# FreeBSD Manual Pages

PDSYGS2(l) ) PDSYGS2(l)NAMEPDSYGS2 - reduce a real symmetric-definite generalized eigenproblem to standard formSYNOPSISSUBROUTINE PDSYGS2( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, DE- SCB, INFO ) CHARACTER UPLO INTEGER IA, IB, IBTYPE, INFO, JA, JB, N INTEGER DESCA( * ), DESCB( * ) DOUBLE PRECISION A( * ), B( * )PURPOSEPDSYGS2 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 vec- tor. This vector stores the information required to establish the map- ping 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 as- sume that its process grid has dimension p x q. LOCr( K ) denotes the number of elements of K that a process would re- ceive 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_AARGUMENTSIBTYPE (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 lead- ing N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangu- lar 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 sub- matrix 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 sub- matrix 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. 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. ScaLAPACK version 1.7 13 August 2001 PDSYGS2(l)

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