1 SUBROUTINE PCGELQF( M, N, 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, LWORK, M, N 11* .. 12* .. Array Arguments .. 13 INTEGER DESCA( * ) 14 COMPLEX A( * ), TAU( * ), WORK( * ) 15* .. 16* 17* Purpose 18* ======= 19* 20* PCGELQF computes a LQ factorization of a complex distributed M-by-N 21* matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. 22* 23* Notes 24* ===== 25* 26* Each global data object is described by an associated description 27* vector. This vector stores the information required to establish 28* the mapping between an object element and its corresponding process 29* and memory location. 30* 31* Let A be a generic term for any 2D block cyclicly distributed array. 32* Such a global array has an associated description vector DESCA. 33* In the following comments, the character _ should be read as 34* "of the global array". 35* 36* NOTATION STORED IN EXPLANATION 37* --------------- -------------- -------------------------------------- 38* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 39* DTYPE_A = 1. 40* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 41* the BLACS process grid A is distribu- 42* ted over. The context itself is glo- 43* bal, but the handle (the integer 44* value) may vary. 45* M_A (global) DESCA( M_ ) The number of rows in the global 46* array A. 47* N_A (global) DESCA( N_ ) The number of columns in the global 48* array A. 49* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 50* the rows of the array. 51* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 52* the columns of the array. 53* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 54* row of the array A is distributed. 55* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 56* first column of the array A is 57* distributed. 58* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 59* array. LLD_A >= MAX(1,LOCr(M_A)). 60* 61* Let K be the number of rows or columns of a distributed matrix, 62* and assume that its process grid has dimension p x q. 63* LOCr( K ) denotes the number of elements of K that a process 64* would receive if K were distributed over the p processes of its 65* process column. 66* Similarly, LOCc( K ) denotes the number of elements of K that a 67* process would receive if K were distributed over the q processes of 68* its process row. 69* The values of LOCr() and LOCc() may be determined via a call to the 70* ScaLAPACK tool function, NUMROC: 71* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 72* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 73* An upper bound for these quantities may be computed by: 74* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 75* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 76* 77* Arguments 78* ========= 79* 80* M (global input) INTEGER 81* The number of rows to be operated on, i.e. the number of rows 82* of the distributed submatrix sub( A ). M >= 0. 83* 84* N (global input) INTEGER 85* The number of columns to be operated on, i.e. the number of 86* columns of the distributed submatrix sub( A ). N >= 0. 87* 88* A (local input/local output) COMPLEX pointer into the 89* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). 90* On entry, the local pieces of the M-by-N distributed matrix 91* sub( A ) which is to be factored. On exit, the elements on 92* and below the diagonal of sub( A ) contain the M by min(M,N) 93* lower trapezoidal matrix L (L is lower triangular if M <= N); 94* the elements above the diagonal, with the array TAU, repre- 95* sent the unitary matrix Q as a product of elementary 96* reflectors (see Further Details). 97* 98* IA (global input) INTEGER 99* The row index in the global array A indicating the first 100* row of sub( A ). 101* 102* JA (global input) INTEGER 103* The column index in the global array A indicating the 104* first column of sub( A ). 105* 106* DESCA (global and local input) INTEGER array of dimension DLEN_. 107* The array descriptor for the distributed matrix A. 108* 109* TAU (local output) COMPLEX, array, dimension 110* LOCr(IA+MIN(M,N)-1). This array contains the scalar factors 111* of the elementary reflectors. TAU is tied to the distributed 112* matrix A. 113* 114* WORK (local workspace/local output) COMPLEX array, 115* dimension (LWORK) 116* On exit, WORK(1) returns the minimal and optimal LWORK. 117* 118* LWORK (local or global input) INTEGER 119* The dimension of the array WORK. 120* LWORK is local input and must be at least 121* LWORK >= MB_A * ( Mp0 + Nq0 + MB_A ), where 122* 123* IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), 124* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), 125* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), 126* Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ), 127* Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ), 128* 129* and NUMROC, INDXG2P are ScaLAPACK tool functions; 130* MYROW, MYCOL, NPROW and NPCOL can be determined by calling 131* the subroutine BLACS_GRIDINFO. 132* 133* If LWORK = -1, then LWORK is global input and a workspace 134* query is assumed; the routine only calculates the minimum 135* and optimal size for all work arrays. Each of these 136* values is returned in the first entry of the corresponding 137* work array, and no error message is issued by PXERBLA. 138* 139* INFO (global output) INTEGER 140* = 0: successful exit 141* < 0: If the i-th argument is an array and the j-entry had 142* an illegal value, then INFO = -(i*100+j), if the i-th 143* argument is a scalar and had an illegal value, then 144* INFO = -i. 145* 146* Further Details 147* =============== 148* 149* The matrix Q is represented as a product of elementary reflectors 150* 151* Q = H(ia+k-1)' H(ia+k-2)' . . . H(ia)', where k = min(m,n). 152* 153* Each H(i) has the form 154* 155* H(i) = I - tau * v * v' 156* 157* where tau is a complex scalar, and v is a complex vector with 158* v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in 159* A(ia+i-1,ja+i:ja+n-1), and tau in TAU(ia+i-1). 160* 161* ===================================================================== 162* 163* .. Parameters .. 164 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 165 $ LLD_, MB_, M_, NB_, N_, RSRC_ 166 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 167 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 168 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 169* .. 170* .. Local Scalars .. 171 LOGICAL LQUERY 172 CHARACTER COLBTOP, ROWBTOP 173 INTEGER I, IACOL, IAROW, IB, ICTXT, IINFO, IN, IPW, 174 $ IROFF, J, K, LWMIN, MP0, MYCOL, MYROW, NPCOL, 175 $ NPROW, NQ0 176* .. 177* .. Local Arrays .. 178 INTEGER IDUM1( 1 ), IDUM2( 1 ) 179* .. 180* .. External Subroutines .. 181 EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PCGELQ2, 182 $ PCLARFB, PCLARFT, PB_TOPGET, PB_TOPSET, PXERBLA 183* .. 184* .. External Functions .. 185 INTEGER ICEIL, INDXG2P, NUMROC 186 EXTERNAL ICEIL, INDXG2P, NUMROC 187* .. 188* .. Intrinsic Functions .. 189 INTRINSIC CMPLX, MIN, MOD, REAL 190* .. 191* .. Executable Statements .. 192* 193* Get grid parameters 194* 195 ICTXT = DESCA( CTXT_ ) 196 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 197* 198* Test the input parameters 199* 200 INFO = 0 201 IF( NPROW.EQ.-1 ) THEN 202 INFO = -(600+CTXT_) 203 ELSE 204 CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) 205 IF( INFO.EQ.0 ) THEN 206 IROFF = MOD( IA-1, DESCA( MB_ ) ) 207 IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 208 $ NPROW ) 209 IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 210 $ NPCOL ) 211 MP0 = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) 212 NQ0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), 213 $ MYCOL, IACOL, NPCOL ) 214 LWMIN = DESCA( MB_ ) * ( MP0 + NQ0 + DESCA( MB_ ) ) 215* 216 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 217 LQUERY = ( LWORK.EQ.-1 ) 218 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) 219 $ INFO = -9 220 END IF 221 IF( LWORK.EQ.-1 ) THEN 222 IDUM1( 1 ) = -1 223 ELSE 224 IDUM1( 1 ) = 1 225 END IF 226 IDUM2( 1 ) = 9 227 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2, 228 $ INFO ) 229 END IF 230* 231 IF( INFO.NE.0 ) THEN 232 CALL PXERBLA( ICTXT, 'PCGELQF', -INFO ) 233 RETURN 234 ELSE IF( LQUERY ) THEN 235 RETURN 236 END IF 237* 238* Quick return if possible 239* 240 IF( M.EQ.0 .OR. N.EQ.0 ) 241 $ RETURN 242* 243 K = MIN( M, N ) 244 IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1 245 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 246 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 247 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 248 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) 249* 250* Handle the first block of rows separately 251* 252 IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 ) 253 IB = IN - IA + 1 254* 255* Compute the LQ factorization of the first block A(ia:in:ja:ja+n-1) 256* 257 CALL PCGELQ2( IB, N, A, IA, JA, DESCA, TAU, WORK, LWORK, IINFO ) 258* 259 IF( IA+IB.LE.IA+M-1 ) THEN 260* 261* Form the triangular factor of the block reflector 262* H = H(ia) H(ia+1) . . . H(in) 263* 264 CALL PCLARFT( 'Forward', 'Rowwise', N, IB, A, IA, JA, DESCA, 265 $ TAU, WORK, WORK( IPW ) ) 266* 267* Apply H to A(ia+ib:ia+m-1,ja:ja+n-1) from the right 268* 269 CALL PCLARFB( 'Right', 'No transpose', 'Forward', 'Rowwise', 270 $ M-IB, N, IB, A, IA, JA, DESCA, WORK, A, IA+IB, 271 $ JA, DESCA, WORK( IPW ) ) 272 END IF 273* 274* Loop over the remaining blocks of rows 275* 276 DO 10 I = IN+1, IA+K-1, DESCA( MB_ ) 277 IB = MIN( K-I+IA, DESCA( MB_ ) ) 278 J = JA + I - IA 279* 280* Compute the LQ factorization of the current block 281* A(i:i+ib-1:j:ja+n-1) 282* 283 CALL PCGELQ2( IB, N-I+IA, A, I, J, DESCA, TAU, WORK, LWORK, 284 $ IINFO ) 285* 286 IF( I+IB.LE.IA+M-1 ) THEN 287* 288* Form the triangular factor of the block reflector 289* H = H(i) H(i+1) . . . H(i+ib-1) 290* 291 CALL PCLARFT( 'Forward', 'Rowwise', N-I+IA, IB, A, I, J, 292 $ DESCA, TAU, WORK, WORK( IPW ) ) 293* 294* Apply H to A(i+ib:ia+m-1,j:ja+n-1) from the right 295* 296 CALL PCLARFB( 'Right', 'No transpose', 'Forward', 'Rowwise', 297 $ M-I-IB+IA, N-J+JA, IB, A, I, J, DESCA, WORK, 298 $ A, I+IB, J, DESCA, WORK( IPW ) ) 299 END IF 300* 301 10 CONTINUE 302* 303 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 304 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 305* 306 WORK( 1 ) = CMPLX( REAL( LWMIN ) ) 307* 308 RETURN 309* 310* End of PCGELQF 311* 312 END 313