SUBROUTINE PCGBTRS( 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. * August 7, 2001 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER BWU, BWL, IB, INFO, JA, LAF, LWORK, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ), IPIV(*) COMPLEX A( * ), AF( * ), B( * ), WORK( * ) * .. * * * Purpose * ======= * * PCGBTRS 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 PCGBTRF. * A(1:N, JA:JA+N-1) is an N-by-N complex * banded distributed * matrix with bandwidth BWL, BWU. * * Routine PCGBTRF MUST be called first. * * ===================================================================== * * Arguments * ========= * * * TRANS (global input) CHARACTER * = 'N': Solve with A(1:N, JA:JA+N-1); * = 'C': Solve with conjugate_transpose( A(1:N, JA:JA+N-1) ); * * 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) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension LAF. * Auxiliary Fillin Space. * Fillin is created during the factorization routine * PCGBTRF and this is stored in AF. If a linear system * is to be solved using PCGBTRS 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) * COMPLEX 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 Marbwus Hegland, Australian Natonal University. Feb., 1997. * Based on code written by : Peter Arbenz, ETH Zurich, 1996. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0 ) PARAMETER ( ZERO = 0.0E+0 ) COMPLEX CONE, CZERO PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) PARAMETER ( CZERO = ( 0.0E+0, 0.0E+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_GRIDINFO, DESC_CONVERT, GLOBCHK, PXERBLA, $ RESHAPE * .. * .. External Functions .. LOGICAL LSAME INTEGER NUMROC EXTERNAL LSAME EXTERNAL NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, 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 ) ENDIF * CALL DESC_CONVERT( DESCB, DESCB_PX1, RETURN_CODE ) * IF( RETURN_CODE .NE. 0) THEN INFO = -( 11*100 + 2 ) ENDIF * * Consistency checks for DESCA and DESCB. * * Context must be the same IF( DESCA_1XP( 2 ) .NE. DESCB_PX1( 2 ) ) THEN INFO = -( 11*100 + 2 ) ENDIF * * 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 ) ENDIF * * Source processor must be the same * IF( DESCA_1XP( 5 ) .NE. DESCB_PX1( 5 ) ) THEN INFO = -( 11*100 + 5 ) ENDIF * * 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, 'C' ) ) THEN IDUM2 = ICHAR( 'C' ) ELSE INFO = -1 END IF * IF( LWORK .LT. -1) THEN INFO = -16 ELSE IF ( LWORK .EQ. -1 ) THEN IDUM3 = -1 ELSE IDUM3 = 1 ENDIF * IF( N .LT. 0 ) THEN INFO = -2 ENDIF * IF( N+JA-1 .GT. STORE_N_A ) THEN INFO = -( 8*100 + 6 ) ENDIF * IF(( BWL .GT. N-1 ) .OR. $ ( BWL .LT. 0 ) ) THEN INFO = -3 ENDIF * IF(( BWU .GT. N-1 ) .OR. $ ( BWU .LT. 0 ) ) THEN INFO = -4 ENDIF * IF( LLDA .LT. (2*BWL+2*BWU+1) ) THEN INFO = -( 8*100 + 6 ) ENDIF * IF( NB .LE. 0 ) THEN INFO = -( 8*100 + 4 ) ENDIF * BW = BWU+BWL * IF( N+IB-1 .GT. STORE_M_B ) THEN INFO = -( 11*100 + 3 ) ENDIF * IF( LLDB .LT. NB ) THEN INFO = -( 11*100 + 6 ) ENDIF * IF( NRHS .LT. 0 ) THEN INFO = -5 ENDIF * * Current alignment restriction * IF( JA .NE. IB) THEN INFO = -7 ENDIF * * Argument checking that is specific to Divide & Conquer routine * IF( NPROW .NE. 1 ) THEN INFO = -( 8*100+2 ) ENDIF * IF( N .GT. NP*NB-MOD( JA-1, NB )) THEN INFO = -( 2 ) CALL PXERBLA( ICTXT, $ 'PCGBTRS, D&C alg.: only 1 block per proc', $ -INFO ) RETURN ENDIF * IF((JA+N-1.GT.NB) .AND. ( NB.LT.(BWL+BWU+1) )) THEN INFO = -( 8*100+4 ) CALL PXERBLA( ICTXT, $ 'PCGBTRS, D&C alg.: NB too small', $ -INFO ) RETURN ENDIF * * * 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, $ 'PCGBTRS: worksize error ', $ -INFO ) ENDIF RETURN ENDIF * * 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, 'PCGBTRS', -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 ENDIF * IF ( MYCOL .LT. CSRC ) THEN PART_OFFSET = PART_OFFSET - NB ENDIF * * 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 GOTO 1234 ENDIF * * * * Begin main code * * Move data into workspace - communicate/copy (overlap) * IF (MYCOL .LT. NPCOL-1) THEN CALL CGESD2D( ICTXT, BWU, NRHS, B(NB-BWU+1), LLDB, $ 0, MYCOL + 1) ENDIF * IF (MYCOL .LT. NPCOL-1) THEN LM = NB-BWU ELSE LM = NB ENDIF * IF (MYCOL .GT. 0) THEN WPTR = BWU+1 ELSE WPTR = 1 ENDIF * LDW = NB+BWU + 2*BW+BWU * CALL CLACPY( 'G', LM, NRHS, B(1), LLDB, WORK( WPTR ), LDW ) * * Zero out rest of work * DO 1501 J=1, NRHS DO 1502 L=WPTR+LM, LDW WORK( (J-1)*LDW+L ) = CZERO 1502 CONTINUE 1501 CONTINUE * IF (MYCOL .GT. 0) THEN CALL CGERV2D( ICTXT, BWU, NRHS, WORK(1), LDW, $ 0, MYCOL-1) ENDIF * ******************************************************************** * 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 ENDIF * 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 ) ENDIF * DO 21 J = 1, LN * LMJ = MIN(LBWL,LM-J) L = IPIV( J ) * IF( L.NE.J ) THEN CALL CSWAP(NRHS, WORK(L), LDW, WORK(J), LDW) ENDIF * LPTR = BW+1 + (J-1)*LLDA + APTR * CALL CGERU(LMJ,NRHS,-CONE, A(LPTR),1, WORK(J),LDW, $ WORK(J+1),LDW) * 21 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) ENDIF * * 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 CGETRS( 'N', N-LN, NRHS, AF(BBPTR+BW*LDBB), LDBB, $ IPIV(LN+1), WORK( LN+1 ), LDW, INFO) * ENDIF * * 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 200 IF (NPACT .LE. 1) GOTO 300 * * 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 ENDIF * CALL CGESD2D( ICTXT, BM, NRHS, $ WORK(LN+1), LDW, 0, NEICOL ) * IF( NPACT .NE. 2 )THEN * * Receive answers back from partner processor * CALL CGERV2D(ICTXT, BM+BMN-BW, NRHS, $ WORK( LN+1 ), LDW, 0, NEICOL ) * BM = BM+BMN-BW * ENDIF * ENDIF * ELSE * NEICOL = MYCOL - NPSTR * IF (NEICOL .EQ. 0) THEN BMN = BW - BWU ELSE BMN = BW ENDIF * CALL CLACPY( 'G', BM, NRHS, WORK(LN+1), LDW, $ WORK(NB+BWU+BMN+1), LDW ) * CALL CGERV2D( 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 CLASWP( NRHS, WORK(NB+BWU+1), LDW, 1, BW, $ IPIV(LN+1), 1) * CALL CTRSM('L','L','N','U', BW, NRHS, CONE, $ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+1), LDW) * * Use soln just calculated to update RHS * CALL CGEMM( 'N', 'N', BM+BMN-BW, NRHS, BW, $ -CONE, AF(BBPTR+BW*LDBB+BW), LDBB, $ WORK(NB+BWU+1), LDW, $ CONE, WORK(NB+BWU+1+BW), LDW ) * * Give answers back to partner processor * CALL CGESD2D( ICTXT, BM+BMN-BW, NRHS, $ WORK(NB+BWU+1+BW), LDW, 0, NEICOL ) * ELSE * * Finish up calculations for final level * CALL CLASWP( NRHS, WORK(NB+BWU+1), LDW, 1, BM+BMN, $ IPIV(LN+1), 1) * CALL CTRSM('L','L','N','U', BM+BMN, NRHS, CONE, $ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+1), LDW) ENDIF * ENDIF * NPACT = (NPACT + 1)/2 NPSTR = NPSTR * 2 GOTO 200 * ENDIF * 300 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 * CGETRS in the frontsolve. * ENDIF * * 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 * 2200 IF( NPACT .GE. NPCOL ) GOTO 2300 * 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) ) ENDIF * * 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) ) ENDIF * IF( NPACT .GT. 2 ) THEN * CALL CGESD2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ), $ LDW, 0, NEICOL ) * CALL CGERV2D( ICTXT, BW, NRHS, WORK( LN+1 ), $ LDW, 0, NEICOL ) * ELSE * CALL CGERV2D( ICTXT, BW, NRHS, WORK( LN+1 ), $ LDW, 0, NEICOL ) * ENDIF * ENDIF * ELSE * This processor is odd on this level * NEICOL = MYCOL - NPSTR * IF (NEICOL .EQ. 0) THEN BMN = BW - BWU ELSE BMN = BW ENDIF * IF( NEICOL .LT. NPCOL-1 ) THEN BNN = BW ELSE BNN = MIN(BW, NUMROC(N, NB, NEICOL, 0, NPCOL) ) ENDIF * IF( NPACT .GT. 2 ) THEN * * Move RHS to make room for received solutions * CALL CLACPY( 'G', BW, NRHS, WORK(NB+BWU+1), $ LDW, WORK(NB+BWU+BW+1), LDW ) * CALL CGERV2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ), $ LDW, 0, NEICOL ) * CALL CGEMM( 'N', 'N', BW, NRHS, BN, $ -CONE, AF(BBPTR), LDBB, $ WORK(LN+1), LDW, $ CONE, WORK(NB+BWU+BW+1), LDW ) * * IF( MYCOL .GT. NPSTR ) THEN * CALL CGEMM( 'N', 'N', BW, NRHS, BW, $ -CONE, AF(BBPTR+2*BW*LDBB), LDBB, $ WORK(LN+BW+1), LDW, $ CONE, WORK(NB+BWU+BW+1), LDW ) * ENDIF * CALL CTRSM('L','U','N','N', BW, NRHS, CONE, $ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+BW+1), LDW) * * Send new solution to neighbor * CALL CGESD2D( ICTXT, BW, NRHS, $ WORK( NB+BWU+BW+1 ), LDW, 0, NEICOL ) * * Copy new solution into expected place * CALL CLACPY( 'G', BW, NRHS, WORK(NB+BWU+1+BW), $ LDW, WORK(LN+BW+1), LDW ) * ELSE * * Solve with local diagonal block * CALL CTRSM( 'L','U','N','N', BN+BNN, NRHS, CONE, $ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+1), LDW) * * Send new solution to neighbor * CALL CGESD2D( ICTXT, BW, NRHS, $ WORK(NB+BWU+1), LDW, 0, NEICOL ) * * Shift solutions into expected positions * CALL CLACPY( '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 1064 J=1, BW CALL CCOPY( NRHS, WORK(NB+BWU+J), LDW, $ WORK(LN+BW+J), LDW ) 1064 CONTINUE * ENDIF * ENDIF * ENDIF * GOTO 2200 * 2300 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 ENDIF * * First metastep is to account for the fillin blocks AF * IF( MYCOL .LT. NPCOL-1 ) THEN * CALL CGESD2D( ICTXT, BW, NRHS, WORK( NB-BW+1 ), $ LDW, 0, MYCOL+1 ) * ENDIF * IF( MYCOL .GT. 0 ) THEN * CALL CGERV2D( ICTXT, BW, NRHS, WORK( NB+BWU+1 ), $ LDW, 0, MYCOL-1 ) * * Modify local right hand sides with received rhs's * CALL CGEMM( 'N', 'N', LM-BM, NRHS, BW, -CONE, $ AF( 1 ), LM, WORK( NB+BWU+1 ), LDW, CONE, $ WORK( 1 ), LDW ) * ENDIF * DO 2021 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 CGEMV( 'T', LMJ, NRHS, -CONE, WORK( J+1), LDW, $ A( LPTR ), LLDA-1, CONE, WORK( J ), LDW ) * * Divide by diagonal element * CALL CSCAL( NRHS, CONE/A( LPTR-LLDA+1 ), $ WORK( J ), LDW ) 2021 CONTINUE * * * CALL CLACPY( '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 ) ENDIF * 1234 CONTINUE * * Restore saved input parameters * NP = NP_SAVE * * Output worksize * WORK( 1 ) = WORK_SIZE_MIN * RETURN * * End of PCGBTRS * END

Generated by Doxygen 1.6.0 Back to index