Number - Scala Mathematical Library/com.phasmidsoftware.number/com.phasmidsoftware.number.algebra/com.phasmidsoftware.number.algebra.eager/Functional

Functional

com.phasmidsoftware.number.algebra.eager.Functional

See theFunctional companion object

trait Functional extends Structure, MaybeFuzzy, Ordered[Functional]

The Functional trait serves as an abstraction for entities that wrap Number, such as Angle, NaturalExponential, etc. These are the types that can potentially have fuzz.

Classes or traits that extend Functional encapsulate a Number instance, providing a consistent interface to access and work with numerical values. It is particularly useful in scenarios where mathematical operations or transformations are required on numbers.

Attributes

Companion: object
Graph
Supertypes: trait Ordered[Functional]

trait Comparable[Functional]

trait MaybeFuzzy

trait Structure

trait Negatable[Structure]

trait WithFuzziness

trait Eager

trait DyadicOps

trait Approximate

trait Valuable

trait TypeSafe

trait Normalizable[Valuable]

trait Exactitude

trait Unitary

trait Zeroable

trait Numeric

trait Renderable

class Object

trait Matchable

class Any
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Known subtypes: trait Radians

class Angle

trait Transformed

class Exponential

class BinaryExponential

class NaturalExponential

class InversePower
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Members list

Value members

Abstract methods

Retrieves the value associated with this Functional instance.

This method provides access to the underlying numerical representation encapsulated as a Number type. The value can represent exact or approximate numerical quantities, facilitating mathematical operations or transformations.

Attributes

Returns: the Number associated with this instance

Concrete methods

Converts the current instance of Functional into a Real representation.

The conversion is achieved by applying the scaleFunction to the value derived from the number method, and optionally utilizing maybeFuzz if available. This process encapsulates the numerical transformation, resulting in the Real type.

Attributes

Returns: a Real object representing the scaled and transformed value of the current instance.

Inherited methods

Returns true if this is less than that

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

Returns true if this is less than or equal to that.

Attributes

Inherited from:: Ordered

Returns true if this is greater than that.

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

Returns true if this is greater than or equal to that.

Attributes

Inherited from:: Ordered

Adds the specified Structure instance to the current instance, producing a new Structure.

Value parameters

y: The Structure instance to be added.

Attributes

Returns: A Try wrapping the resulting Structure instance, or a failure if the operation cannot be completed.
Inherited from:: Structure

Adds the current Eager instance to another Eager instance using the DyadicOperator mechanism. The addition operation is implemented by delegating to the addEagers function for specific behavior, ensuring proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to be added to this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the addition if successful, or a failure if the operation fails
Inherited from:: Eager

Computes an approximate representation of the current value.

This method utilizes the approximation mechanism to derive the most likely value in the form of a Real. Should the approximation fail, an AlgebraException will be raised to indicate the error.

Attributes

Returns: the approximate value as a Real if successful; throws an AlgebraException otherwise.
Inherited from:: Approximate

Attempts to approximate the current instance to a Real value. If the instance is already of type Real, it is simply returned, wrapped inside Some. Otherwise, depending on the value of force, it either attempts a conversion to a default Real (if force is true), or returns None.

NOTE that this method tries to keep exact quantities exact.

Value parameters

force: a boolean flag indicating whether to force the conversion to a default Real value when the current instance is not of type Real

Attributes

Returns: an Option[Real] containing the approximated value if successful, or None if approximation fails
Inherited from:: Structure

Attempts to compute an approximate complex representation of the current value.

This method provides an optional approximation in the form of an Eager type. By default, it does not perform the computation unless explicitly requested through the force flag. The method may return None if no approximation can be computed or if the operation fails.

Value parameters

force: a boolean flag indicating whether to force computation of the approximation. If true, the method will attempt to perform a complex approximation even if it is resource-intensive or otherwise unwarranted.

Attributes

Returns: an Option containing the approximate value as an Eager if successful, or None if no approximation is available.
Inherited from:: Approximate

Converts this Structure object into an optional java.lang.Number provided that the conversion can be performed without loss of precision.

The method determines whether the current Structure object can be represented as a java.lang.Number by leveraging the asNumber method and further evaluating certain conditions:

If the Structure object is an ExactNumber and its factor is PureNumber, the result is converted using Value.asJavaNumber.
If the Structure object is a Real with a wiggle value below a specified tolerance, the result is also converted using Value.asJavaNumber.
In all other cases, None is returned.

Attributes

Returns: an optional java.lang.Number representation of this object. The result is Some(java.lang.Number) if the conversion is successful under the stated conditions; otherwise, None.
Inherited from:: Structure

Returns the category of this value in the Valuable type hierarchy.

Attributes

Returns: a string indicating the high-level category (e.g., "Expression", "Structure", "Nat", "Complex")
Inherited from:: TypeSafe

Compares two instances of Eager and determines their relative ordering. This method is not yet implemented and will raise an com.phasmidsoftware.number.algebra.util.AlgebraException if called.

Value parameters

x: the first Eager instance to compare
y: the second Eager instance to compare

Attributes

Returns: a Try[Int] that contains the comparison result: - 0 if x and y are equal, - a negative result if x is less than y, - and a positive result if x is greater than y. As the method is unimplemented, it will always return a failure with an AlgebraException.
Inherited from:: Eager

Result of comparing this with operand that.

Value parameters

that: the instance to compare against

Attributes

Inherited from:: Ordered

Returns a descriptive string combining category and type name. Useful for debugging to understand both the hierarchy level and concrete type.

Attributes

Returns: a string in the format "Category.TypeName" (e.g., "Structure.WholeNumber")
Inherited from:: TypeSafe

Divides the current Structure instance by another Structure instance. The operation is performed using the DyadicOperator defined for Structure. The result is wrapped in a Try to handle potential failures during the operation.

Value parameters

y: the Structure instance to divide the current instance by

Attributes

Returns: a Try[Structure] containing the result of the division if successful, or a failure if the operation cannot be performed
Inherited from:: Structure

Performs division of the current Eager instance by another Eager instance. This operation is implemented using the DyadicOperator mechanism, delegating the actual division logic to the divideEagers function.

Value parameters

y: the Eager instance to divide the current instance by

Attributes

Returns: a Try[Eager] containing the result of the division if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

Compares this Eager instance with another Eager instance for equality. This method is unimplemented and currently returns a failure with an AlgebraException.

Value parameters

that: the Eager instance to compare against

Attributes

Returns: a Try[Boolean] indicating whether the two instances are equal. As the method is unimplemented, it always returns a failure containing an AlgebraException.
Inherited from:: Eager

Attempts to convert the current object to an instance of Eager using an approximation method. If the conversion fails, it recovers by throwing an AlgebraException with a descriptive error message.

Attributes

Returns: An instance of Eager if the approximation is successful.
Inherited from:: Eager

Performs a fuzzy comparison between two Eager instances. The comparison is based on a specified tolerance and determines their relative ordering. If the comparison cannot be performed, an AlgebraException is returned as a failure.

Value parameters

p: the tolerance (as a Double) to be used for the comparison
x: the first Eager instance to be compared
y: the second Eager instance to be compared

Attributes

Returns: a Try[Int] representing the result of the comparison: - A negative integer if x is less than y - Zero if x is approximately equal to y within the tolerance p - A positive integer if x is greater than y - A Failure(AlgebraException) if the comparison cannot be performed
Inherited from:: Eager

Performs a fuzzy equality comparison between the current Structure instance and another Eager instance. The comparison is based on a specified tolerance level.

If both instances are of type Structure, this method attempts to convert them to Real and performs a fuzzy equality check with the specified tolerance. If the conversion or comparison fails, a failure with an appropriate AlgebraException is returned.

If either of the instances is not of type Structure, a failure with an AlgebraException is returned.

Value parameters

confidence: the tolerance level (as a Double) to be used for the fuzzy equality comparison.
that: the Eager instance to compare against the current instance.

Attributes

Returns: a Try[Boolean] indicating whether the two instances are fuzzy equal within the specified tolerance. Returns a Success(true) or Success(false) if the comparison completes successfully, or a Failure(AlgebraException) if an error occurs.
Definition Classes: Structure -> Eager -> DyadicOps
Inherited from:: Structure

Multiplies the current Structure instance by the specified Structure operand. The result of the operation is wrapped in a Try, allowing for safe handling of failures.

Value parameters

y: the Structure operand with which the current instance is multiplied

Attributes

Returns: a Try[Structure] containing the result of the multiplication if successful, or a failure if the operation is not valid or cannot be performed
Inherited from:: Structure

Multiplies the current Eager instance with another Eager instance. The multiplication operation is carried out using the DyadicOperator mechanism, which delegates to the multiplyEagers function for specific behavior. This ensures proper handling of various subtypes of Eager.

Value parameters

y: the Eager instance to multiply with this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the multiplication if successful, or a failure if the operation cannot be performed
Inherited from:: Eager

Obtains the product of this Valuable instance and another Valuable instance. The behavior of the method is determined by whether the instances are of type Lazy or Eager. If the provided instances do not conform to the expected types, an AlgebraException is thrown. CONSIDER supporting sum also.

CONSIDER using lazify

Value parameters

other: the other Valuable instance to compute the product with

Attributes

Returns: a Valuable instance representing the product of this and the other instance
Note: throws AlgebraException if the computation involves unsupported Valuable types
Inherited from:: Valuable

Renders and returns a string representation of the object. By default, this is the same as render but it can be overridden in subclasses.

Attributes

Returns: a string representing the object
Inherited from:: Valuable

Subtracts the given Structure instance (y) from the current instance. The operation is performed using a dyadic operator that ensures type safety and handles any failures during the subtraction via a Try.

Value parameters

y: the Structure instance to be subtracted from the current instance

Attributes

Returns: a Try[Structure] containing the result of the subtraction if successful, or a failure if the subtraction operation cannot be performed
Inherited from:: Structure

Subtracts the given Eager instance y from the current Eager instance. This operation is performed using the DyadicOperator mechanism, which delegates to the subtractEagers function to handle the specific subtraction behavior.

Value parameters

y: the Eager instance to be subtracted from this Eager instance

Attributes

Returns: a Try[Eager] containing the result of the subtraction if successful, or a failure if the operation fails
Inherited from:: Eager

Returns a simple string representation of the runtime type. Useful for debugging and logging.

Attributes

Returns: the simple class name (e.g., "WholeNumber", "RationalNumber")
Inherited from:: TypeSafe

Inherited and Abstract methods

Result of comparing this with operand that.

Implement this method to determine how instances of A will be sorted.

Returns x where:

x < 0 when this < that
x == 0 when this == that
x > 0 when this > that

Value parameters

that: the instance to compare against

Attributes

Returns: an integer whose sign indicates the ordering relation between this and that
Inherited from:: Ordered

Converts the given Structure object to an optional instance of the same type.

TODO refactor this method to use a type class instance of CanConvert[T, Structure] instead of ClassTag.

Value parameters

t: the input object of type T which is a subtype of Structure.

Attributes

Returns: an Option containing a transformed instance of type T if the conversion is successful, or None otherwise.
Inherited from:: Structure

Retrieves an optional fuzziness value associated with this instance.

The fuzziness value, if present, provides information about the level of uncertainty or imprecision, modeled as a Fuzziness[Double].

Attributes

Returns: an Option containing the Fuzziness[Double] value if defined, or None if no fuzziness is specified.
Inherited from:: WithFuzziness

Determines whether this object is exact, i.e., is not any kind of approximation.

CONSIDER it may be possible that there are non-approximatable entities that are not exact either.

The method returns true if the value is represented exactly in IEEE 754 format, or Two's complement or the exact value must be represented symbolically. Examples of the first type include the number one (represented here as either WholeNumber(1) or Succ(NatZero). Examples of the second type include 1.5 or the square root of two (represented here as InversePower(2,2)).

When we are forced to approximate a value, for example when we want to print the decimal value of 𝛗, the Golden Ratio, then we mark such a representation as approximate, i.e., this method returns false.

Attributes

Returns: a Boolean indicating whether the entity is exact (true) or is an approximation (false).
Inherited from:: Exactitude

Determines whether this object represents unity.

Attributes

Returns: true if the object represents unity, false otherwise
Inherited from:: Unitary

Determines if the current number is equal to zero.

Attributes

Returns: true if the number is zero, false otherwise
Inherited from:: Zeroable

Attempts to retrieve a factor based on the provided context. This method evaluates whether there is an applicable factor within the given context.

Value parameters

context: the context in which the factor is evaluated.

Attributes

Returns: an optional Factor if one qualifies under the provided context; otherwise, None.
Inherited from:: Valuable

Retrieves an optional name associated with this instance.

Attributes

Returns: an Option[String] containing the name if present, otherwise None
Inherited from:: Eager

Returns a new instance of T that is the negation of the current instance. CONSIDER sorting out the use of CanNegate so that we can extend that for Structure.

Attributes

Returns: a Structure representing the negation of this instance
Inherited from:: Negatable

Normalizes the current instance of Eager. This operation ensures that the instance is in its standard or canonical form. Be very wary of changing the way normalization works! One place that we don't routinely normalize (maybe we should) is in the Eq and FuzzyEq comparisons.

Attributes

Returns: the normalized instance of Eager as Self
Inherited from:: Eager

Method to render this Valuable for presentation to the user. NOTE to implementors: never ever invoke this.toString in your implementation lest you get a StackOverflow.

Attributes

Returns: a String
Inherited from:: Renderable

Determines the sign of the Structure value represented by this instance. Returns an integer indicating whether the value is positive, negative, or zero.

Attributes

Returns: 1 if the value is positive, -1 if the value is negative, and 0 if the value is zero
Inherited from:: Zeroable

Abstract fields

Represents the derivative function associated with this Functional instance. That's to say d(f(number)) by d(number) where f is this Functional. For a Structure, the derivative should be positive, however, it is possible that it is not positive for certain types of Functional.

The derivativeFunction provides a mathematical operation that computes the derivative with respect to a given input value. It is typically used to evaluate rates of change or sensitivity in the context of numerical transformations.

Attributes

Returns: A function that accepts a Double value and returns the computed derivative as a Double.

This yields the scale function for this Functional.

Attributes

Returns: a function to transform the nominal value into the actual value as it would appear in a PureNumber context.

Concrete fields

If this Valuable is exact, it returns the exact value as a Double. Otherwise, it returns None. NOTE: do NOT implement this method to return a Double for a fuzzy Real--only for exact numbers.

Attributes

Returns: Some(x) where x is a Double if this is exact, else None.

Retrieves an optional fuzziness value for a given number.

Attributes

Returns: An Option containing the fuzziness representation of the number, or None if not available.

Retrieves the nominal (non-fuzzy) value associated with the entity.

This value represents the precise or primary measurement or parameter of the entity, without considering any associated fuzziness or uncertainty.

Attributes

Returns: The nominal value as a Double.

Inherited fields

Casts this Valuable instance into a Structure type if it already is a Structure. If the instance is not a Structure, an AlgebraException is thrown. CONSIDER returning Option[Structure] instead.

Attributes

Returns: the current instance as a Structure
Note: Throws com.phasmidsoftware.number.algebra.util.AlgebraException if the instance is not of type Structure
Inherited from:: Valuable

Attempts to cast this instance to a Number. If the instance is of type Number, it is wrapped in an Option and returned. Otherwise, returns None.

Attributes

Returns: an Option containing the instance as a Number if applicable, or None if not.
Inherited from:: Valuable

Converts the current Lazy instance into an Eager instance by forcing the resolution or evaluation of its underlying value.

The materialize method ensures that the computation of the value represented by this Lazy instance is completed and encapsulated within an appropriate Eager representation. This is particularly useful in scenarios where deferred computation needs to be explicitly resolved prior to further processing.

Attributes

Returns: the materialized Eager instance representing the resolved value
Inherited from:: Eager

Converts the approximate representation of this number into a Double.

This method attempts to approximate the value of this number by invoking the approximation method with force = true. If the approximation exists, it is converted to a Double. If no approximation can be obtained, an AlgebraException is thrown to indicate a logic error.

Attributes

Returns: the approximate value as a Double.
Note: Throws an com.phasmidsoftware.number.algebra.util.AlgebraException if no approximation can be obtained.
Inherited from:: Approximate

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