spire.math

Jet

final case class Jet[T](real: T, infinitesimal: Array[T]) extends ScalaNumber with ScalaNumericConversions with Serializable with Product

Self Type
Jet[T]
Annotations
@SerialVersionUID( 0L )
Linear Supertypes
Product, Equals, Serializable, ScalaNumericConversions, ScalaNumericAnyConversions, ScalaNumber, java.lang.Number, Serializable, AnyRef, Any
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Inherited
  1. Jet
  2. Product
  3. Equals
  4. Serializable
  5. ScalaNumericConversions
  6. ScalaNumericAnyConversions
  7. ScalaNumber
  8. Number
  9. Serializable
  10. AnyRef
  11. Any
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Visibility
  1. Public
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Instance Constructors

  1. new Jet(real: T, infinitesimal: Array[T])

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. def %(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

  5. def *(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  6. def *(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  7. def **(b: Jet[T])(implicit c: ClassTag[T], e: Eq[T], f: Field[T], r: IsReal[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

  8. def **(b: Int)(implicit e: Eq[T], f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  9. def +(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  10. def +(b: T)(implicit f: Field[T]): Jet[T]

  11. def -(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  12. def -(b: T)(implicit f: Field[T]): Jet[T]

  13. def /(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  14. def /(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  15. def /%(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): (Jet[T], Jet[T])

  16. def /~(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

  17. def =!=(that: Jet[_]): Boolean

  18. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  19. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  20. def ===(that: Jet[_]): Boolean

  21. def abs()(implicit f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

    abs(x + du) ~= x + du or -(x + du)

  22. def acos()(implicit f: Field[T], n: NRoot[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    acos(a + du) ~= acos(a) - 1 / sqrt(1 - a**2) du

  23. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  24. def asTuple: (T, Array[T])

  25. def asin()(implicit f: Field[T], n: NRoot[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    asin(a + du) ~= asin(a) - 1 / sqrt(1 - a**2) du

  26. def atan()(implicit f: Field[T], n: NRoot[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    atan(a + du) ~= atan(a) + 1 / (1 + a**2) du

  27. def atan2(a: Jet[T])(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    Defined with "this" as the y coordinate: this.

    Defined with "this" as the y coordinate: this.atan2(a) == atan2(this, a) == atan(this / a) atan2(b + dv, a + du) ~= atan2(b, a) + (- b du + a dv) / (a2 + b2)

  28. def byteValue(): Byte

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  29. def ceil()(implicit c: ClassTag[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

  30. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  31. def cos()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    cos(a + du) ~= cos(a) - sin(a) du

  32. def cosh()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    cosh(a + du) ~= cosh(a) + sinh(a) du

  33. def dimension: Int

  34. def doubleValue(): Double

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  35. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  36. def equals(that: Any): Boolean

    Definition Classes
    Jet → Equals → AnyRef → Any

  37. def eqv(b: Jet[T])(implicit o: Eq[T]): Boolean

  38. def exp()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    exp(a + du) ~= exp(a) + exp(a) du

  39. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  40. def floatValue(): Float

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  41. def floor()(implicit c: ClassTag[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

  42. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  43. def hashCode(): Int

    Definition Classes
    Jet → AnyRef → Any

  44. val infinitesimal: Array[T]

  45. def intValue(): Int

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  46. def isInfinitesimal(implicit r: IsReal[T]): Boolean

  47. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  48. def isReal: Boolean

  49. def isValidByte: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  50. def isValidChar: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  51. def isValidInt: Boolean

    Definition Classes
    Jet → ScalaNumericAnyConversions

  52. def isValidShort: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  53. def isWhole(): Boolean

    Definition Classes
    Jet → ScalaNumericAnyConversions → ScalaNumber

  54. def isZero: Boolean

  55. implicit def jetDimension: JetDim

  56. def log()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    log(a + du) ~= log(a) + du / a

  57. def longValue(): Long

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  58. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  59. def neqv(b: Jet[T])(implicit o: Eq[T]): Boolean

  60. final def notify(): Unit

    Definition Classes
    AnyRef

  61. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  62. def nroot(k: Int)(implicit e: Eq[T], f: Field[T], r: IsReal[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

  63. def pow(b: Jet[T])(implicit c: ClassTag[T], e: Eq[T], f: Field[T], m: Module[Array[T], T], r: IsReal[T], t: Trig[T]): Jet[T]

    pow -- both base (this) and exponent are differentiable functions.

    pow -- both base (this) and exponent are differentiable functions. (a + du)(b + dv) ~= ab + b * a(b-1) du + ab log(a) dv

  64. def pow(p: Int)(implicit f: Field[T], e: Eq[T], v: VectorSpace[Array[T], T]): Jet[T]

  65. def pow(p: T)(implicit e: Eq[T], f: Field[T], r: IsReal[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    pow -- base (this) is a differentiable function, exponent is a constant.

    pow -- base (this) is a differentiable function, exponent is a constant. pow(a + du, p) ~= pow(a, p) + p * pow(a, p-1) du

  66. def powScalarToJet(a: T)(implicit c: ClassTag[T], e: Eq[T], f: Field[T], m: Module[Array[T], T], r: IsReal[T], t: Trig[T]): Jet[T]

  67. val real: T

  68. def round()(implicit c: ClassTag[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]

  69. def shortValue(): Short

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  70. def signum()(implicit r: Signed[T]): Int

    This is consistent with abs

  71. def sin()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    sin(a + du) ~= sin(a) + cos(a) du

  72. def sinh()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    sinh(a + du) ~= sinh(a) + cosh(a) du

  73. def sqrt()(implicit f: Field[T], n: NRoot[T], v: VectorSpace[Array[T], T]): Jet[T]

    sqrt(a + du) ~= sqrt(a) + du / (2 sqrt(a))

  74. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef

  75. def tan()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    tan(a + du) ~= tan(a) + (1 + tan(a)**2) du

  76. def tanh()(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

    tanh(a + du) ~= tanh(a) + (1 - tanh(a)**2) du

  77. def toByte: Byte

    Definition Classes
    ScalaNumericAnyConversions

  78. def toChar: Char

    Definition Classes
    ScalaNumericAnyConversions

  79. def toDouble: Double

    Definition Classes
    ScalaNumericAnyConversions

  80. def toFloat: Float

    Definition Classes
    ScalaNumericAnyConversions

  81. def toInt: Int

    Definition Classes
    ScalaNumericAnyConversions

  82. def toLong: Long

    Definition Classes
    ScalaNumericAnyConversions

  83. def toShort: Short

    Definition Classes
    ScalaNumericAnyConversions

  84. def toString(): String

    Definition Classes
    Jet → AnyRef → Any

  85. def unary_-()(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]

  86. def underlying(): AnyRef

    Definition Classes
    Jet → ScalaNumericConversions → ScalaNumericAnyConversions → ScalaNumber

  87. def unifiedPrimitiveEquals(x: Any): Boolean

    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions

  88. def unifiedPrimitiveHashcode(): Int

    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions

  89. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  90. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  91. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Product

Inherited from Equals

Inherited from Serializable

Inherited from ScalaNumericConversions

Inherited from ScalaNumericAnyConversions

Inherited from ScalaNumber

Inherited from java.lang.Number

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

Ungrouped