1 SUBROUTINE PDGETF2( M, N, A, IA, JA, DESCA, IPIV, INFO ) 2* 3* -- ScaLAPACK routine (version 1.7) -- 4* University of Tennessee, Knoxville, Oak Ridge National Laboratory, 5* and University of California, Berkeley. 6* May 1, 1997 7* 8* .. Scalar Arguments .. 9 INTEGER IA, INFO, JA, M, N 10* .. 11* .. Array Arguments .. 12 INTEGER DESCA( * ), IPIV( * ) 13 DOUBLE PRECISION A( * ) 14* .. 15* 16* Purpose 17* ======= 18* 19* PDGETF2 computes an LU factorization of a general M-by-N 20* distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using 21* partial pivoting with row interchanges. 22* 23* The factorization has the form sub( A ) = P * L * U, where P is a 24* permutation matrix, L is lower triangular with unit diagonal 25* elements (lower trapezoidal if m > n), and U is upper triangular 26* (upper trapezoidal if m < n). 27* 28* This is the right-looking Parallel Level 2 BLAS version of the 29* algorithm. 30* 31* Notes 32* ===== 33* 34* Each global data object is described by an associated description 35* vector. This vector stores the information required to establish 36* the mapping between an object element and its corresponding process 37* and memory location. 38* 39* Let A be a generic term for any 2D block cyclicly distributed array. 40* Such a global array has an associated description vector DESCA. 41* In the following comments, the character _ should be read as 42* "of the global array". 43* 44* NOTATION STORED IN EXPLANATION 45* --------------- -------------- -------------------------------------- 46* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 47* DTYPE_A = 1. 48* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 49* the BLACS process grid A is distribu- 50* ted over. The context itself is glo- 51* bal, but the handle (the integer 52* value) may vary. 53* M_A (global) DESCA( M_ ) The number of rows in the global 54* array A. 55* N_A (global) DESCA( N_ ) The number of columns in the global 56* array A. 57* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 58* the rows of the array. 59* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 60* the columns of the array. 61* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 62* row of the array A is distributed. 63* CSRC_A (global) DESCA( CSRC_ ) The process column over which the 64* first column of the array A is 65* distributed. 66* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 67* array. LLD_A >= MAX(1,LOCr(M_A)). 68* 69* Let K be the number of rows or columns of a distributed matrix, 70* and assume that its process grid has dimension p x q. 71* LOCr( K ) denotes the number of elements of K that a process 72* would receive if K were distributed over the p processes of its 73* process column. 74* Similarly, LOCc( K ) denotes the number of elements of K that a 75* process would receive if K were distributed over the q processes of 76* its process row. 77* The values of LOCr() and LOCc() may be determined via a call to the 78* ScaLAPACK tool function, NUMROC: 79* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 80* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 81* An upper bound for these quantities may be computed by: 82* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 83* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 84* 85* This routine requires N <= NB_A-MOD(JA-1, NB_A) and square block 86* decomposition ( MB_A = NB_A ). 87* 88* Arguments 89* ========= 90* 91* M (global input) INTEGER 92* The number of rows to be operated on, i.e. the number of rows 93* of the distributed submatrix sub( A ). M >= 0. 94* 95* N (global input) INTEGER 96* The number of columns to be operated on, i.e. the number of 97* columns of the distributed submatrix sub( A ). 98* NB_A-MOD(JA-1, NB_A) >= N >= 0. 99* 100* A (local input/local output) DOUBLE PRECISION pointer into the 101* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). 102* On entry, this array contains the local pieces of the M-by-N 103* distributed matrix sub( A ). On exit, this array contains 104* the local pieces of the factors L and U from the factoriza- 105* tion sub( A ) = P*L*U; the unit diagonal elements of L are 106* not stored. 107* 108* IA (global input) INTEGER 109* The row index in the global array A indicating the first 110* row of sub( A ). 111* 112* JA (global input) INTEGER 113* The column index in the global array A indicating the 114* first column of sub( A ). 115* 116* DESCA (global and local input) INTEGER array of dimension DLEN_. 117* The array descriptor for the distributed matrix A. 118* 119* IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A ) 120* This array contains the pivoting information. 121* IPIV(i) -> The global row local row i was swapped with. 122* This array is tied to the distributed matrix A. 123* 124* INFO (local output) INTEGER 125* = 0: successful exit 126* < 0: If the i-th argument is an array and the j-entry had 127* an illegal value, then INFO = -(i*100+j), if the i-th 128* argument is a scalar and had an illegal value, then 129* INFO = -i. 130* > 0: If INFO = K, U(IA+K-1,JA+K-1) is exactly zero. 131* The factorization has been completed, but the factor U 132* is exactly singular, and division by zero will occur if 133* it is used to solve a system of equations. 134* 135* ===================================================================== 136* 137* .. Parameters .. 138 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 139 $ LLD_, MB_, M_, NB_, N_, RSRC_ 140 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 141 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 142 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 143 DOUBLE PRECISION ONE, ZERO 144 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 145* .. 146* .. Local Scalars .. 147 CHARACTER ROWBTOP 148 INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IIA, IROFF, J, 149 $ JJA, MN, MYCOL, MYROW, NPCOL, NPROW 150 DOUBLE PRECISION GMAX 151* .. 152* .. External Subroutines .. 153 EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, IGEBR2D, 154 $ IGEBS2D, INFOG2L, PDAMAX, PDGER, 155 $ PDSCAL, PDSWAP, PB_TOPGET, PXERBLA 156* .. 157* .. Intrinsic Functions .. 158 INTRINSIC MIN, MOD 159* .. 160* .. Executable Statements .. 161* 162* Get grid parameters. 163* 164 ICTXT = DESCA( CTXT_ ) 165 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 166* 167* Test the input parameters. 168* 169 INFO = 0 170 IF( NPROW.EQ.-1 ) THEN 171 INFO = -(600+CTXT_) 172 ELSE 173 CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) 174 IF( INFO.EQ.0 ) THEN 175 IROFF = MOD( IA-1, DESCA( MB_ ) ) 176 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 177 IF( N+ICOFF.GT.DESCA( NB_ ) ) THEN 178 INFO = -2 179 ELSE IF( IROFF.NE.0 ) THEN 180 INFO = -4 181 ELSE IF( ICOFF.NE.0 ) THEN 182 INFO = -5 183 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN 184 INFO = -(600+NB_) 185 END IF 186 END IF 187 END IF 188* 189 IF( INFO.NE.0 ) THEN 190 CALL PXERBLA( ICTXT, 'PDGETF2', -INFO ) 191 CALL BLACS_ABORT( ICTXT, 1 ) 192 RETURN 193 END IF 194* 195* Quick return if possible 196* 197 IF( M.EQ.0 .OR. N.EQ.0 ) 198 $ RETURN 199* 200 MN = MIN( M, N ) 201 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 202 $ IAROW, IACOL ) 203 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 204* 205 IF( MYCOL.EQ.IACOL ) THEN 206 DO 10 J = JA, JA+MN-1 207 I = IA + J - JA 208* 209* Find pivot and test for singularity. 210* 211 CALL PDAMAX( M-J+JA, GMAX, IPIV( IIA+J-JA ), A, I, J, 212 $ DESCA, 1 ) 213 IF( GMAX.NE.ZERO ) THEN 214* 215* Apply the row interchanges to columns JA:JA+N-1 216* 217 CALL PDSWAP( N, A, I, JA, DESCA, DESCA( M_ ), A, 218 $ IPIV( IIA+J-JA ), JA, DESCA, DESCA( M_ ) ) 219* 220* Compute elements I+1:IA+M-1 of J-th column. 221* 222 IF( J-JA+1.LT.M ) 223 $ CALL PDSCAL( M-J+JA-1, ONE / GMAX, A, I+1, J, 224 $ DESCA, 1 ) 225 ELSE IF( INFO.EQ.0 ) THEN 226 INFO = J - JA + 1 227 END IF 228* 229* Update trailing submatrix 230* 231 IF( J-JA+1.LT.MN ) THEN 232 CALL PDGER( M-J+JA-1, N-J+JA-1, -ONE, A, I+1, J, DESCA, 233 $ 1, A, I, J+1, DESCA, DESCA( M_ ), A, I+1, 234 $ J+1, DESCA ) 235 END IF 236 10 CONTINUE 237* 238 CALL IGEBS2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ), 239 $ MN ) 240* 241 ELSE 242* 243 CALL IGEBR2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ), 244 $ MN, MYROW, IACOL ) 245* 246 END IF 247* 248 RETURN 249* 250* End of PDGETF2 251* 252 END 253