/* BiCG.f -- translated by f2c (version of 20 August 1993 13:15:44). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static integer c__1 = 1; static doublereal c_b5 = -1.; static doublereal c_b6 = 0.; static doublereal c_b28 = 1.; /* -- 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). * * Purpose * ======= * * BiCG solves the linear system Ax = b using the * BiConjugate Gradient iterative method with preconditioning. * * Convergence test: ( norm( b - A*x ) / norm( b ) ) < TOL. * For other measures, see the above reference. * * 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 (workspace) DOUBLE PRECISION array, dimension (LDW,6). * 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. * * 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. * * MATVECTRANS (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 the tranpose of a matrix A. Vector x must remain * unchanged. * The solution is over-written on vector y. * * The call is: * * CALL MATVECTRANS( ALPHA, X, BETA, Y ) * * The matrix is passed into the routine in a common block. * * PSOLVE (external subroutine) * The user must provide a subroutine to perform the * preconditioner solve routine for the linear system * * M*x = b, * * where x and b are vectors, and M a matrix. Vector b must * remain unchanged. * The solution is over-written on vector x. * * The call is: * * CALL PSOLVE( X, B ) * * The preconditioner is passed into the routine in a common block * * PSOLVETRANS (external subroutine) * The user must provide a subroutine to perform the * preconditioner solve routine for the linear system * * M'*x = b, * * where x and y are vectors, and M' is the tranpose of a * matrix M. Vector b must remain unchanged. The solution * is over-written on vector x. * * The call is: * * CALL PSOLVETRANS( X, B ) * * The preconditioner 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. * * -1: matrix dimension N < 0 * -2: LDW < N * -3: Maximum number of iterations ITER <= 0. * * BREAKDOWN: If parameters RHO or OMEGA become smaller * than some tolerance, the program will terminate. * Here we check against tolerance BREAKTOL. * * -10: RHO < BREAKTOL: RHO and RTLD have become * orthogonal. * * BREAKTOL is set in function GETBREAK. * * BLAS CALLS: DAXPY, DCOPY, DDOT, DNRM2 * ============================================================ */ int bicg_(n, b, x, work, ldw, iter, resid, matvec, matvectrans, psolve, psolvetrans, info) integer *n, *ldw, *iter, *info; doublereal *b, *x, *work, *resid; int (*matvec) (), (*matvectrans) (), (*psolve) (), (*psolvetrans) (); { /* System generated locals */ integer work_dim1, work_offset; doublereal d__1; /* Local variables */ static doublereal beta; extern doublereal ddot_(); static integer ptld, rtld, qtld; extern doublereal getbreak_(); static integer ztld; static doublereal bnrm2; extern doublereal dnrm2_(); static integer p, q, r; static doublereal alpha; static integer z; extern /* Subroutine */ int dcopy_(); static integer maxit; extern /* Subroutine */ int daxpy_(); static doublereal rhotol, rho, tol, rho1; /* Parameter adjustments */ work_dim1 = *ldw; work_offset = work_dim1 + 1; work -= work_offset; --x; --b; /* Executable Statements */ *info = 0; /* Test the input parameters. */ if (*n < 0) { *info = -1; } else if (*ldw < max(1,*n)) { *info = -2; } else if (*iter <= 0) { *info = -3; } if (*info != 0) { return 0; } maxit = *iter; tol = *resid; /* Alias workspace columns. */ r = 1; rtld = 2; z = 3; ztld = 4; p = 5; ptld = 6; q = 3; qtld = 4; /* Set breakdown parameters. */ rhotol = getbreak_(); /* Set initial residual. */ dcopy_(n, &b[1], &c__1, &work[r * work_dim1 + 1], &c__1); if (dnrm2_(n, &x[1], &c__1) != 0.) { (*matvec)(&c_b5, &x[1], &c_b28, &work[r * work_dim1 + 1]); if (dnrm2_(n, &work[r * work_dim1 + 1], &c__1) <= tol) { goto L30; } } dcopy_(n, &work[r * work_dim1 + 1], &c__1, &work[rtld * work_dim1 + 1], & c__1); bnrm2 = dnrm2_(n, &b[1], &c__1); if (bnrm2 == 0.) { bnrm2 = 1.; } *iter = 0; L10: /* Perform BiConjugate Gradient iteration. */ ++(*iter); /* Compute direction vectors PK and PTLD. */ (*psolve)(&work[z * work_dim1 + 1], &work[r * work_dim1 + 1]); (*psolvetrans)(&work[ztld * work_dim1 + 1], &work[rtld * work_dim1 + 1]); rho = ddot_(n, &work[z * work_dim1 + 1], &c__1, &work[rtld * work_dim1 + 1], &c__1); if (abs(rho) < rhotol) { goto L25; } if (*iter > 1) { beta = rho / rho1; daxpy_(n, &beta, &work[p * work_dim1 + 1], &c__1, &work[z * work_dim1 + 1], &c__1); daxpy_(n, &beta, &work[ptld * work_dim1 + 1], &c__1, &work[ztld * work_dim1 + 1], &c__1); dcopy_(n, &work[z * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1], & c__1); dcopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[ptld * work_dim1 + 1], &c__1); } else { dcopy_(n, &work[z * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1], & c__1); dcopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[ptld * work_dim1 + 1], &c__1); } (*matvec)(&c_b28, &work[p * work_dim1 + 1], &c_b6, &work[q * work_dim1 + 1]); (*matvectrans)(&c_b28, &work[ptld * work_dim1 + 1], &c_b6, &work[qtld * work_dim1 + 1]); alpha = rho / ddot_(n, &work[ptld * work_dim1 + 1], &c__1, &work[q * work_dim1 + 1], &c__1); /* Compute current solution vector x. */ daxpy_(n, &alpha, &work[p * work_dim1 + 1], &c__1, &x[1], &c__1); /* Compute residual vector rk, find norm, */ /* then check for tolerance. */ d__1 = -alpha; daxpy_(n, &d__1, &work[q * work_dim1 + 1], &c__1, &work[r * work_dim1 + 1] , &c__1); *resid = dnrm2_(n, &work[r * work_dim1 + 1], &c__1) / bnrm2; if (*resid <= tol) { goto L30; } if (*iter == maxit) { goto L20; } d__1 = -alpha; daxpy_(n, &d__1, &work[qtld * work_dim1 + 1], &c__1, &work[rtld * work_dim1 + 1], &c__1); rho1 = rho; goto L10; L20: /* Iteration fails. */ *info = 1; return 0; L25: /* Set breakdown flag. */ *info = -10; return 0; L30: /* Iteration successful; return. */ return 0; /* End of BICG */ }