scalation.math

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Type Members

trait Combinatorics extends Error

This trait provides several common combinatorics functions.
class Complex extends AnyRef

This class is used to represent complex numbers (a + bi) as (a, b), e.
case class DoubleWithExp (x: Double) extends Product with Serializable

This class defines an expontiation operator '~^' for Doubles.
class Eigenvalue extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to find the eigenvalues of an n by n matrix 'a' using an iterative technique that applies similarity transformations to convert 'a' into an upper triangular matrix, so that the eigenvalues appear along the diagonal.
class EigenvalueSym extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to find the eigenvalues of an n by n symmetric matrix 'a' using an iterative technique, the Symmetric QR Algorithm.
class Eigenvector extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to find the eigenvectors of an n by n matrix 'a' by solving equations of the form (a - eI)v = 0 where e is the eigenvalue and v is the eigenvector.
class Hessenburg extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to reduce, via similarity transformations, an n by n matrix 'a' to Hessenburg form 'h', where all elements two below the main diagonal are zero (or close to zero).
class Householder extends Error

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
case class IntWithExp (x: Int) extends Product with Serializable

This class defines an expontiation operator '~^' for Ints.
class Matrix [T] extends Error

The Matrix class is abstract and defines the operations to be defined by three concrete subclasses: MatrixN, SparseMatrixN and SymTriMatrix.
class MatrixN [T] extends Matrix[T] with Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: The MatrixN class stores and operates on Numeric Matrices of various sizes and types.
case class ProbNumber (x: Double, p: Double) extends Numeric[ProbNumber] with Ordered[ProbNumber] with Error with Product with Serializable

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to represent probabilistic numbers (x, p) where x is a a real number and p is its probability of occurrence.
class QRdecomposition extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class is used to decompose an m by n matrix 'a' into an orthogonal m by n matrix 'q' and an n by n right upper triangular matrix 'r' such that a = q * r.
class SparseMatrixN [T] extends Matrix[T] with Error

The SparseMatrixN class stores and operates on Numeric Matrices of various sizes and types.
class SymTriMatrixN [T] extends Matrix[T] with Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: The SymTriMatrixN class stores and operates on symmetric tridiagonal matrices.
class SymmetricQRstep extends Error

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This class performs a symmetric QR step with a Wilkinson shift.
class VectorN [T] extends PartiallyOrdered[VectorN[T]] with Error

The VectorN class stores and operates on Numeric Vectors of various sizes and types.

Value Members

object Calculus extends AnyRef

This object contains function for computing derivatives, gradients and Jacobians.
object CalculusTest extends App

This object is used to test the Calculus object.
object CombinatoricsTest extends App with Combinatorics

This objects test the methods in the Combinatorics trait.
object ComplexTest extends App

This object is used to test the Complex class.
object DoubleWithExp extends Serializable

Implicit conversion from Double to DoubleWithExp allowing '~^' to be applied to Doubles.
object DoubleWithExpTest extends App

This object is used to test DoubleWithExp.
object EigenTest extends App

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This object is used to test the all the classes used in computing Eigenvalues and Eigenvectors for the non-symmetric/general case.
object EigenTest2 extends App

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This object is used to test the all the classes used in computing Eigenvalues and Eigenvectors for the symmetric/special case.
object IntWithExp extends Serializable

Implicit conversion from Int to IntWithExp allowing '~^' to be applied to Ints.
object IntWithExpTest extends App

This object is used to test IntWithExp.
object Matrices extends AnyRef

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Convenience definitions for commonly used types of matrices.
object MatrixNTest extends App

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: The MatrixN object tests the operations provided by MatrixN.
object Primes extends AnyRef

This object provides an array of 1000 prime numbers as well as methods to generate prime numbers within a given range.
object PrimesTest extends App

This object is use to perform timing test on the Primes object.
object ProbNumberTest extends App

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This object is used to test the ProbNumber class.
object SparseMatrices extends AnyRef

Convenience definitions for commonly used types of sparse matrices.
object SparseMatrixNTest extends App

This object is used to test the SparseMatrixN class.
object SymTriMatrices extends AnyRef

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Convenience definitions for commonly used types of symmetric tridiagonal matrices.
object SymTriMatrixNtest extends App

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: This object is used to test the SymTriMatrixN class.
object SymmetricQRstep extends Error
object VectorNTest extends App

The VectorNTest object tests the operations provided by VectorN.
object Vectors extends AnyRef

Convenience definitions for commonly used types of vectors.

math

package math

Type Members

trait Combinatorics extends Error

class Complex extends AnyRef

case class DoubleWithExp (x: Double) extends Product with Serializable

class Eigenvalue extends Error

class EigenvalueSym extends Error

class Eigenvector extends Error

class Hessenburg extends Error

class Householder extends Error

case class IntWithExp (x: Int) extends Product with Serializable

class Matrix [T] extends Error

class MatrixN [T] extends Matrix[T] with Error

case class ProbNumber (x: Double, p: Double) extends Numeric[ProbNumber] with Ordered[ProbNumber] with Error with Product with Serializable

class QRdecomposition extends Error

class SparseMatrixN [T] extends Matrix[T] with Error

class SymTriMatrixN [T] extends Matrix[T] with Error

class SymmetricQRstep extends Error

class VectorN [T] extends PartiallyOrdered[VectorN[T]] with Error

Value Members

object Calculus extends AnyRef

object CalculusTest extends App

object CombinatoricsTest extends App with Combinatorics

object ComplexTest extends App

object DoubleWithExp extends Serializable

object DoubleWithExpTest extends App

object EigenTest extends App

object EigenTest2 extends App

object IntWithExp extends Serializable

object IntWithExpTest extends App

object Matrices extends AnyRef

object MatrixNTest extends App

object Primes extends AnyRef

object PrimesTest extends App

object ProbNumberTest extends App

object SparseMatrices extends AnyRef

object SparseMatrixNTest extends App

object SymTriMatrices extends AnyRef

object SymTriMatrixNtest extends App

object SymmetricQRstep extends Error

object VectorNTest extends App

object Vectors extends AnyRef