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ruby/lib/matrix.rb

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#--
# 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", "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, 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, "+", self.class, m.class
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, "-", self.class, m.class
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, -1], [0, -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 |ii|
next if ii == k
q = a[ii][k].quo(akk)
a[ii][k] = 0
(k + 1 ... size).each do |j|
a[ii][j] -= a[k][j] * q
end
size.times do |j|
@rows[ii][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 ErrOperationNotImplemented, "**", self.class, other.class
else
Matrix.Raise ErrOperationNotDefined, "**", self.class, other.class
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 {|ii|
a[ii][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 |ii|
q = a[ii][k].quo(akk)
(k + 1 ... size).each do |j|
a[ii][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 {|ii|
a[ii][k] != 0
}
return 0 if i.nil?
a[i], a[k] = a[k], a[i]
det *= -1
end
(k + 1 ... size).each do |ii|
q = a[ii][k].quo(a[k][k])
(k ... size).each do |j|
a[ii][j] -= a[k][j] * q
end
unless a[ii][k].zero?
a[ii], a[k] = a[k], a[ii]
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 {|ii|
a[ii][k] != 0
}
if i
a[i], a[k] = a[k], a[i]
akk = a[k][k]
else
i = (k+1 ... a_column_size).find {|ii|
a[k][ii] != 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 |ii|
q = a[ii][k].quo(akk)
(k + 1... a_column_size).each do |j|
a[ii][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 ErrOperationNotDefined, "+", @value.class, other.class
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 ErrOperationNotDefined, "-", @value.class, other.class
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 ErrOperationNotDefined, "/", @value.class, other.class
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 ErrOperationNotDefined, "**", @value.class, other.class
when Matrix
#other.powered_by(self)
Scalar.Raise ErrOperationNotImplemented, "**", @value.class, other.class
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
include Enumerable
#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
#
def each(&block)
return to_enum(:each) unless block_given?
@elements.each(&block)
self
end
#
# 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, v) unless block_given?
size.times do |i|
yield @elements[i], v[i]
end
self
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, v) unless block_given?
size.times.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
when Vector
Vector.Raise ErrOperationNotDefined, "*", self.class, x.class
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 division.
#
def /(x)
case x
when Numeric
els = @elements.collect{|e| e / x}
Vector.elements(els, false)
when Matrix, Vector
Vector.Raise ErrOperationNotDefined, "/", self.class, x.class
else
s, x = x.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, v) 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
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