SUBROUTINE PDGBTRS( TRANS, N, BWL, BWU, NRHS, A, JA, DESCA, IPIV, $ B, IB, DESCB, AF, LAF, WORK, LWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * April 3, 2000 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER BWL, BWU, IB, INFO, JA, LAF, LWORK, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ), IPIV( * ) DOUBLE PRECISION A( * ), AF( * ), B( * ), WORK( * ) * .. * * Purpose * ======= * * PDGBTRS solves a system of linear equations * * A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) * or * A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) * * where A(1:N, JA:JA+N-1) is the matrix used to produce the factors * stored in A(1:N,JA:JA+N-1) and AF by PDGBTRF. * A(1:N, JA:JA+N-1) is an N-by-N real * banded distributed * matrix with bandwidth BWL, BWU. * * Routine PDGBTRF MUST be called first. * * ===================================================================== * * Arguments * ========= * * * TRANS (global input) CHARACTER * = 'N': Solve with A(1:N, JA:JA+N-1); * = 'T' or 'C': Solve with A(1:N, JA:JA+N-1)^T; * * N (global input) INTEGER * The number of rows and columns to be operated on, i.e. the * order of the distributed submatrix A(1:N, JA:JA+N-1). N >= 0. * * BWL (global input) INTEGER * Number of subdiagonals. 0 <= BWL <= N-1 * * BWU (global input) INTEGER * Number of superdiagonals. 0 <= BWU <= N-1 * * NRHS (global input) INTEGER * The number of right hand sides, i.e., the number of columns * of the distributed submatrix B(IB:IB+N-1, 1:NRHS). * NRHS >= 0. * * A (local input/local output) DOUBLE PRECISION pointer into * local memory to an array with first dimension * LLD_A >=(2*bwl+2*bwu+1) (stored in DESCA). * On entry, this array contains the local pieces of the * N-by-N unsymmetric banded distributed Cholesky factor L or * L^T A(1:N, JA:JA+N-1). * This local portion is stored in the packed banded format * used in LAPACK. Please see the Notes below and the * ScaLAPACK manual for more detail on the format of * distributed matrices. * * JA (global input) INTEGER * The index in the global array A that points to the start of * the matrix to be operated on (which may be either all of A * or a submatrix of A). * * DESCA (global and local input) INTEGER array of dimension DLEN. * if 1D type (DTYPE_A=501), DLEN >= 7; * if 2D type (DTYPE_A=1), DLEN >= 9 . * The array descriptor for the distributed matrix A. * Contains information of mapping of A to memory. Please * see NOTES below for full description and options. * * IPIV (local output) INTEGER array, dimension >= DESCA( NB ). * Pivot indices for local factorizations. * Users *should not* alter the contents between * factorization and solve. * * B (local input/local output) DOUBLE PRECISION pointer into * local memory to an array of local lead dimension lld_b>=NB. * On entry, this array contains the * the local pieces of the right hand sides * B(IB:IB+N-1, 1:NRHS). * On exit, this contains the local piece of the solutions * distributed matrix X. * * IB (global input) INTEGER * The row index in the global array B that points to the first * row of the matrix to be operated on (which may be either * all of B or a submatrix of B). * * DESCB (global and local input) INTEGER array of dimension DLEN. * if 1D type (DTYPE_B=502), DLEN >=7; * if 2D type (DTYPE_B=1), DLEN >= 9. * The array descriptor for the distributed matrix B. * Contains information of mapping of B to memory. Please * see NOTES below for full description and options. * * AF (local output) DOUBLE PRECISION array, dimension LAF. * Auxiliary Fillin Space. * Fillin is created during the factorization routine * PDGBTRF and this is stored in AF. If a linear system * is to be solved using PDGBTRS after the factorization * routine, AF *must not be altered* after the factorization. * * LAF (local input) INTEGER * Size of user-input Auxiliary Fillin space AF. Must be >= * (NB+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) * If LAF is not large enough, an error code will be returned * and the minimum acceptable size will be returned in AF( 1 ) * * WORK (local workspace/local output) * DOUBLE PRECISION temporary workspace. This space may * be overwritten in between calls to routines. WORK must be * the size given in LWORK. * On exit, WORK( 1 ) contains the minimal LWORK. * * LWORK (local input or global input) INTEGER * Size of user-input workspace WORK. * If LWORK is too small, the minimal acceptable size will be * returned in WORK(1) and an error code is returned. LWORK>= * NRHS*(NB+2*bwl+4*bwu) * * INFO (global 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. * * ===================================================================== * * Restrictions * ============ * * The following are restrictions on the input parameters. Some of these * are temporary and will be removed in future releases, while others * may reflect fundamental technical limitations. * * Non-cyclic restriction: VERY IMPORTANT! * P*NB>= mod(JA-1,NB)+N. * The mapping for matrices must be blocked, reflecting the nature * of the divide and conquer algorithm as a task-parallel algorithm. * This formula in words is: no processor may have more than one * chunk of the matrix. * * Blocksize cannot be too small: * If the matrix spans more than one processor, the following * restriction on NB, the size of each block on each processor, * must hold: * NB >= (BWL+BWU)+1 * The bulk of parallel computation is done on the matrix of size * O(NB) on each processor. If this is too small, divide and conquer * is a poor choice of algorithm. * * Submatrix reference: * JA = IB * Alignment restriction that prevents unnecessary communication. * * ===================================================================== * * Notes * ===== * * If the factorization routine and the solve routine are to be called * separately (to solve various sets of righthand sides using the same * coefficient matrix), the auxiliary space AF *must not be altered* * between calls to the factorization routine and the solve routine. * * The best algorithm for solving banded and tridiagonal linear systems * depends on a variety of parameters, especially the bandwidth. * Currently, only algorithms designed for the case N/P >> bw are * implemented. These go by many names, including Divide and Conquer, * Partitioning, domain decomposition-type, etc. * * Algorithm description: Divide and Conquer * * The Divide and Conqer algorithm assumes the matrix is narrowly * banded compared with the number of equations. In this situation, * it is best to distribute the input matrix A one-dimensionally, * with columns atomic and rows divided amongst the processes. * The basic algorithm divides the banded matrix up into * P pieces with one stored on each processor, * and then proceeds in 2 phases for the factorization or 3 for the * solution of a linear system. * 1) Local Phase: * The individual pieces are factored independently and in * parallel. These factors are applied to the matrix creating * fillin, which is stored in a non-inspectable way in auxiliary * space AF. Mathematically, this is equivalent to reordering * the matrix A as P A P^T and then factoring the principal * leading submatrix of size equal to the sum of the sizes of * the matrices factored on each processor. The factors of * these submatrices overwrite the corresponding parts of A * in memory. * 2) Reduced System Phase: * A small (max(bwl,bwu)* (P-1)) system is formed representing * interaction of the larger blocks, and is stored (as are its * factors) in the space AF. A parallel Block Cyclic Reduction * algorithm is used. For a linear system, a parallel front solve * followed by an analagous backsolve, both using the structure * of the factored matrix, are performed. * 3) Backsubsitution Phase: * For a linear system, a local backsubstitution is performed on * each processor in parallel. * * * Descriptors * =========== * * Descriptors now have *types* and differ from ScaLAPACK 1.0. * * Note: banded codes can use either the old two dimensional * or new one-dimensional descriptors, though the processor grid in * both cases *must be one-dimensional*. We describe both types below. * * 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 * * * One-dimensional descriptors: * * One-dimensional descriptors are a new addition to ScaLAPACK since * version 1.0. They simplify and shorten the descriptor for 1D * arrays. * * Since ScaLAPACK supports two-dimensional arrays as the fundamental * object, we allow 1D arrays to be distributed either over the * first dimension of the array (as if the grid were P-by-1) or the * 2nd dimension (as if the grid were 1-by-P). This choice is * indicated by the descriptor type (501 or 502) * as described below. * * IMPORTANT NOTE: the actual BLACS grid represented by the * CTXT entry in the descriptor may be *either* P-by-1 or 1-by-P * irrespective of which one-dimensional descriptor type * (501 or 502) is input. * This routine will interpret the grid properly either way. * ScaLAPACK routines *do not support intercontext operations* so that * the grid passed to a single ScaLAPACK routine *must be the same* * for all array descriptors passed to that routine. * * NOTE: In all cases where 1D descriptors are used, 2D descriptors * may also be used, since a one-dimensional array is a special case * of a two-dimensional array with one dimension of size unity. * The two-dimensional array used in this case *must* be of the * proper orientation: * If the appropriate one-dimensional descriptor is DTYPEA=501 * (1 by P type), then the two dimensional descriptor must * have a CTXT value that refers to a 1 by P BLACS grid; * If the appropriate one-dimensional descriptor is DTYPEA=502 * (P by 1 type), then the two dimensional descriptor must * have a CTXT value that refers to a P by 1 BLACS grid. * * * Summary of allowed descriptors, types, and BLACS grids: * DTYPE 501 502 1 1 * BLACS grid 1xP or Px1 1xP or Px1 1xP Px1 * ----------------------------------------------------- * A OK NO OK NO * B NO OK NO OK * * Note that a consequence of this chart is that it is not possible * for *both* DTYPE_A and DTYPE_B to be 2D_type(1), as these lead * to opposite requirements for the orientation of the BLACS grid, * and as noted before, the *same* BLACS context must be used in * all descriptors in a single ScaLAPACK subroutine call. * * Let A be a generic term for any 1D 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( 1 ) The descriptor type. For 1D grids, * TYPE_A = 501: 1-by-P grid. * TYPE_A = 502: P-by-1 grid. * CTXT_A (global) DESCA( 2 ) 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. * N_A (global) DESCA( 3 ) The size of the array dimension being * distributed. * NB_A (global) DESCA( 4 ) The blocking factor used to distribute * the distributed dimension of the array. * SRC_A (global) DESCA( 5 ) The process row or column over which the * first row or column of the array * is distributed. * LLD_A (local) DESCA( 6 ) The leading dimension of the local array * storing the local blocks of the distri- * buted array A. Minimum value of LLD_A * depends on TYPE_A. * TYPE_A = 501: LLD_A >= * size of undistributed dimension, 1. * TYPE_A = 502: LLD_A >=NB_A, 1. * Reserved DESCA( 7 ) Reserved for future use. * * ===================================================================== * * Implemented for ScaLAPACK by: * Andrew J. Cleary, Livermore National Lab and University of Tenn., * and Markus Hegland, Australian National University. Feb., 1997. * Based on code written by : Peter Arbenz, ETH Zurich, 1996. * Last modified by: Peter Arbenz, Institute of Scientific Computing, * ETH, Zurich. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) INTEGER INT_ONE PARAMETER ( INT_ONE = 1 ) INTEGER DESCMULT, BIGNUM PARAMETER ( DESCMULT = 100, BIGNUM = DESCMULT*DESCMULT ) INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, $ LLD_, MB_, M_, NB_, N_, RSRC_ 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 ) * .. * .. Local Scalars .. INTEGER APTR, BBPTR, BM, BMN, BN, BNN, BW, CSRC, $ FIRST_PROC, ICTXT, ICTXT_NEW, ICTXT_SAVE, $ IDUM2, IDUM3, J, JA_NEW, L, LBWL, LBWU, LDBB, $ LDW, LLDA, LLDB, LM, LMJ, LN, LPTR, MYCOL, $ MYROW, NB, NEICOL, NP, NPACT, NPCOL, NPROW, $ NPSTR, NP_SAVE, ODD_SIZE, PART_OFFSET, $ RECOVERY_VAL, RETURN_CODE, STORE_M_B, $ STORE_N_A, WORK_SIZE_MIN, WPTR * .. * .. Local Arrays .. INTEGER DESCA_1XP( 7 ), DESCB_PX1( 7 ), $ PARAM_CHECK( 17, 3 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDEXIT, BLACS_GRIDINFO, DCOPY, $ DESC_CONVERT, DGEMM, DGEMV, DGER, DGERV2D, $ DGESD2D, DGETRS, DLACPY, DLASWP, DSCAL, DSWAP, $ DTRSM, GLOBCHK, PXERBLA, RESHAPE * .. * .. External Functions .. LOGICAL LSAME INTEGER NUMROC EXTERNAL LSAME, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, MAX, MIN, MOD * .. * .. Executable Statements .. * * * Test the input parameters * INFO = 0 * * Convert descriptor into standard form for easy access to * parameters, check that grid is of right shape. * DESCA_1XP( 1 ) = 501 DESCB_PX1( 1 ) = 502 * CALL DESC_CONVERT( DESCA, DESCA_1XP, RETURN_CODE ) * IF( RETURN_CODE.NE.0 ) THEN INFO = -( 8*100+2 ) END IF * CALL DESC_CONVERT( DESCB, DESCB_PX1, RETURN_CODE ) * IF( RETURN_CODE.NE.0 ) THEN INFO = -( 11*100+2 ) END IF * * Consistency checks for DESCA and DESCB. * * Context must be the same IF( DESCA_1XP( 2 ).NE.DESCB_PX1( 2 ) ) THEN INFO = -( 11*100+2 ) END IF * * These are alignment restrictions that may or may not be removed * in future releases. -Andy Cleary, April 14, 1996. * * Block sizes must be the same IF( DESCA_1XP( 4 ).NE.DESCB_PX1( 4 ) ) THEN INFO = -( 11*100+4 ) END IF * * Source processor must be the same * IF( DESCA_1XP( 5 ).NE.DESCB_PX1( 5 ) ) THEN INFO = -( 11*100+5 ) END IF * * Get values out of descriptor for use in code. * ICTXT = DESCA_1XP( 2 ) CSRC = DESCA_1XP( 5 ) NB = DESCA_1XP( 4 ) LLDA = DESCA_1XP( 6 ) STORE_N_A = DESCA_1XP( 3 ) LLDB = DESCB_PX1( 6 ) STORE_M_B = DESCB_PX1( 3 ) * * Get grid parameters * * CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) NP = NPROW*NPCOL * * * IF( LSAME( TRANS, 'N' ) ) THEN IDUM2 = ICHAR( 'N' ) ELSE IF( LSAME( TRANS, 'T' ) ) THEN IDUM2 = ICHAR( 'T' ) ELSE IF( LSAME( TRANS, 'C' ) ) THEN IDUM2 = ICHAR( 'T' ) ELSE INFO = -1 END IF * IF( LWORK.LT.-1 ) THEN INFO = -16 ELSE IF( LWORK.EQ.-1 ) THEN IDUM3 = -1 ELSE IDUM3 = 1 END IF * IF( N.LT.0 ) THEN INFO = -2 END IF * IF( N+JA-1.GT.STORE_N_A ) THEN INFO = -( 8*100+6 ) END IF * IF( ( BWL.GT.N-1 ) .OR. ( BWL.LT.0 ) ) THEN INFO = -3 END IF * IF( ( BWU.GT.N-1 ) .OR. ( BWU.LT.0 ) ) THEN INFO = -4 END IF * IF( LLDA.LT.( 2*BWL+2*BWU+1 ) ) THEN INFO = -( 8*100+6 ) END IF * IF( NB.LE.0 ) THEN INFO = -( 8*100+4 ) END IF * BW = BWU + BWL * IF( N+IB-1.GT.STORE_M_B ) THEN INFO = -( 11*100+3 ) END IF * IF( LLDB.LT.NB ) THEN INFO = -( 11*100+6 ) END IF * IF( NRHS.LT.0 ) THEN INFO = -5 END IF * * Current alignment restriction * IF( JA.NE.IB ) THEN INFO = -7 END IF * * Argument checking that is specific to Divide & Conquer routine * IF( NPROW.NE.1 ) THEN INFO = -( 8*100+2 ) END IF * IF( N.GT.NP*NB-MOD( JA-1, NB ) ) THEN INFO = -( 2 ) CALL PXERBLA( ICTXT, 'PDGBTRS, D&C alg.: only 1 block per proc' $ , -INFO ) RETURN END IF * IF( ( JA+N-1.GT.NB ) .AND. ( NB.LT.( BWL+BWU+1 ) ) ) THEN INFO = -( 8*100+4 ) CALL PXERBLA( ICTXT, 'PDGBTRS, D&C alg.: NB too small', -INFO ) RETURN END IF * * * Check worksize * WORK_SIZE_MIN = NRHS*( NB+2*BWL+4*BWU ) * WORK( 1 ) = WORK_SIZE_MIN * IF( LWORK.LT.WORK_SIZE_MIN ) THEN IF( LWORK.NE.-1 ) THEN INFO = -16 CALL PXERBLA( ICTXT, 'PDGBTRS: worksize error ', -INFO ) END IF RETURN END IF * * Pack params and positions into arrays for global consistency check * PARAM_CHECK( 17, 1 ) = DESCB( 5 ) PARAM_CHECK( 16, 1 ) = DESCB( 4 ) PARAM_CHECK( 15, 1 ) = DESCB( 3 ) PARAM_CHECK( 14, 1 ) = DESCB( 2 ) PARAM_CHECK( 13, 1 ) = DESCB( 1 ) PARAM_CHECK( 12, 1 ) = IB PARAM_CHECK( 11, 1 ) = DESCA( 5 ) PARAM_CHECK( 10, 1 ) = DESCA( 4 ) PARAM_CHECK( 9, 1 ) = DESCA( 3 ) PARAM_CHECK( 8, 1 ) = DESCA( 1 ) PARAM_CHECK( 7, 1 ) = JA PARAM_CHECK( 6, 1 ) = NRHS PARAM_CHECK( 5, 1 ) = BWU PARAM_CHECK( 4, 1 ) = BWL PARAM_CHECK( 3, 1 ) = N PARAM_CHECK( 2, 1 ) = IDUM3 PARAM_CHECK( 1, 1 ) = IDUM2 * PARAM_CHECK( 17, 2 ) = 1105 PARAM_CHECK( 16, 2 ) = 1104 PARAM_CHECK( 15, 2 ) = 1103 PARAM_CHECK( 14, 2 ) = 1102 PARAM_CHECK( 13, 2 ) = 1101 PARAM_CHECK( 12, 2 ) = 10 PARAM_CHECK( 11, 2 ) = 805 PARAM_CHECK( 10, 2 ) = 804 PARAM_CHECK( 9, 2 ) = 803 PARAM_CHECK( 8, 2 ) = 801 PARAM_CHECK( 7, 2 ) = 7 PARAM_CHECK( 6, 2 ) = 5 PARAM_CHECK( 5, 2 ) = 4 PARAM_CHECK( 4, 2 ) = 3 PARAM_CHECK( 3, 2 ) = 2 PARAM_CHECK( 2, 2 ) = 16 PARAM_CHECK( 1, 2 ) = 1 * * Want to find errors with MIN( ), so if no error, set it to a big * number. If there already is an error, multiply by the the * descriptor multiplier. * IF( INFO.GE.0 ) THEN INFO = BIGNUM ELSE IF( INFO.LT.-DESCMULT ) THEN INFO = -INFO ELSE INFO = -INFO*DESCMULT END IF * * Check consistency across processors * CALL GLOBCHK( ICTXT, 17, PARAM_CHECK, 17, PARAM_CHECK( 1, 3 ), $ INFO ) * * Prepare output: set info = 0 if no error, and divide by DESCMULT * if error is not in a descriptor entry. * IF( INFO.EQ.BIGNUM ) THEN INFO = 0 ELSE IF( MOD( INFO, DESCMULT ).EQ.0 ) THEN INFO = -INFO / DESCMULT ELSE INFO = -INFO END IF * IF( INFO.LT.0 ) THEN CALL PXERBLA( ICTXT, 'PDGBTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( NRHS.EQ.0 ) $ RETURN * * * Adjust addressing into matrix space to properly get into * the beginning part of the relevant data * PART_OFFSET = NB*( ( JA-1 ) / ( NPCOL*NB ) ) * IF( ( MYCOL-CSRC ).LT.( JA-PART_OFFSET-1 ) / NB ) THEN PART_OFFSET = PART_OFFSET + NB END IF * IF( MYCOL.LT.CSRC ) THEN PART_OFFSET = PART_OFFSET - NB END IF * * Form a new BLACS grid (the "standard form" grid) with only procs * holding part of the matrix, of size 1xNP where NP is adjusted, * starting at csrc=0, with JA modified to reflect dropped procs. * * First processor to hold part of the matrix: * FIRST_PROC = MOD( ( JA-1 ) / NB+CSRC, NPCOL ) * * Calculate new JA one while dropping off unused processors. * JA_NEW = MOD( JA-1, NB ) + 1 * * Save and compute new value of NP * NP_SAVE = NP NP = ( JA_NEW+N-2 ) / NB + 1 * * Call utility routine that forms "standard-form" grid * CALL RESHAPE( ICTXT, INT_ONE, ICTXT_NEW, INT_ONE, FIRST_PROC, $ INT_ONE, NP ) * * Use new context from standard grid as context. * ICTXT_SAVE = ICTXT ICTXT = ICTXT_NEW DESCA_1XP( 2 ) = ICTXT_NEW DESCB_PX1( 2 ) = ICTXT_NEW * * Get information about new grid. * CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Drop out processors that do not have part of the matrix. * IF( MYROW.LT.0 ) THEN GO TO 100 END IF * * * * Begin main code * * Move data into workspace - communicate/copy (overlap) * IF( MYCOL.LT.NPCOL-1 ) THEN CALL DGESD2D( ICTXT, BWU, NRHS, B( NB-BWU+1 ), LLDB, 0, $ MYCOL+1 ) END IF * IF( MYCOL.LT.NPCOL-1 ) THEN LM = NB - BWU ELSE LM = NB END IF * IF( MYCOL.GT.0 ) THEN WPTR = BWU + 1 ELSE WPTR = 1 END IF * LDW = NB + BWU + 2*BW + BWU * CALL DLACPY( 'G', LM, NRHS, B( 1 ), LLDB, WORK( WPTR ), LDW ) * * Zero out rest of work * DO 20 J = 1, NRHS DO 10 L = WPTR + LM, LDW WORK( ( J-1 )*LDW+L ) = ZERO 10 CONTINUE 20 CONTINUE * IF( MYCOL.GT.0 ) THEN CALL DGERV2D( ICTXT, BWU, NRHS, WORK( 1 ), LDW, 0, MYCOL-1 ) END IF * ******************************************************************** * PHASE 1: Local computation phase -- Solve L*X = B ******************************************************************** * * Size of main (or odd) partition in each processor * ODD_SIZE = NUMROC( N, NB, MYCOL, 0, NPCOL ) * IF( MYCOL.NE.0 ) THEN LBWL = BW LBWU = 0 APTR = 1 ELSE LBWL = BWL LBWU = BWU APTR = 1 + BWU END IF * IF( MYCOL.NE.NPCOL-1 ) THEN LM = NB - LBWU LN = NB - BW ELSE IF( MYCOL.NE.0 ) THEN LM = ODD_SIZE + BWU LN = MAX( ODD_SIZE-BW, 0 ) ELSE LM = N LN = MAX( N-BW, 0 ) END IF * DO 30 J = 1, LN * LMJ = MIN( LBWL, LM-J ) L = IPIV( J ) * IF( L.NE.J ) THEN CALL DSWAP( NRHS, WORK( L ), LDW, WORK( J ), LDW ) END IF * LPTR = BW + 1 + ( J-1 )*LLDA + APTR * CALL DGER( LMJ, NRHS, -ONE, A( LPTR ), 1, WORK( J ), LDW, $ WORK( J+1 ), LDW ) * 30 CONTINUE * ******************************************************************** * PHASE 2: Global computation phase -- Solve L*X = B ******************************************************************** * * Define the initial dimensions of the diagonal blocks * The offdiagonal blocks (for MYCOL > 0) are of size BM by BW * IF( MYCOL.NE.NPCOL-1 ) THEN BM = BW - LBWU BN = BW ELSE BM = MIN( BW, ODD_SIZE ) + BWU BN = MIN( BW, ODD_SIZE ) END IF * * Pointer to first element of block bidiagonal matrix in AF * Leading dimension of block bidiagonal system * BBPTR = ( NB+BWU )*BW + 1 LDBB = 2*BW + BWU * IF( NPCOL.EQ.1 ) THEN * * In this case the loop over the levels will not be * performed. CALL DGETRS( 'N', N-LN, NRHS, AF( BBPTR+BW*LDBB ), LDBB, $ IPIV( LN+1 ), WORK( LN+1 ), LDW, INFO ) * END IF * * Loop over levels ... * * The two integers NPACT (nu. of active processors) and NPSTR * (stride between active processors) is used to control the * loop. * NPACT = NPCOL NPSTR = 1 * * Begin loop over levels 40 CONTINUE IF( NPACT.LE.1 ) $ GO TO 50 * * Test if processor is active IF( MOD( MYCOL, NPSTR ).EQ.0 ) THEN * * Send/Receive blocks * IF( MOD( MYCOL, 2*NPSTR ).EQ.0 ) THEN * NEICOL = MYCOL + NPSTR * IF( NEICOL / NPSTR.LE.NPACT-1 ) THEN * IF( NEICOL / NPSTR.LT.NPACT-1 ) THEN BMN = BW ELSE BMN = MIN( BW, NUMROC( N, NB, NEICOL, 0, NPCOL ) ) + $ BWU END IF * CALL DGESD2D( ICTXT, BM, NRHS, WORK( LN+1 ), LDW, 0, $ NEICOL ) * IF( NPACT.NE.2 ) THEN * * Receive answers back from partner processor * CALL DGERV2D( ICTXT, BM+BMN-BW, NRHS, WORK( LN+1 ), $ LDW, 0, NEICOL ) * BM = BM + BMN - BW * END IF * END IF * ELSE * NEICOL = MYCOL - NPSTR * IF( NEICOL.EQ.0 ) THEN BMN = BW - BWU ELSE BMN = BW END IF * CALL DLACPY( 'G', BM, NRHS, WORK( LN+1 ), LDW, $ WORK( NB+BWU+BMN+1 ), LDW ) * CALL DGERV2D( ICTXT, BMN, NRHS, WORK( NB+BWU+1 ), LDW, 0, $ NEICOL ) * * and do the permutations and eliminations * IF( NPACT.NE.2 ) THEN * * Solve locally for BW variables * CALL DLASWP( NRHS, WORK( NB+BWU+1 ), LDW, 1, BW, $ IPIV( LN+1 ), 1 ) * CALL DTRSM( 'L', 'L', 'N', 'U', BW, NRHS, ONE, $ AF( BBPTR+BW*LDBB ), LDBB, WORK( NB+BWU+1 ), $ LDW ) * * Use soln just calculated to update RHS * CALL DGEMM( 'N', 'N', BM+BMN-BW, NRHS, BW, -ONE, $ AF( BBPTR+BW*LDBB+BW ), LDBB, $ WORK( NB+BWU+1 ), LDW, ONE, $ WORK( NB+BWU+1+BW ), LDW ) * * Give answers back to partner processor * CALL DGESD2D( ICTXT, BM+BMN-BW, NRHS, $ WORK( NB+BWU+1+BW ), LDW, 0, NEICOL ) * ELSE * * Finish up calculations for final level * CALL DLASWP( NRHS, WORK( NB+BWU+1 ), LDW, 1, BM+BMN, $ IPIV( LN+1 ), 1 ) * CALL DTRSM( 'L', 'L', 'N', 'U', BM+BMN, NRHS, ONE, $ AF( BBPTR+BW*LDBB ), LDBB, WORK( NB+BWU+1 ), $ LDW ) END IF * END IF * NPACT = ( NPACT+1 ) / 2 NPSTR = NPSTR*2 GO TO 40 * END IF * 50 CONTINUE * * ************************************** * BACKSOLVE ******************************************************************** * PHASE 2: Global computation phase -- Solve U*Y = X ******************************************************************** * IF( NPCOL.EQ.1 ) THEN * * In this case the loop over the levels will not be * performed. * In fact, the backsolve portion was done in the call to * DGETRS in the frontsolve. * END IF * * Compute variable needed to reverse loop structure in * reduced system. * RECOVERY_VAL = NPACT*NPSTR - NPCOL * * Loop over levels * Terminal values of NPACT and NPSTR from frontsolve are used * 60 CONTINUE IF( NPACT.GE.NPCOL ) $ GO TO 80 * NPSTR = NPSTR / 2 * NPACT = NPACT*2 * * Have to adjust npact for non-power-of-2 * NPACT = NPACT - MOD( ( RECOVERY_VAL / NPSTR ), 2 ) * * Find size of submatrix in this proc at this level * IF( MYCOL / NPSTR.LT.NPACT-1 ) THEN BN = BW ELSE BN = MIN( BW, NUMROC( N, NB, NPCOL-1, 0, NPCOL ) ) END IF * * If this processor is even in this level... * IF( MOD( MYCOL, 2*NPSTR ).EQ.0 ) THEN * NEICOL = MYCOL + NPSTR * IF( NEICOL / NPSTR.LE.NPACT-1 ) THEN * IF( NEICOL / NPSTR.LT.NPACT-1 ) THEN BMN = BW BNN = BW ELSE BMN = MIN( BW, NUMROC( N, NB, NEICOL, 0, NPCOL ) ) + BWU BNN = MIN( BW, NUMROC( N, NB, NEICOL, 0, NPCOL ) ) END IF * IF( NPACT.GT.2 ) THEN * CALL DGESD2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ), LDW, 0, $ NEICOL ) * CALL DGERV2D( ICTXT, BW, NRHS, WORK( LN+1 ), LDW, 0, $ NEICOL ) * ELSE * CALL DGERV2D( ICTXT, BW, NRHS, WORK( LN+1 ), LDW, 0, $ NEICOL ) * END IF * END IF * ELSE * This processor is odd on this level * NEICOL = MYCOL - NPSTR * IF( NEICOL.EQ.0 ) THEN BMN = BW - BWU ELSE BMN = BW END IF * IF( NEICOL.LT.NPCOL-1 ) THEN BNN = BW ELSE BNN = MIN( BW, NUMROC( N, NB, NEICOL, 0, NPCOL ) ) END IF * IF( NPACT.GT.2 ) THEN * * Move RHS to make room for received solutions * CALL DLACPY( 'G', BW, NRHS, WORK( NB+BWU+1 ), LDW, $ WORK( NB+BWU+BW+1 ), LDW ) * CALL DGERV2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ), LDW, 0, $ NEICOL ) * CALL DGEMM( 'N', 'N', BW, NRHS, BN, -ONE, AF( BBPTR ), LDBB, $ WORK( LN+1 ), LDW, ONE, WORK( NB+BWU+BW+1 ), $ LDW ) * * IF( MYCOL.GT.NPSTR ) THEN * CALL DGEMM( 'N', 'N', BW, NRHS, BW, -ONE, $ AF( BBPTR+2*BW*LDBB ), LDBB, WORK( LN+BW+1 ), $ LDW, ONE, WORK( NB+BWU+BW+1 ), LDW ) * END IF * CALL DTRSM( 'L', 'U', 'N', 'N', BW, NRHS, ONE, $ AF( BBPTR+BW*LDBB ), LDBB, WORK( NB+BWU+BW+1 ), $ LDW ) * * Send new solution to neighbor * CALL DGESD2D( ICTXT, BW, NRHS, WORK( NB+BWU+BW+1 ), LDW, 0, $ NEICOL ) * * Copy new solution into expected place * CALL DLACPY( 'G', BW, NRHS, WORK( NB+BWU+1+BW ), LDW, $ WORK( LN+BW+1 ), LDW ) * ELSE * * Solve with local diagonal block * CALL DTRSM( 'L', 'U', 'N', 'N', BN+BNN, NRHS, ONE, $ AF( BBPTR+BW*LDBB ), LDBB, WORK( NB+BWU+1 ), $ LDW ) * * Send new solution to neighbor * CALL DGESD2D( ICTXT, BW, NRHS, WORK( NB+BWU+1 ), LDW, 0, $ NEICOL ) * * Shift solutions into expected positions * CALL DLACPY( 'G', BNN+BN-BW, NRHS, WORK( NB+BWU+1+BW ), LDW, $ WORK( LN+1 ), LDW ) * * IF( ( NB+BWU+1 ).NE.( LN+1+BW ) ) THEN * * Copy one row at a time since spaces may overlap * DO 70 J = 1, BW CALL DCOPY( NRHS, WORK( NB+BWU+J ), LDW, $ WORK( LN+BW+J ), LDW ) 70 CONTINUE * END IF * END IF * END IF * GO TO 60 * 80 CONTINUE * End of loop over levels * ******************************************************************** * PHASE 1: (Almost) Local computation phase -- Solve U*Y = X ******************************************************************** * * Reset BM to value it had before reduced system frontsolve... * IF( MYCOL.NE.NPCOL-1 ) THEN BM = BW - LBWU ELSE BM = MIN( BW, ODD_SIZE ) + BWU END IF * * First metastep is to account for the fillin blocks AF * IF( MYCOL.LT.NPCOL-1 ) THEN * CALL DGESD2D( ICTXT, BW, NRHS, WORK( NB-BW+1 ), LDW, 0, $ MYCOL+1 ) * END IF * IF( MYCOL.GT.0 ) THEN * CALL DGERV2D( ICTXT, BW, NRHS, WORK( NB+BWU+1 ), LDW, 0, $ MYCOL-1 ) * * Modify local right hand sides with received rhs's * CALL DGEMM( 'T', 'N', LM-BM, NRHS, BW, -ONE, AF( 1 ), BW, $ WORK( NB+BWU+1 ), LDW, ONE, WORK( 1 ), LDW ) * END IF * DO 90 J = LN, 1, -1 * LMJ = MIN( BW, ODD_SIZE-1 ) * LPTR = BW - 1 + J*LLDA + APTR * * In the following, the TRANS=T option is used to reverse * the order of multiplication, not as a true transpose * CALL DGEMV( 'T', LMJ, NRHS, -ONE, WORK( J+1 ), LDW, A( LPTR ), $ LLDA-1, ONE, WORK( J ), LDW ) * * Divide by diagonal element * CALL DSCAL( NRHS, ONE / A( LPTR-LLDA+1 ), WORK( J ), LDW ) 90 CONTINUE * * * CALL DLACPY( 'G', ODD_SIZE, NRHS, WORK( 1 ), LDW, B( 1 ), LLDB ) * * Free BLACS space used to hold standard-form grid. * ICTXT = ICTXT_SAVE IF( ICTXT.NE.ICTXT_NEW ) THEN CALL BLACS_GRIDEXIT( ICTXT_NEW ) END IF * 100 CONTINUE * * Restore saved input parameters * NP = NP_SAVE * * Output worksize * WORK( 1 ) = WORK_SIZE_MIN * RETURN * * End of PDGBTRS * END

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