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

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Instance Constructors

  1. new QRDecomp(a: MatrixD)

    a

    the matrix to decompose into q and r

Value Members

  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. final def asInstanceOf[T0]: T0

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  7. 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

  8. def clone(): AnyRef

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  9. final def eq(arg0: AnyRef): Boolean

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  10. def equals(arg0: Any): Boolean

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  11. def finalize(): Unit

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  12. 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

  13. final def getClass(): Class[_]

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  14. def getQ: MatrixD

    Get the orthogonal q matrix.

  15. def getQR: (MatrixD, MatrixD)

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

  16. def getR: MatrixD

    Get the right upper triangular r matrix.

  17. def hashCode(): Int

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  18. final def isInstanceOf[T0]: Boolean

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  19. final def ne(arg0: AnyRef): Boolean

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  20. final def notify(): Unit

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  21. final def notifyAll(): Unit

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  22. 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

  23. 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.

  24. 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

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

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  26. def toString(): String

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  27. final def wait(): Unit

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  28. final def wait(arg0: Long, arg1: Int): Unit

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  29. final def wait(arg0: Long): Unit

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