table of contents
PZGEQRF(l) | LAPACK routine (version 1.5) | PZGEQRF(l) |
NAME¶
PZGEQRF - compute a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * RSYNOPSIS¶
- SUBROUTINE PZGEQRF(
- M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
PURPOSE¶
PZGEQRF computes a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. NotesDTYPE_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¶
- 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) COMPLEX*16 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, the elements on and above the diagonal of sub( A ) contain the min(M,N) by N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal, with the array TAU, represent the unitary 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) COMPLEX*16, array, dimension
- LOCc(JA+MIN(M,N)-1). This array contains the scalar factors TAU of the elementary reflectors. TAU is tied to the distributed matrix A.
- WORK (local workspace/local output) COMPLEX*16 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_A * ( Mp0 + Nq0 + NB_A ), where IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ), Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ), and NUMROC, INDXG2P 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 elementary reflectorsQ = H(ja) H(ja+1) . . . H(ja+k-1), where k = min(m,n). Each H(i) has the form
H(j) = I - tau * v * v'
12 May 1997 | LAPACK version 1.5 |