SUBROUTINE PDLAGGE( M, N, 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, LWORK, M, N, ORDER * .. * .. Array Arguments .. INTEGER DESCA( * ), ISEED( 4 ) DOUBLE PRECISION A( * ), D( * ), WORK( * ) * .. * * Purpose * ======= * * PDLAGGE generates a real symmetric matrix A, by pre- and post- * multiplying a real diagonal matrix D with a random orthogonal * matrices: A = U*D*VT. * * This is just a quick implementation which will be replaced in the * future. The random matrix A1(m,n) is generated and random left * orthogonal matrix U(m,m) is obtained by running QR on A1: * A1(m,n) = U(m,m)*R, * where U(m,m) is a product of min(m,n) Householder rotations. * Afterwards the space of A1 is reused for a second random matrix * A2(m,n), which is used to obtain the right orthogonal matrix VT(n,n) * by running LQ on A2: * A2(m,n) = L*VT(n,n). * This requires vastly more computation than necessary, but not * significantly more communication than is used in the rest of this * routine, and hence is not that much slower than an efficient * solution. * * 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 * * Arguments * ========= * * M (global input) INTEGER * Number of rows of the matrix A. M >= 0. * * N (global input) INTEGER * Number of columns of matrix A. N >= 0. * * D (local input) DOUBLE PRECISION array, dimension (N) * The diagonal elements of the diagonal matrix D. * * A (local output) DOUBLE PRECISION array * Global dimension (M, N), local dimension (MP, NQ) * * IA (global input) INTEGER * The global row index of the submatrix of the distributed * matrix A to operate on. * * JA (global input) INTEGER * The global column index of the submatrix of the distributed * matrix A to operate 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) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (local input) INTEGER dimension of WORK * LWORK >= MAX( QR_WORK, LQ_WORK ) * QR_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU1 ) + * MAX( SIZEMQRLEFT, SIZEQRF) * LQ_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU2) + * MAX( SIZEMLQRIGHT, SIZEQRF ) * Where: * LDAA = DESCA( LLD_ ) * MB_A = DESCA( MB_ ) * NB_A = DESCA( NB_ ) * RSRC_A = DESCA( RSRC_ ) * CSRC_A = DESCA( CSRC_ ) * LCM = ILCM( NPROW, NPCOL ) * LCMQ = LCM / NPCOL * IROFFA = MOD( IA-1, MB_A ) * ICOFFA = MOD( JA-1, NB_A ) * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ) * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ) * MP = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ) * NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ) * DTAU1 = NUMROC( JA + SIZE- 1, NB_A, MYCOL, IACOL, NPROW ) * DTAU2 = NUMROC( IA + SIZE- 1, MB_A, MYROW, IAROW, NPROW ) * SIZEMQRLEFT = MAX( (MB_A*(MB_A-1))/2, ( MP + NQ ) * MB_A ) * + ( MP + NB_A ) * NB_A * SIZEMLQRIGHT = MAX( (MB_A*(MB_A-1))/2, (MP + NQ)*MB_A ) + * MB_A * MB_A * SIZEQRF = NB_A*NP + MB_A*NQ + NB_A*NB_A * * 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 ) DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER CSRC_A, DTAU1, DTAU2, I, IACOL, IAROW, ICOFFA, $ IROFFA, LCM, LCMQ, LDAA, LQ_WORK, LWMIN, MB_A, $ MP, MYCOL, MYROW, NB_A, NPCOL, NPROW, NQ, $ PTR2AA, PTR2TAU, PTR2WORK, QR_WORK, RSRC_A, $ SIZE, SIZELQF, SIZEMLQRIGHT, SIZEMQRLEFT, $ SIZEQRF * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PDELSET, PDGELQF, $ PDGEQRF, PDLASET, PDMATGEN, PDORMLQ, PDORMQR, $ PXERBLA * .. * .. External Functions .. INTEGER ILCM, INDXG2P, NUMROC EXTERNAL ILCM, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. Executable Statements .. * This is just to keep ftnchek happy IF( BLOCK_CYCLIC_2D*DLEN_*DTYPE_*M_*N_.LT.0 )RETURN * * Initialize grid information. * CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) * * Check LWORK. * INFO = 0 SIZE = MIN( M, N ) IF( NPROW.EQ.-1 ) THEN INFO = -607 ELSE CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 8, INFO ) END IF * Calculation of a minimum workspace. LDAA = DESCA( LLD_ ) MB_A = DESCA( MB_ ) NB_A = DESCA( NB_ ) RSRC_A = DESCA( RSRC_ ) CSRC_A = DESCA( CSRC_ ) LCM = ILCM( NPROW, NPCOL ) LCMQ = LCM / NPCOL IROFFA = MOD( IA-1, MB_A ) ICOFFA = MOD( JA-1, NB_A ) IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ) IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ) DTAU1 = NUMROC( JA+SIZE-1, NB_A, MYCOL, IACOL, NPCOL ) DTAU2 = NUMROC( IA+SIZE-1, MB_A, MYROW, IAROW, NPROW ) MP = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ) * SIZEMQRLEFT = MAX( ( MB_A*( MB_A-1 ) ) / 2, ( MP+NQ )*MB_A ) + $ ( MP+NB_A )*NB_A SIZEMLQRIGHT = MAX( ( MB_A*( MB_A-1 ) ) / 2, ( MP+NQ )*MB_A ) + $ MB_A*MB_A SIZEQRF = NB_A*MP + MB_A*NQ + NB_A*NB_A + 100 SIZELQF = NB_A*( MP+NQ+NB_A ) + 100 * QR_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU1 ) + $ MAX( SIZEMQRLEFT, SIZEQRF ) LQ_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU2 ) + $ MAX( SIZEMLQRIGHT, SIZELQF ) LWMIN = MAX( QR_WORK, LQ_WORK ) WORK( 1 ) = LWMIN IF( LWORK.EQ.-1 ) $ GO TO 20 * * Test the input arguments. * IF( INFO.EQ.0 ) THEN IF( SIZE.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_ ), 'PDLAGGE', -INFO ) RETURN END IF * * Build a diagonal matrix A with the eigenvalues specified in D. * CALL PDLASET( 'Full', M, N, ZERO, ZERO, A, IA, JA, DESCA ) DO 10 I = 1, SIZE CALL PDELSET( A, I, I, DESCA, D( I ) ) 10 CONTINUE * * Local dimension of array TAU in tis case is LOCc(JA+MIN(M,N)-1). * PTR2AA = 2 PTR2TAU = PTR2AA + LDAA*MAX( 1, NQ ) + 100 PTR2WORK = PTR2TAU + MAX( 1, DTAU1 ) + 100 * CALL PDLASET( 'All', M, N, ZERO, ZERO, WORK( PTR2AA ), IA, JA, $ DESCA ) * * Build a random matrix AA1. * CALL PDMATGEN( DESCA( CTXT_ ), 'N', 'N', M, N, DESCA( MB_ ), $ DESCA( NB_ ), WORK( PTR2AA ), DESCA( LLD_ ), $ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED( 1 ), 0, MP, $ 0, NQ, MYROW, MYCOL, NPROW, NPCOL ) * * Produce QR decomposition AA1 -> U*R. * CALL PDGEQRF( M, N, WORK( PTR2AA ), IA, JA, DESCA, $ WORK( PTR2TAU ), WORK( PTR2WORK ), SIZEQRF, INFO ) * * A = U*A. * CALL PDORMQR( 'L', 'N', M, N, SIZE, WORK( PTR2AA ), IA, JA, DESCA, $ WORK( PTR2TAU ), A, IA, JA, DESCA, WORK( PTR2WORK ), $ SIZEMQRLEFT, INFO ) * * Reinitialize pointer to WORK array. Dimension of array TAU in * this case is LOCr(IA+MIN(M,N)-1). * PTR2WORK = PTR2TAU + MAX( 1, DTAU2 ) + 100 * * Use the same workspace to generate a random matrix AA2. * CALL PDMATGEN( DESCA( CTXT_ ), 'N', 'N', M, N, DESCA( MB_ ), $ DESCA( NB_ ), WORK( PTR2AA ), DESCA( LLD_ ), $ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED( 2 ), 0, MP, $ 0, NQ, MYROW, MYCOL, NPROW, NPCOL ) * * Produce LQ decomposition of random matrix AA2 -> L*VT. * CALL PDGELQF( M, N, WORK( PTR2AA ), IA, JA, DESCA, $ WORK( PTR2TAU ), WORK( PTR2WORK ), SIZELQF, INFO ) * * Calculate A = A*VT. * CALL PDORMLQ( 'R', 'N', M, N, SIZE, WORK( PTR2AA ), IA, JA, DESCA, $ WORK( PTR2TAU ), A, IA, JA, DESCA, WORK( PTR2WORK ), $ SIZEMLQRIGHT, INFO ) * * End of PDLAGGE * 20 CONTINUE RETURN END