Package org.hipparchus

Interface CalculusFieldElement<T extends FieldElement<T>>

    • Method Summary

      All Methods Instance Methods Abstract Methods Default Methods 
      Modifier and Type Method Description
      T abs()
      absolute value.
      T acos()
      Arc cosine operation.
      T acosh()
      Inverse hyperbolic cosine operation.
      default T add​(double a)
      '+' operator.
      T asin()
      Arc sine operation.
      T asinh()
      Inverse hyperbolic sine operation.
      T atan()
      Arc tangent operation.
      T atan2​(T x)
      Two arguments arc tangent operation.
      T atanh()
      Inverse hyperbolic tangent operation.
      default T cbrt()
      Cubic root.
      default T ceil()
      Get the smallest whole number larger than instance.
      default T copySign​(double sign)
      Returns the instance with the sign of the argument.
      T copySign​(T sign)
      Returns the instance with the sign of the argument.
      T cos()
      Cosine operation.
      T cosh()
      Hyperbolic cosine operation.
      default T divide​(double a)
      '÷' operator.
      default T divide​(T a)
      Compute this ÷ a.
      T exp()
      Exponential.
      T expm1()
      Exponential minus 1.
      default T floor()
      Get the largest whole number smaller than instance.
      T getAddendum()
      Get the addendum to the real value of the number.
      default int getExponent()
      Return the exponent of the instance, removing the bias.
      default T getPi()
      Get the Archimedes constant π.
      T hypot​(T y)
      Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
      default boolean isFinite()
      Check if the instance is finite (neither infinite nor NaN).
      default boolean isInfinite()
      Check if the instance is infinite.
      default boolean isNaN()
      Check if the instance is Not a Number.
      default T linearCombination​(double[] a, T[] b)
      Compute a linear combination.
      default T linearCombination​(double a1, T b1, double a2, T b2)
      Compute a linear combination.
      default T linearCombination​(double a1, T b1, double a2, T b2, double a3, T b3)
      Compute a linear combination.
      default T linearCombination​(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4)
      Compute a linear combination.
      T linearCombination​(T[] a, T[] b)
      Compute a linear combination.
      T linearCombination​(T a1, T b1, T a2, T b2)
      Compute a linear combination.
      T linearCombination​(T a1, T b1, T a2, T b2, T a3, T b3)
      Compute a linear combination.
      T linearCombination​(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4)
      Compute a linear combination.
      T log()
      Natural logarithm.
      T log10()
      Base 10 logarithm.
      T log1p()
      Shifted natural logarithm.
      default T multiply​(double a)
      '×' operator.
      default T multiply​(int n)
      Compute n × this.
      T newInstance​(double value)
      Create an instance corresponding to a constant real value.
      default double norm()
      norm.
      default T pow​(double p)
      Power operation.
      default T pow​(int n)
      Integer power operation.
      T pow​(T e)
      Power operation.
      T remainder​(double a)
      IEEE remainder operator.
      T remainder​(T a)
      IEEE remainder operator.
      default T rint()
      Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
      default T rootN​(int n)
      Nth root.
      default long round()
      Get the closest long to instance real value.
      T scalb​(int n)
      Multiply the instance by a power of 2.
      default T sign()
      Compute the sign of the instance.
      T sin()
      Sine operation.
      default FieldSinCos<T> sinCos()
      Combined Sine and Cosine operation.
      T sinh()
      Hyperbolic sine operation.
      default FieldSinhCosh<T> sinhCosh()
      Combined hyperbolic sine and cosine operation.
      default T sqrt()
      Square root.
      default T square()
      Compute this × this.
      default T subtract​(double a)
      '-' operator.
      default T subtract​(T a)
      Compute this - a.
      default T tan()
      Tangent operation.
      default T tanh()
      Hyperbolic tangent operation.
      default T toDegrees()
      Convert radians to degrees, with error of less than 0.5 ULP
      default T toRadians()
      Convert degrees to radians, with error of less than 0.5 ULP
      default T ulp()
      Compute least significant bit (Unit in Last Position) for a number.

    • Method Detail

      • getAddendum

        T getAddendum()
        Get the addendum to the real value of the number.

        The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.

        Returns:
        real value
        Since:
        4.0

      • getPi

        default T getPi()
        Get the Archimedes constant π.

        Archimedes constant is the ratio of a circle's circumference to its diameter.

        Returns:
        Archimedes constant π
        Since:
        2.0

      • newInstance

        T newInstance​(double value)
        Create an instance corresponding to a constant real value.
        Parameters:
        value - constant real value
        Returns:
        instance corresponding to a constant real value

      • add

        default T add​(double a)
        '+' operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this+a

      • subtract

        default T subtract​(double a)
        '-' operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this-a

      • subtract

        default T subtract​(T a)
        Compute this - a.
        Specified by:
        subtract in interface FieldElement<T extends FieldElement<T>>
        Parameters:
        a - element to subtract
        Returns:
        a new element representing this - a

      • multiply

        default T multiply​(double a)
        '×' operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this×a

      • multiply

        default T multiply​(int n)
        Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]
        Specified by:
        multiply in interface FieldElement<T extends FieldElement<T>>
        Parameters:
        n - Number of times this must be added to itself.
        Returns:
        A new element representing n × this.

      • divide

        default T divide​(double a)
        '÷' operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this÷a

      • getExponent

        default int getExponent()
        Return the exponent of the instance, removing the bias.

        For double numbers of the form 2x, the unbiased exponent is exactly x.

        Returns:
        exponent for the instance, without bias

      • scalb

        T scalb​(int n)
        Multiply the instance by a power of 2.
        Parameters:
        n - power of 2
        Returns:
        this × 2n

      • ulp

        default T ulp()
        Compute least significant bit (Unit in Last Position) for a number.
        Returns:
        ulp(this)
        Since:
        2.0

      • hypot

        T hypot​(T y)
 throws MathIllegalArgumentException
        Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
        • If either argument is infinite, then the result is positive infinity.
        • else, if either argument is NaN then the result is NaN.
        Parameters:
        y - a value
        Returns:
        sqrt(this2 +y2)
        Throws:
        MathIllegalArgumentException - if number of free parameters or orders are inconsistent

      • divide

        default T divide​(T a)
        Compute this ÷ a.
        Specified by:
        divide in interface FieldElement<T extends FieldElement<T>>
        Parameters:
        a - element to divide by
        Returns:
        a new element representing this ÷ a

      • sqrt

        default T sqrt()
        Square root.
        Returns:
        square root of the instance

      • cbrt

        default T cbrt()
        Cubic root.
        Returns:
        cubic root of the instance

      • rootN

        default T rootN​(int n)
        Nth root.
        Parameters:
        n - order of the root
        Returns:
        nth root of the instance

      • square

        default T square()
        Compute this × this.
        Returns:
        a new element representing this × this
        Since:
        3.1

      • pow

        default T pow​(double p)
        Power operation.
        Parameters:
        p - power to apply
        Returns:
        thisp

      • pow

        default T pow​(int n)
        Integer power operation.
        Parameters:
        n - power to apply
        Returns:
        thisn

      • exp

        T exp()
        Exponential.
        Returns:
        exponential of the instance

      • expm1

        T expm1()
        Exponential minus 1.
        Returns:
        exponential minus one of the instance

      • log

        T log()
        Natural logarithm.
        Returns:
        logarithm of the instance

      • log1p

        T log1p()
        Shifted natural logarithm.
        Returns:
        logarithm of one plus the instance

      • log10

        T log10()
        Base 10 logarithm.
        Returns:
        base 10 logarithm of the instance

      • cos

        T cos()
        Cosine operation.
        Returns:
        cos(this)

      • sin

        T sin()
        Sine operation.
        Returns:
        sin(this)

      • sinCos

        default FieldSinCos<T> sinCos()
        Combined Sine and Cosine operation.
        Returns:
        [sin(this), cos(this)]
        Since:
        1.4

      • tan

        default T tan()
        Tangent operation.
        Returns:
        tan(this)

      • acos

        T acos()
        Arc cosine operation.
        Returns:
        acos(this)

      • asin

        T asin()
        Arc sine operation.
        Returns:
        asin(this)

      • atan

        T atan()
        Arc tangent operation.
        Returns:
        atan(this)

      • atan2

        T atan2​(T x)
 throws MathIllegalArgumentException
        Two arguments arc tangent operation.

        Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.

        Parameters:
        x - second argument of the arc tangent
        Returns:
        atan2(this, x)
        Throws:
        MathIllegalArgumentException - if number of free parameters or orders are inconsistent

      • cosh

        T cosh()
        Hyperbolic cosine operation.
        Returns:
        cosh(this)

      • sinh

        T sinh()
        Hyperbolic sine operation.
        Returns:
        sinh(this)

      • sinhCosh

        default FieldSinhCosh<T> sinhCosh()
        Combined hyperbolic sine and cosine operation.
        Returns:
        [sinh(this), cosh(this)]
        Since:
        2.0

      • tanh

        default T tanh()
        Hyperbolic tangent operation.
        Returns:
        tanh(this)

      • acosh

        T acosh()
        Inverse hyperbolic cosine operation.
        Returns:
        acosh(this)

      • asinh

        T asinh()
        Inverse hyperbolic sine operation.
        Returns:
        asin(this)

      • atanh

        T atanh()
        Inverse hyperbolic tangent operation.
        Returns:
        atanh(this)

      • toDegrees

        default T toDegrees()
        Convert radians to degrees, with error of less than 0.5 ULP
        Returns:
        instance converted into degrees

      • toRadians

        default T toRadians()
        Convert degrees to radians, with error of less than 0.5 ULP
        Returns:
        instance converted into radians

      • ceil

        default T ceil()
        Get the smallest whole number larger than instance.
        Returns:
        ceil(this)

      • floor

        default T floor()
        Get the largest whole number smaller than instance.
        Returns:
        floor(this)

      • rint

        default T rint()
        Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
        Returns:
        a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5

      • remainder

        T remainder​(double a)
        IEEE remainder operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this - n × a where n is the closest integer to this/a

      • remainder

        T remainder​(T a)
        IEEE remainder operator.
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this - n × a where n is the closest integer to this/a

      • sign

        default T sign()
        Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)
        Returns:
        -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

      • copySign

        T copySign​(T sign)
        Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
        Parameters:
        sign - the sign for the returned value
        Returns:
        the instance with the same sign as the sign argument

      • copySign

        default T copySign​(double sign)
        Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
        Parameters:
        sign - the sign for the returned value
        Returns:
        the instance with the same sign as the sign argument

      • isInfinite

        default boolean isInfinite()
        Check if the instance is infinite.
        Returns:
        true if the instance is infinite

      • isFinite

        default boolean isFinite()
        Check if the instance is finite (neither infinite nor NaN).
        Returns:
        true if the instance is finite (neither infinite nor NaN)
        Since:
        2.0

      • isNaN

        default boolean isNaN()
        Check if the instance is Not a Number.
        Returns:
        true if the instance is Not a Number

      • norm

        default double norm()
        norm.
        Returns:
        norm(this)
        Since:
        2.0

      • abs

        T abs()
        absolute value.
        Returns:
        abs(this)

      • round

        default long round()
        Get the closest long to instance real value.
        Returns:
        closest long to FieldElement.getReal()