SUBROUTINE PZGBTRS( TRANS, N, BWL, BWU, NRHS, A, JA, DESCA, IPIV,
$ B, IB, DESCB, AF, LAF, WORK, LWORK, INFO )
*
*
*
* -- ScaLAPACK routine (version 1.6) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* November 15, 1997
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER BWU, BWL, IB, INFO, JA, LAF, LWORK, N, NRHS
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCB( * ), IPIV(*)
COMPLEX*16 A( * ), AF( * ), B( * ), WORK( * )
* ..
*
*
* Purpose
* =======
*
* PZGBTRS 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 PZGBTRF.
* A(1:N, JA:JA+N-1) is an N-by-N complex
* banded distributed
* matrix with bandwidth BWL, BWU.
*
* Routine PZGBTRF 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*16 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*16 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*16 array, dimension LAF.
* Auxiliary Fillin Space.
* Fillin is created during the factorization routine
* PZGBTRF and this is stored in AF. If a linear system
* is to be solved using PZGBTRS 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*16 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 ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0 )
PARAMETER ( ZERO = 0.0D+0 )
COMPLEX*16 CONE, CZERO
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
PARAMETER ( CZERO = ( 0.0D+0, 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_GRIDINFO, DESC_CONVERT, GLOBCHK, PXERBLA
* ..
* .. 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,
$ 'PZGBTRS, 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,
$ 'PZGBTRS, 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,
$ 'PZGBTRS: 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, 'PZGBTRS', -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 ZGESD2D( 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 ZLACPY( '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 ZGERV2D( 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 ZSWAP(NRHS, WORK(L), LDW, WORK(J), LDW)
ENDIF
*
LPTR = BW+1 + (J-1)*LLDA + APTR
*
CALL ZGERU(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 ZGETRS( '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 ZGESD2D( ICTXT, BM, NRHS,
$ WORK(LN+1), LDW, 0, NEICOL )
*
IF( NPACT .NE. 2 )THEN
*
* Receive answers back from partner processor
*
CALL ZGERV2D(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 ZLACPY( 'G', BM, NRHS, WORK(LN+1), LDW,
$ WORK(NB+BWU+BMN+1), LDW )
*
CALL ZGERV2D( 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 ZLASWP( NRHS, WORK(NB+BWU+1), LDW, 1, BW,
$ IPIV(LN+1), 1)
*
CALL ZTRSM('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 ZGEMM( '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 ZGESD2D( ICTXT, BM+BMN-BW, NRHS,
$ WORK(NB+BWU+1+BW), LDW, 0, NEICOL )
*
ELSE
*
* Finish up calculations for final level
*
CALL ZLASWP( NRHS, WORK(NB+BWU+1), LDW, 1, BM+BMN,
$ IPIV(LN+1), 1)
*
CALL ZTRSM('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
* ZGETRS 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 ZGESD2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ),
$ LDW, 0, NEICOL )
*
CALL ZGERV2D( ICTXT, BW, NRHS, WORK( LN+1 ),
$ LDW, 0, NEICOL )
*
ELSE
*
CALL ZGERV2D( 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 ZLACPY( 'G', BW, NRHS, WORK(NB+BWU+1),
$ LDW, WORK(NB+BWU+BW+1), LDW )
*
CALL ZGERV2D( ICTXT, 2*BW, NRHS, WORK( LN+1 ),
$ LDW, 0, NEICOL )
*
CALL ZGEMM( '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 ZGEMM( '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 ZTRSM('L','U','N','N', BW, NRHS, CONE,
$ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+BW+1), LDW)
*
* Send new solution to neighbor
*
CALL ZGESD2D( ICTXT, BW, NRHS,
$ WORK( NB+BWU+BW+1 ), LDW, 0, NEICOL )
*
* Copy new solution into expected place
*
CALL ZLACPY( 'G', BW, NRHS, WORK(NB+BWU+1+BW),
$ LDW, WORK(LN+BW+1), LDW )
*
ELSE
*
* Solve with local diagonal block
*
CALL ZTRSM( 'L','U','N','N', BN+BNN, NRHS, CONE,
$ AF(BBPTR+BW*LDBB), LDBB, WORK(NB+BWU+1), LDW)
*
* Send new solution to neighbor
*
CALL ZGESD2D( ICTXT, BW, NRHS,
$ WORK(NB+BWU+1), LDW, 0, NEICOL )
*
* Shift solutions into expected positions
*
CALL ZLACPY( '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 ZCOPY( 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 ZGESD2D( ICTXT, BW, NRHS, WORK( NB-BW+1 ),
$ LDW, 0, MYCOL+1 )
*
ENDIF
*
IF( MYCOL .GT. 0 ) THEN
*
CALL ZGERV2D( ICTXT, BW, NRHS, WORK( NB+BWU+1 ),
$ LDW, 0, MYCOL-1 )
*
* Modify local right hand sides with received rhs's
*
CALL ZGEMM( '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 ZGEMV( 'T', LMJ, NRHS, -CONE, WORK( J+1), LDW,
$ A( LPTR ), LLDA-1, CONE, WORK( J ), LDW )
*
* Divide by diagonal element
*
CALL ZSCAL( NRHS, CONE/A( LPTR-LLDA+1 ),
$ WORK( J ), LDW )
2021 CONTINUE
*
*
*
CALL ZLACPY( '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 PZGBTRS
*
END