1 SUBROUTINE PCGEQRRV( 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* PCGEQRRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from Q, R 20* computed by PCGEQRF. 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 Q and R computed 90* by PCGEQRF. 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 104* LOCc(JA+MIN(M,N)-1). This array contains the scalar factors 105* TAU of the elementary reflectors computed by PCGEQRF. TAU 106* is tied to the distributed matrix A. 107* 108* WORK (local workspace) COMPLEX array, dimension (LWORK) 109* LWORK = NB_A * ( 2*Mp0 + Nq0 + NB_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* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 119* the subroutine BLACS_GRIDINFO. 120* 121* ===================================================================== 122* 123* .. Parameters .. 124 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 125 $ LLD_, MB_, M_, NB_, N_, RSRC_ 126 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 127 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 128 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 129 COMPLEX ONE, ZERO 130 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), 131 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 132* .. 133* .. Local Scalars .. 134 CHARACTER COLBTOP, ROWBTOP 135 INTEGER IACOL, IAROW, I, ICTXT, IIA, IPT, IPV, IPW, 136 $ IROFF, IV, J, JB, JJA, JL, JN, K, MP, MYCOL, 137 $ MYROW, NPCOL, NPROW 138* .. 139* .. Local Arrays .. 140 INTEGER DESCV( DLEN_ ) 141* .. 142* .. External Subroutines .. 143 EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCLACPY, 144 $ PCLARFB, PCLARFT, PCLASET, PB_TOPGET, 145 $ PB_TOPSET 146* .. 147* .. External Functions .. 148 INTEGER ICEIL, INDXG2P, NUMROC 149 EXTERNAL ICEIL, INDXG2P, NUMROC 150* .. 151* .. Intrinsic Functions .. 152 INTRINSIC MAX, MIN, MOD 153* .. 154* .. Executable Statements .. 155* 156* Get grid parameters 157* 158 ICTXT = DESCA( CTXT_ ) 159 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 160* 161 IROFF = MOD( IA-1, DESCA( MB_ ) ) 162 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 163 $ IAROW, IACOL ) 164 MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) 165 IPV = 1 166 IPT = IPV + MP * DESCA( NB_ ) 167 IPW = IPT + DESCA( NB_ ) * DESCA( NB_ ) 168 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 169 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 170 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'D-ring' ) 171 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) 172* 173 K = MIN( M, N ) 174 JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+K-1 ) 175 JL = MAX( ( (JA+K-2) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1, JA ) 176* 177 CALL DESCSET( DESCV, M+IROFF, DESCA( NB_ ), DESCA( MB_ ), 178 $ DESCA( NB_ ), IAROW, INDXG2P( JL, DESCA( NB_ ), 179 $ MYCOL, DESCA( CSRC_ ), NPCOL ), ICTXT, 180 $ MAX( 1, MP ) ) 181* 182 DO 10 J = JL, JN+1, -DESCA( NB_ ) 183 JB = MIN( JA+K-J, DESCA( NB_ ) ) 184 I = IA + J - JA 185 IV = 1 + J - JA + IROFF 186* 187* Compute upper triangular matrix T 188* 189 CALL PCLARFT( 'Forward', 'Columnwise', M-I+IA, JB, A, I, J, 190 $ DESCA, TAU, WORK( IPT ), WORK( IPW ) ) 191* 192* Copy Householder vectors into workspace 193* 194 CALL PCLACPY( 'Lower', M-I+IA, JB, A, I, J, DESCA, WORK( IPV ), 195 $ IV, 1, DESCV ) 196 CALL PCLASET( 'Upper', M-I+IA, JB, ZERO, ONE, WORK( IPV ), IV, 197 $ 1, DESCV ) 198* 199* Zeroes the strict lower triangular part of sub( A ) to get 200* block column of R 201* 202 CALL PCLASET( 'Lower', M-I+IA-1, JB, ZERO, ZERO, A, I+1, J, 203 $ DESCA ) 204* 205* Apply block Householder transformation 206* 207 CALL PCLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise', 208 $ M-I+IA, N-J+JA, JB, WORK( IPV ), IV, 1, DESCV, 209 $ WORK( IPT ), A, I, J, DESCA, WORK( IPW ) ) 210* 211 DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL ) 212* 213 10 CONTINUE 214* 215* Handle first block separately 216* 217 JB = JN - JA + 1 218* 219* Compute upper triangular matrix T 220* 221 CALL PCLARFT( 'Forward', 'Columnwise', M, JB, A, IA, JA, DESCA, 222 $ TAU, WORK( IPT ), WORK( IPW ) ) 223* 224* Copy Householder vectors into workspace 225* 226 CALL PCLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPV ), 227 $ IROFF+1, 1, DESCV ) 228 CALL PCLASET( 'Upper', M, JB, ZERO, ONE, WORK, IROFF+1, 1, DESCV ) 229* 230* Zeroes the strict lower triangular part of sub( A ) to get block 231* column of R 232* 233 CALL PCLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA ) 234* 235* Apply block Householder transformation 236* 237 CALL PCLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise', M, 238 $ N, JB, WORK( IPV ), IROFF+1, 1, DESCV, WORK( IPT ), 239 $ A, IA, JA, DESCA, WORK( IPW ) ) 240* 241 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 242 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 243* 244 RETURN 245* 246* End of PCGEQRRV 247* 248 END 249