1 SUBROUTINE PZLAWIL( II, JJ, M, A, DESCA, H44, H33, H43H34, V ) 2* 3* -- ScaLAPACK routine (version 1.7) -- 4* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 5* and University of California, Berkeley. 6* July 31, 2001 7* 8* .. Scalar Arguments .. 9 INTEGER II, JJ, M 10 COMPLEX*16 H33, H43H34, H44 11* .. 12* .. Array Arguments .. 13 INTEGER DESCA( * ) 14 COMPLEX*16 A( * ), V( * ) 15* .. 16* 17* Purpose 18* ======= 19* 20* PZLAWIL gets the transform given by H44,H33, & H43H34 into V 21* starting at row M. 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* II (global input) INTEGER 81* Row owner of H(M+2,M+2) 82* 83* JJ (global input) INTEGER 84* Column owner of H(M+2,M+2) 85* 86* M (global input) INTEGER 87* On entry, this is where the transform starts (row M.) 88* Unchanged on exit. 89* 90* A (global input) COMPLEX*16 array, dimension 91* (DESCA(LLD_),*) 92* On entry, the Hessenberg matrix. 93* Unchanged on exit. 94* 95* DESCA (global and local input) INTEGER array of dimension DLEN_. 96* The array descriptor for the distributed matrix A. 97* Unchanged on exit. 98* 99* H44 100* H33 101* H43H34 (global input) COMPLEX*16 102* These three values are for the double shift QR iteration. 103* Unchanged on exit. 104* 105* V (global output) COMPLEX*16 array of size 3. 106* Contains the transform on ouput. 107* 108* Further Details 109* =============== 110* 111* Implemented by: M. Fahey, May 28, 1999 112* 113* ===================================================================== 114* 115* .. Parameters .. 116 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 117 $ LLD_, MB_, M_, NB_, N_, RSRC_ 118 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 119 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 120 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 121* .. 122* .. Local Scalars .. 123 INTEGER CONTXT, DOWN, HBL, ICOL, IROW, JSRC, LDA, LEFT, 124 $ MODKM1, MYCOL, MYROW, NPCOL, NPROW, NUM, RIGHT, 125 $ RSRC, UP 126 DOUBLE PRECISION S 127 COMPLEX*16 CDUM, H11, H12, H21, H22, H33S, H44S, V1, V2, 128 $ V3 129* .. 130* .. Local Arrays .. 131 COMPLEX*16 BUF( 4 ) 132* .. 133* .. External Subroutines .. 134 EXTERNAL BLACS_GRIDINFO, INFOG2L, ZGERV2D, ZGESD2D 135* .. 136* .. Intrinsic Functions .. 137 INTRINSIC ABS, DBLE, DIMAG, MOD 138* .. 139* .. Statement Functions .. 140 DOUBLE PRECISION CABS1 141* .. 142* .. Statement Function definitions .. 143 CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) 144* .. 145* .. Executable Statements .. 146* 147 HBL = DESCA( MB_ ) 148 CONTXT = DESCA( CTXT_ ) 149 LDA = DESCA( LLD_ ) 150 CALL BLACS_GRIDINFO( CONTXT, NPROW, NPCOL, MYROW, MYCOL ) 151 LEFT = MOD( MYCOL+NPCOL-1, NPCOL ) 152 RIGHT = MOD( MYCOL+1, NPCOL ) 153 UP = MOD( MYROW+NPROW-1, NPROW ) 154 DOWN = MOD( MYROW+1, NPROW ) 155 NUM = NPROW*NPCOL 156* 157* On node (II,JJ) collect all DIA,SUP,SUB info from M, M+1 158* 159 MODKM1 = MOD( M+1, HBL ) 160 IF( MODKM1.EQ.0 ) THEN 161 IF( ( MYROW.EQ.II ) .AND. ( RIGHT.EQ.JJ ) .AND. 162 $ ( NPCOL.GT.1 ) ) THEN 163 CALL INFOG2L( M+2, M+1, DESCA, NPROW, NPCOL, MYROW, MYCOL, 164 $ IROW, ICOL, RSRC, JSRC ) 165 BUF( 1 ) = A( ( ICOL-1 )*LDA+IROW ) 166 CALL ZGESD2D( CONTXT, 1, 1, BUF, 1, II, JJ ) 167 END IF 168 IF( ( DOWN.EQ.II ) .AND. ( RIGHT.EQ.JJ ) .AND. ( NUM.GT.1 ) ) 169 $ THEN 170 CALL INFOG2L( M, M, DESCA, NPROW, NPCOL, MYROW, MYCOL, IROW, 171 $ ICOL, RSRC, JSRC ) 172 BUF( 1 ) = A( ( ICOL-1 )*LDA+IROW ) 173 BUF( 2 ) = A( ( ICOL-1 )*LDA+IROW+1 ) 174 BUF( 3 ) = A( ICOL*LDA+IROW ) 175 BUF( 4 ) = A( ICOL*LDA+IROW+1 ) 176 CALL ZGESD2D( CONTXT, 4, 1, BUF, 4, II, JJ ) 177 END IF 178 IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN 179 CALL INFOG2L( M+2, M+2, DESCA, NPROW, NPCOL, MYROW, MYCOL, 180 $ IROW, ICOL, RSRC, JSRC ) 181 IF( NPCOL.GT.1 ) THEN 182 CALL ZGERV2D( CONTXT, 1, 1, V3, 1, MYROW, LEFT ) 183 ELSE 184 V3 = A( ( ICOL-2 )*LDA+IROW ) 185 END IF 186 IF( NUM.GT.1 ) THEN 187 CALL ZGERV2D( CONTXT, 4, 1, BUF, 4, UP, LEFT ) 188 H11 = BUF( 1 ) 189 H21 = BUF( 2 ) 190 H12 = BUF( 3 ) 191 H22 = BUF( 4 ) 192 ELSE 193 H11 = A( ( ICOL-3 )*LDA+IROW-2 ) 194 H21 = A( ( ICOL-3 )*LDA+IROW-1 ) 195 H12 = A( ( ICOL-2 )*LDA+IROW-2 ) 196 H22 = A( ( ICOL-2 )*LDA+IROW-1 ) 197 END IF 198 END IF 199 END IF 200 IF( MODKM1.EQ.1 ) THEN 201 IF( ( DOWN.EQ.II ) .AND. ( RIGHT.EQ.JJ ) .AND. ( NUM.GT.1 ) ) 202 $ THEN 203 CALL INFOG2L( M, M, DESCA, NPROW, NPCOL, MYROW, MYCOL, IROW, 204 $ ICOL, RSRC, JSRC ) 205 CALL ZGESD2D( CONTXT, 1, 1, A( ( ICOL-1 )*LDA+IROW ), 1, II, 206 $ JJ ) 207 END IF 208 IF( ( DOWN.EQ.II ) .AND. ( MYCOL.EQ.JJ ) .AND. ( NPROW.GT.1 ) ) 209 $ THEN 210 CALL INFOG2L( M, M+1, DESCA, NPROW, NPCOL, MYROW, MYCOL, 211 $ IROW, ICOL, RSRC, JSRC ) 212 CALL ZGESD2D( CONTXT, 1, 1, A( ( ICOL-1 )*LDA+IROW ), 1, II, 213 $ JJ ) 214 END IF 215 IF( ( MYROW.EQ.II ) .AND. ( RIGHT.EQ.JJ ) .AND. 216 $ ( NPCOL.GT.1 ) ) THEN 217 CALL INFOG2L( M+1, M, DESCA, NPROW, NPCOL, MYROW, MYCOL, 218 $ IROW, ICOL, RSRC, JSRC ) 219 CALL ZGESD2D( CONTXT, 1, 1, A( ( ICOL-1 )*LDA+IROW ), 1, II, 220 $ JJ ) 221 END IF 222 IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN 223 CALL INFOG2L( M+2, M+2, DESCA, NPROW, NPCOL, MYROW, MYCOL, 224 $ IROW, ICOL, RSRC, JSRC ) 225 IF( NUM.GT.1 ) THEN 226 CALL ZGERV2D( CONTXT, 1, 1, H11, 1, UP, LEFT ) 227 ELSE 228 H11 = A( ( ICOL-3 )*LDA+IROW-2 ) 229 END IF 230 IF( NPROW.GT.1 ) THEN 231 CALL ZGERV2D( CONTXT, 1, 1, H12, 1, UP, MYCOL ) 232 ELSE 233 H12 = A( ( ICOL-2 )*LDA+IROW-2 ) 234 END IF 235 IF( NPCOL.GT.1 ) THEN 236 CALL ZGERV2D( CONTXT, 1, 1, H21, 1, MYROW, LEFT ) 237 ELSE 238 H21 = A( ( ICOL-3 )*LDA+IROW-1 ) 239 END IF 240 H22 = A( ( ICOL-2 )*LDA+IROW-1 ) 241 V3 = A( ( ICOL-2 )*LDA+IROW ) 242 END IF 243 END IF 244 IF( ( MYROW.NE.II ) .OR. ( MYCOL.NE.JJ ) ) 245 $ RETURN 246* 247 IF( MODKM1.GT.1 ) THEN 248 CALL INFOG2L( M+2, M+2, DESCA, NPROW, NPCOL, MYROW, MYCOL, 249 $ IROW, ICOL, RSRC, JSRC ) 250 H11 = A( ( ICOL-3 )*LDA+IROW-2 ) 251 H21 = A( ( ICOL-3 )*LDA+IROW-1 ) 252 H12 = A( ( ICOL-2 )*LDA+IROW-2 ) 253 H22 = A( ( ICOL-2 )*LDA+IROW-1 ) 254 V3 = A( ( ICOL-2 )*LDA+IROW ) 255 END IF 256* 257 H44S = H44 - H11 258 H33S = H33 - H11 259 V1 = ( H33S*H44S-H43H34 ) / H21 + H12 260 V2 = H22 - H11 - H33S - H44S 261 S = CABS1( V1 ) + CABS1( V2 ) + CABS1( V3 ) 262 V1 = V1 / S 263 V2 = V2 / S 264 V3 = V3 / S 265 V( 1 ) = V1 266 V( 2 ) = V2 267 V( 3 ) = V3 268* 269 RETURN 270* 271* End of PZLAWIL 272* 273 END 274