1 SUBROUTINE PDGETRRV( M, N, A, IA, JA, DESCA, IPIV, 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( * ), IPIV( * ) 13 DOUBLE PRECISION A( * ), WORK( * ) 14* .. 15* 16* Purpose 17* ======= 18* 19* PDGETRRV reforms sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from the 20* triangular matrices L and U returned by PDGETRF. It multiplies 21* an upper triangular matrix stored in the upper triangle of sub( A ) 22* times the unit lower triangular matrix stored in the lower triangle. 23* To accomplish this, the routine basically performs the PDGETRF 24* routine in reverse. 25* 26* It computes L*U first, and then apply P: P*L*U => sub( A ). In the 27* J-th loop, the block column (or column panel), which has the lower 28* triangular unit matrix L is multiplied with the block row (or row 29* panel), which contains the upper triangular matrix U. 30* 31* ( L1 ) ( 0 0 ) ( L1*U1 L1*U2 ) 32* A` = L * U + A` = ( ) * (U1 U2) + ( ) = ( ) 33* ( L2 ) ( 0 A`) ( L2*U1 L2*U2+A` ) 34* 35* where L1 is a lower unit triangular matrix and U1 is an upper 36* triangular matrix. 37* 38* Notes 39* ===== 40* 41* Each global data object is described by an associated description 42* vector. This vector stores the information required to establish 43* the mapping between an object element and its corresponding process 44* and memory location. 45* 46* Let A be a generic term for any 2D block cyclicly distributed array. 47* Such a global array has an associated description vector DESCA. 48* In the following comments, the character _ should be read as 49* "of the global array". 50* 51* NOTATION STORED IN EXPLANATION 52* --------------- -------------- -------------------------------------- 53* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 54* DTYPE_A = 1. 55* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 56* the BLACS process grid A is distribu- 57* ted over. The context itself is glo- 58* bal, but the handle (the integer 59* value) may vary. 60* M_A (global) DESCA( M_ ) The number of rows in the global 61* array A. 62* N_A (global) DESCA( N_ ) The number of columns in the global 63* array A. 64* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 65* the rows of the array. 66* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 67* the columns of the array. 68* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 69* row of the array A is distributed. 70* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 71* first column of the array A is 72* distributed. 73* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 74* array. LLD_A >= MAX(1,LOCr(M_A)). 75* 76* Let K be the number of rows or columns of a distributed matrix, 77* and assume that its process grid has dimension p x q. 78* LOCr( K ) denotes the number of elements of K that a process 79* would receive if K were distributed over the p processes of its 80* process column. 81* Similarly, LOCc( K ) denotes the number of elements of K that a 82* process would receive if K were distributed over the q processes of 83* its process row. 84* The values of LOCr() and LOCc() may be determined via a call to the 85* ScaLAPACK tool function, NUMROC: 86* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 87* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 88* An upper bound for these quantities may be computed by: 89* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 90* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 91* 92* Arguments 93* ========= 94* 95* M (global input) INTEGER 96* The number of rows to be operated on, i.e. the number of rows 97* of the distributed submatrix sub( A ). M >= 0. 98* 99* N (global input) INTEGER 100* The number of columns to be operated on, i.e. the number of 101* columns of the distributed submatrix sub( A ). N >= 0. 102* 103* A (local input/local output) DOUBLE PRECISION pointer into the 104* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). 105* On entry, the local pieces of the distributed matrix sub( A ) 106* contains the the factors L and U from the factorization 107* sub( A ) = P*L*U; the unit diagonal elements of L are not 108* stored. On exit, the original distributed matrix sub( A ) 109* is restored. 110* 111* IA (global input) INTEGER 112* The row index in the global array A indicating the first 113* row of sub( A ). 114* 115* JA (global input) INTEGER 116* The column index in the global array A indicating the 117* first column of sub( A ). 118* 119* DESCA (global and local input) INTEGER array of dimension DLEN_. 120* The array descriptor for the distributed matrix A. 121* 122* IPIV (local input) INTEGER array, dimension ( LOCr(M_A)+MB_A ) 123* This array contains the pivoting information. 124* IPIV(i) -> The global row local row i was swapped with. 125* This array is tied to the distributed matrix A. 126* 127* WORK (local workspace) DOUBLE PRECISION array of dimension (LWORK) 128* LWORK >= MpA0 * NB_A + NqA0 * MB_A, where 129* 130* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), 131* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), 132* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), 133* MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), 134* NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), 135* 136* WORK is used to store a block of columns of L, and a block of 137* rows of U. INDXG2P and NUMROC are ScaLAPACK tool functions; 138* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 139* the subroutine BLACS_GRIDINFO. 140* 141* ===================================================================== 142* 143* .. Parameters .. 144 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 145 $ LLD_, MB_, M_, NB_, N_, RSRC_ 146 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 147 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 148 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 149 DOUBLE PRECISION ONE, ZERO 150 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 151* .. 152* .. Local Scalars .. 153 CHARACTER COLBTOP, ROWBTOP 154 INTEGER IACOL, IAROW, ICTXT, IL, IPL, IPU, IROFF, J, 155 $ JB, JL, JN, MN, MP, MYCOL, MYROW, NPCOL, NPROW 156* .. Local Arrays .. 157 INTEGER DESCIP( DLEN_ ), DESCL( DLEN_ ), 158 $ DESCU( DLEN_ ), IDUM( 1 ) 159* .. 160* .. External Subroutines .. 161 EXTERNAL BLACS_GRIDINFO, DESCSET, PDGEMM, PDLACPY, 162 $ PDLAPIV, PDLASET, PB_TOPGET, PB_TOPSET 163* .. 164* .. External Functions .. 165 INTEGER ICEIL, INDXG2P, NUMROC 166 EXTERNAL ICEIL, INDXG2P, NUMROC 167* .. 168* .. Intrinsic Functions .. 169 INTRINSIC MAX, MIN, MOD 170* .. 171* .. Executable Statements .. 172* 173* Get grid parameters. 174* 175 ICTXT = DESCA( CTXT_ ) 176 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 177* 178 IROFF = MOD( IA-1, DESCA( MB_ ) ) 179 IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) 180 MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) 181 IPL = 1 182 IPU = IPL + MP * DESCA( NB_ ) 183 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 184 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 185 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' ) 186 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) 187* 188* Define array descriptors for L and U 189* 190 MN = MIN( M, N ) 191 IL = MAX( ( ( IA+MN-2 ) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) 192 JL = MAX( ( ( JA+MN-2 ) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1, JA ) 193 JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+MN-1 ) 194 IAROW = INDXG2P( IL, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) 195 IACOL = INDXG2P( JL, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL ) 196* 197 CALL DESCSET( DESCL, IA+M-IL, DESCA( NB_ ), DESCA( MB_ ), 198 $ DESCA( NB_ ), IAROW, IACOL, ICTXT, MAX( 1, MP ) ) 199* 200 CALL DESCSET( DESCU, DESCA( MB_ ), JA+N-JL, DESCA( MB_ ), 201 $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) 202* 203 CALL DESCSET( DESCIP, DESCA( M_ ) + DESCA( MB_ )*NPROW, 1, 204 $ DESCA( MB_ ), 1, DESCA( RSRC_ ), MYCOL, ICTXT, 205 $ NUMROC( DESCA( M_ ), DESCA( MB_ ), MYROW, 206 $ DESCA( RSRC_ ), NPROW ) + DESCA( MB_ ) ) 207* 208* 209 DO 10 J = JL, JN+1, -DESCA( NB_ ) 210* 211 JB = MIN( JA+MN-J, DESCA( NB_ ) ) 212* 213* Copy unit lower triangular part of sub( A ) into WORK 214* 215 CALL PDLACPY( 'Lower', M-IL+IA, JB, A, IL, J, DESCA, 216 $ WORK( IPL ), 1, 1, DESCL ) 217 CALL PDLASET( 'Upper', M-IL+IA, JB, ZERO, ONE, WORK( IPL ), 218 $ 1, 1, DESCL ) 219* 220* Copy upper triangular part of sub( A ) into WORK(IPU) 221* 222 CALL PDLACPY( 'Upper', JB, JA+N-J, A, IL, J, DESCA, 223 $ WORK( IPU ), 1, 1, DESCU ) 224 CALL PDLASET( 'Lower', JB-1, JA+N-J, ZERO, ZERO, 225 $ WORK( IPU ), 2, 1, DESCU ) 226* 227* Zero the strict lower triangular piece of the current block. 228* 229 CALL PDLASET( 'Lower', IA+M-IL-1, JB, ZERO, ZERO, A, IL+1, J, 230 $ DESCA ) 231* 232* Zero the upper triangular piece of the current block. 233* 234 CALL PDLASET( 'Upper', JB, JA+N-J, ZERO, ZERO, A, IL, J, 235 $ DESCA ) 236* 237* Update the matrix sub( A ). 238* 239 CALL PDGEMM( 'No transpose', 'No transpose', IA+M-IL, 240 $ JA+N-J, JB, ONE, WORK( IPL ), 1, 1, DESCL, 241 $ WORK( IPU ), 1, 1, DESCU, ONE, A, IL, J, DESCA ) 242* 243 IL = IL - DESCA( MB_ ) 244 DESCL( M_ ) = DESCL( M_ ) + DESCL( MB_ ) 245 DESCL( RSRC_ ) = MOD( DESCL( RSRC_ ) + NPROW - 1, NPROW ) 246 DESCL( CSRC_ ) = MOD( DESCL( CSRC_ ) + NPCOL - 1, NPCOL ) 247 DESCU( N_ ) = DESCU( N_ ) + DESCU( NB_ ) 248 DESCU( RSRC_ ) = DESCL( RSRC_ ) 249 DESCU( CSRC_ ) = DESCL( CSRC_ ) 250* 251 10 CONTINUE 252* 253* Handle first block separately 254* 255 JB = MIN( JN-JA+1, DESCA( NB_ ) ) 256* 257* Copy unit lower triangular part of sub( A ) into WORK 258* 259 CALL PDLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPL ), 260 $ 1, 1, DESCL ) 261 CALL PDLASET( 'Upper', M, JB, ZERO, ONE, WORK( IPL ), 1, 1, 262 $ DESCL ) 263* 264* Copy upper triangular part of sub( A ) into WORK(IPU) 265* 266 CALL PDLACPY( 'Upper', JB, N, A, IA, JA, DESCA, WORK( IPU ), 1, 267 $ 1, DESCU ) 268 CALL PDLASET( 'Lower', JB-1, N, ZERO, ZERO, WORK( IPU ), 2, 1, 269 $ DESCU ) 270* 271* Zero the strict lower triangular piece of the current block. 272* 273 CALL PDLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA ) 274* 275* Zero the upper triangular piece of the current block. 276* 277 CALL PDLASET( 'Upper', JB, N, ZERO, ZERO, A, IA, JA, DESCA ) 278* 279* Update the matrix sub( A ). 280* 281 CALL PDGEMM( 'No transpose', 'No transpose', M, N, JB, ONE, 282 $ WORK( IPL ), 1, 1, DESCL, WORK( IPU ), 1, 1, 283 $ DESCU, ONE, A, IA, JA, DESCA ) 284* 285* Apply pivots so that sub( A ) = P*L*U 286* 287 CALL PDLAPIV( 'Backward', 'Row', 'Col', MIN( M, N ), N, A, IA, JA, 288 $ DESCA, IPIV, IA, 1, DESCIP, IDUM ) 289* 290 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 291 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 292* 293 RETURN 294* 295* End of PDGETRRV 296* 297 END 298