PCGEQR2 - compute a QR factorization of a complex distributed M-by-N matrix sub(
A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R
- SUBROUTINE PCGEQR2(
- M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )
INTEGER IA, INFO, JA, LWORK, M, N INTEGER DESCA( * ) COMPLEX A( * ), TAU( * ),
WORK( * )
PCGEQR2 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. Notes
=====
Each global data object is described by an associated description vector. This
vector stores the information required to establish the mapping between an
object element and its corresponding process and memory location.
Let A be a generic term for any 2D block cyclicly distributed array. Such a
global array has an associated description vector DESCA. In the following
comments, the character _ should be read as "of the global array".
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
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.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
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( K ) denotes the number of elements of K that a process would receive if K
were distributed over the p processes of its process column.
Similarly, LOCc( K ) denotes the number of elements of K that a process would
receive if K were distributed over the q processes of its process row.
The values of LOCr() and LOCc() may be determined via a call to the ScaLAPACK
tool function, NUMROC:
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
- 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 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, 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 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 >= Mp0 + MAX( 1, Nq0 ), 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 (local output) INTEGER
- = 0: successful exit
< 0: If the i-th argument is an array and the j-entry had an illegal
value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an
illegal value, then INFO = -i.
The matrix Q is represented as a product of elementary reflectors
Q = 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'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and
v(i) = 1; v(i+1:m) is stored on exit in
A(ia+i:ia+m-1,ja+i-1), and tau in TAU(ja+i-1).