Packages

class SVD_2by2 extends SVDecomp

The SVD_2by2 is used to solve Singular Value Decomposition for bidiagonal 2-by-2 matrices.

[ f g ] [ 0 h ]

See also

fortranwiki.org/fortran/show/svd

Linear Supertypes
SVDecomp, Factorization, AnyRef, Any
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  1. SVD_2by2
  2. SVDecomp
  3. Factorization
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Instance Constructors

  1. new SVD_2by2(f: Double, g: Double, h: Double)

    f

    the first diagonal element

    g

    the super-diagonal element

    h

    the second diagonal element

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. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  6. 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
  7. def deflate(): VectorD

    Return the two singular values (smallest first) for the bidiagonal 2-by-2 matrix form from the elements f, g and h.

    Return the two singular values (smallest first) for the bidiagonal 2-by-2 matrix form from the elements f, g and h.

    See also

    LAPACK SUBROUTINE DLAS2 (F, G, H, SSMIN, SSMAX)

  8. def deflateV(): (Double, Double, Double, Double, Double, Double)

    Return the two singular values (smallest first) for the bidiagonal 2-by-2 matrix form from the elements f, g and h.

    Return the two singular values (smallest first) for the bidiagonal 2-by-2 matrix form from the elements f, g and h. Also, return the singular vectors.

    See also

    LAPACK SUBROUTINE DLASV2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL)

  9. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  10. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  11. 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
  12. 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
  13. 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
  14. def factor123(): FactorType

    Factor matrix 'a' forming a diagonal matrix consisting of singular values and return the singular values in a vector.

    Factor matrix 'a' forming a diagonal matrix consisting of singular values and return the singular values in a vector.

    Definition Classes
    SVD_2by2SVDecomp
  15. 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
  16. val factored: Boolean

    Flag indicating whether the matrix has been factored

    Flag indicating whether the matrix has been factored

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

    Return the two factored matrices.

    Return the two factored matrices.

    Definition Classes
    SVDecompFactorization
  18. 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
  19. 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
  20. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  26. 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
  27. 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
  28. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  29. def toString(): String
    Definition Classes
    AnyRef → Any
  30. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  31. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  32. 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 SVDecomp

Inherited from Factorization

Inherited from AnyRef

Inherited from Any

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