scalation.linalgebra

QRDecomp

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'. It uses Gram-Schmidt orthogonalization. Note, orthogonal means that 'q.t * q = I'.

See also

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

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

Linear Supertypes
Error, AnyRef, Any
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. QRDecomp
  2. Error
  3. AnyRef
  4. Any
  1. Hide All
  2. Show all
Learn more about member selection
Visibility
  1. Public
  2. All

Instance Constructors

  1. new QRDecomp(a: MatrixD)

    a

    the matrix to decompose 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 backSub(r: MatrixD, b: VectorD): VectorD

    Perform backward substitution to solve for x in r*x = b.

    Perform backward substitution to solve for x in r*x = b.

    r

    the upper triangular matrix

    b

    the constant vector

  6. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  7. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  8. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  9. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  10. 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
  11. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  12. def getQ: MatrixD

    Get the orthogonal q matrix.

  13. def getQR: (MatrixD, MatrixD)

    Get bot the orthogonal q matrix and the right upper triangular r matrix.

  14. def getR: MatrixD

    Get the right upper triangular r matrix.

  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  16. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  17. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  18. final def notify(): Unit

    Definition Classes
    AnyRef
  19. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  20. def nullspace(rank: Int): MatrixD

    Compute the nullspace of matrix a: { x | a*x = 0 } using QR Decomposition qr*x = 0.

    Compute the nullspace of matrix a: { x | a*x = 0 } using QR Decomposition qr*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

  21. def nullspaceV: VectorD

    Compute the nullspace of matrix a: { x | a*x = 0 } using QR Decomposition qr*x = 0.

    Compute the nullspace of matrix a: { x | a*x = 0 } using QR Decomposition qr*x = 0. Gives only one vector in the nullspace.

  22. def solve(b: VectorD): VectorD

    Solve for x in a*x = b using QR Decomposition a = qr via r*x = q.

    Solve for x in a*x = b using QR Decomposition a = qr via r*x = q.t * b.

    b

    the constant vector

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

    Definition Classes
    AnyRef
  24. def toString(): String

    Definition Classes
    AnyRef → Any
  25. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  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( ... )

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped