Packages

class Fac_QR_H3 extends Fac_QR[MatrixD]

The Fac_QR_H3 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 Householder orthogonalization. Note, orthogonal means that 'q.t * q = I'.

See also

5.1 and 5.2 in Matrix Computations

QRDecomposition.java in Jama

www.stat.wisc.edu/~larget/math496/qr.html ------------------------------------------------------------------------------ This implementation is the easiest to understandard, but the least efficient. Caveat: for m < n use Fac_LQ. FIX: change 'aa: MatrixD' to 'aa: MatriD', requires 'times_ip_pre' in trait ------------------------------------------------------------------------------

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  1. Fac_QR_H3
  2. Fac_QR
  3. Error
  4. Factorization
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Instance Constructors

  1. new Fac_QR_H3(aa: MatrixD, needQ: Boolean = true)

    needQ

    whether the full q matrix is need, e.g., Regression does not

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. def computeQ(): Unit

    Compute the full 'q' orthogonal matrix based on updated values in 'a'.

    Compute the full 'q' orthogonal matrix based on updated values in 'a'.

    Definition Classes
    Fac_QR_H3Fac_QR
  7. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  8. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  9. def factor(): Fac_QR_H3

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

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

    Definition Classes
    Fac_QR_H3Factorization
  10. 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
  11. 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
  12. 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
  13. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

    Attributes
    protected
    Definition Classes
    Factorization
  14. 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
  15. 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
  16. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  17. def hReflect(v: VectoD): MatrixD

    Return the Householder reflection matrix 'h' computed from Householder vector 'v'.

    Return the Householder reflection matrix 'h' computed from Householder vector 'v'.

    v

    the Householder vector

  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. def houseV(x: VectoD, α: Double): VectoD

    Return the Householder vector 'v' computed from vector 'x'.

    Return the Householder vector 'v' computed from vector 'x'.

    x

    the given vector for calculating the Householder vector

    α

    the sign adjusted norm of x

  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. val m: Int
    Attributes
    protected
    Definition Classes
    Fac_QR
  22. val n: Int
    Attributes
    protected
    Definition Classes
    Fac_QR
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  26. def nullspace(rank: Int): MatriD

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

    Compute the nullspace of matrix 'a': basis { 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 column vectors)

    Definition Classes
    Fac_QR_H3Fac_QR
  27. 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.

  28. val p: Int
    Attributes
    protected
    Definition Classes
    Fac_QR
  29. val q: MatrixD
    Attributes
    protected
    Definition Classes
    Fac_QR
  30. val r: MatriD
    Attributes
    protected
    Definition Classes
    Fac_QR
  31. 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
  32. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  33. def toString(): String
    Definition Classes
    AnyRef → Any
  34. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    Annotations
    @throws( ... )
  35. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
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    @throws( ... ) @native()
  36. 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 Fac_QR[MatrixD]

Inherited from Error

Inherited from Factorization

Inherited from AnyRef

Inherited from Any

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