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object Fac_LU extends Error

The Fac_LU companion object provides functions related to LU Factorization.

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  1. final def !=(arg0: Any): Boolean
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  2. final def ##(): Int
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  3. final def ==(arg0: Any): Boolean
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  4. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
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    protected[java.lang]
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    @native() @throws( ... )
  6. def conditionNum(a: MatriD, a_lu: Fac_LU[MatriD]): Double

    Compute the condition number of matrix 'a', which equals

    Compute the condition number of matrix 'a', which equals

    ||a|| ||b|| where b = a.inverse

    Requires 'a' to be a square matrix. For rectangular matrices, @see SVDecomp.

    a

    the matrix whose condition number is sought

    a_lu

    LU Factorization of matrix A

  7. def conditionNum2(a: MatriD, a_lu: Fac_LU[MatriD]): Double

    Compute the condition number of matrix 'a', which equals

    Compute the condition number of matrix 'a', which equals

    ||a|| ||b|| where b = a.inverse

    Requires 'a' to be a square matrix. For rectangular matrices, @see SVDecomp.

    a

    the matrix whose condition number is sought

    a_lu

    LU Factorization of matrix A

  8. final def eq(arg0: AnyRef): Boolean
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  9. def equals(arg0: Any): Boolean
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  10. def finalize(): Unit
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    @throws( classOf[java.lang.Throwable] )
  11. 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
  12. final def getClass(): Class[_]
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  13. def hashCode(): Int
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  14. final def isInstanceOf[T0]: Boolean
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  15. final def ne(arg0: AnyRef): Boolean
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  16. def norm1est(a: MatriD, inv: Boolean): Double

    Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum.

    Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum. It uses an adapted version of Hager's algorithm.

    a

    the matrix A whose norm is sought

    inv

    whether or not to compute for inverse (default true)

  17. def norm1est(a: MatriD, a_lu: Fac_LU[MatriD], inv: Boolean = true): Double

    Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum.

    Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum. It uses an adapted version of Hager's algorithm.

    a

    the matrix A whose norm is sought

    a_lu

    LU Factorization of matrix A

    inv

    whether or not to compute for inverse (default true)

    See also

    www.maths.manchester.ac.uk/~higham/narep/narep135.pdf

    Higham, N.J. "Fortran Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation." ACM Trans. Math. Soft., 14, 1988, pp. 381-396.

    Algorithm 4.1 in HIGHAM1998

  18. final def notify(): Unit
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  19. final def notifyAll(): Unit
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  20. def solve(a: MatriD, lu: Fac_LU[MatriD], b: VectoD): VectoD

    Solve a system of linear equations 'a*x = b'.

    Solve a system of linear equations 'a*x = b'.

    a

    the matrix A holding the coefficients of the equations

    lu

    LU Factorization of matrix A

    b

    the constant vector

  21. def solveOver(a: MatriD, b: VectoD): VectoD

    Solve for 'x' in the equation 'a*x = b' in an over determined system of linear equation using least squares.

    Solve for 'x' in the equation 'a*x = b' in an over determined system of linear equation using least squares. Return the solution vector 'x'.

    a

    the matrix A holding the coefficients of the equations

    b

    the constant vector

    See also

    people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf

  22. def solveUnder(a: MatriD, b: VectoD): VectoD

    Solve for 'x' in the equation 'a*x = b' in an under determined system of linear equation by finding the smallest solution.

    Solve for 'x' in the equation 'a*x = b' in an under determined system of linear equation by finding the smallest solution. Return the solution vector 'x'.

    a

    the matrix A holding the coefficients of the equations

    b

    the constant vector

    See also

    people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf

  23. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
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  24. def test(a: MatriD, b: VectoD): Unit

    Test the LU Factorization of matrix 'a' into 'l' and 'u' and its usage in solving a system of linear equations.

    Test the LU Factorization of matrix 'a' into 'l' and 'u' and its usage in solving a system of linear equations.

    a

    the matrix A to be factored

    b

    the constant vector in Ax = b

  25. def toString(): String
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  26. final def wait(): Unit
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  27. final def wait(arg0: Long, arg1: Int): Unit
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  28. final def wait(arg0: Long): Unit
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