slamsh(3) [debian man page]
SLAMSH(l) LAPACK auxiliary routine (version 1.5) SLAMSH(l) NAME
SLAMSH - send multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by sub- sequent shifts in an effort to maximize the number of bulges that can be sent through SYNOPSIS
SUBROUTINE SLAMSH ( S, LDS, NBULGE, JBLK, H, LDH, N, ULP ) INTEGER LDS, NBULGE, JBLK, LDH, N REAL ULP REAL S(LDS,*), H(LDH,*) PURPOSE
SLAMSH sends multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. SLAMSH should only be called when there are multiple shifts/bulges (NBULGE > 1) and the first shift is starting in the middle of an unreduced Hessenberg matrix because of two or more consecutive small subdiagonal elements. ARGUMENTS
S (local input/output) REAL array, (LDS,*) On entry, the matrix of shifts. Only the 2x2 diagonal of S is referenced. It is assumed that S has JBLK double shifts (size 2). On exit, the data is rearranged in the best order for applying. LDS (local input) INTEGER On entry, the leading dimension of S. Unchanged on exit. 1 < NBULGE <= JBLK <= LDS/2 NBULGE (local input/output) INTEGER On entry, the number of bulges to send through H ( >1 ). NBULGE should be less than the maximum determined (JBLK). 1 < NBULGE <= JBLK <= LDS/2 On exit, the maximum number of bulges that can be sent through. JBLK (local input) INTEGER On entry, the number of shifts determined for S. Unchanged on exit. H (local input/output) REAL array (LDH,N) On entry, the local matrix to apply the shifts on. H should be aligned so that the starting row is 2. On exit, the data is destroyed. LDS (local input) INTEGER On entry, the leading dimension of S. Unchanged on exit. N (local input) INTEGER On entry, the size of H. If all the bulges are expected to go through, N should be at least 4*NBULGE+2. Otherwise, NBULGE may be reduced by this routine. ULP (local input) REAL On entry, machine precision Unchanged on exit. Implemented by: G. Henry, May 1, 1997 LAPACK version 1.5 12 May 1997 SLAMSH(l)
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PSLASMSUB(l) LAPACK routine (version 1.5 ) PSLASMSUB(l) NAME
PSLASMSUB - look for a small subdiagonal element from the bottom of the matrix that it can safely set to zero SYNOPSIS
SUBROUTINE PSLASMSUB( A, DESCA, I, L, K, SMLNUM, BUF, LWORK ) INTEGER I, K, L, LWORK REAL SMLNUM INTEGER DESCA( * ) REAL A( * ), BUF( * ) PURPOSE
PSLASMSUB looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero. 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 col- umn. 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 ARGUMENTS
A (global input) REAL array, dimension (DESCA(LLD_),*) On entry, the Hessenberg matrix whose tridiagonal part is being scanned. Unchanged on exit. DESCA (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix A. I (global input) INTEGER The global location of the bottom of the unreduced submatrix of A. Unchanged on exit. L (global input) INTEGER The global location of the top of the unreduced submatrix of A. Unchanged on exit. K (global output) INTEGER On exit, this yields the bottom portion of the unreduced submatrix. This will satisfy: L <= M <= I-1. SMLNUM (global input) REAL On entry, a "small number" for the given matrix. Unchanged on exit. BUF (local output) REAL array of size LWORK. LWORK (global input) INTEGER On exit, LWORK is the size of the work buffer. This must be at least 2*Ceil( Ceil( (I-L)/HBL ) / LCM(NPROW,NPCOL) ) Here LCM is least common multiple, and NPROWxNPCOL is the logical grid size. Notes: This routine does a global maximum and must be called by all processes. This code is basically a parallelization of the following snip of LAPACK code from SLAHQR: Look for a single small subdiagonal element. DO 20 K = I, L + 1, -1 TST1 = ABS( H( K-1, K-1 ) ) + ABS( H( K, K ) ) IF( TST1.EQ.ZERO ) $ TST1 = SLANHS( '1', I-L+1, H( L, L ), LDH, WORK ) IF( ABS( H( K, K-1 ) ).LE.MAX( ULP*TST1, SMLNUM ) ) $ GO TO 30 20 CONTINUE 30 CONTINUE Implemented by: G. Henry, November 17, 1996 LAPACK version 1.5 12 May 1997 PSLASMSUB(l)