1 SUBROUTINE PCUNGLQ( 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 A( * ), TAU( * ), WORK( * ) 15* .. 16* 17* Purpose 18* ======= 19* 20* PCUNGLQ 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 22* the first M rows of a product of K elementary reflectors of order N 23* 24* Q = H(k)' . . . H(2)' H(1)' 25* 26* as returned by PCGELQF. 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 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 <= i <= IA+K-1, as 101* returned by PCGELQF in the K rows of its distributed matrix 102* argument A(IA:IA+K-1,JA:*). On exit, this array contains the 103* 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, array, dimension LOCr(IA+K-1). 117* This array contains the scalar factors TAU(i) of the 118* elementary reflectors H(i) as returned by PCGELQF. 119* TAU is tied to the distributed matrix A. 120* 121* WORK (local workspace/local output) COMPLEX 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 >= MB_A * ( MpA0 + 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* 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 (global 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 ZERO 163 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) 164* .. 165* .. Local Scalars .. 166 LOGICAL LQUERY 167 CHARACTER COLBTOP, ROWBTOP 168 INTEGER I, IACOL, IAROW, IB, ICTXT, IINFO, IL, IN, IPW, 169 $ J, LWMIN, MPA0, MYCOL, MYROW, NPCOL, NPROW, 170 $ NQA0 171* .. 172* .. Local Arrays .. 173 INTEGER IDUM1( 2 ), IDUM2( 2 ) 174* .. 175* .. External Subroutines .. 176 EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PCLARFB, 177 $ PCLARFT, PCLASET, PCUNGL2, PB_TOPGET, 178 $ PB_TOPSET, PXERBLA 179* .. 180* .. External Functions .. 181 INTEGER ICEIL, INDXG2P, NUMROC 182 EXTERNAL ICEIL, INDXG2P, NUMROC 183* .. 184* .. Intrinsic Functions .. 185 INTRINSIC CMPLX, MAX, MIN, MOD, REAL 186* .. 187* .. Executable Statements .. 188* 189* Get grid parameters 190* 191 ICTXT = DESCA( CTXT_ ) 192 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 193* 194* Test the input parameters 195* 196 INFO = 0 197 IF( NPROW.EQ.-1 ) THEN 198 INFO = -(700+CTXT_) 199 ELSE 200 CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO ) 201 IF( INFO.EQ.0 ) THEN 202 IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 203 $ NPROW ) 204 IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 205 $ NPCOL ) 206 MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ), 207 $ MYROW, IAROW, NPROW ) 208 NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), 209 $ MYCOL, IACOL, NPCOL ) 210 LWMIN = DESCA( MB_ ) * ( MPA0 + NQA0 + DESCA( MB_ ) ) 211* 212 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 213 LQUERY = ( LWORK.EQ.-1 ) 214 IF( N.LT.M ) THEN 215 INFO = -2 216 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 217 INFO = -3 218 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 219 INFO = -10 220 END IF 221 END IF 222 IDUM1( 1 ) = K 223 IDUM2( 1 ) = 3 224 IF( LWORK.EQ.-1 ) THEN 225 IDUM1( 2 ) = -1 226 ELSE 227 IDUM1( 2 ) = 1 228 END IF 229 IDUM2( 2 ) = 10 230 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, 2, IDUM1, IDUM2, 231 $ INFO ) 232 END IF 233* 234 IF( INFO.NE.0 ) THEN 235 CALL PXERBLA( ICTXT, 'PCUNGLQ', -INFO ) 236 RETURN 237 ELSE IF( LQUERY ) THEN 238 RETURN 239 END IF 240* 241* Quick return if possible 242* 243 IF( M.LE.0 ) 244 $ RETURN 245* 246 IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1 247 IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 ) 248 IL = MAX( ( (IA+K-2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) 249 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 250 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 251 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 252 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' ) 253* 254 CALL PCLASET( 'All', IA+M-IL, IL-IA, ZERO, ZERO, A, IL, JA, 255 $ DESCA ) 256* 257* Use unblocked code for the last or only block. 258* 259 CALL PCUNGL2( IA+M-IL, N-IL+IA, IA+K-IL, A, IL, JA+IL-IA, DESCA, 260 $ TAU, WORK, LWORK, IINFO ) 261* 262* Is there at least one block of rows to loop over ? 263* 264 IF( IL.GT.IN+1 ) THEN 265* 266* Use blocked code 267* 268 DO 10 I = IL-DESCA( MB_ ), IN+1, -DESCA( MB_ ) 269 IB = MIN( DESCA( MB_ ), IA+M-I ) 270 J = JA + I - IA 271* 272 IF( I+IB.LE.IA+M-1 ) THEN 273* 274* Form the triangular factor of the block reflector 275* H = H(i) H(i+1) . . . H(i+ib-1) 276* 277 CALL PCLARFT( 'Forward', 'Rowwise', N-I+IA, IB, A, I, J, 278 $ DESCA, TAU, WORK, WORK( IPW ) ) 279* 280* Apply H' to A(i+ib:ia+m-1,j:ja+n-1) from the right 281* 282 CALL PCLARFB( 'Right', 'Conjugate transpose', 'Forward', 283 $ 'Rowwise', M-I-IB+IA, N-I+IA, IB, A, I, J, 284 $ DESCA, WORK, A, I+IB, J, DESCA, 285 $ WORK( IPW ) ) 286 END IF 287* 288* Apply H' to columns j:ja+n-1 of current block 289* 290 CALL PCUNGL2( IB, N-I+IA, IB, A, I, J, DESCA, TAU, WORK, 291 $ LWORK, IINFO ) 292* 293* Set columns ia:i-1 of current block to zero 294* 295 CALL PCLASET( 'All', IB, I-IA, ZERO, ZERO, A, I, JA, DESCA ) 296 10 CONTINUE 297* 298 END IF 299* 300* Handle first block separately 301* 302 IF( IL.GT.IA ) THEN 303* 304 IB = IN - IA + 1 305* 306* Form the triangular factor of the block reflector 307* H = H(i) H(i+1) . . . H(i+ib-1) 308* 309 CALL PCLARFT( 'Forward', 'Rowwise', N, IB, A, IA, JA, DESCA, 310 $ TAU, WORK, WORK( IPW ) ) 311* 312* Apply H' to A(ia+ib:ia+m-1,ja:ja+n-1) from the right 313* 314 CALL PCLARFB( 'Right', 'Conjugate transpose', 'Forward', 315 $ 'Rowwise', M-IB, N, IB, A, IA, JA, DESCA, WORK, 316 $ A, IA+IB, JA, DESCA, WORK( IPW ) ) 317* 318* Apply H' to columns ja:ja+n-1 of current block 319* 320 CALL PCUNGL2( IB, N, IB, A, IA, JA, DESCA, TAU, WORK, LWORK, 321 $ IINFO ) 322* 323 END IF 324* 325 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 326 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 327* 328 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 329* 330 RETURN 331* 332* End of PCUNGLQ 333* 334 END 335