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/*
* MLNLS.C - non-linear Newton solver for PML
* - courtesy of Jeff Painter
*
* Source Version: 2.0
* Software Release #92-0043
*
*/
#include "cpyright.h"
#include "pml.h"
static void
SC_DECLARE(_PM_settol,
(int neqns, REAL *tol, REAL *y, double atol, double rtol));
static double
SC_DECLARE(_PM_wvnorm, (int neqns, REAL *x, REAL *tol));
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/* PM_NEWTONDL - a simple nonlinear solver designed to be conveniently called
* - by Alpal-generated codes. This uses Newton's method to
* - solve f(Y)=0, with Y an array of length NEQNS. On input,
* - NEQNS and the maximum number of iterations MAXITER need to
* - be set along with ATOL and RTOL which are the absolute and
* - relative error tolerance parameters (good values are 1.0e-4
* - and 1.0e-3 respectively). Initial y values come in through Y
* - and the solution values are returned in Y.
* - One subroutine must be passed in through LINSOLV.
* - LINSOLV(x, y, iter) computes the Jacobian and the right-hand
* - side in the equation:
* -
* - J.dy = -f(y1) where J = (df/dy) at y1
* - y1 = y[iter-1]
* - dy = y[iter] - y1
* -
* - and returns the solution of the equation. Iter is the Newton
* - iteration index.
* -
* - Returns 0 iff we converged.
* - The convergence criterion is simple minded:
* -
* - Norm(dy)/(atol + rtol*abs(y2[i])) < 1
* -
* - where, dy is the correction to the solution found in
* - the last iteration.
*/
double PM_newtondl(neqns, y, dy, tol, maxiter, atol, rtol, linsolv, arg)
int neqns;
REAL *y, *dy, *tol;
int maxiter;
double atol, rtol;
PFVoid linsolv;
byte *arg;
{double err;
int i, n, iter;
iter = 0;
err = 2.0;
n = neqns*sizeof(double);
while ((err > 1.0) && (iter++ < maxiter))
/* initial iterate */
{memset(dy, 0, n);
/* solve J.dy = -f(y) */
linsolv(neqns, dy, y, iter, arg);
/* update y */
for (i = 0; i < neqns; i++)
y[i] += dy[i];
_PM_settol(neqns, tol, y, atol, rtol);
err = _PM_wvnorm(neqns, dy, tol);};
return((err <= 1.0) ? 0.0 : err);}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/* PM_NEWTONUL - a simple nonlinear solver designed to be conveniently called
* - by Alpal-generated codes. This uses Newton's method to
* - solve f(Y)=0, with Y an array of length NEQNS. On input,
* - NEQNS and the maximum number of iterations MAXITER need to
* - be set along with ATOL and RTOL which are the absolute and
* - relative error tolerance parameters (good values are 1.0e-4
* - and 1.0e-3 respectively). Initial y values come in through Y
* - and the solution values are returned in Y.
* - One subroutine must be passed in through LINSOLV.
* - LINSOLV(x, y, iter) computes the Jacobian and the right-hand
* - side in the equation:
* -
* - J.y2 = J.y1 - f(y1) where J = (df/dy) at y1
* - y1 = y[iter-1]
* - y2 = y[iter]
* -
* - and returns the solution of the equation. Iter is the Newton
* - iteration index.
* -
* - Returns 0 iff we converged.
* - The convergence criterion is simple minded:
* -
* - Norm(delta - y1[i])/(atol + rtol*abs(y2[i])) < 1
* -
* - where, delta - y1 is the correction to the solution found in
* - the last iteration.
*/
double PM_newtonul(neqns, y2, y1, tol, maxiter, atol, rtol, linsolv, arg)
int neqns;
REAL *y2, *y1, *tol;
int maxiter;
double atol, rtol;
PFVoid linsolv;
byte *arg;
{double err;
int i, iter, n;
iter = 0;
err = 2.0;
n = neqns*sizeof(double);
while ((err > 1.0) && (iter++ < maxiter))
/* initial iterate */
{memset(y1, 0, n);
/* solve J.y1 = -f(y2) */
linsolv(neqns, y1, y2, iter, arg);
/* update y2 and set y1 to the correction made in this iteration
* use tol for temporary storage to allow vectorization
*/
for (i = 0; i < neqns; i++)
tol[i] = y1[i] - y2[i];
for (i = 0; i < neqns; i++)
y2[i] = y1[i];
for (i = 0; i < neqns; i++)
y1[i] = tol[i];
_PM_settol(neqns, tol, y2, atol, rtol);
err = _PM_wvnorm(neqns, y1, tol);};
return((err <= 1.0) ? 0.0 : err);}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/* _PM_SETTOL - set the tolerances */
static void _PM_settol(neqns, tol, x, atol, rtol)
int neqns;
REAL *tol, *x;
double atol, rtol;
{int i;
for (i = 0; i < neqns; i++)
tol[i] = 1.0 / (atol + rtol*ABS(x[i]));
return;}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/* _PM_WVNORM - weighted vector norm */
static double _PM_wvnorm(neqns, x, tol)
int neqns;
REAL *x, *tol;
{int i;
double val, t;
val = 0.0;
for (i = 0; i < neqns; i++)
{t = tol[i]*x[i];
val += t*t;};
return(sqrt(val));}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
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