1 SUBROUTINE PCUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, IA, JA, DESCA, 2 $ TAU, C, IC, JC, DESCC, WORK, LWORK, 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 1, 1997 8* 9* .. Scalar Arguments .. 10 CHARACTER SIDE, TRANS 11 INTEGER IA, IC, IHI, ILO, INFO, JA, JC, LWORK, M, N 12* .. 13* .. Array Arguments .. 14 INTEGER DESCA( * ), DESCC( * ) 15 COMPLEX A( * ), C( * ), TAU( * ), WORK( * ) 16* .. 17* 18* Purpose 19* ======= 20* 21* PCUNMHR overwrites the general complex M-by-N distributed matrix 22* sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with 23* 24* SIDE = 'L' SIDE = 'R' 25* TRANS = 'N': Q * sub( C ) sub( C ) * Q 26* TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H 27* 28* where Q is a complex unitary distributed matrix of order nq, with 29* nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the 30* product of IHI-ILO elementary reflectors, as returned by PCGEHRD: 31* 32* Q = H(ilo) H(ilo+1) . . . H(ihi-1). 33* 34* Notes 35* ===== 36* 37* Each global data object is described by an associated description 38* vector. This vector stores the information required to establish 39* the mapping between an object element and its corresponding process 40* and memory location. 41* 42* Let A be a generic term for any 2D block cyclicly distributed array. 43* Such a global array has an associated description vector DESCA. 44* In the following comments, the character _ should be read as 45* "of the global array". 46* 47* NOTATION STORED IN EXPLANATION 48* --------------- -------------- -------------------------------------- 49* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 50* DTYPE_A = 1. 51* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 52* the BLACS process grid A is distribu- 53* ted over. The context itself is glo- 54* bal, but the handle (the integer 55* value) may vary. 56* M_A (global) DESCA( M_ ) The number of rows in the global 57* array A. 58* N_A (global) DESCA( N_ ) The number of columns in the global 59* array A. 60* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 61* the rows of the array. 62* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 63* the columns of the array. 64* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 65* row of the array A is distributed. 66* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 67* first column of the array A is 68* distributed. 69* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 70* array. LLD_A >= MAX(1,LOCr(M_A)). 71* 72* Let K be the number of rows or columns of a distributed matrix, 73* and assume that its process grid has dimension p x q. 74* LOCr( K ) denotes the number of elements of K that a process 75* would receive if K were distributed over the p processes of its 76* process column. 77* Similarly, LOCc( K ) denotes the number of elements of K that a 78* process would receive if K were distributed over the q processes of 79* its process row. 80* The values of LOCr() and LOCc() may be determined via a call to the 81* ScaLAPACK tool function, NUMROC: 82* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 83* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 84* An upper bound for these quantities may be computed by: 85* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 86* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 87* 88* Arguments 89* ========= 90* 91* SIDE (global input) CHARACTER 92* = 'L': apply Q or Q**H from the Left; 93* = 'R': apply Q or Q**H from the Right. 94* 95* TRANS (global input) CHARACTER 96* = 'N': No transpose, apply Q; 97* = 'C': Conjugate transpose, apply Q**H. 98* 99* M (global input) INTEGER 100* The number of rows to be operated on i.e the number of rows 101* of the distributed submatrix sub( C ). M >= 0. 102* 103* N (global input) INTEGER 104* The number of columns to be operated on i.e the number of 105* columns of the distributed submatrix sub( C ). N >= 0. 106* 107* ILO (global input) INTEGER 108* IHI (global input) INTEGER 109* ILO and IHI must have the same values as in the previous call 110* of PCGEHRD. Q is equal to the unit matrix except in the 111* distributed submatrix Q(ia+ilo:ia+ihi-1,ia+ilo:ja+ihi-1). 112* If SIDE = 'L', 1 <= ILO <= IHI <= max(1,M); 113* if SIDE = 'R', 1 <= ILO <= IHI <= max(1,N); 114* ILO and IHI are relative indexes. 115* 116* A (local input) COMPLEX pointer into the local memory 117* to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', 118* and (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'. The vectors which 119* define the elementary reflectors, as returned by PCGEHRD. 120* 121* IA (global input) INTEGER 122* The row index in the global array A indicating the first 123* row of sub( A ). 124* 125* JA (global input) INTEGER 126* The column index in the global array A indicating the 127* first column of sub( A ). 128* 129* DESCA (global and local input) INTEGER array of dimension DLEN_. 130* The array descriptor for the distributed matrix A. 131* 132* TAU (local input) COMPLEX, array, dimension LOCc(JA+M-2) 133* if SIDE = 'L', and LOCc(JA+N-2) if SIDE = 'R'. This array 134* contains the scalar factors TAU(j) of the elementary 135* reflectors H(j) as returned by PCGEHRD. TAU is tied to 136* the distributed matrix A. 137* 138* C (local input/local output) COMPLEX pointer into the 139* local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). 140* On entry, the local pieces of the distributed matrix sub(C). 141* On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) 142* or sub( C )*Q' or sub( C )*Q. 143* 144* IC (global input) INTEGER 145* The row index in the global array C indicating the first 146* row of sub( C ). 147* 148* JC (global input) INTEGER 149* The column index in the global array C indicating the 150* first column of sub( C ). 151* 152* DESCC (global and local input) INTEGER array of dimension DLEN_. 153* The array descriptor for the distributed matrix C. 154* 155* WORK (local workspace/local output) COMPLEX array, 156* dimension (LWORK) 157* On exit, WORK(1) returns the minimal and optimal LWORK. 158* 159* LWORK (local or global input) INTEGER 160* The dimension of the array WORK. 161* LWORK is local input and must be at least 162* 163* IAA = IA + ILO; JAA = JA+ILO-1; 164* If SIDE = 'L', 165* MI = IHI-ILO; NI = N; ICC = IC + ILO; JCC = JC; 166* LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + 167* NB_A * NB_A 168* else if SIDE = 'R', 169* MI = M; NI = IHI-ILO; ICC = IC; JCC = JC + ILO; 170* LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 + 171* NUMROC( NUMROC( NI+ICOFFC, NB_A, 0, 0, NPCOL ), 172* NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) + 173* NB_A * NB_A 174* end if 175* 176* where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ), 177* 178* IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), 179* IAROW = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ), 180* NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW, IAROW, NPROW ), 181* 182* IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), 183* ICROW = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), 184* ICCOL = INDXG2P( JCC, NB_C, MYCOL, CSRC_C, NPCOL ), 185* MpC0 = NUMROC( MI+IROFFC, MB_C, MYROW, ICROW, NPROW ), 186* NqC0 = NUMROC( NI+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ), 187* 188* ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions; 189* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 190* the subroutine BLACS_GRIDINFO. 191* 192* If LWORK = -1, then LWORK is global input and a workspace 193* query is assumed; the routine only calculates the minimum 194* and optimal size for all work arrays. Each of these 195* values is returned in the first entry of the corresponding 196* work array, and no error message is issued by PXERBLA. 197* 198* 199* INFO (global output) INTEGER 200* = 0: successful exit 201* < 0: If the i-th argument is an array and the j-entry had 202* an illegal value, then INFO = -(i*100+j), if the i-th 203* argument is a scalar and had an illegal value, then 204* INFO = -i. 205* 206* Alignment requirements 207* ====================== 208* 209* The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1) 210* must verify some alignment properties, namely the following 211* expressions should be true: 212* 213* If SIDE = 'L', 214* ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND. IAROW.EQ.ICROW ) 215* If SIDE = 'R', 216* ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC ) 217* 218* ===================================================================== 219* 220* .. Parameters .. 221 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 222 $ LLD_, MB_, M_, NB_, N_, RSRC_ 223 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 224 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 225 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 226* .. 227* .. Local Scalars .. 228 LOGICAL LEFT, LQUERY, NOTRAN 229 INTEGER IAA, IAROW, ICC, ICCOL, ICOFFC, ICROW, ICTXT, 230 $ IINFO, IROFFA, IROFFC, JAA, JCC, LCM, LCMQ, 231 $ LWMIN, MI, MPC0, MYCOL, MYROW, NH, NI, NPA0, 232 $ NPCOL, NPROW, NQ, NQC0 233* .. 234* .. Local Arrays .. 235 INTEGER IDUM1( 5 ), IDUM2( 5 ) 236* .. 237* .. External Subroutines .. 238 EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PCUNMQR, 239 $ PXERBLA 240* .. 241* .. External Functions .. 242 LOGICAL LSAME 243 INTEGER ILCM, INDXG2P, NUMROC 244 EXTERNAL ILCM, INDXG2P, LSAME, NUMROC 245* .. 246* .. Intrinsic Functions .. 247 INTRINSIC CMPLX, ICHAR, MAX, MIN, MOD, REAL 248* .. 249* .. Executable Statements .. 250* 251* Get grid parameters 252* 253 ICTXT = DESCA( CTXT_ ) 254 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 255* 256* Test the input parameters 257* 258 INFO = 0 259 NH = IHI - ILO 260 IF( NPROW.EQ.-1 ) THEN 261 INFO = -(1000+CTXT_) 262 ELSE 263 LEFT = LSAME( SIDE, 'L' ) 264 NOTRAN = LSAME( TRANS, 'N' ) 265 IAA = IA + ILO 266 JAA = JA + ILO - 1 267* 268* NQ is the order of Q 269* 270 IF( LEFT ) THEN 271 NQ = M 272 MI = NH 273 NI = N 274 ICC = IC + ILO 275 JCC = JC 276 CALL CHK1MAT( M, 3, M, 3, IA, JA, DESCA, 10, INFO ) 277 ELSE 278 NQ = N 279 MI = M 280 NI = NH 281 ICC = IC 282 JCC = JC + ILO 283 CALL CHK1MAT( N, 4, N, 4, IA, JA, DESCA, 10, INFO ) 284 END IF 285 CALL CHK1MAT( M, 3, N, 4, IC, JC, DESCC, 15, INFO ) 286 IF( INFO.EQ.0 ) THEN 287 IROFFA = MOD( IAA-1, DESCA( MB_ ) ) 288 IROFFC = MOD( ICC-1, DESCC( MB_ ) ) 289 ICOFFC = MOD( JCC-1, DESCC( NB_ ) ) 290 IAROW = INDXG2P( IAA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 291 $ NPROW ) 292 ICROW = INDXG2P( ICC, DESCC( MB_ ), MYROW, DESCC( RSRC_ ), 293 $ NPROW ) 294 ICCOL = INDXG2P( JCC, DESCC( NB_ ), MYCOL, DESCC( CSRC_ ), 295 $ NPCOL ) 296 MPC0 = NUMROC( MI+IROFFC, DESCC( MB_ ), MYROW, ICROW, 297 $ NPROW ) 298 NQC0 = NUMROC( NI+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, 299 $ NPCOL ) 300* 301 IF( LEFT ) THEN 302 LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) / 2, 303 $ ( MPC0 + NQC0 ) * DESCA( NB_ ) ) + 304 $ DESCA( NB_ ) * DESCA( NB_ ) 305 ELSE 306 NPA0 = NUMROC( NI+IROFFA, DESCA( MB_ ), MYROW, IAROW, 307 $ NPROW ) 308 LCM = ILCM( NPROW, NPCOL ) 309 LCMQ = LCM / NPCOL 310 LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) 311 $ / 2, ( NQC0 + MAX( NPA0 + NUMROC( NUMROC( 312 $ NI+ICOFFC, DESCA( NB_ ), 0, 0, NPCOL ), 313 $ DESCA( NB_ ), 0, 0, LCMQ ), MPC0 ) ) * 314 $ DESCA( NB_ ) ) + DESCA( NB_ ) * DESCA( NB_ ) 315 END IF 316* 317 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 318 LQUERY = ( LWORK.EQ.-1 ) 319 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 320 INFO = -1 321 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN 322 INFO = -2 323 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN 324 INFO = -5 325 ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN 326 INFO = -6 327 ELSE IF( .NOT.LEFT .AND. DESCA( MB_ ).NE.DESCC( NB_ ) ) THEN 328 INFO = -(1000+NB_) 329 ELSE IF( LEFT .AND. IROFFA.NE.IROFFC ) THEN 330 INFO = -13 331 ELSE IF( LEFT .AND. IAROW.NE.ICROW ) THEN 332 INFO = -13 333 ELSE IF( .NOT.LEFT .AND. IROFFA.NE.ICOFFC ) THEN 334 INFO = -14 335 ELSE IF( LEFT .AND. DESCA( MB_ ).NE.DESCC( MB_ ) ) THEN 336 INFO = -(1500+MB_) 337 ELSE IF( ICTXT.NE.DESCC( CTXT_ ) ) THEN 338 INFO = -(1500+CTXT_) 339 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 340 INFO = -17 341 END IF 342 END IF 343* 344 IF( LEFT ) THEN 345 IDUM1( 1 ) = ICHAR( 'L' ) 346 ELSE 347 IDUM1( 1 ) = ICHAR( 'R' ) 348 END IF 349 IDUM2( 1 ) = 1 350 IF( NOTRAN ) THEN 351 IDUM1( 2 ) = ICHAR( 'N' ) 352 ELSE 353 IDUM1( 2 ) = ICHAR( 'C' ) 354 END IF 355 IDUM2( 2 ) = 2 356 IDUM1( 3 ) = ILO 357 IDUM2( 3 ) = 5 358 IDUM1( 4 ) = IHI 359 IDUM2( 4 ) = 6 360 IF( LWORK.EQ.-1 ) THEN 361 IDUM1( 5 ) = -1 362 ELSE 363 IDUM1( 5 ) = 1 364 END IF 365 IDUM2( 5 ) = 17 366 IF( LEFT ) THEN 367 CALL PCHK2MAT( M, 3, M, 3, IA, JA, DESCA, 10, M, 3, N, 4, 368 $ IC, JC, DESCC, 15, 5, IDUM1, IDUM2, INFO ) 369 ELSE 370 CALL PCHK2MAT( N, 4, N, 4, IA, JA, DESCA, 10, M, 3, N, 4, 371 $ IC, JC, DESCC, 15, 5, IDUM1, IDUM2, INFO ) 372 END IF 373 END IF 374* 375 IF( INFO.NE.0 ) THEN 376 CALL PXERBLA( ICTXT, 'PCUNMHR', -INFO ) 377 RETURN 378 ELSE IF( LQUERY ) THEN 379 RETURN 380 END IF 381* 382* Quick return if possible 383* 384 IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) 385 $ RETURN 386* 387 CALL PCUNMQR( SIDE, TRANS, MI, NI, NH, A, IAA, JAA, DESCA, TAU, 388 $ C, ICC, JCC, DESCC, WORK, LWORK, IINFO ) 389* 390 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 391* 392 RETURN 393* 394* End of PCUNMHR 395* 396 END 397