table of contents
PDGERQF(l) | LAPACK routine (version 1.5) | PDGERQF(l) |
NAME¶
PDGERQF - compute a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * QSYNOPSIS¶
- SUBROUTINE PDGERQF(
- M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
- INTEGER
- IA, INFO, JA, LWORK, M, N
- INTEGER
- DESCA( * )
- DOUBLE
- PRECISION A( * ), TAU( * ), WORK( * )
PURPOSE¶
PDGERQF computes a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q.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¶
- M (global input) INTEGER
- The number of rows to be operated on, i.e. the number of rows of the distributed submatrix sub( A ). M >= 0.
- N (global input) INTEGER
- The number of columns to be operated on, i.e. the number of columns of the distributed submatrix sub( A ). 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, the local pieces of the M-by-N distributed matrix sub( A ) which is to be factored. On exit, if M <= N, the upper triangle of A( IA:IA+M-1, JA+N-M:JA+N-1 ) contains the M by M upper triangular matrix R; if M >= N, the elements on and above the (M-N)-th subdiagonal contain the M by N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent 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 LOCr(IA+M-1)
- This array contains the scalar factors of the elementary reflectors. 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 >= MB_A * ( Mp0 + Nq0 + MB_A ), where
- INFO (global output) INTEGER
- = 0: successful exit
FURTHER DETAILS¶
The matrix Q is represented as a product of elementary reflectorsQ = H(ia) H(ia+1) . . . H(ia+k-1), where k = min(m,n).
H(i) = I - tau * v * v'
12 May 1997 | LAPACK version 1.5 |