scalation

linalgebra

package linalgebra

The linalgebra package contains classes, traits and objects for linear algebra, including vectors and matrices for real and complex numbers.

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  1. class BidMatrixD extends Matrix with Error with Serializable

    The BidMatrixD class stores and operates on bidiagoanl matrices.

  2. class Bidiagonal extends Error

    The Bidiagonal class is used to creates a bidiagonal matrix for matrix 'a'.

  3. class Cholesky extends Error

    The Cholesky class provides a method to factor symmetric positive definite matrices 'a' into 'l * l.

  4. trait Eigen extends AnyRef

    The Eigen trait defines constants used by classes and objects the Eigen group.

  5. class Eigenvalue extends Eigen with Error

    The Eigenvalue 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.

  6. class EigenvalueSym extends Eigen with Error

    The EigenvalueSym class is used to find the eigenvalues of an 'n' by 'n' symmetric matrix 'a' using an iterative technique, the Symmetric QR Algorithm.

  7. class Eigenvector extends Eigen with Error

    The Eigenvector class is used to find the eigenvectors of an 'n' by 'n' matrix 'a' by solving equations of the form

  8. class Hessenburg extends Eigen with Error

    The Hessenburg 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).

  9. class HouseholderT extends Eigen with Error

    The HouseholderT class performs a Householder Tridiagonalization on a symmetric matrix.

  10. trait Matric extends Error

    The Matric trait specifies the operations to be defined by three concrete implemeting classes: MatrixC, SparseMatrixC and SymTriMatrixC.

  11. trait Matrir extends Error

    The Matrir trait specifies the operations to be defined by three concrete implemeting classes: MatrixR, SparseMatrixR and SymTriMatrixR.

  12. trait Matrix extends Error

    The Matrix trait specifies the operations to be defined by four concrete implemeting classes: MatrixD, ParMatrixD, SparseMatrixD and SymTriMatrixD.

  13. class MatrixC extends Matric with Error with Serializable

    The MatrixC class stores and operates on Numeric Matrices of type Complex.

  14. class MatrixD extends Matrix with Error with Serializable

    The MatrixD class stores and operates on Numeric Matrices of type Double.

  15. class MatrixR extends Matrir with Error with Serializable

    The MatrixR class stores and operates on Numeric Matrices of type Rational.

  16. class ParMatrixD extends Matrix with Error with Serializable

    The ParMatrixD class stores and operates parallel on Numeric Matrices of type Double.

  17. class ParSparseMatrixD extends Matrix with Error with Serializable

    The ParSparseMatrixD class stores and operates on Matrices of Doubles.

  18. class QRDecomp extends Error

    The QRDecomp 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'.

  19. case class Rotation(cs: Double, sn: Double, r: Double) extends Product with Serializable

    The Rotation class is a data structure for holding the results of rotating by angle a.

  20. class SVD extends SVDecomp

    The SVD class is used to solve Singular Value Decomposition for bidiagonal matrices.

  21. class SVD2 extends SVDecomp

    The SVD2 class performs Single Value Decompositions (SVDs) using the Eigen class.

  22. class SVD3 extends SVDecomp with Error

    The SVD3 class is used to compute the Singlar Value Decomposition (SVD) of matrix 'aa' using the Golub-Kahan-Reinsch Algorithm.

  23. class SVD_2by2 extends SVDecomp

    The SVD_2by2 is used to solve Singular Value Decomposition for bidiagonal 2-by-2 matrices.

  24. trait SVDecomp extends AnyRef

    The SVDDecomp trait specifies the major methods for Singular Value Decomposition implementations.

  25. class SparseMatrixC extends Matric with Error with Serializable

    The SparseMatrixC class stores and operates on Matrices of Complex numbers.

  26. class SparseMatrixD extends Matrix with Error with Serializable

    The SparseMatrixD class stores and operates on Matrices of Doubles.

  27. class SymTriMatrixC extends Matric with Error with Serializable

    The SymTriMatrixC class stores and operates on symmetric tridiagonal matrices.

  28. class SymTriMatrixD extends Matrix with Error with Serializable

    The SymTriMatrixD class stores and operates on symmetric tridiagonal matrices.

  29. class VectorC extends Traversable[Complex] with PartiallyOrdered[VectorC] with Error with Serializable

    The VectorC class stores and operates on Numeric Vectors of base type Complex.

  30. class VectorD extends Traversable[Double] with PartiallyOrdered[VectorD] with Error with Serializable

    The VectorD class stores and operates on Numeric Vectors of base type Double.

  31. class VectorR extends Traversable[Rational] with PartiallyOrdered[VectorR] with Error with Serializable

    The VectorR class stores and operates on Numeric Vectors of base type Rational.

Value Members

  1. object BidMatrixDTest extends App

    The BidMatrixDTest object is used to test the BidMatrixD class.

  2. object BidiagonalTest extends App

    The BidiagonalTest object is used to test the Bidiagonal class.

  3. object CholeskyTest extends App

    The CholeskyTest object is used to test the Cholesky class.

  4. object EigenTest extends App

    The EigenTest object is used to test the all the classes used in computing Eigenvalues and Eigenvectors for the non-symmetric/general case.

  5. object Eigen_2by2 extends Error

    The Eigen_2by2 object provides simple methods for computing eigenvalues and eigenvectors for 2-by-2 matrices.

  6. object Eigen_2by2Test extends App

    The Eigen_2by2Test is used to test the Eigen_2by2 object.

  7. object Givens

    The Givens objects has methods for determinng values 'c = cos(theta)' and 's = sin(theta) for Givens rotation matrices as well as methods for applying Givens rotations.

  8. object GivensTest extends App

    The GivensTest object tests the Givens object by using two rotations to turn matrix 'a' into an upper triangular matrix, clearing positions (1, 0) and (2, 1).

  9. object Householder

    The Householder object provides methods to compute Householder vectors and reflector matrices.

  10. object HouseholderTest extends App

    The HouseholderTest object is used to test Householder object.

  11. object MatrixC extends Error with Serializable

    The MatrixC companion object provides operations for MatrixC that don't require 'this' (like static methods in Java).

  12. object MatrixCTest extends App

    The MatrixCTest object tests the operations provided by MatrixC class.

  13. object MatrixD extends Error with Serializable

    The MatrixD companion object provides operations for MatrixD that don't require 'this' (like static methods in Java).

  14. object MatrixDTest extends App

    The MatrixDTest object tests the operations provided by MatrixD class.

  15. object MatrixR extends Error with Serializable

    The MatrixR companion object provides operations for MatrixR that don't require 'this' (like static methods in Java).

  16. object MatrixRTest extends App

    The MatrixRTest object tests the operations provided by MatrixR class.

  17. object ParMatrixD extends Error with Serializable

    The ParMatrixD companion object provides operations for ParMatrixD that don't require 'this' (like static methods in Java).

  18. object ParMatrixDTest extends App

    The ParMatrixDTest object tests the operations provided by ParMatrixD class.

  19. object ParSparseMatrixDTest extends App

    The ParSparseMatrixDTest object is used to test the ParSparseMatrixD class.

  20. object QRDecompTest extends App

    The QRDecompTest object is used to test the QRDecomp class.

  21. object Rotation extends Serializable

    The Rotation object provides methods for rotating in a plane.

  22. object RotationTest extends App

    The RotationTest object is used to test the Rotation object,

  23. object SVD2Test extends App

    The SVD2Test object is used to test the SVD2 class.

  24. object SVD2Test2 extends App

    The SVD2Test2 object is used to test the SVD2 class.

  25. object SVD3

    The SVD3 companion object.

  26. object SVD3Test extends App

    The SVD3Test object is used to test the SVD3 class starting with a matrix that is already bidiagonalized and gives eigenvalues of 28, 18 for the first step.

  27. object SVD3Test2 extends App

    The SVD3Test2 object is used to test the SVD3 class starting with a general matrix.

  28. object SVD3Test3 extends App

    The SVD3Test3 object is used to test the SVD3 companion object.

  29. object SVDTest extends App

    The SVDTest is used to test the SVD class.

  30. object SVDTest2 extends App

    The SVDTest2 is used to test the SVD class.

  31. object SVD_2by2Test extends App

    The SVD_2by2Test is used to test the SVD_2by2 class.

  32. object SparseMatrixC extends Serializable

    The SparseMatrixC objecxt is the companion object for the SparseMatrixC class.

  33. object SparseMatrixCTest extends App

    The SparseMatrixCTest object is used to test the SparseMatrixC class.

  34. object SparseMatrixD extends Serializable

    The SparseMatrixD object is the companion object for the SparseMatrixD class.

  35. object SparseMatrixDTest extends App

    The SparseMatrixDTest object is used to test the SparseMatrixD class.

  36. object SymTriMatrixCTest extends App

    The SymTriMatrixCTest object is used to test the SymTriMatrixC class.

  37. object SymTriMatrixDTest extends App

    The SymTriMatrixDTest object is used to test the SymTriMatrixD class.

  38. object SymmetricQRstep extends Eigen with Error

    The SymmetricQRstep object performs a symmetric QR step with a Wilkinson shift.

  39. object VectorC extends Serializable

    The VectorC object is the companion object for VectorC class.

  40. object VectorCTest extends App

    The VectorCTest object tests the operations provided by VectorC class.

  41. object VectorD extends Serializable

    The VectorD object is the companion object for the VectorD class.

  42. object VectorDTest extends App

    The VectorDTest object tests the operations provided by VectorD.

  43. object VectorR extends Serializable

    The VectorR object is the companion object for Vector class.

  44. object VectorRTest extends App

    The VectorRTest object tests the operations provided by VectorR class.

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