# FreeBSD Manual Pages

PZGETRS(l) ) PZGETRS(l)NAMEPZGETRS - solve a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) us- ing the LU factorization computed by PZGETRFSYNOPSISSUBROUTINE PZGETRS( TRANS, N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB, DESCB, INFO ) CHARACTER TRANS INTEGER IA, IB, INFO, JA, JB, N, NRHS INTEGER DESCA( * ), DESCB( * ), IPIV( * ) COMPLEX*16 A( * ), B( * )PURPOSEPZGETRS solves a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PZGETRF. sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A, A**T or A**H and sub( B ) denotes B(IB:IB+N-1,JB:JB+NRHS-1). 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_A This routine requires square block data decomposition ( MB_A=NB_A ).ARGUMENTSTRANS (global input) CHARACTER Specifies the form of the system of equations: = 'N': sub( A ) * X = sub( B ) (No transpose) = 'T': sub( A )**T * X = sub( B ) (Transpose) = 'C': sub( A )**H * X = sub( B ) (Conjugate transpose) N (global input) INTEGER The number of rows and columns to be operated on, i.e. the or- der of the distributed submatrix sub( A ). N >= 0. NRHS (global input) INTEGER The number of right hand sides, i.e., the number of columns of the distributed submatrix sub( B ). NRHS >= 0. A (local input) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). On en- try, this array contains the local pieces of the factors L and U from the factorization sub( A ) = P*L*U; the unit diagonal elements of L are not stored. 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. IPIV (local input) INTEGER array, dimension ( LOCr(M_A)+MB_A ) This array contains the pivoting information. IPIV(i) -> The global row local row i was swapped with. This array is tied to the distributed matrix A. B (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_B,LOCc(JB+NRHS-1)). On entry, the right hand sides sub( B ). On exit, sub( B ) is overwritten by the solution distributed matrix X. IB (global input) INTEGER The row index in the global array B indicating the first row of sub( B ). JB (global input) INTEGER The column index in the global array B indicating the first column of sub( B ). 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 PZGETRS(l)

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