verry.intervalseries.IntervalSeries

class verry.intervalseries.IntervalSeries(coeffs, intvl)

Bases: Scalar, Generic

Interval series.

Parameters:

• coeffs – Sequence of coefficients with respect to the monomial basis.

• intvl (type[Interval] | None) – Type of each coefficient.

__call__(arg)

Return compose(arg) or eval(arg) depending on the type of arg.

See also

compose, eval

compose(arg)

Return the composition.

See also

eval, __call__

Examples

>>> from verry import FloatInterval as FI
>>> f = IntervalSeries([4, 3, 1], intvl=FI)
>>> g = IntervalSeries([2, -1, 5], intvl=FI)
>>> h = f.compose(g)
>>> print([coeff.mid() for coeff in h.coeffs])
[14.0, -7.0, 36.0, -10.0, 25.0]

copy()

Return a copy of the series.

eval(arg)

Return an interval containing the image of arg.

See also

compose, __call__

Examples

>>> from verry import FloatInterval as FI
>>> f = IntervalSeries([8, 2, -1], intvl=FI)
>>> y1 = f.eval(2)
>>> print(format(y1, ".2f"))
[8.00, 8.00]
>>> y2 = f.eval(FI(-1, 1))
>>> FI(5, 9).issubset(y2)
True

integrate()

Integrate the series in a term by term.

Examples

>>> from verry import FloatInterval as FI
>>> x = IntervalSeries([0, 1], intvl=FI)
>>> y = 3 * x**2 + 4 * x + 5
>>> z = y.integrate()
>>> z == x**3 + 2 * x**2 + 5 * x
True

reciprocal()

Return the reciprocal of the series.

Raises:

ZeroDivisionError – If the constant term contains zero.

round_type1(deg)

Round the series in Type-I PSA. This method modifies the series in-place.

Parameters:

deg – Truncation degree.

See also

round_type2

Examples

>>> from verry import FloatInterval as FI
>>> f = IntervalSeries([1, 2, -3], intvl=FI)
>>> g = IntervalSeries([1, -1, 1], intvl=FI)
>>> h1 = f * g
>>> h2 = h1.copy()
>>> h2.round_type1(deg=2)
>>> h1(1).issubset(h2(1))
False

round_type2(deg, domain)

Round the series in Type-II PSA. This method modifies the series in-place.

Parameters:

deg – Truncation degree.

See also

round_type1

Examples

>>> from verry import FloatInterval as FI
>>> f = IntervalSeries([1, 2, -3], intvl=FI)
>>> g = IntervalSeries([1, -1, 1], intvl=FI)
>>> h1 = f * g
>>> h2 = h1.copy()
>>> h2.round_type2(deg=2, domain=FI(0, 2))
>>> h1(1).issubset(h2(1))
True