Packages

  • package root
    Definition Classes
    root
  • package scalation

    The scalation package specifies system-wide constants for directory paths.

    The scalation package specifies system-wide constants for directory paths. Sub-packages may wish to define 'BASE-DIR = DATA_DIR + ⁄ + <package>' in their own 'package.scala' files. For maintainability, directory paths should only be specified in 'package.scala' files.

    Definition Classes
    root
  • package linalgebra

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

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

    Definition Classes
    scalation
  • package par

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

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

    Definition Classes
    linalgebra
  • Fac_Cholesky
  • Fac_CholeskyTest
  • Fac_QR
  • Fac_QRTest
  • MatrixD
  • MatrixDTest
  • SparseMatrixD
  • SparseMatrixDTest
  • VectorD
  • VectorDTest

class Fac_QR extends Factorization with Error

The Fac_QR class provides methods to factor an 'm-by-n' matrix 'a' into the product of two matrices:

'q' - an 'm-by-n' orthogonal matrix and 'r' - an 'n-by-n' right upper triangular matrix

such that 'a = q * r'. It uses Gram-Schmidt orthogonalization. Note, orthogonal means that 'q.t * q = I'. This version uses parallel processing to speed up execution.

See also

http://www.stat.wisc.edu/~larget/math496/qr.html

http://en.wikipedia.org/wiki/Gram–Schmidt_process (stabilized Gram–Schmidt orthonormalization)

Linear Supertypes
Error, Factorization, AnyRef, Any
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Inherited
  1. Fac_QR
  2. Error
  3. Factorization
  4. AnyRef
  5. Any
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Visibility
  1. Public
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Instance Constructors

  1. new Fac_QR(a: MatrixD)

    a

    the matrix to be factor into q and r

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native() @HotSpotIntrinsicCandidate()
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  7. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  8. def factor(): Fac_QR

    Factor matrix 'a' into the product of two matrices, 'a = q * r', returning both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.

    Factor matrix 'a' into the product of two matrices, 'a = q * r', returning both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.

    Definition Classes
    Fac_QRFactorization
  9. def factor1(): MatriD

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.

    Definition Classes
    Factorization
  10. def factor12(): (MatriD, MatriD)

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.

    Definition Classes
    Factorization
  11. def factor2(): MatriD

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.

    Definition Classes
    Factorization
  12. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

    Attributes
    protected
    Definition Classes
    Factorization
  13. def factors: (MatriD, MatriD)

    Return both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.

    Return both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.

    Definition Classes
    Fac_QRFactorization
  14. final def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  15. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  17. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  18. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  19. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  20. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. def nullspace(rank: Int): MatrixD

    Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'.

    Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'. Gives a basis of dimension 'n' - rank for the nullspace

    rank

    the rank of the matrix (number of linearly independent row vectors) FIX: should work, but it does not

  22. def nullspaceV: VectorD

    Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'.

    Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'. Gives only one vector in the nullspace.

  23. def solve(b: VectoD): VectoD

    Solve for 'x' in 'a*x = b' using the QR Factorization 'a = q*r' via 'r*x = q.t * b'.

    Solve for 'x' in 'a*x = b' using the QR Factorization 'a = q*r' via 'r*x = q.t * b'.

    b

    the constant vector

    Definition Classes
    Fac_QRFactorization
  24. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  25. def toString(): String
    Definition Classes
    AnyRef → Any
  26. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  27. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  28. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] ) @Deprecated
    Deprecated

Inherited from Error

Inherited from Factorization

Inherited from AnyRef

Inherited from Any

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