# FreeBSD Manual Pages

PZUNGQR(l) ) PZUNGQR(l)NAMEPZUNGQR - generate an M-by-N complex distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2)SYNOPSISSUBROUTINE PZUNGQR( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO ) INTEGER IA, INFO, JA, K, LWORK, M, N INTEGER DESCA( * ) COMPLEX*16 A( * ), TAU( * ), WORK( * )PURPOSEPZUNGQR generates an M-by-N complex distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by PZGEQRF. 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_AARGUMENTSM (global input) INTEGER The number of rows to be operated on i.e the number of rows of the distributed submatrix Q. M >= 0. N (global input) INTEGER The number of columns to be operated on i.e the number of col- umns of the distributed submatrix Q. M >= N >= 0. K (global input) INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On entry, the j-th column must contain the vector which defines the elementary reflector H(j), JA <= j <= JA+K-1, as returned by PZGEQRF in the K columns of its distributed matrix argument A(IA:*,JA:JA+K-1). On exit, this array contains the local pieces of the M-by-N distributed matrix Q. 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 input) COMPLEX*16, array, dimension LOCc(JA+K-1) This array contains the scalar factors TAU(j) of the elementary reflectors H(j) as returned by PZGEQRF. TAU is tied to the distributed matrix A. WORK (local workspace/local output) COMPLEX*16 array, dimension (LWORK) On exit, WORK(1) returns the minimal and op- timal LWORK. LWORK (local or global input) INTEGER The dimension of the array WORK. LWORK is local input and must be at least LWORK >= NB_A * ( NqA0 + MpA0 + NB_A ), where IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), INDXG2P and NUMROC 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 (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 PZUNGQR(l)

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