scalation.linalgebra

SVD

class SVD extends Error

This class is used to compute the Singlar Value Decomposition (SVD) of matrix 'a', i.e., decompose matrix 'a' into 'u * b * v.t'.

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Instance Constructors

  1. new SVD(a: MatrixD)

    a

    the m-by-n matrix to decompose (requires m >= n)

Value Members

  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. final def asInstanceOf[T0]: T0

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  7. def bidiagonalization(): (MatrixD, MatrixD, MatrixD)

    Use the Householder Bidiagonalization Algorithm to compute unitary matrices u and v such that u.

    Use the Householder Bidiagonalization Algorithm to compute unitary matrices u and v such that u.t * a * v = b where matrix b is bidiagonal. The b matrix will only have non-zero elements on its main diagonal and its super diagonal (the diagonal above the main). This implementation computes b in-place in matrix a.

    See also

    Matrix Computations: Algorithm 5.4.2 Householder Bidiagonalization

  8. def bidiagonalization2(): (VectorD, VectorD)

    Use the Golub-Kahan Bidiagonalization Algorithm to compute unitary matrices u and v such that u.

    Use the Golub-Kahan Bidiagonalization Algorithm to compute unitary matrices u and v such that u.t * a * v = b where matrix b is bidiagonal (nonzero elements on the main diagonal and the diagonal above it). Solve a * v = u * b by computing column vectors u_k and v_k and diagonals c and d. Use transposes of u and v since row access is more efficient than column access. Caveat: assumes bidiagonals elements are non-negative and need to add re-orthogonalization steps.

    See also

    web.eecs.utk.edu/~dongarra/etemplates/node198.html

  9. def clone(): AnyRef

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  10. final def eq(arg0: AnyRef): Boolean

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  11. def equals(arg0: Any): Boolean

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  12. def finalize(): Unit

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  13. 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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  14. final def getClass(): java.lang.Class[_]

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  15. def hashCode(): Int

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  16. final def isInstanceOf[T0]: Boolean

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  17. final def ne(arg0: AnyRef): Boolean

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  18. final def notify(): Unit

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  19. final def notifyAll(): Unit

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  20. final def synchronized[T0](arg0: ⇒ T0): T0

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  21. def toString(): String

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  22. final def wait(): Unit

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  23. final def wait(arg0: Long, arg1: Int): Unit

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  24. final def wait(arg0: Long): Unit

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