core/spire.math/Jet

Jet

@SerialVersionUID(0L)
final case class Jet[@specialized(Float, Double) T](real: T, infinitesimal: Array[T]) extends ScalaNumber with ScalaNumericConversions with Serializable
Companion:
object
trait Product
trait Equals
class Number
class Object
trait Matchable
class Any
Jet[T]

Value members

Concrete methods

def %(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]
def *(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def *(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def **(b: Int)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def **(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], o: Order[T], s: Signed[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]
def +(b: T)(implicit f: Field[T]): Jet[T]
def +(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def -(b: T)(implicit f: Field[T]): Jet[T]
def -(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /%(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): (Jet[T], Jet[T])
def /~(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]
def =!=(that: Jet[_]): Boolean
def ===(that: Jet[_]): Boolean
def abs(implicit f: Field[T], o: Order[T], s: Signed[T], v: VectorSpace[Array[T], T]): Jet[T]

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

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

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

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

def asTuple: (T, Array[T])
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

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

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

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

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

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:

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) / (a^2 + b^2)
override def byteValue: Byte
Definition Classes
def ceil(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
def cos(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

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

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

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

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

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

override def doubleValue: Double
Definition Classes
override def equals(that: Any): Boolean
Definition Classes
Equals -> Any
def eqv(b: Jet[T])(implicit o: Eq[T]): Boolean
def exp(implicit t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

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

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

override def floatValue: Float
Definition Classes
def floor(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
override def hashCode: Int
Definition Classes
Any
override def intValue: Int
Definition Classes
override def isValidInt: Boolean
Definition Classes
override def isWhole: Boolean
def log(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

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

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

override def longValue: Long
Definition Classes
def neqv(b: Jet[T])(implicit o: Eq[T]): Boolean
def nroot(k: Int)(implicit f: Field[T], o: Order[T], s: Signed[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]
def pow(p: T)(implicit f: Field[T], o: Order[T], s: Signed[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
def pow(p: Int)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def pow(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], m: CModule[Array[T], T], o: Order[T], s: Signed[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) ~= a^b + b * a^(b-1) du + a^b log(a) dv
def powScalarToJet(a: T)(implicit c: ClassTag[T], f: Field[T], m: CModule[Array[T], T], o: Order[T], s: Signed[T], t: Trig[T]): Jet[T]
def round(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
override def shortValue: Short
Definition Classes
def signum(implicit r: Signed[T]): Int

This is consistent with abs

This is consistent with abs

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

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

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

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

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

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

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))

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

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

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

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

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

override def toString: String
Definition Classes
Any
def unary_-(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
override def underlying: Object

Inherited methods

def productIterator: Iterator[Any]
Inherited from:
Product
protected def unifiedPrimitiveEquals(x: Any): Boolean

Implicits

Implicits

implicit def jetDimension: JetDim