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scalation/scalation/scalation.mathstat/Bidiagonal

Bidiagonal

scalation.mathstat.Bidiagonal
class Bidiagonal(a: MatrixD)

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) v is an n-by-n matrix

Value parameters

a

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

Attributes

Graph
Supertypes
class Object
trait Matchable
class Any

Members list

Value members

Concrete methods

def bidiagonalize(): (MatrixD, MatrixD, MatrixD)

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.

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.

Attributes

def bmax: Double

Return the maximum column magnitude from bidiagonal matrix b.

Return the maximum column magnitude from bidiagonal matrix b.

Attributes

def e_q: (VectorD, VectorD)

Return the super-diagonal e and main diagonal q as vectors.

Return the super-diagonal e and main diagonal q as vectors.

Attributes

def sdot(v1: VectorD, v2: VectorD, from: Int): Double

Compute the sliced dot product. Take the dot product of two row/column vectors starting from the 'from' parameter.

Compute the sliced dot product. Take the dot product of two row/column vectors starting from the 'from' parameter.

Value parameters

from

the offset from which to compute the sliced dot product

v1

the first vector

v2

the second vector

Attributes

def test(): Unit

Test whether the product of factorization equals the orginal matrix.

Test whether the product of factorization equals the orginal matrix.

Attributes

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