* * SUBROUTINE PSLAGSY( N, K, D, A, IA, JA, DESCA, ISEED, ORDER, WORK, $ LWORK, INFO ) * * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. INTEGER IA, INFO, JA, K, LWORK, N, ORDER * .. * .. Array Arguments .. INTEGER DESCA( * ), ISEED( 4 ) REAL A( * ), D( * ), WORK( * ) * .. * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * Purpose * ======= * * PSLAGSY generates a real symmetric matrix A, by pre- and post- * multiplying a real diagonal matrix D with a random orthogonal matrix: * A = U*D*U'. * * This is just a quick implementation which will be replaced in the * future. The random orthogonal matrix is computed by creating a * random matrix and running QR on it. This requires vastly more * computation than necessary, but not significantly more communication * than is used in the rest of this rouinte, and hence is not that much * slower than an efficient solution. * * Arguments * ========= * * N (global input) INTEGER * The size of the matrix A. N >= 0. * * K (global input) INTEGER * The number of nonzero subdiagonals within the band of A. * 0 <= K <= N-1. * ### K must be 0 or N-1, 0 < K < N-1 is not supported yet. * * D (global input) REAL array, dimension (N) * The diagonal elements of the diagonal matrix D. * * A (local output) REAL array * Global dimension (N, N), local dimension (NP, NQ) * The generated n by n symmetric matrix A (the full matrix is * stored). * * IA (global input) INTEGER * A's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JA (global input) INTEGER * A's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * ISEED (global input/output) INTEGER array, dimension (4) * On entry, the seed of the random number generator; the array * elements must be between 0 and 4095, and ISEED(4) must be * odd. * On exit, the seed is updated and will remain identical on * all processes in the context. * * ORDER (global input) INTEGER * Number of reflectors in the matrix Q * At present, ORDER .NE. N is not supported * * WORK (local workspace) REAL array, dimension (LWORK) * * LWORK (local input) INTEGER dimension of WORK * LWORK >= SIZETMS as returned by PSLASIZESEP * * * INFO (local output) INTEGER * = 0: successful exit * < 0: If the i-th argument is an array and the j-entry had * an illegal value, then INFO = -(i*100+j), if the i-th * argument is a scalar and had an illegal value, then * INFO = -i. * * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_, $ MB_, NB_, RSRC_, CSRC_, LLD_ PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER CSRC_A, I, IACOL, IAROW, ICOFFA, II, IIROW, $ INDAA, INDTAU, INDWORK, IPOSTPAD, IPREPAD, $ IROFFA, ISIZESUBTST, ISIZESYEVX, ISIZETST, $ JJCOL, LDAA, LII, LIII, LJJ, LJJJ, LWMIN, MAXI, $ MB_A, MYCOL, MYROW, NB_A, NP, NPCOL, NPROW, NQ, $ RSRC_A, SIZECHK, SIZEMQRLEFT, SIZEMQRRIGHT, $ SIZEQRF, SIZEQTQ, SIZESUBTST, SIZESYEVX, $ SIZETMS, SIZETST * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PSGEQRF, PSLASIZESEP, $ PSMATGEN, PSORMQR, PXERBLA, SLASET * .. * .. External Functions .. INTEGER INDXG2P, NUMROC EXTERNAL INDXG2P, NUMROC * .. * .. Intrinsic Functions .. * INTRINSIC MAX, MIN, MOD * .. * .. Executable Statements .. * This is just to keep ftnchek happy IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* $ RSRC_.LT.0 )RETURN * * Initialize grid information * CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) * * Check LWORK * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -( 700+CTXT_ ) ELSE CALL CHK1MAT( N, 1, N, 1, IA, JA, DESCA, 7, INFO ) END IF * LDAA = DESCA( LLD_ ) MB_A = DESCA( MB_ ) NB_A = DESCA( NB_ ) RSRC_A = DESCA( RSRC_ ) CSRC_A = DESCA( CSRC_ ) IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ) IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ) IROFFA = MOD( IA-1, MB_A ) ICOFFA = MOD( JA-1, NB_A ) NP = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ) IPREPAD = 0 IPOSTPAD = 0 CALL PSLASIZESEP( DESCA, IPREPAD, IPOSTPAD, SIZEMQRLEFT, $ SIZEMQRRIGHT, SIZEQRF, SIZETMS, SIZEQTQ, $ SIZECHK, SIZESYEVX, ISIZESYEVX, SIZESUBTST, $ ISIZESUBTST, SIZETST, ISIZETST ) LWMIN = SIZETMS * * Test the input arguments * IF( INFO.EQ.0 ) THEN IF( K.LT.0 .OR. K.GT.N-1 ) THEN INFO = -2 ELSE IF( N.NE.ORDER ) THEN INFO = -9 ELSE IF( LWORK.LT.LWMIN ) THEN INFO = -11 END IF END IF IF( INFO.LT.0 ) THEN CALL PXERBLA( DESCA( CTXT_ ), 'PSLAGSY', -INFO ) RETURN END IF * INDAA = 1 INDTAU = INDAA + LDAA*MAX( 1, NQ ) INDWORK = INDTAU + MAX( 1, NQ ) * IF( K.NE.0 ) THEN CALL SLASET( 'A', LDAA, NQ, ZERO, ZERO, WORK( INDAA ), LDAA ) * * * Build a random matrix * * CALL PSMATGEN( DESCA( CTXT_ ), 'N', 'N', N, ORDER, $ DESCA( MB_ ), DESCA( NB_ ), WORK( INDAA ), $ DESCA( LLD_ ), DESCA( RSRC_ ), DESCA( CSRC_ ), $ ISEED( 1 ), 0, NP, 0, NQ, MYROW, MYCOL, NPROW, $ NPCOL ) CALL PSGEQRF( N, ORDER, WORK( INDAA ), IA, JA, DESCA, $ WORK( INDTAU ), WORK( INDWORK ), SIZEQRF, INFO ) * END IF * * Build a diagonal matrix A with the eigenvalues specified in D * CALL SLASET( 'A', NP, NQ, ZERO, ZERO, A, DESCA( LLD_ ) ) * IIROW = 0 JJCOL = 0 LII = 1 LJJ = 1 * DO 20 II = 1, N, DESCA( MB_ ) MAXI = MIN( N, II+DESCA( MB_ )-1 ) IF( ( MYROW.EQ.IIROW ) .AND. ( MYCOL.EQ.JJCOL ) ) THEN LIII = LII LJJJ = LJJ DO 10 I = II, MAXI A( LIII+( LJJJ-1 )*DESCA( LLD_ ) ) = D( I ) LIII = LIII + 1 LJJJ = LJJJ + 1 10 CONTINUE END IF IF( MYROW.EQ.IIROW ) $ LII = LII + DESCA( MB_ ) IF( MYCOL.EQ.JJCOL ) $ LJJ = LJJ + DESCA( MB_ ) IIROW = MOD( IIROW+1, NPROW ) JJCOL = MOD( JJCOL+1, NPCOL ) 20 CONTINUE * * A = Q * A * IF( K.NE.0 ) THEN * CALL PSORMQR( 'L', 'Transpose', N, N, ORDER, WORK( INDAA ), IA, $ JA, DESCA, WORK( INDTAU ), A, IA, JA, DESCA, $ WORK( INDWORK ), SIZEMQRLEFT, INFO ) * * * A = A * Q' * * CALL PSORMQR( 'R', 'N', N, N, ORDER, WORK( INDAA ), IA, JA, $ DESCA, WORK( INDTAU ), A, IA, JA, DESCA, $ WORK( INDWORK ), SIZEMQRRIGHT, INFO ) * END IF * * End of PSLAGSY * END