cas

Type Members

1. case class Abs(x: Scalar) extends Scalar with Product with Serializable

   

   abs(x)

2. case class Add(x: Scalar, y: Scalar) extends Scalar with Product with Serializable

   

   x + y

3. case class AddMatrix(A: Matrix, B: Matrix) extends Matrix with Product with Serializable

   

   A + B

4. case class AddVector(x: Vector, y: Vector) extends Vector with Product with Serializable

   

   x + y

5. case class ArcCos(x: Scalar) extends Scalar with Product with Serializable

   

   acos(x)

6. case class ArcCot(x: Scalar) extends Scalar with Product with Serializable

   

   acot(x)

7. case class ArcSin(x: Scalar) extends Scalar with Product with Serializable

   

   asin(x)

8. case class ArcTan(x: Scalar) extends Scalar with Product with Serializable

   

   atan(x)

9. case class Ceil(x: Scalar) extends IntScalar with Product with Serializable

   

   ceil(x)

10. case class Const(symbol: String) extends Scalar with Product with Serializable

    

    Constant value.

11. case class ConstMatrix(symbol: String, size: (IntScalar, IntScalar) = (IntConst("m"), IntConst("n"))) extends Matrix with Product with Serializable

    

    Constant matrix.

12. case class ConstVector(symbol: String, size: IntScalar = IntConst("n")) extends Vector with Product with Serializable

    

    Constant vector.

    Constant vector. Different from VectorVal that has concrete values, this is of constant yet abstract value.

13. case class Cos(x: Scalar) extends Scalar with Product with Serializable

    

    cos(x)

14. case class Cot(x: Scalar) extends Scalar with Product with Serializable

    

    cot(x)

15. case class DiagonalMatrix(x: Scalar*) extends Matrix with Product with Serializable

    

    Diagonal matrix

16. case class Div(x: Scalar, y: Scalar) extends Scalar with Product with Serializable

    

    x / y

17. case class Exp(x: Scalar) extends Scalar with Product with Serializable

    

    exp(x)

18. case class Floor(x: Scalar) extends IntScalar with Product with Serializable

    

    floor(x)

19. case class GradientVector(y: Var, x: VectorVar) extends Vector with Product with Serializable

    

    The derivative of a scalar y with respect to a vector x.

20. case class IdentityMatrix(size: (IntScalar, IntScalar) = (IntConst("n"), IntConst("n"))) extends Matrix with Product with Serializable

    

    Identity matrix

21. case class InnerProduct(x: Vector, y: Vector) extends Scalar with Product with Serializable

    

    Inner product (x * y)

22. case class Int2Scalar(x: IntScalar) extends Scalar with Product with Serializable

    

    Explicit conversion of int to float.

23. case class IntAdd(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x + y

24. case class IntConst(symbol: String) extends IntScalar with Product with Serializable

    

    Integer constant value.

25. case class IntDiv(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x / y

26. case class IntMul(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x * y

27. case class IntNeg(x: IntScalar) extends IntScalar with Product with Serializable

    

    -x

28. case class IntPower(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x ** y

29. trait IntScalar extends Tensor

    

    Scalar: rank-0 tensor.

30. case class IntSub(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x - y

31. case class IntVal(x: Int) extends IntScalar with Product with Serializable

    

    Integer scalar value.

32. case class IntVar(symbol: String) extends IntScalar with Product with Serializable

    

    Integer scalar variable

33. case class Log(x: Scalar) extends Scalar with Product with Serializable

    

    log(x)

34. trait Matrix extends Tensor

    

    Matrix: rank-2 tensor.

35. case class MatrixInverse(A: Matrix) extends Matrix with Product with Serializable

    

    inv(A)

36. case class MatrixProduct(A: Matrix, B: Matrix) extends Matrix with Product with Serializable

    

    Matrix multiplication (A * B)

37. case class MatrixTranspose(A: Matrix) extends Matrix with Product with Serializable

    

    A'

38. case class MatrixVar(symbol: String, size: (IntScalar, IntScalar) = (IntConst("m"), IntConst("n"))) extends Matrix with Product with Serializable

    

    Abstract matrix variable

39. case class MatrixVectorProduct(A: Matrix, x: Vector) extends Vector with Product with Serializable

    

    Matrix vector multiplication (A * x)

40. case class Mod(x: IntScalar, y: IntScalar) extends IntScalar with Product with Serializable

    

    x % y

41. case class Mul(x: Scalar, y: Scalar) extends Scalar with Product with Serializable

    

    x * y

42. case class Neg(x: Scalar) extends Scalar with Product with Serializable

    

    -x

43. case class NegMatrix(A: Matrix) extends Matrix with Product with Serializable

    

    -A

44. case class NegVector(x: Vector) extends Vector with Product with Serializable

    

    -x

45. case class OneMatrix(size: (IntScalar, IntScalar) = (IntConst("m"), IntConst("n"))) extends Matrix with Product with Serializable

    

    Matrix of all 1's

46. case class OneVector(size: IntScalar = IntConst("n")) extends Vector with Product with Serializable

    

    Vector of all 1's

47. case class OuterProduct(x: Vector, y: Vector) extends Matrix with Product with Serializable

    

    Outer product (x ** y)

48. case class Power(x: Scalar, y: Scalar) extends Scalar with Product with Serializable

    

    x ** y

49. case class Round(x: Scalar) extends IntScalar with Product with Serializable

    

    round(x)

50. case class RowMatrix(x: Vector*) extends Matrix with Product with Serializable

    

    Row-wise matrix

51. trait Scalar extends Tensor

    

    Scalar: rank-0 tensor.

52. case class ScalarMatrixProduct(a: Scalar, A: Matrix) extends Matrix with Product with Serializable

    

    a * A

53. case class ScalarVectorProduct(a: Scalar, x: Vector) extends Vector with Product with Serializable

    

    a * x

54. case class Sin(x: Scalar) extends Scalar with Product with Serializable

    

    sin(x)

55. case class Sub(x: Scalar, y: Scalar) extends Scalar with Product with Serializable

    

    x - y

56. case class Tan(x: Scalar) extends Scalar with Product with Serializable

    

    tan(x)

57. case class TangentMatrix(y: MatrixVar, x: Var) extends Matrix with Product with Serializable

    

    The derivative of a matrix y with respect to a scalar x.

58. case class TangentVector(y: VectorVar, x: Var) extends Vector with Product with Serializable

    

    The derivative of a vector y with respect to a scalar x.

59. trait Tensor extends AnyRef

    

    A tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space.

    A tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors (which are often, but not always, understood as arrows with length that point in a direction) and scalars (which are often familiar numbers such as the real numbers), and, recursively, even other tensors. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system.

    The shape of tensor (the number of dimensions and the size of each dimension) might be only partially known.

60. case class Val(x: Double) extends Scalar with Product with Serializable

    

    Scalar value.

61. case class Var(symbol: String) extends Scalar with Product with Serializable

    

    Scalar variable

62. case class Vars(x: Scalar*) extends Vector with Product with Serializable

    

    Vector variable

63. trait Vector extends Tensor

    

    Vector: rank-1 tensor.

64. case class VectorVal(x: Array[Double]) extends Vector with Product with Serializable

    

    Vector value.

65. case class VectorVar(symbol: String, size: IntScalar = IntConst("n")) extends Vector with Product with Serializable

    

    Abstract vector variable

66. case class ZeroMatrix(size: (IntScalar, IntScalar) = (IntConst("m"), IntConst("n"))) extends Matrix with Product with Serializable

    

    Matrix of all 0's

67. case class ZeroVector(size: IntScalar = IntConst("n")) extends Vector with Product with Serializable

    

    Vector of all 0's