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* NEWS: List all changes to lib/matrix

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* lib/matrix.rb: Improve doc and style. Trivial optimizations.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@27585 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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marcandre 2010-05-02 05:43:29 +00:00
parent c8e50abfe8
commit ec8b5d0625
2 changed files with 114 additions and 87 deletions
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24
NEWS
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@ -224,6 +224,30 @@ with all sufficient information, see the ChangeLog file.
* do not raise ShiftingError if an aged file already exists. * do not raise ShiftingError if an aged file already exists.
(no ShiftingError will be raised from 1.2.7, just warn() instead) (no ShiftingError will be raised from 1.2.7, just warn() instead)
* matrix
* API change to adhere strictly to mathematical definitions:
* Matrices must now be rectangular.
* trace, regular?, singular? are defined only for square matrices
* support for empty matrices
* all integer matrices now have the right determinant (also an integer)
* Matrix and Vector include Enumerable.
* new methods:
* Matrix.build
* Matrix.empty
* Matrix#conj
* Matrix#conjugate
* Matrix#each
* Matrix#each_with_index
* Matrix#empty?
* Matrix#imag
* Matrix#imaginary
* Matrix#real
* Matrix#real?
* Matrix#rect
* Matrix#rectangular
* net/http * net/http
* merged net/https. * merged net/https.

145
lib/matrix.rb
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@ -1,21 +1,15 @@
#-- # encoding: utf-8
# 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 # = matrix.rb
# #
# An implementation of Matrix and Vector classes. # 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. # See classes Matrix and Vector for documentation.
# #
# Current Maintainer:: Marc-André Lafortune
# Original Author:: Keiju ISHITSUKA
# Original Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly))
##
require "e2mmap.rb" require "e2mmap.rb"
@ -31,15 +25,9 @@ module ExceptionForMatrix # :nodoc:
end end
# #
# The +Matrix+ class represents a mathematical matrix, and provides methods for creating # The +Matrix+ class represents a mathematical matrix. It provides methods for creating
# special-case matrices (zero, identity, diagonal, singular, vector), operating on them # matrices, operating on them arithmetically and algebraically,
# arithmetically and algebraically, and determining their mathematical properties (trace, rank, # and determining their mathematical properties (trace, rank, inverse, determinant).
# 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 # == Method Catalogue
# #
@ -115,9 +103,6 @@ end
# * <tt> #inspect </tt> # * <tt> #inspect </tt>
# #
class Matrix class Matrix
@RCS_ID='-$Id: matrix.rb,v 1.13 2001/12/09 14:22:23 keiju Exp keiju $-'
# extend Exception2MessageMapper
include Enumerable include Enumerable
include ExceptionForMatrix include ExceptionForMatrix
@ -145,13 +130,13 @@ class Matrix
# -1 66 # -1 66
# #
def Matrix.rows(rows, copy = true) def Matrix.rows(rows, copy = true)
rows = Matrix.convert_to_array(rows) rows = convert_to_array(rows)
rows.map! do |row| rows.map! do |row|
Matrix.convert_to_array(row, copy) convert_to_array(row, copy)
end end
size = (rows[0] || []).size size = (rows[0] || []).size
rows.each do |row| rows.each do |row|
Matrix.Raise ErrDimensionMismatch, "element size differs (#{row.size} should be #{size})" unless row.size == size Matrix.Raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size
end end
new rows, size new rows, size
end end
@ -200,7 +185,7 @@ class Matrix
def Matrix.diagonal(*values) def Matrix.diagonal(*values)
size = values.size size = values.size
rows = (0 ... size).collect {|j| rows = (0 ... size).collect {|j|
row = Array.new(size).fill(0, 0, size) row = Array.new(size, 0)
row[j] = values[j] row[j] = values[j]
row row
} }
@ -215,7 +200,7 @@ class Matrix
# 0 5 # 0 5
# #
def Matrix.scalar(n, value) def Matrix.scalar(n, value)
Matrix.diagonal(*Array.new(n).fill(value, 0, n)) Matrix.diagonal(*Array.new(n, value))
end end
# #
@ -249,7 +234,7 @@ class Matrix
# => 4 5 6 # => 4 5 6
# #
def Matrix.row_vector(row) def Matrix.row_vector(row)
row = Matrix.convert_to_array(row) row = convert_to_array(row)
new [row] new [row]
end end
@ -262,13 +247,13 @@ class Matrix
# 6 # 6
# #
def Matrix.column_vector(column) def Matrix.column_vector(column)
column = Matrix.convert_to_array(column) column = convert_to_array(column)
new [column].transpose, 1 new [column].transpose, 1
end end
# #
# Creates a empty matrix of +row_size+ x +column_size+. # Creates a empty matrix of +row_size+ x +column_size+.
# +row_size+ or +column_size+ must be 0. # At least one of +row_size+ or +column_size+ must be 0.
# #
# m = Matrix.empty(2, 0) # m = Matrix.empty(2, 0)
# m == Matrix[ [], [] ] # m == Matrix[ [], [] ]
@ -417,7 +402,7 @@ class Matrix
# #
# Returns a section of the matrix. The parameters are either: # Returns a section of the matrix. The parameters are either:
# * start_row, nrows, start_col, ncols; OR # * start_row, nrows, start_col, ncols; OR
# * col_range, row_range # * row_range, col_range
# #
# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2) # Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
# => 9 0 0 # => 9 0 0
@ -430,17 +415,19 @@ class Matrix
def minor(*param) def minor(*param)
case param.size case param.size
when 2 when 2
from_row = param[0].first row_range, col_range = param
from_row = row_range.first
from_row += row_size if from_row < 0 from_row += row_size if from_row < 0
to_row = param[0].end to_row = row_range.end
to_row += row_size if to_row < 0 to_row += row_size if to_row < 0
to_row += 1 unless param[0].exclude_end? to_row += 1 unless row_range.exclude_end?
size_row = to_row - from_row size_row = to_row - from_row
from_col = param[1].first
from_col = col_range.first
from_col += column_size if from_col < 0 from_col += column_size if from_col < 0
to_col = param[1].end to_col = col_range.end
to_col += column_size if to_col < 0 to_col += column_size if to_col < 0
to_col += 1 unless param[1].exclude_end? to_col += 1 unless col_range.exclude_end?
size_col = to_col - from_col size_col = to_col - from_col
when 4 when 4
from_row, size_row, from_col, size_col = param from_row, size_row, from_col, size_col = param
@ -521,7 +508,7 @@ class Matrix
# There should be no good reason to do this since Matrices are immutable. # There should be no good reason to do this since Matrices are immutable.
# #
def clone def clone
new_matrix @rows.map{|row| row.dup}, column_size new_matrix @rows.map(&:dup), column_size
end end
# #
@ -654,21 +641,18 @@ class Matrix
# #
def inverse def inverse
Matrix.Raise ErrDimensionMismatch unless square? Matrix.Raise ErrDimensionMismatch unless square?
Matrix.I(row_size).inverse_from(self) Matrix.I(row_size).send(:inverse_from, self)
end end
alias inv inverse alias inv inverse
# def inverse_from(src) # :nodoc:
# Not for public consumption? last = row_size - 1
#
def inverse_from(src)
size = row_size
a = src.to_a a = src.to_a
size.times do |k| 0.upto(last) do |k|
i = k i = k
akk = a[k][k].abs akk = a[k][k].abs
(k+1 ... size).each do |j| (k+1).upto(last) do |j|
v = a[j][k].abs v = a[j][k].abs
if v > akk if v > akk
i = j i = j
@ -682,39 +666,40 @@ class Matrix
end end
akk = a[k][k] akk = a[k][k]
size.times do |ii| 0.upto(last) do |ii|
next if ii == k next if ii == k
q = a[ii][k].quo(akk) q = a[ii][k].quo(akk)
a[ii][k] = 0 a[ii][k] = 0
(k + 1 ... size).each do |j| (k + 1).upto(last) do |j|
a[ii][j] -= a[k][j] * q a[ii][j] -= a[k][j] * q
end end
size.times do |j| 0.upto(last) do |j|
@rows[ii][j] -= @rows[k][j] * q @rows[ii][j] -= @rows[k][j] * q
end end
end end
(k + 1 ... size).each do |j| (k+1).upto(last) do |j|
a[k][j] = a[k][j].quo(akk) a[k][j] = a[k][j].quo(akk)
end end
size.times do |j| 0.upto(last) do |j|
@rows[k][j] = @rows[k][j].quo(akk) @rows[k][j] = @rows[k][j].quo(akk)
end end
end end
self self
end end
#alias reciprocal inverse private :inverse_from
# #
# Matrix exponentiation. Defined for integer powers only. Equivalent to # Matrix exponentiation. Currently implemented for integer powers only.
# multiplying the matrix by itself N times. # Equivalent to multiplying the matrix by itself N times.
# Matrix[[7,6], [3,9]] ** 2 # Matrix[[7,6], [3,9]] ** 2
# => 67 96 # => 67 96
# 48 99 # 48 99
# #
def ** (other) def ** (other)
if other.kind_of?(Integer) case other
when Integer
x = self x = self
if other <= 0 if other <= 0
x = self.inverse x = self.inverse
@ -727,7 +712,7 @@ class Matrix
return z if (other >>= 1).zero? return z if (other >>= 1).zero?
x *= x x *= x
end end
elsif other.kind_of?(Float) || defined?(Rational) && other.kind_of?(Rational) when Float, Rational
Matrix.Raise ErrOperationNotImplemented, "**", self.class, other.class Matrix.Raise ErrOperationNotImplemented, "**", self.class, other.class
else else
Matrix.Raise ErrOperationNotDefined, "**", self.class, other.class Matrix.Raise ErrOperationNotDefined, "**", self.class, other.class
@ -796,8 +781,8 @@ class Matrix
# It has the same computational cost order O(n^3) as standard Gaussian elimination. # It has the same computational cost order O(n^3) as standard Gaussian elimination.
# Intermediate results are fraction free and of lower complexity. # Intermediate results are fraction free and of lower complexity.
# A matrix of Integers will have thus intermediate results that are also Integers, # A matrix of Integers will have thus intermediate results that are also Integers,
# with smaller bignums (if any), while a matrix of Float will usually have more # with smaller bignums (if any), while a matrix of Float will usually have
# precise intermediate results. # intermediate results with better precision.
# #
def determinant_bareiss def determinant_bareiss
size = row_size size = row_size
@ -973,7 +958,11 @@ class Matrix
#++ #++
# #
# FIXME: describe #coerce. # The coerce method provides support for Ruby type coercion.
# This coercion mechanism is used by Ruby to handle mixed-type
# numeric operations: it is intended to find a compatible common
# type between the two operands of the operator.
# See also Numeric#coerce.
# #
def coerce(other) def coerce(other)
case other case other
@ -1010,17 +999,17 @@ class Matrix
end end
def elements_to_f def elements_to_f
warn "#{caller(1)[0]}: warning: Matrix#elements_to_f is deprecated" warn "#{caller(1)[0]}: warning: Matrix#elements_to_f is deprecated, use map(&:to_f)"
map(&:to_f) map(&:to_f)
end end
def elements_to_i def elements_to_i
warn "#{caller(1)[0]}: warning: Matrix#elements_to_i is deprecated" warn "#{caller(1)[0]}: warning: Matrix#elements_to_i is deprecated, use map(&:to_i)"
map(&:to_i) map(&:to_i)
end end
def elements_to_r def elements_to_r
warn "#{caller(1)[0]}: warning: Matrix#elements_to_r is deprecated" warn "#{caller(1)[0]}: warning: Matrix#elements_to_r is deprecated, use map(&:to_r)"
map(&:to_r) map(&:to_r)
end end
@ -1052,11 +1041,14 @@ class Matrix
end end
end end
# Private helper modules
module ConversionHelper # :nodoc:
# #
# Converts the obj to an Array. If copy is set to true # Converts the obj to an Array. If copy is set to true
# a copy of obj will be made if necessary. # a copy of obj will be made if necessary.
# #
def Matrix.convert_to_array(obj, copy = false) def convert_to_array(obj, copy = false) # :nodoc:
case obj case obj
when Array when Array
copy ? obj.dup : obj copy ? obj.dup : obj
@ -1072,10 +1064,16 @@ class Matrix
converted converted
end end
end end
private :convert_to_array
end
# Private helper module extend ConversionHelper
module CoercionHelper # :nodoc: module CoercionHelper # :nodoc:
#
# Applies the operator +oper+ with argument +obj+
# through coercion of +obj+
#
def apply_through_coercion(obj, oper) def apply_through_coercion(obj, oper)
coercion = obj.coerce(self) coercion = obj.coerce(self)
raise TypeError unless coercion.is_a?(Array) && coercion.length == 2 raise TypeError unless coercion.is_a?(Array) && coercion.length == 2
@ -1085,10 +1083,12 @@ class Matrix
end end
private :apply_through_coercion private :apply_through_coercion
#
# Helper method to coerce a value into a specific class. # Helper method to coerce a value into a specific class.
# Raises a TypeError if the coercion fails or the returned value # Raises a TypeError if the coercion fails or the returned value
# is not of the right class. # is not of the right class.
# (from Rubinius) # (from Rubinius)
#
def self.coerce_to(obj, cls, meth) # :nodoc: def self.coerce_to(obj, cls, meth) # :nodoc:
return obj if obj.kind_of?(cls) return obj if obj.kind_of?(cls)
@ -1227,17 +1227,19 @@ class Vector
include ExceptionForMatrix include ExceptionForMatrix
include Enumerable include Enumerable
include Matrix::CoercionHelper include Matrix::CoercionHelper
extend Matrix::ConversionHelper
#INSTANCE CREATION #INSTANCE CREATION
private_class_method :new private_class_method :new
attr_reader :elements attr_reader :elements
protected :elements protected :elements
# #
# Creates a Vector from a list of elements. # Creates a Vector from a list of elements.
# Vector[7, 4, ...] # Vector[7, 4, ...]
# #
def Vector.[](*array) def Vector.[](*array)
new Matrix.convert_to_array(array, copy = false) new convert_to_array(array, copy = false)
end end
# #
@ -1245,7 +1247,7 @@ class Vector
# whether the array itself or a copy is used internally. # whether the array itself or a copy is used internally.
# #
def Vector.elements(array, copy = true) def Vector.elements(array, copy = true)
new Matrix.convert_to_array(array, copy) new convert_to_array(array, copy)
end end
# #
@ -1502,7 +1504,11 @@ class Vector
end end
# #
# FIXME: describe Vector#coerce. # The coerce method provides support for Ruby type coercion.
# This coercion mechanism is used by Ruby to handle mixed-type
# numeric operations: it is intended to find a compatible common
# type between the two operands of the operator.
# See also Numeric#coerce.
# #
def coerce(other) def coerce(other)
case other case other
@ -1531,6 +1537,3 @@ class Vector
str = "Vector"+@elements.inspect str = "Vector"+@elements.inspect
end end
end end
# Documentation comments:
# - Matrix#coerce and Vector#coerce need to be documented