPID; row dst has not |
| 58 | 1 | equemene | been moved yet. |
| 59 | 1 | equemene | |
| 60 | 1 | equemene | Note that when src is equal to dst, the pair (dst,src) should not be |
| 61 | 1 | equemene | added to IPID in order to avoid duplicated entries in this array. |
| 62 | 1 | equemene | During the construction of the array IPID, we make sure that the |
| 63 | 1 | equemene | first N entries are such that IPID(k) with k odd is equal to IA+k/2. |
| 64 | 1 | equemene | For k in [0..K/2), the row of global index IPID(2*k) should be |
| 65 | 1 | equemene | mapped onto the row of global index IPID(2*k+1). |
| 66 | 1 | equemene | |
| 67 | 1 | equemene | <H1>Arguments</H1> |
| 68 | 1 | equemene | <PRE>
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| 69 | 1 | equemene | PANEL (local input/output) HPL_T_panel * |
| 70 | 1 | equemene | On entry, PANEL points to the data structure containing the |
| 71 | 1 | equemene | panel information. |
| 72 | 1 | equemene | </PRE>
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| 73 | 1 | equemene | <PRE>
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| 74 | 1 | equemene | K (global output) int * |
| 75 | 1 | equemene | On exit, K specifies the number of entries in IPID. K is at |
| 76 | 1 | equemene | least 2*N, and at most 4*N. |
| 77 | 1 | equemene | </PRE>
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| 78 | 1 | equemene | <PRE>
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| 79 | 1 | equemene | IPID (global output) int * |
| 80 | 1 | equemene | On entry, IPID is an array of length 4*N. On exit, the first |
| 81 | 1 | equemene | K entries of that array contain the src and final destination |
| 82 | 1 | equemene | resulting from the application of the N interchanges as |
| 83 | 1 | equemene | specified by DPIV. The pairs (src,dst) are contiguously |
| 84 | 1 | equemene | stored and sorted so that IPID(2*i+1) is equal to IA+i with i |
| 85 | 1 | equemene | in [0..N) |
| 86 | 1 | equemene | </PRE>
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| 87 | 1 | equemene | |
| 88 | 1 | equemene | <H1>See Also</H1> |
| 89 | 1 | equemene | <A HREF="HPL_pdlaswp00N.html">HPL_pdlaswp00N</A>, |
| 90 | 1 | equemene | <A HREF="HPL_pdlaswp00T.html">HPL_pdlaswp00T</A>, |
| 91 | 1 | equemene | <A HREF="HPL_pdlaswp01N.html">HPL_pdlaswp01N</A>, |
| 92 | 1 | equemene | <A HREF="HPL_pdlaswp01T.html">HPL_pdlaswp01T</A>. |
| 93 | 1 | equemene | |
| 94 | 1 | equemene | </BODY>
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| 95 | 1 | equemene | </HTML> |