1 SUBROUTINE PCGERQRV( M, N, A, IA, JA, DESCA, TAU, WORK ) 2* 3* -- ScaLAPACK routine (version 1.7) -- 4* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 5* and University of California, Berkeley. 6* May 28, 2001 7* 8* .. Scalar Arguments .. 9 INTEGER IA, JA, M, N 10* .. 11* .. Array Arguments .. 12 INTEGER DESCA( * ) 13 COMPLEX A( * ), TAU( * ), WORK( * ) 14* .. 15* 16* Purpose 17* ======= 18* 19* PCGERQRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from R, Q 20* computed by PCGERQF. 21* 22* Notes 23* ===== 24* 25* Each global data object is described by an associated description 26* vector. This vector stores the information required to establish 27* the mapping between an object element and its corresponding process 28* and memory location. 29* 30* Let A be a generic term for any 2D block cyclicly distributed array. 31* Such a global array has an associated description vector DESCA. 32* In the following comments, the character _ should be read as 33* "of the global array". 34* 35* NOTATION STORED IN EXPLANATION 36* --------------- -------------- -------------------------------------- 37* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 38* DTYPE_A = 1. 39* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 40* the BLACS process grid A is distribu- 41* ted over. The context itself is glo- 42* bal, but the handle (the integer 43* value) may vary. 44* M_A (global) DESCA( M_ ) The number of rows in the global 45* array A. 46* N_A (global) DESCA( N_ ) The number of columns in the global 47* array A. 48* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 49* the rows of the array. 50* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 51* the columns of the array. 52* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 53* row of the array A is distributed. 54* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 55* first column of the array A is 56* distributed. 57* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 58* array. LLD_A >= MAX(1,LOCr(M_A)). 59* 60* Let K be the number of rows or columns of a distributed matrix, 61* and assume that its process grid has dimension p x q. 62* LOCr( K ) denotes the number of elements of K that a process 63* would receive if K were distributed over the p processes of its 64* process column. 65* Similarly, LOCc( K ) denotes the number of elements of K that a 66* process would receive if K were distributed over the q processes of 67* its process row. 68* The values of LOCr() and LOCc() may be determined via a call to the 69* ScaLAPACK tool function, NUMROC: 70* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 71* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 72* An upper bound for these quantities may be computed by: 73* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 74* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 75* 76* Arguments 77* ========= 78* 79* M (global input) INTEGER 80* The number of rows to be operated on, i.e. the number of rows 81* of the distributed submatrix sub( A ). M >= 0. 82* 83* N (global input) INTEGER 84* The number of columns to be operated on, i.e. the number of 85* columns of the distributed submatrix sub( A ). N >= 0. 86* 87* A (local input/local output) COMPLEX pointer into the 88* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). 89* On entry, sub( A ) contains the the factors R and Q computed 90* by PCGERQF. On exit, the original matrix is restored. 91* 92* IA (global input) INTEGER 93* The row index in the global array A indicating the first 94* row of sub( A ). 95* 96* JA (global input) INTEGER 97* The column index in the global array A indicating the 98* first column of sub( A ). 99* 100* DESCA (global and local input) INTEGER array of dimension DLEN_. 101* The array descriptor for the distributed matrix A. 102* 103* TAU (local input) COMPLEX, array, dimension LOCr(M_A). 104* This array contains the scalar factors TAU of the elementary 105* reflectors computed by PCGERQF. TAU is tied to the dis- 106* tributed matrix A. 107* 108* WORK (local workspace) COMPLEX array, dimension (LWORK) 109* LWORK = MB_A * ( Mp0 + 2*Nq0 + MB_A ), where 110* Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ) * NB_A, 111* Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ) * MB_A, 112* IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), 113* IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 114* NPROW ), 115* IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 116* NPCOL ), 117* and NUMROC, INDXG2P are ScaLAPACK tool functions. 118* 119* ===================================================================== 120* 121* .. Parameters .. 122 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 123 $ LLD_, MB_, M_, NB_, N_, RSRC_ 124 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 125 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 126 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 127 COMPLEX ONE, ZERO 128 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), 129 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 130* .. 131* .. Local Scalars .. 132 CHARACTER COLBTOP, ROWBTOP 133 INTEGER I, IACOL, IAROW, IB, ICOFF, ICTXT, IIA, IN, 134 $ IPT, IPV, IPW, JJA, JV, K, MYCOL, MYROW, NPCOL, 135 $ NPROW, NQ 136* .. 137* .. Local Arrays .. 138 INTEGER DESCV( DLEN_ ) 139* .. 140* .. External Subroutines .. 141 EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCLACPY, 142 $ PCLARFB, PCLARFT, PCLASET, PB_TOPGET, 143 $ PB_TOPSET 144* .. 145* .. External Functions .. 146 INTEGER ICEIL, NUMROC 147 EXTERNAL ICEIL, NUMROC 148* .. 149* .. Intrinsic Functions .. 150 INTRINSIC MAX, MIN, MOD 151* .. 152* .. Executable Statements .. 153* 154* Get grid parameters 155* 156 ICTXT = DESCA( CTXT_ ) 157 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 158* 159 K = MIN( M, N ) 160 IN = MIN( ICEIL( IA+M-K, DESCA( MB_ ) ) * DESCA( MB_ ), IA+M-1 ) 161* 162 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 163 CALL INFOG2L( IA+M-K, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, 164 $ IIA, JJA, IAROW, IACOL ) 165 NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) 166 IPV = 1 167 IPT = IPV + NQ * DESCA( MB_ ) 168 IPW = IPT + DESCA( MB_ ) * DESCA( MB_ ) 169 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 170 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 171 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 172 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) 173* 174 CALL DESCSET( DESCV, DESCA( MB_), N + ICOFF, DESCA( MB_ ), 175 $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) 176* 177* Handle first block separately 178* 179 IB = IN - IA - M + K + 1 180 JV = 1 + N - K + ICOFF 181* 182* Compute upper triangular matrix T 183* 184 CALL PCLARFT( 'Backward', 'Rowwise', N-M+IN-IA+1, IB, A, IA+M-K, 185 $ JA, DESCA, TAU, WORK( IPT ), WORK( IPW ) ) 186* 187* Copy Householder vectors into workspace 188* 189 CALL PCLACPY( 'All', IB, N-M+IN-IA+1, A, IA+M-K, JA, DESCA, 190 $ WORK( IPV ), 1, ICOFF+1, DESCV ) 191 CALL PCLASET( 'Upper', IB, IB, ZERO, ONE, WORK( IPV ), 1, JV, 192 $ DESCV ) 193* 194* Zeoes the strict lower triangular part of sub( A ) to get block 195* column of R 196* 197 CALL PCLASET( 'All', IB, N-K, ZERO, ZERO, A, IA+M-K, JA, 198 $ DESCA ) 199 CALL PCLASET( 'Lower', IB-1, IB, ZERO, ZERO, A, IA+M-K+1, 200 $ JA+N-K, DESCA ) 201* 202* Apply block Householder transformation 203* 204 CALL PCLARFB( 'Right', 'Conjugate transpose', 'Backward', 205 $ 'Rowwise', IN-IA+1, N-M+IN-IA+1, IB, WORK( IPV ), 1, 206 $ ICOFF+1, DESCV, WORK( IPT ), A, IA, JA, DESCA, 207 $ WORK( IPW ) ) 208* 209 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 210* 211* Loop over the remaining row blocks 212* 213 DO 10 I = IN+1, IA+M-1, DESCA( MB_ ) 214 IB = MIN( IA+M-I, DESCA( MB_ ) ) 215 JV = 1 + N - M + I - IA + ICOFF 216* 217* Compute upper triangular matrix T 218* 219 CALL PCLARFT( 'Backward', 'Rowwise', N-M+I+IB-IA, IB, A, I, JA, 220 $ DESCA, TAU, WORK( IPT ), WORK( IPW ) ) 221* 222* Copy Householder vectors into workspace 223* 224 CALL PCLACPY( 'All', IB, N-M+I+IB-IA, A, I, JA, DESCA, 225 $ WORK( IPV ), 1, ICOFF+1, DESCV ) 226 CALL PCLASET( 'Upper', IB, IB, ZERO, ONE, WORK( IPV ), 1, JV, 227 $ DESCV ) 228* 229* Zeoes the strict Lower triangular part of sub( A ) to get 230* block column of R 231* 232 CALL PCLASET( 'All', IB, N-M+I-IA, ZERO, ZERO, A, I, JA, 233 $ DESCA ) 234 CALL PCLASET( 'Lower', IB-1, IB, ZERO, ZERO, A, I+1, 235 $ JA+N-M+I-IA, DESCA ) 236* 237* Apply block Householder transformation 238* 239 CALL PCLARFB( 'Right', 'Conjugate transpose', 'Backward', 240 $ 'Rowwise', I+IB-IA, N-M+I+IB-IA, IB, WORK( IPV ), 241 $ 1, ICOFF+1, DESCV, WORK( IPT ), A, IA, JA, DESCA, 242 $ WORK( IPW ) ) 243* 244 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 245* 246 10 CONTINUE 247* 248 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 249 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 250* 251 RETURN 252* 253* End of PCGERQRV 254* 255 END 256