class Bidiagonal[MatT <: MatriD] extends Error
The Bidiagonal class is used to create a bidiagonal matrix from matrix 'a'.
It uses the Householder Bidiagonalization Algorithm to compute orthogonal
matrices 'u' and 'v' such that
u.t * a * v = b a = u * b * v.t
where matrix 'b' is bidiagonal, i.e., it will only have non-zero elements on its main diagonal and its super-diagonal (the diagonal above the main).
u is an m-by-n matrix
b is an n-by-n matrix (bidiagonal - FIX: use BidMatrixD)
v is an n-by-n matrix
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Instance Constructors
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new
Bidiagonal(a: MatT)
- a
the m-by-n matrix to bidiagonalize (requires m >= n)
Value Members
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def
bidiagonalize(): (MatriD, MatriD, MatriD)
Bidiagonalize matrix 'a' using the Householder Bidiagonalization Algorithm to compute orthogonal matrices 'u' and 'v' such that 'u.t * a * v = b' where matrix 'b' is bidiagonal.
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def
bmax: Double
Return the maximum column magnitude from bidiagonal matrix 'b'.
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def
e_q: (VectorD, VectorD)
Return the super-diagonal 'e' and main diagonal 'q' as vectors.
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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
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def
sdot(v1: VectoD, v2: VectoD, from: Int = 0): Double
Compute the sliced dot product.
Compute the sliced dot product. Take the dot product of two row/column vectors starting from the 'from' parameter.
- v1
the first vector
- v2
the second vector
- from
the offset from which to compute the sliced dot product
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def
test(): Unit
Test whether the product of factorization equals the orginal matrix.