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abstract class Fac_QR[MatT <: MatriD] extends Factorization with Error

The Fac_QR abstarct class provides base methods to factor an 'm-by-n' matrix 'aa' 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 'aa = q * r'. ------------------------------------------------------------------------------

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Error, Factorization, AnyRef, Any
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  2. Protected

Instance Constructors

  1. new Fac_QR(aa: MatT, needQ: Boolean = true)

    aa

    the matrix to be factor into q and r

    needQ

    flag indicating whether a full q matrix is needed

Abstract Value Members

  1. abstract def computeQ(): Unit

    Compute values for the full 'q' matrix.

  2. abstract def factor(): Factorization

    Factor a matrix into the product of two matrices without returning the two factored matrices.

    Factor a matrix into the product of two matrices without returning the two factored matrices. Allows for example skipping the computation of the Q matrix in QR factorization when it is not needed, e.g., for regression. Class implementing the 'factor' method should set 'factored = true'.

    Definition Classes
    Factorization
  3. abstract def nullspace(rank: Int): MatriD

    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)

Concrete 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(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  7. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  8. 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
  9. 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
  10. 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
  11. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

    Attributes
    protected
    Definition Classes
    Factorization
  12. 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
  13. 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
  14. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  15. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  17. val m: Int
    Attributes
    protected
  18. val n: Int
    Attributes
    protected
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. val p: Int
    Attributes
    protected
  23. val q: MatrixD
    Attributes
    protected
  24. val r: MatriD
    Attributes
    protected
  25. def solve(b: VectoD): VectoD

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

    Solve for 'x' in 'aa*x = b' using the QR Factorization 'aa = q*r' via 'r*x = q.t * b'. Requires calculating 'q' matrix first.

    b

    the constant vector@param y the constant vector

    Definition Classes
    Fac_QRFactorization
  26. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  27. def toString(): String
    Definition Classes
    AnyRef → Any
  28. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  29. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  30. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

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

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