Calculus

Value Members

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

   

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2. final def ##(): Int

   

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

   

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4. final def asInstanceOf[T0]: T0

   

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5. def clone(): AnyRef

   

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6. def derivative(f: FunctionS2S, x: Double): Double

   

   Estimate the derivative of the scalar-to-scalar function f at x using a 2-sided method (central difference).

   Estimate the derivative of the scalar-to-scalar function f at x using a 2-sided method (central difference). Approximate the tangent line at (x, f(x)) with the secant line through points (x-h, f(x-h)) and (x+h, f(x+h)). Tends to be MORE ACCURATE than the 1-sided method.

   f

   the function whose derivative is sought

   x

   the point (scalar) at which to estimate the derivative

   See also

   http://www.math.montana.edu/frankw/ccp/modeling/continuous/heatflow2/firstder.htm

7. def derivative1(f: FunctionS2S, x: Double): Double

   

   Estimate the derivative of the scalar-to-scalar function f at x using a 1-sided method (forward difference).

   Estimate the derivative of the scalar-to-scalar function f at x using a 1-sided method (forward difference). Approximate the tangent line at (x, f(x)) with the secant line through points (x, f(x)) and (x+h, f(x+h)).

   f

   the function whose derivative is sought

   x

   the point (scalar) at which to estimate the derivative

8. def derivative2(f: FunctionS2S, x: Double): Double

   

   Estimate the second derivative of the scalar-to-scalar function f at x using the central difference formula for second derivatives.

   Estimate the second derivative of the scalar-to-scalar function f at x using the central difference formula for second derivatives.

   f

   the function whose second derivative is sought

   x

   the point (scalar) at which to estimate the derivative

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

   

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10. def equals(arg0: Any): Boolean

    

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11. def finalize(): Unit

    

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

    

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13. def gradient(f: FunctionV2S, x: VectorD): VectorD

    

    Estimate the gradient of the vector-to-scalar function f at point x returning a value for the partial derivative for each dimension of x.

    Estimate the gradient of the vector-to-scalar function f at point x returning a value for the partial derivative for each dimension of x.

    f

    the function whose gradient is sought

    x

    the point (vector) at which to estimate the gradient

14. def gradientD(d: Array[FunctionV2S], x: VectorD): VectorD

    

    Compute the gradient of the vector-to-scalar function f using partial derivative functions evaluated at point x.

    Compute the gradient of the vector-to-scalar function f using partial derivative functions evaluated at point x. Return a value for the partial derivative for each dimension of the vector x.

    d

    the array of partial derivative functions

    x

    the point (vector) at which to compute the gradient

15. def hashCode(): Int

    

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16. def hessian(f: FunctionV2S, x: VectorD): MatrixD

    

    Estimate the Hessian of the vector-to-scalar function f at point x returning a matrix of second partial derivative.

    Estimate the Hessian of the vector-to-scalar function f at point x returning a matrix of second partial derivative.

    f

    the function whose Hessian is sought

    x

    the point (vector) at which to estimate the Hessian

17. final def isInstanceOf[T0]: Boolean

    

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18. def jacobian(f: Array[FunctionV2S], x: VectorD): MatrixD

    

    Compute the Jacobian matrix for a vector-valued function represented as an array of scalar-valued functions.

    Compute the Jacobian matrix for a vector-valued function represented as an array of scalar-valued functions. The i-th row in the matrix is the gradient of the i-th function.

    f

    the array of functions whose Jacobian is sought

    x

    the point (vector) at which to estimate the Jacobian

19. def laplacian(f: FunctionV2S, x: VectorD): Double

    

    Estimate the Laplacian of the vector-to-scalar function f at point x returning the sum of the pure second partial derivatives.

    Estimate the Laplacian of the vector-to-scalar function f at point x returning the sum of the pure second partial derivatives.

    f

    the function whose Hessian is sought

    x

    the point (vector) at which to estimate the Hessian

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

    

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21. final def notify(): Unit

    

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22. final def notifyAll(): Unit

    

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23. def partial(f: FunctionV2S, x: VectorD, i: Int): Double

    

    Estimate the ith partial derivative of the vector-to-scalar function f at point x returning the value for the partial derivative for dimension i.

    Estimate the ith partial derivative of the vector-to-scalar function f at point x returning the value for the partial derivative for dimension i.

    f

    the function whose partial derivative is sought

    x

    the point (vector) at which to estimate the partial derivative

    i

    the dimension to compute the partial derivative on

24. def partial2(f: FunctionV2S, x: VectorD, i: Int, j: Int): Double

    

    Estimate the (i,j)th second partial derivative of the vector-to-scalar function f at point x returning the value for the second partial derivative for dimensions (i, j).

    Estimate the (i,j)th second partial derivative of the vector-to-scalar function f at point x returning the value for the second partial derivative for dimensions (i, j). If i = j, the second partial derivative is called "pure", otherwise it is a "cross" second partial derivative.

    f

    the function whose second partial derivative is sought

    x

    the point (vector) at which to estimate the second partial derivative

    i

    the first dimension to compute the second partial derivative on

    j

    the second dimension to compute the second partial derivative on

25. def resetH(step: Double): Unit

    

    Reset the step size from its default step size to one more suitable for your function.

    Reset the step size from its default step size to one more suitable for your function. A heuristic for the central difference method is to let h = max (|x|,1) * (machine-epsilon)^(1/3) For double precision, the machine-epsilon is about 1E-16.

    step

    the new step size to reset h to

    See also

    http://www.karenkopecky.net/Teaching/eco613614/Notes_NumericalDifferentiation.pdf

26. def slope(f: FunctionV2S, x: VectorD, n: Int = 0): VectorD

    

    Compute the slope of the vector-to-scalar function f defined on mixed real/integer vectors.

    Compute the slope of the vector-to-scalar function f defined on mixed real/integer vectors.

    f

    the function whose slope is sought

    x

    the point (vector) at which to estimate the slope

    n

    the number of dimensions that are real-valued (rest are integers)

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

    

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28. def toString(): String

    

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29. final def wait(): Unit

    

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

    

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

    

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