1 SUBROUTINE PZUNGR2( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, 2 $ INFO ) 3* 4* -- ScaLAPACK routine (version 1.7) -- 5* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 6* and University of California, Berkeley. 7* May 25, 2001 8* 9* .. Scalar Arguments .. 10 INTEGER IA, INFO, JA, K, LWORK, M, N 11* .. 12* .. Array Arguments .. 13 INTEGER DESCA( * ) 14 COMPLEX*16 A( * ), TAU( * ), WORK( * ) 15* .. 16* 17* Purpose 18* ======= 19* 20* PZUNGR2 generates an M-by-N complex distributed matrix Q denoting 21* A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the 22* last M rows of a product of K elementary reflectors of order N 23* 24* Q = H(1)' H(2)' . . . H(k)' 25* 26* as returned by PZGERQF. 27* 28* Notes 29* ===== 30* 31* Each global data object is described by an associated description 32* vector. This vector stores the information required to establish 33* the mapping between an object element and its corresponding process 34* and memory location. 35* 36* Let A be a generic term for any 2D block cyclicly distributed array. 37* Such a global array has an associated description vector DESCA. 38* In the following comments, the character _ should be read as 39* "of the global array". 40* 41* NOTATION STORED IN EXPLANATION 42* --------------- -------------- -------------------------------------- 43* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 44* DTYPE_A = 1. 45* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 46* the BLACS process grid A is distribu- 47* ted over. The context itself is glo- 48* bal, but the handle (the integer 49* value) may vary. 50* M_A (global) DESCA( M_ ) The number of rows in the global 51* array A. 52* N_A (global) DESCA( N_ ) The number of columns in the global 53* array A. 54* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 55* the rows of the array. 56* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 57* the columns of the array. 58* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 59* row of the array A is distributed. 60* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 61* first column of the array A is 62* distributed. 63* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 64* array. LLD_A >= MAX(1,LOCr(M_A)). 65* 66* Let K be the number of rows or columns of a distributed matrix, 67* and assume that its process grid has dimension p x q. 68* LOCr( K ) denotes the number of elements of K that a process 69* would receive if K were distributed over the p processes of its 70* process column. 71* Similarly, LOCc( K ) denotes the number of elements of K that a 72* process would receive if K were distributed over the q processes of 73* its process row. 74* The values of LOCr() and LOCc() may be determined via a call to the 75* ScaLAPACK tool function, NUMROC: 76* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 77* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 78* An upper bound for these quantities may be computed by: 79* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 80* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 81* 82* Arguments 83* ========= 84* 85* M (global input) INTEGER 86* The number of rows to be operated on i.e the number of rows 87* of the distributed submatrix Q. M >= 0. 88* 89* N (global input) INTEGER 90* The number of columns to be operated on i.e the number of 91* columns of the distributed submatrix Q. N >= M >= 0. 92* 93* K (global input) INTEGER 94* The number of elementary reflectors whose product defines the 95* matrix Q. M >= K >= 0. 96* 97* A (local input/local output) COMPLEX*16 pointer into the 98* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). 99* On entry, the i-th row must contain the vector which defines 100* the elementary reflector H(i), IA+M-K <= i <= IA+M-1, as 101* returned by PZGERQF in the K rows of its distributed 102* matrix argument A(IA+M-K:IA+M-1,JA:*). On exit, this array 103* contains the local pieces of the M-by-N distributed matrix Q. 104* 105* IA (global input) INTEGER 106* The row index in the global array A indicating the first 107* row of sub( A ). 108* 109* JA (global input) INTEGER 110* The column index in the global array A indicating the 111* first column of sub( A ). 112* 113* DESCA (global and local input) INTEGER array of dimension DLEN_. 114* The array descriptor for the distributed matrix A. 115* 116* TAU (local input) COMPLEX*16, array, dimension LOCr(IA+M-1) 117* This array contains the scalar factors TAU(i) of the 118* elementary reflectors H(i) as returned by PZGERQF. 119* TAU is tied to the distributed matrix A. 120* 121* WORK (local workspace/local output) COMPLEX*16 array, 122* dimension (LWORK) 123* On exit, WORK(1) returns the minimal and optimal LWORK. 124* 125* LWORK (local or global input) INTEGER 126* The dimension of the array WORK. 127* LWORK is local input and must be at least 128* LWORK >= NqA0 + MAX( 1, MpA0 ), 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* INDXG2P and NUMROC are ScaLAPACK tool functions; 137* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 138* the subroutine BLACS_GRIDINFO. 139* 140* If LWORK = -1, then LWORK is global input and a workspace 141* query is assumed; the routine only calculates the minimum 142* and optimal size for all work arrays. Each of these 143* values is returned in the first entry of the corresponding 144* work array, and no error message is issued by PXERBLA. 145* 146* 147* INFO (local output) INTEGER 148* = 0: successful exit 149* < 0: If the i-th argument is an array and the j-entry had 150* an illegal value, then INFO = -(i*100+j), if the i-th 151* argument is a scalar and had an illegal value, then 152* INFO = -i. 153* 154* ===================================================================== 155* 156* .. Parameters .. 157 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 158 $ LLD_, MB_, M_, NB_, N_, RSRC_ 159 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 160 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 161 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 162 COMPLEX*16 ONE, ZERO 163 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), 164 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 165* .. 166* .. Local Scalars .. 167 LOGICAL LQUERY 168 CHARACTER COLBTOP, ROWBTOP 169 INTEGER IACOL, IAROW, I, ICTXT, II, LWMIN, MP, MPA0, 170 $ MYCOL, MYROW, NPCOL, NPROW, NQA0 171 COMPLEX*16 TAUI 172* .. 173* .. External Subroutines .. 174 EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, 175 $ PB_TOPGET, PB_TOPSET, PXERBLA, PZELSET, 176 $ PZLACGV, PZLARFC, PZLASET, PZSCAL 177* .. 178* .. External Functions .. 179 INTEGER INDXG2L, INDXG2P, NUMROC 180 EXTERNAL INDXG2L, INDXG2P, NUMROC 181* .. 182* .. Intrinsic Functions .. 183 INTRINSIC DBLE, DCMPLX, DCONJG, MAX, MIN, MOD 184* .. 185* .. Executable Statements .. 186* 187* Get grid parameters 188* 189 ICTXT = DESCA( CTXT_ ) 190 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 191* 192* Test the input parameters 193* 194 INFO = 0 195 IF( NPROW.EQ.-1 ) THEN 196 INFO = -(700+CTXT_) 197 ELSE 198 CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO ) 199 IF( INFO.EQ.0 ) THEN 200 IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 201 $ NPROW ) 202 IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 203 $ NPCOL ) 204 MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ), 205 $ MYROW, IAROW, NPROW ) 206 NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), 207 $ MYCOL, IACOL, NPCOL ) 208 LWMIN = NQA0 + MAX( 1, MPA0 ) 209* 210 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) 211 LQUERY = ( LWORK.EQ.-1 ) 212 IF( N.LT.M ) THEN 213 INFO = -2 214 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 215 INFO = -3 216 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 217 INFO = -10 218 END IF 219 END IF 220 END IF 221 IF( INFO.NE.0 ) THEN 222 CALL PXERBLA( ICTXT, 'PZUNGR2', -INFO ) 223 CALL BLACS_ABORT( ICTXT, 1 ) 224 RETURN 225 ELSE IF( LQUERY ) THEN 226 RETURN 227 END IF 228* 229* Quick return if possible 230* 231 IF( M.LE.0 ) 232 $ RETURN 233* 234 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 235 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 236 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 237 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) 238* 239 IF( K.LT.M ) THEN 240* 241* Initialise rows ia:ia+m-k-1 to rows of the unit matrix 242* 243 CALL PZLASET( 'All', M-K, N-M, ZERO, ZERO, A, IA, JA, DESCA ) 244 CALL PZLASET( 'All', M-K, M, ZERO, ONE, A, IA, JA+N-M, DESCA ) 245* 246 END IF 247* 248 TAUI = ZERO 249 MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) 250* 251 DO 10 I = IA+M-K, IA+M-1 252* 253* Apply H(i)' to A(ia:i,ja:ja+n-m+i-ia) from the right 254* 255 CALL PZLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) ) 256 CALL PZELSET( A, I, JA+N-M+I-IA, DESCA, ONE ) 257 CALL PZLARFC( 'Right', I-IA, I-IA+N-M+1, A, I, JA, DESCA, 258 $ DESCA( M_ ), TAU, A, IA, JA, DESCA, WORK ) 259 II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) 260 IAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 261 $ NPROW ) 262 IF( MYROW.EQ.IAROW ) 263 $ TAUI = TAU( MIN( II, MP ) ) 264 CALL PZSCAL( I-IA+N-M, -TAUI, A, I, JA, DESCA, DESCA( M_ ) ) 265 CALL PZLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) ) 266 CALL PZELSET( A, I, JA+N-M+I-IA, DESCA, ONE-DCONJG( TAUI ) ) 267* 268* Set A(i,ja+n-m+i-ia+1:ja+n-1) to zero 269* 270 CALL PZLASET( 'All', 1, IA+M-1-I, ZERO, ZERO, A, I, 271 $ JA+N-M+I-IA+1, DESCA ) 272* 273 10 CONTINUE 274* 275 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 276 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 277* 278 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) 279* 280 RETURN 281* 282* End of PZUNGR2 283* 284 END 285