table of contents
PDGEHRD(l) | LAPACK routine (version 1.5) | PDGEHRD(l) |
NAME¶
PDGEHRD - reduce a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tionSYNOPSIS¶
- SUBROUTINE PDGEHRD(
- N, ILO, IHI, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
PURPOSE¶
PDGEHRD reduces a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tion: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1).DTYPE_A = 1.
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
array A.
array A.
the rows of the array.
the columns of the array.
row of the array A is distributed. CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
array. LLD_A >= MAX(1,LOCr(M_A)). Let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
ARGUMENTS¶
- N (global input) INTEGER
- The number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub( A ). N >= 0.
- ILO (global input) INTEGER
- IHI (global input) INTEGER It is assumed that sub( A ) is already upper triangular in rows IA:IA+ILO-2 and IA+IHI:IA+N-1 and columns JA:JA+ILO-2 and JA+IHI:JA+N-1. See Further Details. If N > 0,
- A (local input/local output) DOUBLE PRECISION pointer into the
- local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On entry, this array contains the local pieces of the N-by-N general distributed matrix sub( A ) to be reduced. On exit, the upper triangle and the first subdiagonal of sub( A ) are overwritten with the upper Hessenberg matrix H, and the ele- ments below the first subdiagonal, with the array TAU, repre- sent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. IA (global input) INTEGER The row index in the global array A indicating the first row of sub( A ).
- JA (global input) INTEGER
- The column index in the global array A indicating the first column of sub( A ).
- DESCA (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix A.
- TAU (local output) DOUBLE PRECISION array, dimension LOCc(JA+N-2)
- The scalar factors of the elementary reflectors (see Further Details). Elements JA:JA+ILO-2 and JA+IHI:JA+N-2 of TAU are set to zero. TAU is tied to the distributed matrix A.
- WORK (local workspace/local output) DOUBLE PRECISION array,
- dimension (LWORK) On exit, WORK( 1 ) returns the minimal and optimal LWORK.
- LWORK (local or global input) INTEGER
- The dimension of the array WORK. LWORK is local input and must be at least LWORK >= NB*NB + NB*MAX( IHIP+1, IHLP+INLQ ) where NB = MB_A = NB_A, IROFFA = MOD( IA-1, NB ), ICOFFA = MOD( JA-1, NB ), IOFF = MOD( IA+ILO-2, NB ), IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ), IHIP = NUMROC( IHI+IROFFA, NB, MYROW, IAROW, NPROW ), ILROW = INDXG2P( IA+ILO-1, NB, MYROW, RSRC_A, NPROW ), IHLP = NUMROC( IHI-ILO+IOFF+1, NB, MYROW, ILROW, NPROW ), ILCOL = INDXG2P( JA+ILO-1, NB, MYCOL, CSRC_A, NPCOL ), INLQ = NUMROC( N-ILO+IOFF+1, NB, MYCOL, ILCOL, NPCOL ), INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO. If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA.
- INFO (global output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The matrix Q is represented as a product of (ihi-ilo) elementary reflectorsQ = H(ilo) H(ilo+1) . . . H(ihi-1).
H(i) = I - tau * v * v'
12 May 1997 | LAPACK version 1.5 |