/* Cheby.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.;


/* Subroutine */ int cheby_(n, b, x, work, ldw, iter, resid, matvec, psolve, 
	info)
integer *n;
real *b, *x, *work;
integer *ldw, *iter;
real *resid;
/* Subroutine */ int (*matvec) (), (*psolve) ();
integer *info;
{
    /* System generated locals */
    integer work_dim1, work_offset;
    real r__1;

    /* Local variables */
    static real beta, bnrm2;
    extern doublereal snrm2_();
    static real c, d;
    static integer p, r;
    static real alpha;
    static integer z, maxit;
    extern /* Subroutine */ int scopy_(), saxpy_(), geteig_();
    static real eigmin, eigmax, tol;


/*  -- 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 */
/*  ======= */

/*  CHEBY solves the linear system Ax = b using the Chebyshev iterative */
/*  method with preconditioning. This version requires explicit */
/*  knowledge of the maximum and minimum eigenvalues. Note that these */
/*  eigenvalues must be positive real numbers, which is the case for the 
*/
/*  symmetric positive definite system. */

/*  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. */

/*          On input, the initial guess. This is commonly set to */
/*          the zero vector. */
/*          On exit, if INFO = 0, the iterated approximate solution. */

/*  WORK    (workspace) REAL array, dimension (LDW,3). */
/*          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) 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. */

/*  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
.*/

/*  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. */

/*  BLAS CALLS:   SAXPY, SCOPY, SNRM2 */
/*  ============================================================ */
/*     .. */
/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Routines .. */

/*     .. 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;

/*     Get extremal eigenvalues. */

    geteig_(&work[work_offset], ldw, &eigmax, &eigmin);

/*     Alias workspace columns. */

    r = 1;
    p = 2;
    z = 3;

/*     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.;
    }

/*     Initialize ellipse parameters. */

    c = (eigmax - eigmin) / (float)2.;
    d = (eigmax + eigmin) / (float)2.;

    *iter = 0;

L10:

/*     Perform Chebyshev iteration. */

    ++(*iter);

    (*psolve)(&work[z * work_dim1 + 1], &work[r * work_dim1 + 1]);
    if (*iter > 1) {
/* Computing 2nd power */
	r__1 = c * alpha / (float)2.;
	beta = r__1 * r__1;
	alpha = (float)1. / (d - beta);
	saxpy_(n, &beta, &work[p * work_dim1 + 1], &c__1, &work[z * work_dim1 
		+ 1], &c__1);
	scopy_(n, &work[z * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1], &
		c__1);
    } else {
	scopy_(n, &work[z * work_dim1 + 1], &c__1, &work[p * work_dim1 + 1], &
		c__1);
	alpha = (float)2. / d;
    }

/*        Compute new approximation vector X; check accuracy. */

    saxpy_(n, &alpha, &work[p * work_dim1 + 1], &c__1, &x[1], &c__1);
    r__1 = -(doublereal)alpha;
    (*matvec)(&r__1, &work[p * work_dim1 + 1], &c_b6, &work[r * work_dim1 + 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;

L30:

/*     Iteration successful; return. */

    return 0;

/*     End of CHEBY.f */

} /* cheby_ */