*
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
REAL RESID
* ..
* .. Array Arguments ..
REAL 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) REAL array, dimension N
* On entry, right hand side vector B.
* Unchanged on exit.
*
* X (input/output) REAL 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) REAL 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) REAL
* 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.
REAL SCLR1, SCLR2
* Vars reqd for STOPTEST2
REAL 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