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 ------------------------------------------------------------------------------
- Alphabetic
- By Inheritance
- Fac_QR_H3
- Fac_QR
- Error
- Factorization
- AnyRef
- Any
- Hide All
- Show All
- Public
- Protected
Instance Constructors
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- def computeQ(): Unit
Compute the full 'q' orthogonal matrix based on updated values in 'a'.
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- 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_H3 → Factorization
- 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
- Definition Classes
- Error
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- 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
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- 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
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- val m: Int
- Attributes
- protected
- Definition Classes
- Fac_QR
- val n: Int
- Attributes
- protected
- Definition Classes
- Fac_QR
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def nullspace(rank: Int): MatriD
Compute the nullspace of matrix 'a': basis { x | a*x = 0 }' using 'QR' Factorization 'q*r*x = 0'.
- 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.
- val p: Int
- Attributes
- protected
- Definition Classes
- Fac_QR
- val q: MatrixD
- Attributes
- protected
- Definition Classes
- Fac_QR
- val r: MatriD
- Attributes
- protected
- Definition Classes
- Fac_QR
- 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
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- AnyRef → Any
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated