Packages

object SVDecomp extends SVDecomp

The SVDecomp object provides several test matrices as well as methods for making full representations, reducing dimensionality, determining rank and testing SVD factorizations.

Linear Supertypes
SVDecomp, Factorization, AnyRef, Any
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  1. SVDecomp
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Type Members

  1. type FactorType = (MatriD, VectoD, MatriD)

    Factor type contains 'u, s, v' which are the left orthogonal matrix, the diagonal matrix/vector containing singular values and the right orthogonal matrix.

    Factor type contains 'u, s, v' which are the left orthogonal matrix, the diagonal matrix/vector containing singular values and the right orthogonal matrix.

    Definition Classes
    SVDecomp
  2. type FactorTypeFull = (MatriD, MatriD, MatriD)
    Definition Classes
    SVDecomp

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. val a1: MatrixD
  5. val a2: MatrixD
  6. val a3: MatrixD
  7. val a4: MatrixD
  8. val a5: MatrixD
  9. val a6: MatrixD
  10. val a7: MatrixD
  11. val a8: MatrixD
  12. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  13. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  14. def conditionNum: Double

    Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest.

    Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest. Note, if not of full rank, it will be infinity.

    Definition Classes
    SVDecomp
  15. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  16. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  17. def factor(): SVDecomp

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Definition Classes
    SVDecompFactorization
  18. 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
  19. 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
  20. def factor123(): FactorType

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero. Then return the vector of singular values (i.e., the main diagonal), along with the left and right singular matrices.

    Definition Classes
    SVDecomp
  21. 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
  22. def factorFull(u_s_v: FactorType): FactorTypeFull

    Convert an SVD factoring to its full representation, returning the result as three matrices.

    Convert an SVD factoring to its full representation, returning the result as three matrices.

    u_s_v

    the 3-way factorization

  23. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

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

    Return the two factored matrices.

    Return the two factored matrices.

    Definition Classes
    SVDecompFactorization
  25. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  26. def flip(u: MatriD, v: MatriD): Unit

    Flip negative main diagonal elements in the singular vectors to positive.

    Flip negative main diagonal elements in the singular vectors to positive.

    u

    the left orthongonal matrix

    v

    the right orthongonal matrix

    Definition Classes
    SVDecomp
  27. def flip(u: MatriD, s: VectoD): Unit

    Flip negative singular values to positive and set singular values close to zero to zero.

    Flip negative singular values to positive and set singular values close to zero to zero.

    u

    the left orthongonal matrix

    s

    the vector of singular values

    Definition Classes
    SVDecomp
  28. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  29. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  30. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  31. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  33. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  34. def rank(s: VectorD): Int

    Determine the rank of a matrix by counting the number of non-zero singular values.

    Determine the rank of a matrix by counting the number of non-zero singular values. The implementation assumes zero singular values are last in the vector.

    s

    the vector of singular values for the matrix whose rank is sought

  35. def reduce(u_s_v: FactorType, k: Int): FactorType

    Reduce the dimensionality of the 'u', 's' and 'v' matrices from 'n' to 'k'.

    Reduce the dimensionality of the 'u', 's' and 'v' matrices from 'n' to 'k'. If 'k = rank', there is no loss of information; when 'k < rank', multiplying the three matrices results in an approximation (little is lost so long as the singular values set to zero (i.e., clipped) are small).

    u_s_v

    the 3-way factorization

    k

    the desired dimensionality

  36. def reorder(ft: FactorType): Unit

    Reorder the singular values to be in non-increasing order.

    Reorder the singular values to be in non-increasing order. Must swap singular vectors in lock step with singular values. To minimize the number of swaps, selection sort is used.

    ft

    the factored matrix (u, s, v)

    Definition Classes
    SVDecomp
  37. def solve(b: VectoD): VectoD

    Solve for 'x' in 'a^t*a*x = b' using SVD.

    Solve for 'x' in 'a^t*a*x = b' using SVD.

    b

    the constant vector

    Definition Classes
    SVDecompFactorization
  38. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  39. def test(a: MatriD, svd: SVDecomp, name: String): Unit

    Test the SVD Factorization algorithm on matrix 'a' by factoring the matrix into a left matrix u, a vector s, and a right matrix v.

    Test the SVD Factorization algorithm on matrix 'a' by factoring the matrix into a left matrix u, a vector s, and a right matrix v. Then multiply back to recover the original matrix 'u ** s * v.t'.

    a

    the orginal matrix

    name

    the name of the test case

  40. def toString(): String
    Definition Classes
    AnyRef → Any
  41. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  43. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )

Inherited from SVDecomp

Inherited from Factorization

Inherited from AnyRef

Inherited from Any

Ungrouped