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- matrix/eigenvalue_decomposition.rb
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Matrix::EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix.
Computes the eigenvalues and eigenvectors of a matrix A.
If A is diagonalizable, this provides matrices V and D such that A = V*D*V.inv, where D is the diagonal matrix with entries equal to the eigenvalues and V is formed by the eigenvectors.
If A is symmetric, then V is orthogonal and thus A = V*D*V.t
Public Class Methods
Constructs the eigenvalue decomposition for a square matrix A
# File matrix/eigenvalue_decomposition.rb, line 18
def initialize(a)
# @d, @e: Arrays for internal storage of eigenvalues.
# @v: Array for internal storage of eigenvectors.
# @h: Array for internal storage of nonsymmetric Hessenberg form.
raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix)
@size = a.row_size
@d = Array.new(@size, 0)
@e = Array.new(@size, 0)
if (@symmetric = a.symmetric?)
@v = a.to_a
tridiagonalize
diagonalize
else
@v = Array.new(@size) { Array.new(@size, 0) }
@h = a.to_a
@ort = Array.new(@size, 0)
reduce_to_hessenberg
hessenberg_to_real_schur
end
end
Public Instance Methods
Returns the block diagonal eigenvalue matrix D
# File matrix/eigenvalue_decomposition.rb, line 72
def eigenvalue_matrix
Matrix.diagonal(*eigenvalues)
end
Returns the eigenvalues in an array
# File matrix/eigenvalue_decomposition.rb, line 58
def eigenvalues
values = @d.dup
@e.each_with_index{|imag, i| values[i] = Complex(values[i], imag) unless imag == 0}
values
end
Returns the eigenvector matrix V
# File matrix/eigenvalue_decomposition.rb, line 42
def eigenvector_matrix
Matrix.send :new, build_eigenvectors.transpose
end
Returns the inverse of the eigenvector matrix V
# File matrix/eigenvalue_decomposition.rb, line 49
def eigenvector_matrix_inv
r = Matrix.send :new, build_eigenvectors
r = r.transpose.inverse unless @symmetric
r
end
Returns an array of the eigenvectors
# File matrix/eigenvalue_decomposition.rb, line 66
def eigenvectors
build_eigenvectors.map{|ev| Vector.send :new, ev}
end
Returns [eigenvector_matrix, #eigenvalue_matrix, #eigenvector_matrix_inv]
# File matrix/eigenvalue_decomposition.rb, line 79
def to_ary
[v, d, v_inv]
end
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