pdsygst(3)
NAME
PDSYGST - reduce a real symmetric-definite generalized eigenproblem to
standard form
SYNOPSIS
SUBROUTINE PDSYGST( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB,
DESCB, SCALE, INFO )
CHARACTER UPLO
INTEGER IA, IB, IBTYPE, INFO, JA, JB, N
DOUBLE PRECISION SCALE
INTEGER DESCA( * ), DESCB( * )
DOUBLE PRECISION A( * ), B( * )
PURPOSE
PDSYGST reduces a real symmetric-definite generalized eigenproblem to
standard form.
In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B
) denotes B( IB:IB+N-1, JB:JB+N-1 ).
If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, and sub(
A ) is overwritten by inv(U**T)*sub( A )*inv(U) or inv(L)*sub( A
)*inv(L**T)
If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or
sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by U*sub( A
)*U**T or L**T*sub( A )*L.
sub( B ) must have been previously factorized as U**T*U or L*L**T by
PDPOTRF.
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 distributed over. The context itself is global, 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
ARGUMENTS
- IBTYPE (global input) INTEGER
- = 1: compute inv(U**T)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L**T); = 2 or 3: compute U*sub( A )*U**T or L**T*sub( A )*L.
- UPLO (global input) CHARACTER
- = 'U': Upper triangle of sub( A ) is stored and sub( B ) is factored as U**T*U; = 'L': Lower triangle of sub( A ) is stored and sub( B ) is factored as L*L**T.
- N (global input) INTEGER
- The order of the matrices sub( A ) and sub( B ). 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, this array contains the local pieces of the N-by-N symmetric distributed matrix sub( A ). If UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.
- On exit, if INFO = 0, the transformed matrix, stored in the same format as sub( A ).
- IA (global input) INTEGER
- A's global row index, which points to the beginning of the submatrix which is to be operated on.
- JA (global input) INTEGER
- A's global column index, which points to the beginning of the submatrix which is to be operated on.
- DESCA (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix A.
- B (local input) DOUBLE PRECISION pointer into the local memory
- to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry, this array contains the local pieces of the triangular factor from the Cholesky factorization of sub( B ), as returned by PDPOTRF.
- IB (global input) INTEGER
- B's global row index, which points to the beginning of the submatrix which is to be operated on.
- JB (global input) INTEGER
- B's global column index, which points to the beginning of the submatrix which is to be operated on.
- DESCB (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix B.
- SCALE (global output) DOUBLE PRECISION
- Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. At present, SCALE is always returned as 1.0, it is returned here to allow for future enhancement.
- INFO (global 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.