* SUBROUTINE CHEBYREVCOM( N, B, X, WORK, LDW, ITER, RESID, INFO, \$ NDX1, NDX2, SCLR1, SCLR2, IJOB) * * -- Iterative template routine -- * Univ. of Tennessee and Oak Ridge National Laboratory * October 1, 1993 * Details of this algorithm are described in "Templates for the * Solution of Linear Systems: Building Blocks for Iterative * Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, * Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications, * 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps). * * .. Scalar Arguments .. INTEGER N, LDW, ITER, INFO DOUBLE PRECISION RESID INTEGER NDX1, NDX2 DOUBLE PRECISION SCLR1, SCLR2 INTEGER IJOB * .. * .. Array Arguments .. DOUBLE PRECISION B( * ), X( * ), WORK( LDW,*) * .. * * Purpose * ======= * * CHEBY solves the linear system Ax = b using the Chebyshev iterative * method with preconditioning. This version requires explicit * knowledge of the maximum and minimum eigenvalues. Note that these * eigenvalues must be DOUBLE PRECISION positive, which is the case for the * symmetric positive definite system. * * Arguments * ========= * * N (input) INTEGER * On entry, the dimension of the matrix. * Unchanged on exit. * * B (input) DOUBLE PRECISION array, dimension N. * On entry, right hand side vector B. * Unchanged on exit. * * On input, the initial guess. This is commonly set to * the zero vector. * On exit, if INFO = 0, the iterated approximate solution. * * WORK (workspace) DOUBLE PRECISION array, dimension (LDW,3). * Workspace for residual, direction vector, etc. * * LDW (input) INTEGER * The leading dimension of the array WORK. LDW >= max(1,N). * * ITER (input/output) INTEGER * On input, the maximum iterations to be performed. * On output, actual number of iterations performed. * * RESID (input/output) DOUBLE PRECISION * On input, the allowable convergence measure for * norm( b - A*x ) / norm( b ). * On output, the final value of this measure. * * INFO (output) INTEGER * * = 0: Successful exit. Iterated approximate solution returned. * * > 0: Convergence to tolerance not achieved. This will be * set to the number of iterations performed. * * < 0: Illegal input parameter, or breakdown occurred * during iteration. * * Illegal parameter: * * -1: matrix dimension N < 0 * -2: LDW < N * -3: Maximum number of iterations ITER <= 0. * -5: Erroneous NDX1/NDX2 in INIT call. * -6: Erroneous RLBL. * * NDX1 (input/output) INTEGER. * NDX2 On entry in INIT call contain indices required by interface * level for stopping test. * All other times, used as output, to indicate indices into * WORK[] for the MATVEC, PSOLVE done by the interface level. * * SCLR1 (output) DOUBLE PRECISION. * SCLR2 Used to pass the scalars used in MATVEC. Scalars are reqd because * original routines use dgemv. * * IJOB (input/output) INTEGER. * Used to communicate job code between the two levels. * * BLAS CALLS: DAXPY, DCOPY, DNRM2 * ============================================================ * .. * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) * .. * .. Local Scalars .. INTEGER R, P, Z, MAXIT, NEED1, NEED2 DOUBLE PRECISION ALPHA, BETA, C, D, BNRM2, EIGMAX, EIGMIN, TOL, \$ DNRM2 * .. * * indicates where to resume from. Only valid when IJOB = 2! INTEGER RLBL * * saving all. SAVE * * .. External Routines .. EXTERNAL DAXPY, DCOPY, DNRM2 * * .. Executable Statements .. * * * Entry point, so test IJOB IF (IJOB .eq. 1) THEN GOTO 1 ELSEIF (IJOB .eq. 2) THEN * here we do resumption handling IF (RLBL .eq. 2) GOTO 2 IF (RLBL .eq. 3) GOTO 3 IF (RLBL .eq. 4) GOTO 4 IF (RLBL .eq. 5) GOTO 5 * if neither of these, then error INFO = -6 GOTO 20 ENDIF * * ***************** 1 CONTINUE ***************** * INFO = 0 * MAXIT = ITER TOL = RESID * * Get extremal eigenvalues. * CALL GETEIG( WORK, LDW, EIGMAX, EIGMIN ) * * Alias workspace columns. * R = 1 P = 2 Z = 3 * * Check if caller will need indexing info. * IF( NDX1.NE.-1 ) THEN IF( NDX1.EQ.1 ) THEN NEED1 = ((R - 1) * LDW) + 1 ELSEIF( NDX1.EQ.2 ) THEN NEED1 = ((P - 1) * LDW) + 1 ELSEIF( NDX1.EQ.3 ) THEN NEED1 = ((Z - 1) * LDW) + 1 ELSE * report error INFO = -5 GO TO 20 ENDIF ELSE NEED1 = NDX1 ENDIF * IF( NDX2.NE.-1 ) THEN IF( NDX2.EQ.1 ) THEN NEED2 = ((R - 1) * LDW) + 1 ELSEIF( NDX2.EQ.2 ) THEN NEED2 = ((P - 1) * LDW) + 1 ELSEIF( NDX2.EQ.3 ) THEN NEED2 = ((Z - 1) * LDW) + 1 ELSE * report error INFO = -5 GO TO 20 ENDIF ELSE NEED2 = NDX2 ENDIF * * Set initial residual. * CALL DCOPY( N, B, 1, WORK(1,R), 1 ) IF ( DNRM2( N, X, 1 ).NE.ZERO ) THEN *********CALL MATVEC( -ONE, X, ONE, WORK(1,R) ) * Note: using P as temp. storage. *********CALL DCOPY(N, X, 1, WORK(1,P), 1) NDX1 = -1 NDX2 = ((R - 1) * LDW) + 1 SCLR1 = -ONE SCLR2 = ONE * * Prepare for resumption & return RLBL = 2 IJOB = 3 RETURN * ***************** 2 CONTINUE ***************** * IF ( DNRM2( N, WORK(1,R), 1 ).LT.TOL ) GO TO 30 ENDIF * BNRM2 = DNRM2( N, B, 1 ) IF ( BNRM2.EQ.ZERO ) BNRM2 = ONE * * Initialize ellipse parameters. * C = ( EIGMAX - EIGMIN ) / TWO D = ( EIGMAX + EIGMIN ) / TWO * ITER = 0 * 10 CONTINUE * * Perform Chebyshev iteration. * ITER = ITER + 1 * *********CALL PSOLVE( WORK(1,Z), WORK(1,R) ) * NDX1 = ((Z - 1) * LDW) + 1 NDX2 = ((R - 1) * LDW) + 1 * Prepare for return & return RLBL = 3 IJOB = 2 RETURN * ***************** 3 CONTINUE ***************** IF ( ITER.GT.1 ) THEN BETA = ( ( C * ALPHA ) / TWO )**2 ALPHA = ONE / ( D - BETA ) CALL DAXPY( N, BETA, WORK(1,P), 1, WORK(1,Z), 1 ) CALL DCOPY( N, WORK(1,Z), 1, WORK(1,P), 1 ) ELSE CALL DCOPY( N, WORK(1,Z), 1, WORK(1,P), 1 ) ALPHA = TWO / D ENDIF * * Compute new approximation vector X; check accuracy. * CALL DAXPY( N, ALPHA, WORK(1,P), 1, X, 1 ) *********CALL MATVEC( -ALPHA, WORK(1,P), ONE, WORK(1,R) ) * NDX1 = ((P - 1) * LDW) + 1 NDX2 = ((R - 1) * LDW) + 1 * Prepare for return & return SCLR1 = -ALPHA SCLR2 = ONE RLBL = 4 IJOB = 1 RETURN * ***************** 4 CONTINUE ***************** * *********RESID = DNRM2( N, WORK(1,R), 1 ) / BNRM2 *********IF ( RESID.LE.TOL ) GO TO 30 * NDX1 = NEED1 NDX2 = NEED2 * Prepare for resumption & return RLBL = 5 IJOB = 4 RETURN * ***************** 5 CONTINUE ***************** IF( INFO.EQ.1 ) GO TO 30 * IF ( ITER.EQ.MAXIT ) THEN INFO = 1 GO TO 20 ENDIF * GO TO 10 * 20 CONTINUE * * Iteration fails. * RLBL = -1 IJOB = -1 RETURN * 30 CONTINUE * * Iteration successful; return. * INFO = 0 RLBL = -1 IJOB = -1 RETURN * * End of CHEBYREVCOM * END