Class: Matrix::EigenvalueDecomposition
- Defined in:
- opal/stdlib/matrix/eigenvalue_decomposition.rb
Overview
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
Instance Method Summary collapse
-
#eigenvalue_matrix ⇒ Object
(also: #d)
Returns the block diagonal eigenvalue matrix +D+.
-
#eigenvalues ⇒ Object
Returns the eigenvalues in an array.
-
#eigenvector_matrix ⇒ Object
(also: #v)
Returns the eigenvector matrix +V+.
-
#eigenvector_matrix_inv ⇒ Object
(also: #v_inv)
Returns the inverse of the eigenvector matrix +V+.
-
#eigenvectors ⇒ Object
Returns an array of the eigenvectors.
-
#initialize(a) ⇒ EigenvalueDecomposition
constructor
Constructs the eigenvalue decomposition for a square matrix +A+.
-
#to_ary ⇒ Object
(also: #to_a)
Returns [eigenvector_matrix, eigenvalue_matrix, eigenvector_matrix_inv].
Constructor Details
#initialize(a) ⇒ EigenvalueDecomposition
Constructs the eigenvalue decomposition for a square matrix +A+
Raises:
- (TypeError)
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 19 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_count @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
Instance Method Details
#eigenvalue_matrix ⇒ Object Also known as: d
Returns the block diagonal eigenvalue matrix +D+
#eigenvalues ⇒ Object
Returns the eigenvalues in an array
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 59 def eigenvalues values = @d.dup @e.each_with_index{|imag, i| values[i] = Complex(values[i], imag) unless imag == 0} values end
#eigenvector_matrix ⇒ Object Also known as: v
Returns the eigenvector matrix +V+
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 43 def eigenvector_matrix Matrix .send(:new, build_eigenvectors.transpose) end
#eigenvector_matrix_inv ⇒ Object Also known as: v_inv
Returns the inverse of the eigenvector matrix +V+
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 50 def eigenvector_matrix_inv r = Matrix .send(:new, build_eigenvectors) r = r.transpose.inverse unless @symmetric r end
#eigenvectors ⇒ Object
Returns an array of the eigenvectors
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 67 def eigenvectors build_eigenvectors.map{|ev| Vector .send(:new, ev)} end
#to_ary ⇒ Object Also known as: to_a
Returns [eigenvector_matrix, eigenvalue_matrix, eigenvector_matrix_inv]
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# File 'opal/stdlib/matrix/eigenvalue_decomposition.rb', line 80 def to_ary [v, d, v_inv] end