1 SUBROUTINE PZUNG2L( 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* PZUNG2L generates an M-by-N complex distributed matrix Q denoting 21* A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as 22* the last N columns of a product of K elementary reflectors of order M 23* 24* Q = H(k) . . . H(2) H(1) 25* 26* as returned by PZGEQLF. 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. M >= N >= 0. 92* 93* K (global input) INTEGER 94* The number of elementary reflectors whose product defines the 95* matrix Q. N >= 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 j-th column must contain the vector which 100* defines the elementary reflector H(j), JA+N-K <= j <= JA+N-1, 101* as returned by PZGEQLF in the K columns of its distributed 102* matrix argument A(IA:*,JA+N-K:JA+N-1). 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 LOCc(JA+N-1) 117* This array contains the scalar factors TAU(j) of the 118* elementary reflectors H(j) as returned by PZGEQLF. 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 >= MpA0 + MAX( 1, NqA0 ), 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, ICTXT, J, JJ, LWMIN, MPA0, MYCOL, 170 $ MYROW, NPCOL, NPROW, NQA0 171 COMPLEX*16 TAUJ 172* .. 173* .. External Subroutines .. 174 EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, 175 $ PB_TOPGET, PB_TOPSET, PXERBLA, PZELSET, PZLARF, 176 $ PZLASET, PZSCAL 177* .. 178* .. External Functions .. 179 INTEGER INDXG2L, INDXG2P, NUMROC 180 EXTERNAL INDXG2L, INDXG2P, NUMROC 181* .. 182* .. Intrinsic Functions .. 183 INTRINSIC DBLE, DCMPLX, 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 = MPA0 + MAX( 1, NQA0 ) 209* 210 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) 211 LQUERY = ( LWORK.EQ.-1 ) 212 IF( N.GT.M ) THEN 213 INFO = -2 214 ELSE IF( K.LT.0 .OR. K.GT.N ) 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, 'PZUNG2L', -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( N.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', 'I-ring' ) 237 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) 238* 239* Initialise columns ja:ja+n-k-1 to columns of the unit matrix 240* 241 CALL PZLASET( 'All', M-N, N-K, ZERO, ZERO, A, IA, JA, DESCA ) 242 CALL PZLASET( 'All', N, N-K, ZERO, ONE, A, IA+M-N, JA, DESCA ) 243* 244 TAUJ = ZERO 245 NQA0 = MAX( 1, NUMROC( JA+N-1, DESCA( NB_ ), MYCOL, 246 $ DESCA( CSRC_ ), NPCOL ) ) 247 DO 10 J = JA+N-K, JA+N-1 248* 249* Apply H(j) to A(ia:ia+m-n+j-ja,ja:j) from the left 250* 251 CALL PZELSET( A, IA+M-N+J-JA, J, DESCA, ONE ) 252 CALL PZLARF( 'Left', M-N+J-JA+1, J-JA, A, IA, J, DESCA, 1, TAU, 253 $ A, IA, JA, DESCA, WORK ) 254* 255 JJ = INDXG2L( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL ) 256 IACOL = INDXG2P( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 257 $ NPCOL ) 258 IF( MYCOL.EQ.IACOL ) 259 $ TAUJ = TAU( MIN( JJ, NQA0 ) ) 260 CALL PZSCAL( M-N+J-JA, -TAUJ, A, IA, J, DESCA, 1 ) 261 CALL PZELSET( A, IA+M-N+J-JA, J, DESCA, ONE-TAUJ ) 262* 263* Set A(ia+m-n+j-ja+1:ia+m-1,j) to zero 264* 265 CALL PZLASET( 'All', JA+N-1-J, 1, ZERO, ZERO, A, IA+M-N+J-JA+1, 266 $ J, DESCA ) 267* 268 10 CONTINUE 269* 270 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 271 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 272* 273 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) 274* 275 RETURN 276* 277* End of PZUNG2L 278* 279 END 280