ComputationEngineNumeric

class poisson_approval.ComputationEngineNumeric

Computation engine: numeric computation.

This engine performs numeric computation, using floats when necessary:

>>> ce = ComputationEngineNumeric
>>> ce.inf
inf
>>> ce.nan
nan
>>> ce.exp(3)
20.085536923187668
>>> ce.log(3)
1.0986122886681098
>>> ce.Rational(1, 3)
Fraction(1, 3)
>>> ce.S(1) / 3
0.3333333333333333
>>> ce.simplify(- ce.Rational(1, 10) - (- ce.sqrt(15) / 5 + ce.sqrt(30) / 10)**2)
-0.151471862576143
>>> ce.sqrt(3)
1.7320508075688772

Usage of look_equal():

>>> ce.look_equal(1, 0.999999999999)
True
>>> ce.look_equal(1, np.float(0.999999999999))
True
>>> ce.look_equal(1, sp.Float(0.999999999999))
False
>>> ce.look_equal(1, Fraction(999999999999, 1000000000000))
False
>>> ce.look_equal(ce.sqrt(2), ce.Rational(14142135623730951, 10000000000000000))
True

classmethod Rational(x, y)

Rational number. Should return a fraction, even in a numeric engine.

classmethod S(x)

Convert the number if necessary.

Return a number that has the same value as x. Cf. function S of the package sympy.

classmethod barycenter(a, b, ratio_b)

Barycenter.

Parameters

• a (Number) –

• b (Number or iterable) –

• ratio_b (Number or iterable) – The ratio of b in the result. If an iterable, must be the same size as b.

Returns

The result of (1 - ratio_b) * a + ratio_b * b. The added value of this function is to preserve the type of a (resp. b) when ratio_b is 0 (resp. 1). If b and ratio_b are iterable, return (1 - sum(ratio_b)) * a + sum(ratio_b * b).

Return type

Number

Examples

In this first example, barycenter preserves the type Fraction, whereas a naive computation returns a float:

>>> from fractions import Fraction
>>> a, b = Fraction(1, 10), 0.7
>>> ratio_b = 0
>>> ComputationEngineNumeric.barycenter(a, b, ratio_b)
Fraction(1, 10)
>>> (1 - ratio_b) * a + ratio_b * b
0.1

The second example is symmetric of the first one, in the sense that it preserves the type of b:

>>> a, b = 0.7, 42
>>> ratio_b = 1
>>> ComputationEngineNumeric.barycenter(a, b, ratio_b)
42
>>> (1 - ratio_b) * a + ratio_b * b
42.0

In the following example, b and ratio_b are iterables:

>>> a = 0
>>> b = [-1 , 1]
>>> ComputationEngineNumeric.barycenter(0, [-1, 1], [Fraction(2, 10), Fraction(3, 10)])
Fraction(1, 10)

classmethod exp(x)

Exponential.

classmethod factorial(x)

Factorial.

inf = inf

Positive infinity.

classmethod log(x)

Logarithm.

classmethod look_equal(x, y, *args, **kwargs)

Test if two numbers can reasonably be considered as equal.

Parameters

• x (Number) –

• y (Number) –

• *args – Cf. math.isclose.

• **kwargs – Cf. math.isclose.

Returns

If x or y is a float or numpy float (but not a sympy float), then return math.isclose(x, y, *args, **kwargs). In all other cases, return True iff x is equal to y.

Return type

bool

classmethod multiply_with_absorbing_zero(x, y)

Multiplication with absorbing zero.

Parameters

• x (Number) –

• y (Number) –

Returns

If x or y is 0, then 0 (even if the other input is nan). Otherwise, the product of x and y.

Return type

Number

nan = nan

Not a Number.

classmethod ones(*args, **kwargs)

Array of ones.

pi = 3.141592653589793

Pi.

classmethod simplify(x)

Simplify the number if necessary.

Return a number that has the same value as x. Cf. function simplify of the package sympy.

classmethod simplify_vector(x)

Simplify the coefficients if necessary.

classmethod sqrt(x)

Square root.

classmethod zeros(*args, **kwargs)

Array of zeros.