table of contents
PSGEHD2(l) | LAPACK auxiliary routine (version 1.5) | PSGEHD2(l) |
NAME¶
PSGEHD2 - reduce a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tionSYNOPSIS¶
- SUBROUTINE PSGEHD2(
- N, ILO, IHI, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
- INTEGER
- IA, IHI, ILO, INFO, JA, LWORK, N
- INTEGER
- DESCA( * )
- REAL
- A( * ), TAU( * ), WORK( * )
PURPOSE¶
PSGEHD2 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)).
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+JLO-2 and JA+JHI:JA+N-1. See Further Details. If N > 0,
- A (local input/local output) REAL 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) REAL 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) REAL 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 + MAX( NpA0, NB )
- INFO (local 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 |