1 SUBROUTINE PCTZRZRV( 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* PCTZRZRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from T, Z 20* computed by PCTZRZF. 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 >= M >= 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 T and Z computed 90* by PCTZRZF. 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 PCTZRZF. 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 ZERO 128 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) 129* .. 130* .. Local Scalars .. 131 CHARACTER COLBTOP, ROWBTOP 132 INTEGER I, IACOL, IAROW, IB, ICOFF, ICTXT, IIA, IN, 133 $ IPT, IPV, IPW, JJA, JM1, JV, L, MYCOL, MYROW, 134 $ NPCOL, NPROW, NQ 135* .. 136* .. Local Arrays .. 137 INTEGER DESCV( DLEN_ ) 138* .. 139* .. External Subroutines .. 140 EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCLACPY, 141 $ PCLARZB, PCLARZT, PCLASET, PB_TOPGET, 142 $ PB_TOPSET 143* .. 144* .. External Functions .. 145 INTEGER ICEIL, NUMROC 146 EXTERNAL ICEIL, NUMROC 147* .. 148* .. Intrinsic Functions .. 149 INTRINSIC MAX, MIN, MOD 150* .. 151* .. Executable Statements .. 152* 153* Get grid parameters 154* 155 ICTXT = DESCA( CTXT_ ) 156 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 157* 158* Quick return if possible 159* 160 IF( N.LT.M ) 161 $ RETURN 162* 163 L = N - M 164 JM1 = JA + MIN( M+1, N ) - 1 165 IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+M-1 ) 166 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 167 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 168 $ IAROW, IACOL ) 169 NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) 170 IPV = 1 171 IPT = IPV + NQ * DESCA( MB_ ) 172 IPW = IPT + DESCA( MB_ ) * DESCA( MB_ ) 173 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 174 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 175 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 176 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) 177* 178 CALL DESCSET( DESCV, DESCA( MB_ ), N + ICOFF, DESCA( MB_ ), 179 $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) 180* 181* Handle first block separately 182* 183 IB = IN - IA + 1 184 JV = ICOFF + JM1 - JA + 1 185* 186* Compute upper triangular matrix T 187* 188 CALL PCLARZT( 'Backward', 'Rowwise', L, IB, A, IA, JM1, DESCA, 189 $ TAU, WORK( IPT ), WORK( IPW ) ) 190* 191* Copy Householder vectors into workspace 192* 193 CALL PCLACPY( 'All', IB, L, A, IA, JM1, DESCA, WORK( IPV ), 1, 194 $ JV, DESCV ) 195* 196* Save temporarily strict lower part of A(IA:IA+IB-1,JA:JA+IB-1) 197* 198 CALL PCLACPY( 'Lower', IB-1, IB-1, A, IA+1, JA, DESCA, 199 $ WORK( IPV ), 1, ICOFF+1, DESCV ) 200* 201* Zeroes the row panel of sub( A ) to get T(IA:IN,JA:JA+N-1) 202* 203 CALL PCLASET( 'All', IB, L, ZERO, ZERO, A, IA, JM1, DESCA ) 204 CALL PCLASET( 'Lower', IB-1, IB-1, ZERO, ZERO, A, IA+1, JA, 205 $ DESCA ) 206* 207* Apply block Householder transformation 208* 209 CALL PCLARZB( 'Right', 'Conjugate transpose', 'Backward', 210 $ 'Rowwise', IN-IA+1, N, IB, L, WORK( IPV ), 1, JV, 211 $ DESCV, WORK( IPT ), A, IA, JA, DESCA, WORK( IPW ) ) 212* 213* Restore strict lower part of A( IA:IA+IB-1, JA:JA+N-1 ) 214* 215 CALL PCLACPY( 'Lower', IB-1, IB-1, WORK( IPV ), 1, ICOFF+1, DESCV, 216 $ A, IA+1, JA, DESCA ) 217* 218 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 219* 220* Loop over the remaining row blocks 221* 222 DO 10 I = IN+1, IA+M-1, DESCA( MB_ ) 223 IB = MIN( IA+M-I, DESCA( MB_ ) ) 224* 225* Compute upper triangular matrix T 226* 227 CALL PCLARZT( 'Backward', 'Rowwise', L, IB, A, I, JM1, DESCA, 228 $ TAU, WORK( IPT ), WORK( IPW ) ) 229* 230* Copy Householder vectors into workspace 231* 232 CALL PCLACPY( 'All', IB, L, A, I, JM1, DESCA, WORK( IPV ), 1, 233 $ JV, DESCV ) 234* 235* Save temporarily strict lower part of A(I:I+IB-1,J:J+IB-1 ) 236* 237 CALL PCLACPY( 'Lower', IB-1, IB-1, A, I+1, JA+I-IA, DESCA, 238 $ WORK( IPV ), 1, ICOFF+1+I-IA, DESCV ) 239* 240* Zeoes the row panel of sub( A ) to get T(IA:I-1,JA+I-IA:JA+N-1) 241* 242 CALL PCLASET( 'All', IB, L, ZERO, ZERO, A, I, JM1, DESCA ) 243 CALL PCLASET( 'Lower', IB-1, IB-1, ZERO, ZERO, A, I+1, JA+I-IA, 244 $ DESCA ) 245* 246* Apply block Householder transformation 247* 248 CALL PCLARZB( 'Right', 'Conjugate transpose', 'Backward', 249 $ 'Rowwise', I+IB-IA, N-I+IA, IB, L, WORK( IPV ), 250 $ 1, JV, DESCV, WORK( IPT ), A, IA, JA+I-IA, DESCA, 251 $ WORK( IPW ) ) 252* 253 CALL PCLACPY( 'Lower', IB-1, IB-1, WORK( IPV ), 1, 254 $ ICOFF+1+I-IA, DESCV, A, I+1, JA+I-IA, DESCA ) 255* 256 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 257* 258 10 CONTINUE 259* 260 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 261 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 262* 263 RETURN 264* 265* End of PCTZRZRV 266* 267 END 268