

SUBROUTINE PSGEQL2(  M, N, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO ) 
INTEGER IA, INFO, JA, LWORK, M, N  
INTEGER DESCA( * )  
REAL A( * ), TAU( * ), WORK( * )  
PSGEQL2 computes a QL factorization of a real distributed MbyN matrix sub( A ) = A(IA:IA+M1,JA:JA+N1) = Q * L. 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) REAL pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N1)). On entry, the local pieces of the MbyN distributed matrix sub( A ) which is to be factored. On exit, if M >= N, the lower triangle of the distributed submatrix A( IA+MN:IA+M1, JA:JA+N1 ) contains the NbyN lower triangular matrix L; if M <= N, the elements on and below the (NM)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 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+N1) This array contains the scalar factors of the elementary reflectors. 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 >= Mp0 + MAX( 1, Nq0 ), where IROFF = MOD( IA1, MB_A ), ICOFF = MOD( JA1, 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 ith argument is an array and the jentry had an illegal value, then INFO = (i*100+j), if the ith argument is a scalar and had an illegal value, then INFO = i.
The matrix Q is represented as a product of elementary reflectorsQ = H(ja+k1) . . . H(ja+1) H(ja), where k = min(m,n).
Each H(i) has the form
H(i) = I  tau * v * v’
where tau is a real scalar, and v is a real vector with
v(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(ia:ia+mk+i2,ja+nk+i1), and tau in TAU(ja+nk+i1).
ScaLAPACK version 1.7  PSGEQL2 (l)  13 August 2001 
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