Packages

class Fac_LU[MatT <: MatriD] extends Factorization with Error

The Fac_LU class provides methods to factor an 'm-by-n' matrix into its lower and upper triangular products:

A = LU when partial pivoting is not needed PA = LU where P is the permutation matrix A = QLU where Q = P.inverse

where 'a' is the given matrix, 'l' is an 'm-by-n' lower triangular matrix, and 'u' is an 'n-by-n' upper triangular matrix. The permutation matrix is represented by the 'piv' vector. Once factored, can be used to solve a system of linear equations.

Solve for x in Ax = b: Ax = QLUx = b => LUx = Pb using steps (1) and (2) (1) Solve Ly = Pb using forward substitution for y (2) Solve Ux = y using backward substitution for x

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Error, Factorization, AnyRef, Any
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Instance Constructors

  1. new Fac_LU(a: MatT)

    a

    the given m-by-n rectangular matrix

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 bsolve(y: VectoD): VectorD

    Solve for 'x' using back substitution in the equation 'u*x = y' where matrix 'u' is upper triangular.

    Solve for 'x' using back substitution in the equation 'u*x = y' where matrix 'u' is upper triangular.

    y

    the constant vector

  6. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  7. def det: Double

    Compute the determinant of matrix 'a'.

    Compute the determinant of matrix 'a'. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).

  8. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  9. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  10. def factor(): Fac_LU[MatT]

    Factor matrix 'a' into the product of 'l' and 'u'.

    Factor matrix 'a' into the product of 'l' and 'u'.

    Definition Classes
    Fac_LUFactorization
  11. 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
  12. 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
  13. 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
  14. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

    Attributes
    protected
    Definition Classes
    Factorization
  15. def factors: (MatriD, MatriD)

    Return the 'l' and 'u' matrices.

    Return the 'l' and 'u' matrices.

    Definition Classes
    Fac_LUFactorization
  16. 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
  17. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. def inverse: MatriD

    Compute the inverse of matrix 'a' from the LU Factorization.

  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. def permute(d: VectoD): VectoD

    Permute vector 'd', equivalent to 'pd', i.e., multiplying by the permutation matrix 'p'.

    Permute vector 'd', equivalent to 'pd', i.e., multiplying by the permutation matrix 'p'.

    d

    the vector to permute

  25. def permute(c: MatriD): Unit

    Permute matrix 'c', equivalent to 'qc', i.e., multiplying by the inverse of the permutation matrix 'p'.

    Permute matrix 'c', equivalent to 'qc', i.e., multiplying by the inverse of the permutation matrix 'p'.

    c

    the matrix to permute

  26. def rank: Int

    Return the rank (number of independent columns) of 'm-by-n' matrix 'a', by counting the number of non-zero diagonal elements in 'u'.

    Return the rank (number of independent columns) of 'm-by-n' matrix 'a', by counting the number of non-zero diagonal elements in 'u'. If 'rank < n', then 'a' is singular.

    See also

    en.wikipedia.org/wiki/Rank_%28linear_algebra%29

    Fac_QR_RR or SVD

  27. def solve(b: VectoD): VectoD

    Solve for 'x' in the equation 'l*u*x = b' via 'l*y = b' and 'u*x = y'.

    Solve for 'x' in the equation 'l*u*x = b' via 'l*y = b' and 'u*x = y'. Return the solution vector 'x'.

    b

    the constant vector

    Definition Classes
    Fac_LUFactorization
  28. def split(): Unit

    Split 'l' into lower and upper triangular matrices by placing the upper portion in 'u' and clearing, so 'l' is properly lower triangular.

  29. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  30. def toString(): String
    Definition Classes
    AnyRef → Any
  31. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  32. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  33. 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

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