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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Instance Constructors
- 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
- abstract def computeQ(): Unit
Compute values for the full 'q' matrix.
- 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
- 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
- final def !=(arg0: Any): Boolean
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- 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
- 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
- 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
- val factored: Boolean
Flag indicating whether the matrix has been factored
Flag indicating whether the matrix has been factored
- Attributes
- protected
- Definition Classes
- Factorization
- 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_QR → Factorization
- 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
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- final def getClass(): Class[_ <: AnyRef]
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- val m: Int
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- val n: Int
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- val p: Int
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- val q: MatrixD
- Attributes
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- val r: MatriD
- Attributes
- protected
- 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_QR → Factorization
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- def finalize(): Unit
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