/* QMR.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 real c_b5 = (float)-1.; static real c_b6 = (float)1.; static real c_b45 = (float)0.; /* Subroutine */ int qmr_(n, b, x, work, ldw, iter, resid, matvec, matvectrans, psolveq, psolvetransq, info) integer *n; real *b, *x, *work; integer *ldw, *iter; real *resid; /* Subroutine */ int (*matvec) (), (*matvectrans) (), (*psolveq) (), (* psolvetransq) (); integer *info; { /* System generated locals */ integer work_dim1, work_offset; real r__1, r__2; /* Builtin functions */ double sqrt(); /* Local variables */ static real beta; static integer ptld; extern doublereal getbreak_(); static integer vtld, wtld; extern doublereal sdot_(); static integer ytld, ztld; static real gammatol, deltatol, bnrm2; extern doublereal snrm2_(); static integer d, p, q, r, s; static real gamma; static integer v, w, y, z; static real delta, theta; extern /* Subroutine */ int sscal_(); static integer maxit; static real c1; extern /* Subroutine */ int scopy_(); static real xitol, gamma1; extern /* Subroutine */ int saxpy_(); static real theta1, xi, epstol, rhotol, eta, eps, rho, tol, betatol, rho1; /* -- 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 .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* .. Function Arguments .. */ /* Purpose */ /* ======= */ /* QMR Method solves the linear system Ax = b using the */ /* Quasi-Minimal Residual 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) 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; on exit, the iterated solution. */ /* WORK (workspace) REAL array, dimension (LDW,11). */ /* Workspace for residual, direction vector, etc. */ /* Note that W and WTLD, Y and YTLD, and Z and ZTLD share */ /* workspace. */ /* 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( 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. */ /* PSOLVEQ (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. As QMR uses left */ /* and right preconditioning and the preconditioners are in */ /* common, we must specify in the call which to use. Vector b */ /* must remain unchanged. */ /* The solution is over-written on vector x. */ /* The call is: */ /* CALL PSOLVEQ( X, B, 'LEFT' ) */ /* The preconditioner is passed into the routine in a common block .*/ /* PSOLVETRANSQ (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. As QMR uses left and right preconditioning and */ /* the preconditioners are in common, we must specify in the */ /* call which to use. Vector b must remain unchanged. */ /* The solution is over-written on vector x. */ /* The call is: */ /* CALL PSOLVETRANSQ( X, B, 'LEFT' ) */ /* 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, or breakdown occurred */ /* during iteration. */ /* Illegal 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. */ /* -11: BETA < BREAKTOL: EPS too small in relation to DEL TA.*/ /* Convergence has stalled. */ /* -12: GAMMA < BREAKTOL: THETA too large. */ /* Convergence has stalled. */ /* -13: DELTA < BREAKTOL: Y and Z have become */ /* orthogonal. */ /* -14: EPS < BREAKTOL: Q and PTLD have become */ /* orthogonal. */ /* -15: XI < BREAKTOL: Z too small. Convergence has sta lled.*/ /* BREAKTOL is set in function GETBREAK. */ /* BLAS CALLS: SAXPY, SCOPY, SDOT, SNRM2, SSCAL */ /* ============================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Routines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ work_dim1 = *ldw; work_offset = work_dim1 + 1; work -= work_offset; --x; --b; /* Function Body */ *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; d = 2; p = 3; ptld = 4; q = 5; s = 6; v = 7; vtld = 8; w = 9; wtld = 9; y = 10; ytld = 10; z = 11; ztld = 11; /* Set breakdown tolerances. */ rhotol = getbreak_(); betatol = getbreak_(); gammatol = getbreak_(); deltatol = getbreak_(); epstol = getbreak_(); xitol = getbreak_(); /* Set initial residual. */ scopy_(n, &b[1], &c__1, &work[r * work_dim1 + 1], &c__1); if (snrm2_(n, &x[1], &c__1) != (float)0.) { (*matvec)(&c_b5, &x[1], &c_b6, &work[r * work_dim1 + 1]); if (snrm2_(n, &work[r * work_dim1 + 1], &c__1) < tol) { goto L30; } } bnrm2 = snrm2_(n, &b[1], &c__1); if (bnrm2 == (float)0.) { bnrm2 = (float)1.; } scopy_(n, &work[r * work_dim1 + 1], &c__1, &work[vtld * work_dim1 + 1], & c__1); (*psolveq)(&work[y * work_dim1 + 1], &work[vtld * work_dim1 + 1], "LEFT", 4L); rho = snrm2_(n, &work[y * work_dim1 + 1], &c__1); scopy_(n, &work[r * work_dim1 + 1], &c__1, &work[wtld * work_dim1 + 1], & c__1); (*psolvetransq)(&work[z * work_dim1 + 1], &work[wtld * work_dim1 + 1], "RIGHT", 5L); xi = snrm2_(n, &work[z * work_dim1 + 1], &c__1); gamma = (float)1.; eta = (float)-1.; theta = (float)0.; *iter = 0; L10: /* Perform Preconditioned QMR iteration. */ ++(*iter); if (dabs(rho) < rhotol || dabs(xi) < xitol) { goto L25; } scopy_(n, &work[vtld * work_dim1 + 1], &c__1, &work[v * work_dim1 + 1], & c__1); r__1 = (float)1. / rho; sscal_(n, &r__1, &work[v * work_dim1 + 1], &c__1); r__1 = (float)1. / rho; sscal_(n, &r__1, &work[y * work_dim1 + 1], &c__1); scopy_(n, &work[wtld * work_dim1 + 1], &c__1, &work[w * work_dim1 + 1], & c__1); r__1 = (float)1. / xi; sscal_(n, &r__1, &work[w * work_dim1 + 1], &c__1); r__1 = (float)1. / xi; sscal_(n, &r__1, &work[z * work_dim1 + 1], &c__1); delta = sdot_(n, &work[z * work_dim1 + 1], &c__1, &work[y * work_dim1 + 1] , &c__1); if (dabs(delta) < deltatol) { goto L25; } (*psolveq)(&work[ytld * work_dim1 + 1], &work[y * work_dim1 + 1], "RIGHT", 5L); (*psolvetransq)(&work[ztld * work_dim1 + 1], &work[z * work_dim1 + 1], "LEFT", 4L); if (*iter > 1) { c1 = -(doublereal)(xi * delta / eps); saxpy_(n, &c1, &work[p * work_dim1 + 1], &c__1, &work[ytld * work_dim1 + 1], &c__1); scopy_(n, &work[ytld * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1] , &c__1); r__1 = -(doublereal)(rho * delta / eps); saxpy_(n, &r__1, &work[q * work_dim1 + 1], &c__1, &work[ztld * work_dim1 + 1], &c__1); scopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[q * work_dim1 + 1] , &c__1); } else { scopy_(n, &work[ytld * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1] , &c__1); scopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[q * work_dim1 + 1] , &c__1); } (*matvec)(&c_b6, &work[p * work_dim1 + 1], &c_b45, &work[ptld * work_dim1 + 1]); eps = sdot_(n, &work[q * work_dim1 + 1], &c__1, &work[ptld * work_dim1 + 1], &c__1); if (dabs(eps) < epstol) { goto L25; } beta = eps / delta; if (dabs(beta) < betatol) { goto L25; } scopy_(n, &work[ptld * work_dim1 + 1], &c__1, &work[vtld * work_dim1 + 1], &c__1); r__1 = -(doublereal)beta; saxpy_(n, &r__1, &work[v * work_dim1 + 1], &c__1, &work[vtld * work_dim1 + 1], &c__1); (*psolveq)(&work[y * work_dim1 + 1], &work[vtld * work_dim1 + 1], "LEFT", 4L); rho1 = rho; rho = snrm2_(n, &work[y * work_dim1 + 1], &c__1); scopy_(n, &work[w * work_dim1 + 1], &c__1, &work[wtld * work_dim1 + 1], & c__1); r__1 = -(doublereal)beta; (*matvectrans)(&c_b6, &work[q * work_dim1 + 1], &r__1, &work[wtld * work_dim1 + 1]); (*psolvetransq)(&work[z * work_dim1 + 1], &work[wtld * work_dim1 + 1], "RIGHT", 5L); xi = snrm2_(n, &work[z * work_dim1 + 1], &c__1); gamma1 = gamma; theta1 = theta; theta = rho / (gamma1 * dabs(beta)); /* Computing 2nd power */ r__1 = theta; gamma = (float)1. / sqrt(r__1 * r__1 + (float)1.); if (dabs(gamma) < gammatol) { goto L25; } /* Computing 2nd power */ r__1 = gamma; /* Computing 2nd power */ r__2 = gamma1; eta = -(doublereal)eta * rho1 * (r__1 * r__1) / (beta * (r__2 * r__2)); if (*iter > 1) { /* Computing 2nd power */ r__2 = theta1 * gamma; r__1 = r__2 * r__2; sscal_(n, &r__1, &work[d * work_dim1 + 1], &c__1); saxpy_(n, &eta, &work[p * work_dim1 + 1], &c__1, &work[d * work_dim1 + 1], &c__1); /* Computing 2nd power */ r__2 = theta1 * gamma; r__1 = r__2 * r__2; sscal_(n, &r__1, &work[s * work_dim1 + 1], &c__1); saxpy_(n, &eta, &work[ptld * work_dim1 + 1], &c__1, &work[s * work_dim1 + 1], &c__1); } else { scopy_(n, &work[p * work_dim1 + 1], &c__1, &work[d * work_dim1 + 1], & c__1); sscal_(n, &eta, &work[d * work_dim1 + 1], &c__1); scopy_(n, &work[ptld * work_dim1 + 1], &c__1, &work[s * work_dim1 + 1] , &c__1); sscal_(n, &eta, &work[s * work_dim1 + 1], &c__1); } /* Compute current solution vector x. */ saxpy_(n, &c_b6, &work[d * work_dim1 + 1], &c__1, &x[1], &c__1); /* Compute residual vector rk, find norm, */ /* then check for tolerance. */ saxpy_(n, &c_b5, &work[s * work_dim1 + 1], &c__1, &work[r * work_dim1 + 1] , &c__1); *resid = snrm2_(n, &work[r * work_dim1 + 1], &c__1) / bnrm2; if (*resid <= tol) { goto L30; } if (*iter == maxit) { goto L20; } goto L10; L20: /* Iteration fails. */ *info = 1; return 0; L25: /* Method breakdown. */ if (dabs(rho) < rhotol) { *info = -10; } else if (dabs(beta) < betatol) { *info = -11; } else if (dabs(gamma) < gammatol) { *info = -12; } else if (dabs(delta) < deltatol) { *info = -13; } else if (dabs(eps) < epstol) { *info = -14; } else if (dabs(xi) < xitol) { *info = -15; } return 0; L30: /* Iteration successful; return. */ return 0; /* End of QMR */ } /* qmr_ */