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()
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: Any): Boolean

    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

    Definition Classes
    AnyRef → Any

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

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

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

  6. 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]

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

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

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

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

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

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

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

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

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

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

    Definition Classes
    AnyRef → Any

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

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

  18. 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

  19. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

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

  21. 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

  22. 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

  23. 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)

  24. def byteValue(): Byte

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  25. def ceil()(implicit f: Field[T], r: IsReal[T]): Jet[T]

  26. def clone(): AnyRef

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

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

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

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

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

  29. def dimension: Int

  30. def doubleValue(): Double

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

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

    Definition Classes
    AnyRef

  32. def equals(that: Any): Boolean

    Definition Classes
    Jet → Equals → AnyRef → Any

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

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

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

  35. def finalize(): Unit

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

  36. def floatValue(): Float

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

  37. def floor()(implicit f: Field[T], r: IsReal[T]): Jet[T]

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

    Definition Classes
    AnyRef → Any

  39. def hashCode(): Int

    Definition Classes
    Jet → AnyRef → Any

  40. val infinitesimal: Array[T]

  41. def intValue(): Int

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

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

  43. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  44. def isReal: Boolean

  45. def isValidByte: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  46. def isValidChar: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  47. def isValidInt: Boolean

    Definition Classes
    Jet → ScalaNumericAnyConversions

  48. def isValidShort: Boolean

    Definition Classes
    ScalaNumericAnyConversions

  49. def isWhole(): Boolean

    Definition Classes
    Jet → ScalaNumericAnyConversions → ScalaNumber

  50. def isZero: Boolean

  51. implicit def jetDimension: JetDim

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

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

  53. def longValue(): Long

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

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

    Definition Classes
    AnyRef

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

  56. final def notify(): Unit

    Definition Classes
    AnyRef

  57. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

  59. def pow(b: Jet[T])(implicit c: ClassTag[T], e: Eq[T], f: Field[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

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

  61. 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

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

  63. val real: T

  64. def round()(implicit f: Field[T], r: IsReal[T]): Jet[T]

  65. def shortValue(): Short

    Definition Classes
    Jet → ScalaNumericAnyConversions → Number

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

    This is consistent with abs

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

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

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

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

  69. 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))

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

    Definition Classes
    AnyRef

  71. 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

  72. 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

  73. def toByte: Byte

    Definition Classes
    ScalaNumericAnyConversions

  74. def toChar: Char

    Definition Classes
    ScalaNumericAnyConversions

  75. def toDouble: Double

    Definition Classes
    ScalaNumericAnyConversions

  76. def toFloat: Float

    Definition Classes
    ScalaNumericAnyConversions

  77. def toInt: Int

    Definition Classes
    ScalaNumericAnyConversions

  78. def toLong: Long

    Definition Classes
    ScalaNumericAnyConversions

  79. def toShort: Short

    Definition Classes
    ScalaNumericAnyConversions

  80. def toString(): String

    Definition Classes
    Jet → AnyRef → Any

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

  82. def underlying(): AnyRef

    Definition Classes
    Jet → ScalaNumericConversions → ScalaNumericAnyConversions → ScalaNumber

  83. def unifiedPrimitiveEquals(x: Any): Boolean

    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions

  84. def unifiedPrimitiveHashcode(): Int

    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions

  85. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  87. 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