scipy.optimize.

# ridder#

scipy.optimize.ridder(f, a, b, args=(), xtol=2e-12, rtol=np.float64(8.881784197001252e-16), maxiter=100, full_output=False, disp=True)[source]#

Find a root of a function in an interval using Ridder’s method.

Parameters:
ffunction

Python function returning a number. f must be continuous, and f(a) and f(b) must have opposite signs.

ascalar

One end of the bracketing interval [a,b].

bscalar

The other end of the bracketing interval [a,b].

xtolnumber, optional

The computed root `x0` will satisfy ```np.allclose(x, x0, atol=xtol, rtol=rtol)```, where `x` is the exact root. The parameter must be positive.

rtolnumber, optional

The computed root `x0` will satisfy ```np.allclose(x, x0, atol=xtol, rtol=rtol)```, where `x` is the exact root. The parameter cannot be smaller than its default value of `4*np.finfo(float).eps`.

maxiterint, optional

If convergence is not achieved in maxiter iterations, an error is raised. Must be >= 0.

argstuple, optional

Containing extra arguments for the function f. f is called by `apply(f, (x)+args)`.

full_outputbool, optional

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.

dispbool, optional

If True, raise RuntimeError if the algorithm didn’t converge. Otherwise, the convergence status is recorded in any `RootResults` return object.

Returns:
rootfloat

Root of f between a and b.

r`RootResults` (present if `full_output = True`)

Object containing information about the convergence. In particular, `r.converged` is True if the routine converged.

Notes

Uses [Ridders1979] method to find a root of the function f between the arguments a and b. Ridders’ method is faster than bisection, but not generally as fast as the Brent routines. [Ridders1979] provides the classic description and source of the algorithm. A description can also be found in any recent edition of Numerical Recipes.

The routine used here diverges slightly from standard presentations in order to be a bit more careful of tolerance.

References

[Ridders1979] (1,2)

Ridders, C. F. J. “A New Algorithm for Computing a Single Root of a Real Continuous Function.” IEEE Trans. Circuits Systems 26, 979-980, 1979.

Examples

```>>> def f(x):
...     return (x**2 - 1)
```
```>>> from scipy import optimize
```
```>>> root = optimize.ridder(f, 0, 2)
>>> root
1.0
```
```>>> root = optimize.ridder(f, -2, 0)
>>> root
-1.0
```