API Documentation Generated by Endo, 2006-08-14

Variables

• CONVERGED

  CONVERGED = 'converged'
  
  

• CONVERR

  CONVERR = 'convergence error'
  
  

• SIGNERR

  SIGNERR = 'sign error'
  
  

• flag_map

  flag_map = { Const(0) : Name('CONVERGED'), UnarySub(Const(1)) : Name('SIGNERR'), UnarySub(Const(2)) : Name('CONVERR') }
  
  

Classes

• RootResults

Function summary

• bisect(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)
• brenth(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)
• brentq(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)
• results_c(full_output, r)
• ridder(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)

Functions

• bisect(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)

  Find root of f in [a,b]

  Basic bisection routine to find a zero of the function f between the arguments a and b. f(a) and f(b) can not have the same signs. Slow but sure.

  f : Python function returning a number.

  a : Number, one end of the bracketing interval.

  b : Number, the other end of the bracketing interval.

  xtol : Number, the routine converges when a root is known

  to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

  maxiter : Number, if convergence is not achieved in

  maxiter iterations, and error is raised. Must be >= 0.

  args : tuple containing extra arguments for the function f.

  f is called by apply(f,(x)+args).

  If full_output is False, the root is returned.

  If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object containing information about the convergence. In particular, r.converged is True if the the routine converged.

• brenth(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)

  Find root of f in [a,b]

  A variation on the classic Brent routine to find a zero of the function f between the arguments a and b that uses hyperbolic extrapolation instead of inverse quadratic extrapolation. There was a paper back in the 1980's ... f(a) and f(b) can not have the same signs. Generally on a par with the brent routine, but not as heavily tested. It is a safe version of the secant method that uses hyperbolic extrapolation. The version here is by Chuck Harris.

  f : Python function returning a number.

  a : Number, one end of the bracketing interval.

  b : Number, the other end of the bracketing interval.

  xtol : Number, the routine converges when a root is known

  to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

  maxiter : Number, if convergence is not achieved in

  maxiter iterations, and error is raised. Must be >= 0.

  args : tuple containing extra arguments for the function f.

  f is called by apply(f,(x)+args).

  If full_output is False, the root is returned.

  If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object containing information about the convergence. In particular, r.converged is True if the the routine converged.

• brentq(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)

  Find root of f in [a,b]

  The classic Brent routine to find a zero of the function f between the arguments a and b. f(a) and f(b) can not have the same signs. Generally the best of the routines here. It is a safe version of the secant method that uses inverse quadratic extrapolation. The version here is a slight modification that uses a different formula in the extrapolation step. A description may be found in Numerical Recipes, but the code here is probably easier to understand.

  f : Python function returning a number.

  a : Number, one end of the bracketing interval.

  b : Number, the other end of the bracketing interval.

  xtol : Number, the routine converges when a root is known

  to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

  maxiter : Number, if convergence is not achieved in

  maxiter iterations, and error is raised. Must be >= 0.

  args : tuple containing extra arguments for the function f.

  f is called by apply(f,(x)+args).

  If full_output is False, the root is returned.

  If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object containing information about the convergence. In particular, r.converged is True if the the routine converged.

• results_c(full_output, r)
• ridder(f, a, b, args = (), xtol = _xtol, rtol = _rtol, maxiter = _iter, full_output = False, disp = False)

  Find root of f in [a,b]

  Ridder routine to find a zero of the function f between the arguments a and b. f(a) and f(b) can not have the same signs. Faster than bisection, but not generaly as fast as the brent rountines. A description may be found in a recent edition of Numerical Recipes. The routine here is modified a bit to be more careful of tolerance.

  f : Python function returning a number.

  a : Number, one end of the bracketing interval.

  b : Number, the other end of the bracketing interval.

  xtol : Number, the routine converges when a root is known

  to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

  maxiter : Number, if convergence is not achieved in

  maxiter iterations, and error is raised. Must be >= 0.

  args : tuple containing extra arguments for the function f.

  f is called by apply(f,(x)+args).

  If full_output is False, the root is returned.

  If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object containing information about the convergence. In particular, r.converged is True if the the routine converged.

Imported names