mod_solver Module Reference

Functions/Subroutines
real(kind(1d0)) function	newtonpolynomial (x0, pcoeff, conv, maxiter)

Function/Subroutine Documentation

newtonpolynomial()

real(kind(1d0)) function mod_solver::newtonpolynomial	(	real(kind(1d0))	x0,
		real(kind(1d0)), dimension(:)	pcoeff,
		real(kind(1d0))	conv,
		integer	maxiter )

Definition at line 206 of file suews_phys_estm.f95.

      !Solves Newton's Method for a polynomial of the form
      !f(x)=Pcoeff(1)*x^n+Pcoeff(2)*x^n-1+...+Pcoeff(n+1)
      !                f(x(i))
      ! x(i+1) = x(i)- -------
      !                f'(x(i))
      !
      !conv is the level required for convergence
      !maxiter is the maximum allowed iterations
      !----------------------------------------------------
      REAL(KIND(1D0)) :: x0, x, conv
      REAL(KIND(1D0)) :: Pcoeff(:)
      REAL(KIND(1D0)) :: e, xprev
      REAL(KIND(1D0)) :: f, fp
      INTEGER :: maxiter
      INTEGER :: niter
      LOGICAL :: converged = .false.
      INTEGER :: n, i, j
 
      e = huge(1.)
      n = SIZE(pcoeff)
      x = x0
      DO i = 1, maxiter
         IF (abs(e) < conv) THEN
            converged = .true.
            EXIT
         END IF
         f = 0; fp = 0
         DO j = 1, n - 1
            f = f + pcoeff(j)*x**(n - j)
            fp = fp + pcoeff(j)*(n - j)*x**(n - j - 1) !!FO!! derivative
         END DO
 
         f = f + pcoeff(n)
         xprev = x
         IF (fp == 0.) fp = tiny(1.)
         x = xprev - f/fp
         e = x - xprev
      END DO
      niter = i - 1
      IF (.NOT. converged) THEN
         print *, "Solution did not converge. Niter=", niter, " Error=", e
         x = x0
      END IF

Referenced by estm_module::estm().

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