Instance Methodswift-numerics 1.0.3RealModule->Swift

    isApproximatelyEqual(to:absoluteTolerance:relativeTolerance:norm:)

    Test if self and other are approximately equal with specified tolerances and norm.

    ApproximateEquality.swift:233
    func isApproximatelyEqual<Magnitude>(to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude) -> Bool where Magnitude : FloatingPoint
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    Parameters

    other

    The value to which self is compared.

    absoluteTolerance

    The absolute tolerance to use in the comparison.

    This value should be non-negative and finite. This constraint on is only checked in debug builds, because a mathematically well-defined result exists for any tolerance, even one out of range.

    relativeTolerance

    The relative tolerance to use in the comparison. Defaults to zero.

    This value should be non-negative and less than or equal to 1. This constraint on is only checked in debug builds, because a mathematically well-defined result exists for any tolerance, even one out of range.

    norm

    The norm to use for the comparison. Defaults to \.magnitude.

    For example, if we wanted to test if a complex value was inside a circle of radius 0.001 centered at (1 + 0i), we could use:

    z.isApproximatelyEqual(
  to: 1,
  absoluteTolerance: 0.001,
  norm: \.length
)

    (if we used the default norm, .magnitude, we would be testing if z were inside a square region instead.)

    true if self and other are equal, or if they are finite and either

    norm(self - other) <= absoluteTolerance

    or

    norm(self - other) <= relativeTolerance * scale

    where scale is max(norm(self), norm(other)).

    Mathematical Properties:

    • isApproximatelyEqual(to:absoluteTolerance:relativeTolerance:norm:) is reflexive for non-exceptional values (such as NaN).

    • isApproximatelyEqual(to:absoluteTolerance:relativeTolerance:norm:) is symmetric.

    • isApproximatelyEqual(to:absoluteTolerance:relativeTolerance:norm:) is not transitive. Because of this, approximately equality is not an equivalence relation, even when restricted to non-exceptional values.

      This means that you must not use approximate equality to implement a conformance to Equatable, as it will violate the invariants of code written against that protocol.

    • For any point a, the set of values that compare approximately equal to a is convex (under the assumption that norm implements a valid norm, which cannot be checked by this function or a protocol).

    See Also:

    • isApproximatelyEqual(to:[relativeTolerance:norm:])

    • isApproximatelyEqual(to:absoluteTolerance:[relativeTolerance:])