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
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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
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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.
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- SVDecomp
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type
FactorTypeFull = (MatriD, MatriD, MatriD)
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- SVDecomp
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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
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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)
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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)
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eq(arg0: AnyRef): Boolean
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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
- SVDecomp → Factorization
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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
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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
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def
factor123(): FactorType
Factor matrix 'a' forming a diagonal matrix consisting of singular values and return the singular values in a vector.
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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
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val
factored: Boolean
Flag indicating whether the matrix has been factored
Flag indicating whether the matrix has been factored
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- Factorization
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def
factors: (MatriD, MatriD)
Return the two factored matrices.
Return the two factored matrices.
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- SVDecomp → Factorization
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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
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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
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- SVDecomp
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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
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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
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