* SUBROUTINE SOR( N, B, X, WORK, LDW, ITER, RESID, MATVEC, \$ BACKSOLVE, INFO ) * * -- 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 * .. * .. Array Arguments .. DOUBLE PRECISION B( * ), X( * ), WORK( * ) * .. * .. Function Arguments .. EXTERNAL MATVEC, BACKSOLVE * * Purpose * ======= * * SOR solves the linear system Ax = b using the Successive * Over-Relaxation iterative method. * The matrix splitting is formed by copying the strict upper * triangular portion of A onto matrix N, stored in WORK. Matrix M * is the lower triangular portion of A. * On exit, matrix A and right hand side b are reset to their * original form. * * Relative error measured: norm( X - X_1 ) / norm( X ). * * 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. * * X (input/output) DOUBLE PRECISION array, dimension N. * On input, the initial guess. This is commonly set to * the zero vector. * On exit, if INFO = 0, the iterated approximate solution. * * WORK (input/workspace) DOUBLE PRECISION array, dimension (N*(N+3)). * The relaxation parameter, OMEGA, should be input in WORK(1). * The amount of workspace can be significantly reduced (to 2*N) * by customizing the matrix-vector product and backsolve. * * 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( x - x_1 ) / norm( x ). * On output, the final value of this measure. * * MATVEC (external subroutine) * The user must provide a subroutine to perform the * matrix-vector product * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are vectors, * and A is a matrix. Vector x must remain unchanged. * The solution is over-written on vector y. * * The call is: * * CALL MATVEC( ALPHA, X, BETA, Y ) * * The matrix is passed into the routine in a common block. * * BACKSOLVE (external subroutine) * The user must provide a subroutine to perform the * linear system solve * * x := M*x, * * where x is a vector and M is a lower triangular matrix. * The solution is over-written on vector x. * * The call is: * * CALL BACKSOLVE( N, M, LDM, X ) * * The matrix is passed into the routine in a common block. * * 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. * -4: Relaxation parameter OMEGA not in interval (0,2). * * ========================================================== * * *This variable used to communicate requests between SOR() and SORREVCOM() *SOR -> SORREVCOM: 1 = init, * 2 = use saved state to resume flow. *SORREVCOM -> SOR: -1 = done, return to main, * 1 = matvec using SCLR1/2, NDX1/2 * 2 = solve using NDX1/2 INTEGER IJOB * * Arg/Result indices into WORK[]. INTEGER NDX1, NDX2 * Scalars passed from SORREVCOM to SOR. DOUBLE PRECISION SCLR1, SCLR2 * Vars reqd for STOPTEST2 DOUBLE PRECISION TOL, XNRM2 * .. * .. External subroutines .. EXTERNAL SORREVCOM, STOPTEST2 * .. * .. Executable Statements .. * INFO = 0 * * Test the input parameters. * IF ( N.LT.0 ) THEN INFO = -1 ELSE IF ( LDW.LT.MAX( 1, N ) ) THEN INFO = -2 ELSE IF ( ITER.LE.0 ) THEN INFO = -3 ELSE IF ( ( WORK( 1 ).LE.0 ).OR.( WORK( 1 ).GE.2 ) ) THEN INFO = -4 ENDIF IF ( INFO.NE.0 ) RETURN * * Stop test may need some indexing info from REVCOM * use the init call to send the request across. REVCOM * will note these requests, and everytime it asks for * stop test to be done, it will provide the indexing info. * * 1 == X1; 2 == TEMP; 3 == MM; -1 == ignore; any other == error NDX1 = 1 NDX2 = -1 TOL = RESID * * First time call always init. * IJOB = 1 1 CONTINUE CALL SORREVCOM(N, B, X, WORK, LDW, ITER, RESID, INFO, \$ NDX1, NDX2, SCLR1, SCLR2, IJOB) * On a return from REVCOM() we use the table * to decode IJOB. IF (IJOB .eq. -1) THEN * revcom wants to terminate, so do it. GOTO 2 ELSEIF (IJOB .eq. 1) THEN * call matvec with X. CALL MATVEC(SCLR1, X, SCLR2, WORK(NDX2)) ELSEIF (IJOB .eq. 2) THEN * call backsolve with X CALL BACKSOLVE(N, WORK(NDX1), LDW, X) ELSEIF (IJOB .EQ. 3) THEN * do stopping test 2 * XNRM2 shld be recomputed everytime. INFO = -1 CALL STOPTEST2(N, WORK(NDX1), X, XNRM2, RESID, TOL, INFO) ENDIF * * done what revcom asked, set IJOB & go back to it. IJOB = 2 GOTO 1 * * come here to terminate 2 CONTINUE * * RETURN * * End of SOR * END