table of contents
PDGEQLF(l) | LAPACK routine (version 1.5) | PDGEQLF(l) |
NAME¶
PDGEQLF - compute a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * LSYNOPSIS¶
- SUBROUTINE PDGEQLF(
- M, N, A, IA, JA, DESCA, TAU, WORK, LWORK,INFO )
PURPOSE¶
PDGEQLF computes a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. 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 rowsof the distributed submatrix sub( A ). M >= 0.
- N (global input) INTEGER
- The number of columns to be operated on, i.e. the number ofcolumns 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 lower triangle of the distributed submatrix A( IA+M-N:IA+M-1, JA:JA+N-1 ) contains the N-by-N lower triangular matrix L; if M <= N, the elements on and below the (N-M)-th superdiagonal contain the M by N lower trapezoidal matrix L; 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 thefirst 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-1)
- This array contains the scalar factors of the elementaryreflectors. 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 leastLWORK >= 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
FURTHERDETAILS¶
The matrix Q is represented as a product of elementary reflectorsQ = H(ja+k-1) . . . H(ja+1) H(ja), where k = min(m,n). Each H(i) has the form
H(i) = I - tau * v * v'
12 May 1997 | LAPACK version 1.5 |