/* 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 doublereal c_b5 = -1.;
static doublereal c_b6 = 0.;
static doublereal c_b44 = 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,4).
*          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.
*
*  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.
*
*                   -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 DELTA.
*                                         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 stalled.
*
*                  BREAKTOL is set in function GETBREAK.
*
*  BLAS CALLS:   DAXPY, DCOPY, DDOT, DNRM2, DSCAL
*  ============================================================ */

int qmr_(n, b, x, work, ldw, iter, resid, matvec, 
	matvectrans, psolveq, psolvetransq, info)

   integer *n, *ldw, *iter, *info;
   doublereal *b, *x, *work, *resid;
   int (*matvec) (), (*matvectrans) (), (*psolveq) (), (*psolvetransq) ();
{
    /* System generated locals */
    integer work_dim1, work_offset;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt();

    /* Local variables */
    static doublereal beta;
    extern doublereal ddot_();
    static integer ptld;
    extern doublereal getbreak_();
    static integer vtld, wtld, ytld, ztld;
    static doublereal gammatol, deltatol, bnrm2;
    extern doublereal dnrm2_();
    static integer d, p, q, r, s;
    static doublereal gamma;
    static integer v, w, y, z;
    static doublereal delta;
    extern /* Subroutine */ int dscal_();
    static doublereal theta;
    extern /* Subroutine */ int dcopy_();
    static integer maxit;
    static doublereal c1;
    extern /* Subroutine */ int daxpy_();
    static doublereal xitol, gamma1, theta1, xi, epstol, rhotol, eta, eps, 
	    rho, tol, betatol, 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;
    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. */

    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_b44, &work[r * work_dim1 + 1]);
	if (dnrm2_(n, &work[r * work_dim1 + 1], &c__1) < tol) {
	    goto L30;
	}
    }

    bnrm2 = dnrm2_(n, &b[1], &c__1);
    if (bnrm2 == 0.) {
	bnrm2 = 1.;
    }

    dcopy_(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 = dnrm2_(n, &work[y * work_dim1 + 1], &c__1);

    dcopy_(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 = dnrm2_(n, &work[z * work_dim1 + 1], &c__1);

    gamma = 1.;
    eta = -1.;
    theta = 0.;

    *iter = 0;

L10:

/*     Perform Preconditioned QMR iteration. */

    ++(*iter);

    if (abs(rho) < rhotol || abs(xi) < xitol) {
	goto L25;
    }

    dcopy_(n, &work[vtld * work_dim1 + 1], &c__1, &work[v * work_dim1 + 1], &
	    c__1);
    d__1 = 1. / rho;
    dscal_(n, &d__1, &work[v * work_dim1 + 1], &c__1);
    d__1 = 1. / rho;
    dscal_(n, &d__1, &work[y * work_dim1 + 1], &c__1);

    dcopy_(n, &work[wtld * work_dim1 + 1], &c__1, &work[w * work_dim1 + 1], &
	    c__1);
    d__1 = 1. / xi;
    dscal_(n, &d__1, &work[w * work_dim1 + 1], &c__1);
    d__1 = 1. / xi;
    dscal_(n, &d__1, &work[z * work_dim1 + 1], &c__1);

    delta = ddot_(n, &work[z * work_dim1 + 1], &c__1, &work[y * work_dim1 + 1]
	    , &c__1);
    if (abs(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 = -(xi * delta / eps);
	daxpy_(n, &c1, &work[p * work_dim1 + 1], &c__1, &work[ytld * 
		work_dim1 + 1], &c__1);
	dcopy_(n, &work[ytld * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1]
		, &c__1);
	d__1 = -(rho * delta / eps);
	daxpy_(n, &d__1, &work[q * work_dim1 + 1], &c__1, &work[ztld * 
		work_dim1 + 1], &c__1);
	dcopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[q * work_dim1 + 1]
		, &c__1);
    } else {
	dcopy_(n, &work[ytld * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1]
		, &c__1);
	dcopy_(n, &work[ztld * work_dim1 + 1], &c__1, &work[q * work_dim1 + 1]
		, &c__1);
    }

    (*matvec)(&c_b44, &work[p * work_dim1 + 1], &c_b6, &work[ptld * work_dim1 
	    + 1]);

    eps = ddot_(n, &work[q * work_dim1 + 1], &c__1, &work[ptld * work_dim1 + 
	    1], &c__1);
    if (abs(eps) < epstol) {
	goto L25;
    }

    beta = eps / delta;
    if (abs(beta) < betatol) {
	goto L25;
    }

    dcopy_(n, &work[ptld * work_dim1 + 1], &c__1, &work[vtld * work_dim1 + 1],
	     &c__1);
    d__1 = -beta;
    daxpy_(n, &d__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 = dnrm2_(n, &work[y * work_dim1 + 1], &c__1);

    dcopy_(n, &work[w * work_dim1 + 1], &c__1, &work[wtld * work_dim1 + 1], &
	    c__1);
    d__1 = -beta;
    (*matvectrans)(&c_b44, &work[q * work_dim1 + 1], &d__1, &work[wtld * 
	    work_dim1 + 1]);
    (*psolvetransq)(&work[z * work_dim1 + 1], &work[wtld * work_dim1 + 1], 
	    "RIGHT", 5L);

    xi = dnrm2_(n, &work[z * work_dim1 + 1], &c__1);

    gamma1 = gamma;
    theta1 = theta;

    theta = rho / (gamma1 * abs(beta));
/* Computing 2nd power */
    d__1 = theta;
    gamma = 1. / sqrt(d__1 * d__1 + 1.);
    if (abs(gamma) < gammatol) {
	goto L25;
    }

/* Computing 2nd power */
    d__1 = gamma;
/* Computing 2nd power */
    d__2 = gamma1;
    eta = -eta * rho1 * (d__1 * d__1) / (beta * (d__2 * d__2));

    if (*iter > 1) {
/* Computing 2nd power */
	d__2 = theta1 * gamma;
	d__1 = d__2 * d__2;
	dscal_(n, &d__1, &work[d * work_dim1 + 1], &c__1);
	daxpy_(n, &eta, &work[p * work_dim1 + 1], &c__1, &work[d * work_dim1 
		+ 1], &c__1);
/* Computing 2nd power */
	d__2 = theta1 * gamma;
	d__1 = d__2 * d__2;
	dscal_(n, &d__1, &work[s * work_dim1 + 1], &c__1);
	daxpy_(n, &eta, &work[ptld * work_dim1 + 1], &c__1, &work[s * 
		work_dim1 + 1], &c__1);
    } else {
	dcopy_(n, &work[p * work_dim1 + 1], &c__1, &work[d * work_dim1 + 1], &
		c__1);
	dscal_(n, &eta, &work[d * work_dim1 + 1], &c__1);
	dcopy_(n, &work[ptld * work_dim1 + 1], &c__1, &work[s * work_dim1 + 1]
		, &c__1);
	dscal_(n, &eta, &work[s * work_dim1 + 1], &c__1);
    }

/*        Compute current solution vector x. */

    daxpy_(n, &c_b44, &work[d * work_dim1 + 1], &c__1, &x[1], &c__1);

/*        Compute residual vector rk, find norm, */
/*        then check for tolerance. */

    daxpy_(n, &c_b5, &work[s * 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;
    }

    goto L10;

L20:

/*     Iteration fails. */

    *info = 1;
    return 0;

L25:

/*     Method breakdown. */

    if (abs(rho) < rhotol) {
	*info = -10;
    } else if (abs(beta) < betatol) {
	*info = -11;
    } else if (abs(gamma) < gammatol) {
	*info = -12;
    } else if (abs(delta) < deltatol) {
	*info = -13;
    } else if (abs(eps) < epstol) {
	*info = -14;
    } else if (abs(xi) < xitol) {
	*info = -15;
    }

    return 0;

L30:

/*     Iteration successful; return. */

    return 0;

/*     End of QMR */

}