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diff --git a/lib/matrix.rb b/lib/matrix.rb deleted file mode 100644 index 3c75751e37..0000000000 --- a/lib/matrix.rb +++ /dev/null @@ -1,1368 +0,0 @@ -#-- -# matrix.rb - -# $Release Version: 1.0$ -# $Revision: 1.13 $ -# Original Version from Smalltalk-80 version -# on July 23, 1985 at 8:37:17 am -# by Keiju ISHITSUKA -#++ -# -# = matrix.rb -# -# An implementation of Matrix and Vector classes. -# -# Author:: Keiju ISHITSUKA -# Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly)) -# -# See classes Matrix and Vector for documentation. -# - -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", "This operation(%s) can\\'t defined") -end - -# -# The +Matrix+ class represents a mathematical matrix, and provides methods for creating -# special-case matrices (zero, identity, diagonal, singular, vector), operating on them -# arithmetically and algebraically, and determining their mathematical properties (trace, rank, -# inverse, determinant). -# -# Note that matrices must be rectangular, otherwise an ErrDimensionMismatch is raised. -# -# Also note that the determinant of integer matrices may be approximated unless you -# also <tt>require 'mathn'</tt>. This may be fixed in the future. -# -# == Method Catalogue -# -# To create a matrix: -# * <tt> Matrix[*rows] </tt> -# * <tt> Matrix.[](*rows) </tt> -# * <tt> Matrix.rows(rows, copy = true) </tt> -# * <tt> Matrix.columns(columns) </tt> -# * <tt> Matrix.diagonal(*values) </tt> -# * <tt> Matrix.scalar(n, value) </tt> -# * <tt> Matrix.identity(n) </tt> -# * <tt> Matrix.unit(n) </tt> -# * <tt> Matrix.I(n) </tt> -# * <tt> Matrix.zero(n) </tt> -# * <tt> Matrix.row_vector(row) </tt> -# * <tt> Matrix.column_vector(column) </tt> -# -# To access Matrix elements/columns/rows/submatrices/properties: -# * <tt> [](i, j) </tt> -# * <tt> #row_size </tt> -# * <tt> #column_size </tt> -# * <tt> #row(i) </tt> -# * <tt> #column(j) </tt> -# * <tt> #collect </tt> -# * <tt> #map </tt> -# * <tt> #minor(*param) </tt> -# -# Properties of a matrix: -# * <tt> #regular? </tt> -# * <tt> #singular? </tt> -# * <tt> #square? </tt> -# -# Matrix arithmetic: -# * <tt> *(m) </tt> -# * <tt> +(m) </tt> -# * <tt> -(m) </tt> -# * <tt> #/(m) </tt> -# * <tt> #inverse </tt> -# * <tt> #inv </tt> -# * <tt> ** </tt> -# -# Matrix functions: -# * <tt> #determinant </tt> -# * <tt> #det </tt> -# * <tt> #rank </tt> -# * <tt> #trace </tt> -# * <tt> #tr </tt> -# * <tt> #transpose </tt> -# * <tt> #t </tt> -# -# Conversion to other data types: -# * <tt> #coerce(other) </tt> -# * <tt> #row_vectors </tt> -# * <tt> #column_vectors </tt> -# * <tt> #to_a </tt> -# -# String representations: -# * <tt> #to_s </tt> -# * <tt> #inspect </tt> -# -class Matrix - @RCS_ID='-$Id: matrix.rb,v 1.13 2001/12/09 14:22:23 keiju Exp keiju $-' - -# extend Exception2MessageMapper - include ExceptionForMatrix - - # 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) - Matrix.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 = Matrix.convert_to_array(rows) - rows.map! do |row| - Matrix.convert_to_array(row, copy) - end - size = (rows[0] || []).size - rows.each do |row| - Matrix.Raise ErrDimensionMismatch, "element 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) - Matrix.rows(columns, false).transpose - end - - # - # Creates a matrix where the diagonal elements are composed of +values+. - # Matrix.diagonal(9, 5, -3) - # => 9 0 0 - # 0 5 0 - # 0 0 -3 - # - def Matrix.diagonal(*values) - size = values.size - rows = (0 ... size).collect {|j| - row = Array.new(size).fill(0, 0, size) - row[j] = values[j] - row - } - new rows - end - - # - # Creates an +n+ by +n+ diagonal matrix where each diagonal element is - # +value+. - # Matrix.scalar(2, 5) - # => 5 0 - # 0 5 - # - def Matrix.scalar(n, value) - Matrix.diagonal(*Array.new(n).fill(value, 0, n)) - end - - # - # Creates an +n+ by +n+ identity matrix. - # Matrix.identity(2) - # => 1 0 - # 0 1 - # - def Matrix.identity(n) - Matrix.scalar(n, 1) - end - class << Matrix - alias unit identity - alias I identity - end - - # - # Creates an +n+ by +n+ zero matrix. - # Matrix.zero(2) - # => 0 0 - # 0 0 - # - def Matrix.zero(n) - Matrix.scalar(n, 0) - end - - # - # Creates a single-row matrix where the values of that row are as given in - # +row+. - # Matrix.row_vector([4,5,6]) - # => 4 5 6 - # - def Matrix.row_vector(row) - row = Matrix.convert_to_array(row) - new [row] - end - - # - # Creates a single-column matrix where the values of that column are as given - # in +column+. - # Matrix.column_vector([4,5,6]) - # => 4 - # 5 - # 6 - # - def Matrix.column_vector(column) - column = Matrix.convert_to_array(column) - new [column].transpose, 1 - end - - # - # Creates a empty matrix of +row_size+ x +column_size+. - # +row_size+ or +column_size+ must be 0. - # - # m = Matrix.empty(2, 0) - # m == Matrix[ [], [] ] - # => true - # n = Matrix.empty(0, 3) - # n == Matrix.columns([ [], [], [] ]) - # => true - # m * n - # => Matrix[[0, 0, 0], [0, 0, 0]] - # - def Matrix.empty(row_size = 0, column_size = 0) - Matrix.Raise ErrDimensionMismatch if column_size != 0 && row_size != 0 - - new([[]]*row_size, column_size) - end - - # - # Matrix.new is private; use Matrix.rows, columns, [], etc... to create. - # - def initialize(rows, column_size = rows[0].size) - # No checking is done at this point. rows must be an Array of Arrays. - # column_size must be the size of the first row, if there is one, - # otherwise it *must* be specified and can be any integer >= 0 - @rows = rows - @column_size = column_size - end - - def new_matrix(rows, column_size = rows[0].size) # :nodoc: - Matrix.send(:new, rows, column_size) # bypass privacy of Matrix.new - end - private :new_matrix - - # - # Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+. - # - def [](i, j) - @rows.fetch(i){return nil}[j] - end - alias element [] - alias component [] - - def []=(i, j, v) - @rows[i][j] = v - end - alias set_element []= - alias set_component []= - private :[]=, :set_element, :set_component - - # - # Returns the number of rows. - # - def row_size - @rows.size - end - - # - # Returns the number of columns. - # - attr_reader :column_size - - # - # Returns row vector number +i+ of the matrix as a Vector (starting at 0 like - # an array). When a block is given, the elements of that vector are iterated. - # - def row(i, &block) # :yield: e - if block_given? - @rows.fetch(i){return self}.each(&block) - self - else - Vector.elements(@rows.fetch(i){return nil}) - end - end - - # - # Returns column vector number +j+ of the matrix as a Vector (starting at 0 - # like an array). When a block is given, the elements of that vector are - # iterated. - # - def column(j) # :yield: e - if block_given? - return self if j >= column_size || j < -column_size - row_size.times do |i| - yield @rows[i][j] - end - self - else - return nil if j >= column_size || j < -column_size - col = (0 ... row_size).collect {|i| - @rows[i][j] - } - Vector.elements(col, false) - end - end - - # - # Returns a matrix that is the result of iteration of the given block over all - # elements of the matrix. - # Matrix[ [1,2], [3,4] ].collect { |e| e**2 } - # => 1 4 - # 9 16 - # - def collect(&block) # :yield: e - return to_enum(:collect) unless block_given? - rows = @rows.collect{|row| row.collect(&block)} - new_matrix rows, column_size - end - alias map collect - - # - # Returns a section of the matrix. The parameters are either: - # * start_row, nrows, start_col, ncols; OR - # * col_range, row_range - # - # Matrix.diagonal(9, 5, -3).minor(0..1, 0..2) - # => 9 0 0 - # 0 5 0 - # - # Like Array#[], negative indices count backward from the end of the - # row or column (-1 is the last element). Returns nil if the starting - # row or column is greater than row_size or column_size respectively. - # - def minor(*param) - case param.size - when 2 - from_row = param[0].first - from_row += row_size if from_row < 0 - to_row = param[0].end - to_row += row_size if to_row < 0 - to_row += 1 unless param[0].exclude_end? - size_row = to_row - from_row - from_col = param[1].first - from_col += column_size if from_col < 0 - to_col = param[1].end - to_col += column_size if to_col < 0 - to_col += 1 unless param[1].exclude_end? - size_col = to_col - from_col - when 4 - from_row, size_row, from_col, size_col = param - return nil if size_row < 0 || size_col < 0 - from_row += row_size if from_row < 0 - from_col += column_size if from_col < 0 - else - Matrix.Raise ArgumentError, param.inspect - end - - return nil if from_row > row_size || from_col > column_size || from_row < 0 || from_col < 0 - rows = @rows[from_row, size_row].collect{|row| - row[from_col, size_col] - } - new_matrix rows, column_size - from_col - end - - #-- - # TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Returns +true+ if this is a regular matrix. - # - def regular? - square? and rank == column_size - end - - # - # Returns +true+ is this is a singular (i.e. non-regular) matrix. - # - def singular? - not regular? - end - - # - # Returns +true+ is this is a square matrix. - # - def square? - column_size == row_size - end - - #-- - # OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Returns +true+ if and only if the two matrices contain equal elements. - # - def ==(other) - return false unless Matrix === other - rows == other.rows - end - - def eql?(other) - return false unless Matrix === other - rows.eql? other.rows - end - - def compare_by_row_vectors(rows, comparison = :==) - return false unless @rows.size == rows.size - - @rows.size.times do |i| - return false unless @rows[i].send(comparison, rows[i]) - end - true - end - - # - # Returns a clone of the matrix, so that the contents of each do not reference - # identical objects. - # There should be no good reason to do this since Matrices are immutable. - # - def clone - new_matrix @rows.map{|row| row.dup}, column_size - end - - # - # Returns a hash-code for the matrix. - # - def hash - @rows.hash - end - - #-- - # ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Matrix multiplication. - # Matrix[[2,4], [6,8]] * Matrix.identity(2) - # => 2 4 - # 6 8 - # - def *(m) # m is matrix or vector or number - case(m) - when Numeric - rows = @rows.collect {|row| - row.collect {|e| - e * m - } - } - return new_matrix rows, column_size - when Vector - m = Matrix.column_vector(m) - r = self * m - return r.column(0) - when Matrix - Matrix.Raise ErrDimensionMismatch if column_size != m.row_size - - rows = (0 ... row_size).collect {|i| - (0 ... m.column_size).collect {|j| - (0 ... column_size).inject(0) do |vij, k| - vij + self[i, k] * m[k, j] - end - } - } - return new_matrix rows, m.column_size - else - x, y = m.coerce(self) - return x * y - end - end - - # - # Matrix addition. - # Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]] - # => 6 0 - # -4 12 - # - def +(m) - case m - when Numeric - Matrix.Raise ErrOperationNotDefined, "+" - when Vector - m = Matrix.column_vector(m) - when Matrix - else - x, y = m.coerce(self) - return x + y - end - - Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size - - rows = (0 ... row_size).collect {|i| - (0 ... column_size).collect {|j| - self[i, j] + m[i, j] - } - } - new_matrix rows, column_size - end - - # - # Matrix subtraction. - # Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]] - # => -8 2 - # 8 1 - # - def -(m) - case m - when Numeric - Matrix.Raise ErrOperationNotDefined, "-" - when Vector - m = Matrix.column_vector(m) - when Matrix - else - x, y = m.coerce(self) - return x - y - end - - Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size - - rows = (0 ... row_size).collect {|i| - (0 ... column_size).collect {|j| - self[i, j] - m[i, j] - } - } - new_matrix rows, column_size - end - - # - # Matrix division (multiplication by the inverse). - # Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]] - # => -7 1 - # -3 -6 - # - def /(other) - case other - when Numeric - rows = @rows.collect {|row| - row.collect {|e| - e / other - } - } - return new_matrix rows, column_size - when Matrix - return self * other.inverse - else - x, y = other.coerce(self) - return x / y - end - end - - # - # Returns the inverse of the matrix. - # Matrix[[1, 2], [2, 1]].inverse - # => -1 1 - # 0 -1 - # - def inverse - Matrix.Raise ErrDimensionMismatch unless square? - Matrix.I(row_size).inverse_from(self) - end - alias inv inverse - - # - # Not for public consumption? - # - def inverse_from(src) - size = row_size - a = src.to_a - - size.times do |k| - i = k - akk = a[k][k].abs - (k+1 ... size).each do |j| - v = a[j][k].abs - if v > akk - i = j - akk = v - end - end - Matrix.Raise ErrNotRegular if akk == 0 - if i != k - a[i], a[k] = a[k], a[i] - @rows[i], @rows[k] = @rows[k], @rows[i] - end - akk = a[k][k] - - size.times do |i| - next if i == k - q = a[i][k].quo(akk) - a[i][k] = 0 - - (k + 1 ... size).each do |j| - a[i][j] -= a[k][j] * q - end - size.times do |j| - @rows[i][j] -= @rows[k][j] * q - end - end - - (k + 1 ... size).each do |j| - a[k][j] = a[k][j].quo(akk) - end - size.times do |j| - @rows[k][j] = @rows[k][j].quo(akk) - end - end - self - end - #alias reciprocal inverse - - # - # Matrix exponentiation. Defined for integer powers only. Equivalent to - # multiplying the matrix by itself N times. - # Matrix[[7,6], [3,9]] ** 2 - # => 67 96 - # 48 99 - # - def ** (other) - if other.kind_of?(Integer) - x = self - if other <= 0 - x = self.inverse - return Matrix.identity(self.column_size) if other == 0 - other = -other - end - z = nil - loop do - z = z ? z * x : x if other[0] == 1 - return z if (other >>= 1).zero? - x *= x - end - elsif other.kind_of?(Float) || defined?(Rational) && other.kind_of?(Rational) - Matrix.Raise ErrOperationNotDefined, "**" - else - Matrix.Raise ErrOperationNotDefined, "**" - end - end - - #-- - # MATRIX FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Returns the determinant of the matrix. If the matrix is not square, the - # result is 0. This method's algorithm is Gaussian elimination method - # and using Numeric#quo(). Beware that using Float values, with their - # usual lack of precision, can affect the value returned by this method. Use - # Rational values or Matrix#det_e instead if this is important to you. - # - # Matrix[[7,6], [3,9]].determinant - # => 45.0 - # - def determinant - return 0 unless square? - - size = row_size - a = to_a - - det = 1 - size.times do |k| - if (akk = a[k][k]) == 0 - i = (k+1 ... size).find {|i| - a[i][k] != 0 - } - return 0 if i.nil? - a[i], a[k] = a[k], a[i] - akk = a[k][k] - det *= -1 - end - - (k + 1 ... size).each do |i| - q = a[i][k].quo(akk) - (k + 1 ... size).each do |j| - a[i][j] -= a[k][j] * q - end - end - det *= akk - end - det - end - alias det determinant - - # - # Returns the determinant of the matrix. If the matrix is not square, the - # result is 0. This method's algorithm is Gaussian elimination method. - # This method uses Euclidean algorithm. If all elements are integer, - # really exact value. But, if an element is a float, can't return - # exact value. - # - # Matrix[[7,6], [3,9]].determinant - # => 63 - # - def determinant_e - return 0 unless square? - - size = row_size - a = to_a - - det = 1 - size.times do |k| - if a[k][k].zero? - i = (k+1 ... size).find {|i| - a[i][k] != 0 - } - return 0 if i.nil? - a[i], a[k] = a[k], a[i] - det *= -1 - end - - (k + 1 ... size).each do |i| - q = a[i][k].quo(a[k][k]) - (k ... size).each do |j| - a[i][j] -= a[k][j] * q - end - unless a[i][k].zero? - a[i], a[k] = a[k], a[i] - det *= -1 - redo - end - end - det *= a[k][k] - end - det - end - alias det_e determinant_e - - # - # Returns the rank of the matrix. Beware that using Float values, - # probably return faild value. Use Rational values or Matrix#rank_e - # for getting exact result. - # - # Matrix[[7,6], [3,9]].rank - # => 2 - # - def rank - if column_size > row_size - a = transpose.to_a - a_column_size = row_size - a_row_size = column_size - else - a = to_a - a_column_size = column_size - a_row_size = row_size - end - rank = 0 - a_column_size.times do |k| - if (akk = a[k][k]) == 0 - i = (k+1 ... a_row_size).find {|i| - a[i][k] != 0 - } - if i - a[i], a[k] = a[k], a[i] - akk = a[k][k] - else - i = (k+1 ... a_column_size).find {|i| - a[k][i] != 0 - } - next if i.nil? - (k ... a_column_size).each do |j| - a[j][k], a[j][i] = a[j][i], a[j][k] - end - akk = a[k][k] - end - end - - (k + 1 ... a_row_size).each do |i| - q = a[i][k].quo(akk) - (k + 1... a_column_size).each do |j| - a[i][j] -= a[k][j] * q - end - end - rank += 1 - end - return rank - end - - # - # Returns the rank of the matrix. This method uses Euclidean - # algorithm. If all elements are integer, really exact value. But, if - # an element is a float, can't return exact value. - # - # Matrix[[7,6], [3,9]].rank - # => 2 - # - def rank_e - a = to_a - a_column_size = column_size - a_row_size = row_size - pi = 0 - a_column_size.times do |j| - if i = (pi ... a_row_size).find{|i0| !a[i0][j].zero?} - if i != pi - a[pi], a[i] = a[i], a[pi] - end - (pi + 1 ... a_row_size).each do |k| - q = a[k][j].quo(a[pi][j]) - (pi ... a_column_size).each do |j0| - a[k][j0] -= q * a[pi][j0] - end - if k > pi && !a[k][j].zero? - a[k], a[pi] = a[pi], a[k] - redo - end - end - pi += 1 - end - end - pi - end - - - # - # Returns the trace (sum of diagonal elements) of the matrix. - # Matrix[[7,6], [3,9]].trace - # => 16 - # - def trace - Matrix.Raise ErrDimensionMismatch unless square? - (0...column_size).inject(0) do |tr, i| - tr + @rows[i][i] - end - end - alias tr trace - - # - # Returns the transpose of the matrix. - # Matrix[[1,2], [3,4], [5,6]] - # => 1 2 - # 3 4 - # 5 6 - # Matrix[[1,2], [3,4], [5,6]].transpose - # => 1 3 5 - # 2 4 6 - # - def transpose - return Matrix.empty(column_size, 0) if row_size.zero? - new_matrix @rows.transpose, row_size - end - alias t transpose - - #-- - # CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # FIXME: describe #coerce. - # - def coerce(other) - case other - when Numeric - return Scalar.new(other), self - else - raise TypeError, "#{self.class} can't be coerced into #{other.class}" - end - end - - # - # Returns an array of the row vectors of the matrix. See Vector. - # - def row_vectors - (0 ... row_size).collect {|i| - row(i) - } - end - - # - # Returns an array of the column vectors of the matrix. See Vector. - # - def column_vectors - (0 ... column_size).collect {|i| - column(i) - } - end - - # - # Returns an array of arrays that describe the rows of the matrix. - # - def to_a - @rows.collect{|row| row.dup} - end - - def elements_to_f - collect{|e| e.to_f} - end - - def elements_to_i - collect{|e| e.to_i} - end - - def elements_to_r - collect{|e| e.to_r} - end - - #-- - # PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Overrides Object#to_s - # - def to_s - if row_size == 0 || column_size == 0 - "Matrix.empty(#{row_size}, #{column_size})" - else - "Matrix[" + @rows.collect{|row| - "[" + row.collect{|e| e.to_s}.join(", ") + "]" - }.join(", ")+"]" - end - end - - alias_method :inspect_org, :inspect - - # - # Overrides Object#inspect - # - def inspect - if row_size == 0 || column_size == 0 - "Matrix.empty(#{row_size}, #{column_size})" - else - "Matrix#{@rows.inspect}" - end - end - - # - # Converts the obj to an Array. If copy is set to true - # a copy of obj will be made if necessary. - # - def Matrix.convert_to_array(obj, copy = false) - case obj - when Array - copy ? obj.dup : obj - when Vector - obj.to_a - else - begin - converted = obj.to_ary - rescue Exception => e - raise TypeError, "can't convert #{obj.class} into an Array (#{e.message})" - end - raise TypeError, "#{obj.class}#to_ary should return an Array" unless converted.is_a? Array - converted - end - end - - # Private CLASS - - class Scalar < Numeric # :nodoc: - include ExceptionForMatrix - - def initialize(value) - @value = value - end - - # ARITHMETIC - def +(other) - case other - when Numeric - Scalar.new(@value + other) - when Vector, Matrix - Scalar.Raise WrongArgType, other.class, "Numeric or Scalar" - when Scalar - Scalar.new(@value + other.value) - else - x, y = other.coerce(self) - x + y - end - end - - def -(other) - case other - when Numeric - Scalar.new(@value - other) - when Vector, Matrix - Scalar.Raise WrongArgType, other.class, "Numeric or Scalar" - when Scalar - Scalar.new(@value - other.value) - else - x, y = other.coerce(self) - x - y - end - end - - def *(other) - case other - when Numeric - Scalar.new(@value * other) - when Vector, Matrix - other.collect{|e| @value * e} - else - x, y = other.coerce(self) - x * y - end - end - - def / (other) - case other - when Numeric - Scalar.new(@value / other) - when Vector - Scalar.Raise WrongArgType, other.class, "Numeric or Scalar or Matrix" - when Matrix - self * other.inverse - else - x, y = other.coerce(self) - x.quo(y) - end - end - - def ** (other) - case other - when Numeric - Scalar.new(@value ** other) - when Vector - Scalar.Raise WrongArgType, other.class, "Numeric or Scalar or Matrix" - when Matrix - other.powered_by(self) - else - x, y = other.coerce(self) - x ** y - end - end - end -end - - -# -# The +Vector+ class represents a mathematical vector, which is useful in its own right, and -# also constitutes a row or column of a Matrix. -# -# == Method Catalogue -# -# To create a Vector: -# * <tt> Vector.[](*array) </tt> -# * <tt> Vector.elements(array, copy = true) </tt> -# -# To access elements: -# * <tt> [](i) </tt> -# -# To enumerate the elements: -# * <tt> #each2(v) </tt> -# * <tt> #collect2(v) </tt> -# -# Vector arithmetic: -# * <tt> *(x) "is matrix or number" </tt> -# * <tt> +(v) </tt> -# * <tt> -(v) </tt> -# -# Vector functions: -# * <tt> #inner_product(v) </tt> -# * <tt> #collect </tt> -# * <tt> #map </tt> -# * <tt> #map2(v) </tt> -# * <tt> #r </tt> -# * <tt> #size </tt> -# -# Conversion to other data types: -# * <tt> #covector </tt> -# * <tt> #to_a </tt> -# * <tt> #coerce(other) </tt> -# -# String representations: -# * <tt> #to_s </tt> -# * <tt> #inspect </tt> -# -class Vector - include ExceptionForMatrix - - #INSTANCE CREATION - - private_class_method :new - attr_reader :elements - protected :elements - # - # Creates a Vector from a list of elements. - # Vector[7, 4, ...] - # - def Vector.[](*array) - new Matrix.convert_to_array(array, copy = false) - end - - # - # Creates a vector from an Array. The optional second argument specifies - # whether the array itself or a copy is used internally. - # - def Vector.elements(array, copy = true) - new Matrix.convert_to_array(array, copy) - end - - # - # Vector.new is private; use Vector[] or Vector.elements to create. - # - def initialize(array) - # No checking is done at this point. - @elements = array - end - - # ACCESSING - - # - # Returns element number +i+ (starting at zero) of the vector. - # - def [](i) - @elements[i] - end - alias element [] - alias component [] - - def []=(i, v) - @elements[i]= v - end - alias set_element []= - alias set_component []= - private :[]=, :set_element, :set_component - - # - # Returns the number of elements in the vector. - # - def size - @elements.size - end - - #-- - # ENUMERATIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Iterate over the elements of this vector and +v+ in conjunction. - # - def each2(v) # :yield: e1, e2 - Vector.Raise ErrDimensionMismatch if size != v.size - return to_enum(:each2) unless block_given? - size.times do |i| - yield @elements[i], v[i] - end - end - - # - # Collects (as in Enumerable#collect) over the elements of this vector and +v+ - # in conjunction. - # - def collect2(v) # :yield: e1, e2 - Vector.Raise ErrDimensionMismatch if size != v.size - return to_enum(:collect2) unless block_given? - (0 ... size).collect do |i| - yield @elements[i], v[i] - end - end - - #-- - # COMPARING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Returns +true+ iff the two vectors have the same elements in the same order. - # - def ==(other) - return false unless Vector === other - @elements == other.elements - end - - def eql?(other) - return false unless Vector === other - @elements.eql? other.elements - end - - def compare_by(elements, comparison = :==) - @elements.send(comparison, elements) - end - - # - # Return a copy of the vector. - # - def clone - Vector.elements(@elements) - end - - # - # Return a hash-code for the vector. - # - def hash - @elements.hash - end - - #-- - # ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Multiplies the vector by +x+, where +x+ is a number or another vector. - # - def *(x) - case x - when Numeric - els = @elements.collect{|e| e * x} - Vector.elements(els, false) - when Matrix - Matrix.column_vector(self) * x - else - s, x = x.coerce(self) - s * x - end - end - - # - # Vector addition. - # - def +(v) - case v - when Vector - Vector.Raise ErrDimensionMismatch if size != v.size - els = collect2(v) {|v1, v2| - v1 + v2 - } - Vector.elements(els, false) - when Matrix - Matrix.column_vector(self) + v - else - s, x = v.coerce(self) - s + x - end - end - - # - # Vector subtraction. - # - def -(v) - case v - when Vector - Vector.Raise ErrDimensionMismatch if size != v.size - els = collect2(v) {|v1, v2| - v1 - v2 - } - Vector.elements(els, false) - when Matrix - Matrix.column_vector(self) - v - else - s, x = v.coerce(self) - s - x - end - end - - #-- - # VECTOR FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Returns the inner product of this vector with the other. - # Vector[4,7].inner_product Vector[10,1] => 47 - # - def inner_product(v) - Vector.Raise ErrDimensionMismatch if size != v.size - - p = 0 - each2(v) {|v1, v2| - p += v1 * v2 - } - p - end - - # - # Like Array#collect. - # - def collect(&block) # :yield: e - return to_enum(:collect) unless block_given? - els = @elements.collect(&block) - Vector.elements(els, false) - end - alias map collect - - # - # Like Vector#collect2, but returns a Vector instead of an Array. - # - def map2(v, &block) # :yield: e1, e2 - return to_enum(:map2) unless block_given? - els = collect2(v, &block) - Vector.elements(els, false) - end - - # - # Returns the modulus (Pythagorean distance) of the vector. - # Vector[5,8,2].r => 9.643650761 - # - def r - Math.sqrt(@elements.inject(0) {|v, e| v + e*e}) - end - - #-- - # CONVERTING - #++ - - # - # Creates a single-row matrix from this vector. - # - def covector - Matrix.row_vector(self) - end - - # - # Returns the elements of the vector in an array. - # - def to_a - @elements.dup - end - - def elements_to_f - collect{|e| e.to_f} - end - - def elements_to_i - collect{|e| e.to_i} - end - - def elements_to_r - collect{|e| e.to_r} - end - - # - # FIXME: describe Vector#coerce. - # - def coerce(other) - case other - when Numeric - return Matrix::Scalar.new(other), self - else - raise TypeError, "#{self.class} can't be coerced into #{other.class}" - end - end - - #-- - # PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- - #++ - - # - # Overrides Object#to_s - # - def to_s - "Vector[" + @elements.join(", ") + "]" - end - - # - # Overrides Object#inspect - # - def inspect - str = "Vector"+@elements.inspect - end -end - -# Documentation comments: -# - Matrix#coerce and Vector#coerce need to be documented |