package calculus
The calculus
package contains classes with methods for computing
derivatives, gradient vectors, Jacobian matrices, integrals and basic
operators in Functional Analysis.
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Type Members
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class
GaussianFunc extends AnyRef
The
GaussianFunc
class implements the Gaussian function, a generalization of the Gaussian/Normal distribution density function.The
GaussianFunc
class implements the Gaussian function, a generalization of the Gaussian/Normal distribution density function.- See also
en.wikipedia.org/wiki/Gaussian_function
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class
Hilbert extends AnyRef
The
Hilbert
class provides operators to add, subtract, mutiply, divide and raise functions.The
Hilbert
class provides operators to add, subtract, mutiply, divide and raise functions. Given two functions, 'f' and 'g', a new function is created. It also provides methods for computing dot/inner products, norms and distances for functions defined in Hilbert Space. On interval [a, b]Lp-norm (f) = [ ∫f(t)p dt ]1/p
- See also
implicit conversion 'functionS2S2Hilbert' in
package.scala
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type
Interval = (Double, Double)
Type definition for an interval [a, b]
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case class
Poly(c: VectorD, x: String = "x") extends Product with Serializable
The
Poly
class provides operations on univariate polynomials.The
Poly
class provides operations on univariate polynomials.Poly (2, 3) => 3 x + 2
Note, reverse order of coefficients, i.e., coefficients for smallest terms first.
- c
the coefficients of the polynomial
- x
the variable/indeterminate of the polynomial
- See also
MPoly' for multivariate polynomials.
Value Members
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def
_0f(x: Double): Double
Zero function.
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def
_1f(x: Double): Double
One function.
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implicit
def
functionS2S2Hilbert(f: FunctionS2S): Hilbert
Implicit conversion from 'FunctionS2S' to 'Hilbert', which supports functional operators.
Implicit conversion from 'FunctionS2S' to 'Hilbert', which supports functional operators.
- f
the function to turn into a Hilbert function
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object
Differential
The
Differential
object contains functions for computing derivatives, partial derivatives, Laplacians, gradient vectors, Hessian matrices and Jacobian matrices. -
object
DifferentialTest extends App
The
DifferentialTest
object is used to test theDifferential
object.The
DifferentialTest
object is used to test theDifferential
object. > runMain scalation.calculus.DifferentialTest -
object
DifferentialTest2 extends App
The
DifferentialTest2
object is used to test theDifferential
object showing trade-offs of using 1-sided and 2-sided derivative approximations as well as different values for h.The
DifferentialTest2
object is used to test theDifferential
object showing trade-offs of using 1-sided and 2-sided derivative approximations as well as different values for h.- See also
www.rose-hulman.edu/~bryan/lottamath/diffgrad.pdf > runMain scalation.calculus.DifferentialTest2
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object
HilbertTest extends App
The
HilbertTest
object is used to test theHilbert
class.The
HilbertTest
object is used to test theHilbert
class. > runMain scalation.calculus.HilbertTest -
object
Integral
The
Integral
object provides implementations for five basic integration methods:The
Integral
object provides implementations for five basic integration methods:∫f(x)dx on interval [a, b]
trap - trapezoidal method - linear simpson - Simpson method - quadratic simpson38 - 3/8 Simpson method - cubic boole - Boole Method - quartic romberg - Romberg method - recursive, uses trap
The first four are Composite Newton-Coates type integrators.
- See also
en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas
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object
IntegralTest extends App
The
IntegralTest2
object tests the numerical integrators on simple problems.The
IntegralTest2
object tests the numerical integrators on simple problems. Easy problems. > runMain scalation.calculus.IntegralTest -
object
IntegralTest2 extends App
The
IntegralTest2
object tests the numerical integrators using the Gauss function that has no analytic solution.The
IntegralTest2
object tests the numerical integrators using the Gauss function that has no analytic solution. Hard problem. > runMain scalation.calculus.IntegralTest2 -
object
Poly extends Serializable
The
Poly
companion object provides factory methods for the 'Poly' class. -
object
PolyTest extends App
The
PolyTest
object is used to test thePoly
class.The
PolyTest
object is used to test thePoly
class. > runMain scalation.calculus.PolyTest