ˆ¾È 0ÁÆ ˆ¾È 0ÁÆ$ˆl–ßi~”ja,je@7q¦n2☴oÉ „iÀ>ÿÅÂÇ?÷# encoding: utf-8 # # = matrix.rb # # An implementation of Matrix and Vector classes. # # See classes Matrix and Vector for documentation. # # Current Maintainer:: Marc-André Lafortune # Original Author:: Keiju ISHITSUKA # Original Documentation:: Gavin Sinclair (sourced from Ruby in a Nutshell (Matsumoto, O'Reilly)) ## require "e2mmap.rb" module ExceptionForMatrix # :nodoc: extend Exception2MessageMapper def_e2message(TypeError, "wrong argument type %s (expected %s)") def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)") def_exception("ErrDimensionMismatch", "\#{self.name} dimension mismatch") def_exception("ErrNotRegular", "Not Regular Matrix") def_exception("ErrOperationNotDefined", "Operation(%s) can\\'t be defined: %s op %s") def_exception("ErrOperationNotImplemented", "Sorry, Operation(%s) not implemented: %s op %s") end # # The +Matrix+ class represents a mathematical matrix. It provides methods for creating # matrices, operating on them arithmetically and algebraically, # and determining their mathematical properties (trace, rank, inverse, determinant). # # == Method Catalogue # # To create a matrix: # * Matrix[*rows] # * Matrix.[](*rows) # * Matrix.rows(rows, copy = true) # * Matrix.columns(columns) # * Matrix.build(row_count, column_count, &block) # * Matrix.diagonal(*values) # * Matrix.scalar(n, value) # * Matrix.identity(n) # * Matrix.unit(n) # * Matrix.I(n) # * Matrix.zero(n) # * Matrix.row_vector(row) # * Matrix.column_vector(column) # # To access Matrix elements/columns/rows/submatrices/properties: # * #[](i, j) # * #row_count (row_size) # * #column_count (column_size) # * #row(i) # * #column(j) # * #collect # * #map # * #each # * #each_with_index # * #find_index # * #minor(*param) # # Properties of a matrix: # * #diagonal? # * #empty? # * #hermitian? # * #lower_triangular? # * #normal? # * #orthogonal? # * #permutation? # * #real? # * #regular? # * #singular? # * #square? # * #symmetric? # * #unitary? # * #upper_triangular? # * #zero? # # Matrix arithmetic: # * #*(m) # * #+(m) # * #-(m) # * #/(m) # * #inverse # * #inv # * #** # # Matrix functions: # * #determinant # * #det # * #rank # * #round # * #trace # * #tr # * #transpose # * #t # # Matrix decompositions: # * #eigen # * #eigensystem # * #lup # * #lup_decomposition # # Complex arithmetic: # * conj # * conjugate # * imag # * imaginary # * real # * rect # * rectangular # # Conversion to other data types: # * #coerce(other) # * #row_vectors # * #column_vectors # * #to_a # # String representations: # * #to_s # * #inspect # class Matrix include Enumerable include ExceptionForMatrix autoload :EigenvalueDecomposition, "matrix/eigenvalue_decomposition" autoload :LUPDecomposition, "matrix/lup_decomposition" # instance creations private_class_method :new attr_reader :rows protected :rows # # Creates a matrix where each argument is a row. # Matrix[ [25, 93], [-1, 66] ] # => 25 93 # -1 66 # def Matrix.[](*rows) rows(rows, false) end # # Creates a matrix where +rows+ is an array of arrays, each of which is a row # of the matrix. If the optional argument +copy+ is false, use the given # arrays as the internal structure of the matrix without copying. # Matrix.rows([[25, 93], [-1, 66]]) # => 25 93 # -1 66 # def Matrix.rows(rows, copy = true) rows = convert_to_array(rows) rows.map! do |row| convert_to_array(row, copy) end size = (rows[0] || []).size rows.each do |row| raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size end new rows, size end # # Creates a matrix using +columns+ as an array of column vectors. # Matrix.columns([[25, 93], [-1, 66]]) # => 25 -1 # 93 66 # def Matrix.columns(columns) rows(columns, false).transpose end # # Creates a matrix of size +row_count+ x +column_count+. # It fills the values by callin