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authormarcandre <marcandre@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2010-05-02 05:43:29 +0000
committermarcandre <marcandre@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2010-05-02 05:43:29 +0000
commitec8b5d06257830ac277e3ea82dacd3761d6771ee (patch)
tree07e23b91b4461c23bbdec0c09366a96eb7c886c5 /lib/matrix.rb
parentc8e50abfe85fc5787b2b399ff00cf56d86dc7c50 (diff)
* NEWS: List all changes to lib/matrix
* 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
Diffstat (limited to 'lib/matrix.rb')
-rw-r--r--lib/matrix.rb177
1 files changed, 90 insertions, 87 deletions
diff --git a/lib/matrix.rb b/lib/matrix.rb
index a339424..ee26cb9 100644
--- a/lib/matrix.rb
+++ b/lib/matrix.rb
@@ -1,21 +1,15 @@
-#--
-# 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
-#++
+# encoding: utf-8
#
# = 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.
#
+# 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"
@@ -31,15 +25,9 @@ module ExceptionForMatrix # :nodoc:
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.
+# 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
#
@@ -115,9 +103,6 @@ end
# * <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 Enumerable
include ExceptionForMatrix
@@ -145,13 +130,13 @@ class Matrix
# -1 66
#
def Matrix.rows(rows, copy = true)
- rows = Matrix.convert_to_array(rows)
+ rows = convert_to_array(rows)
rows.map! do |row|
- Matrix.convert_to_array(row, copy)
+ 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
+ Matrix.Raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size
end
new rows, size
end
@@ -200,7 +185,7 @@ class Matrix
def Matrix.diagonal(*values)
size = values.size
rows = (0 ... size).collect {|j|
- row = Array.new(size).fill(0, 0, size)
+ row = Array.new(size, 0)
row[j] = values[j]
row
}
@@ -215,7 +200,7 @@ class Matrix
# 0 5
#
def Matrix.scalar(n, value)
- Matrix.diagonal(*Array.new(n).fill(value, 0, n))
+ Matrix.diagonal(*Array.new(n, value))
end
#
@@ -249,7 +234,7 @@ class Matrix
# => 4 5 6
#
def Matrix.row_vector(row)
- row = Matrix.convert_to_array(row)
+ row = convert_to_array(row)
new [row]
end
@@ -262,13 +247,13 @@ class Matrix
# 6
#
def Matrix.column_vector(column)
- column = Matrix.convert_to_array(column)
+ column = 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.
+ # At least one of +row_size+ or +column_size+ must be 0.
#
# m = Matrix.empty(2, 0)
# m == Matrix[ [], [] ]
@@ -417,7 +402,7 @@ class Matrix
#
# Returns a section of the matrix. The parameters are either:
# * 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)
# => 9 0 0
@@ -430,17 +415,19 @@ class Matrix
def minor(*param)
case param.size
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
- to_row = param[0].end
+ to_row = row_range.end
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
- from_col = param[1].first
+
+ from_col = col_range.first
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 += 1 unless param[1].exclude_end?
+ to_col += 1 unless col_range.exclude_end?
size_col = to_col - from_col
when 4
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.
#
def clone
- new_matrix @rows.map{|row| row.dup}, column_size
+ new_matrix @rows.map(&:dup), column_size
end
#
@@ -654,21 +641,18 @@ class Matrix
#
def inverse
Matrix.Raise ErrDimensionMismatch unless square?
- Matrix.I(row_size).inverse_from(self)
+ Matrix.I(row_size).send(:inverse_from, self)
end
alias inv inverse
- #
- # Not for public consumption?
- #
- def inverse_from(src)
- size = row_size
+ def inverse_from(src) # :nodoc:
+ last = row_size - 1
a = src.to_a
- size.times do |k|
+ 0.upto(last) do |k|
i = k
akk = a[k][k].abs
- (k+1 ... size).each do |j|
+ (k+1).upto(last) do |j|
v = a[j][k].abs
if v > akk
i = j
@@ -682,39 +666,40 @@ class Matrix
end
akk = a[k][k]
- size.times do |ii|
+ 0.upto(last) do |ii|
next if ii == k
q = a[ii][k].quo(akk)
a[ii][k] = 0
- (k + 1 ... size).each do |j|
+ (k + 1).upto(last) do |j|
a[ii][j] -= a[k][j] * q
end
- size.times do |j|
+ 0.upto(last) do |j|
@rows[ii][j] -= @rows[k][j] * q
end
end
- (k + 1 ... size).each do |j|
+ (k+1).upto(last) do |j|
a[k][j] = a[k][j].quo(akk)
end
- size.times do |j|
+ 0.upto(last) do |j|
@rows[k][j] = @rows[k][j].quo(akk)
end
end
self
end
- #alias reciprocal inverse
+ private :inverse_from
#
- # Matrix exponentiation. Defined for integer powers only. Equivalent to
- # multiplying the matrix by itself N times.
+ # Matrix exponentiation. Currently implemented 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)
+ case other
+ when Integer
x = self
if other <= 0
x = self.inverse
@@ -727,7 +712,7 @@ class Matrix
return z if (other >>= 1).zero?
x *= x
end
- elsif other.kind_of?(Float) || defined?(Rational) && other.kind_of?(Rational)
+ when Float, Rational
Matrix.Raise ErrOperationNotImplemented, "**", self.class, other.class
else
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.
# Intermediate results are fraction free and of lower complexity.
# 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
- # precise intermediate results.
+ # with smaller bignums (if any), while a matrix of Float will usually have
+ # intermediate results with better precision.
#
def determinant_bareiss
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)
case other
@@ -1010,17 +999,17 @@ class Matrix
end
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)
end
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)
end
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)
end
@@ -1052,30 +1041,39 @@ class Matrix
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})"
+ # Private helper modules
+
+ module ConversionHelper # :nodoc:
+ #
+ # Converts the obj to an Array. If copy is set to true
+ # a copy of obj will be made if necessary.
+ #
+ def convert_to_array(obj, copy = false) # :nodoc:
+ 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
- raise TypeError, "#{obj.class}#to_ary should return an Array" unless converted.is_a? Array
- converted
end
+ private :convert_to_array
end
- # Private helper module
+ extend ConversionHelper
module CoercionHelper # :nodoc:
+ #
+ # Applies the operator +oper+ with argument +obj+
+ # through coercion of +obj+
+ #
def apply_through_coercion(obj, oper)
coercion = obj.coerce(self)
raise TypeError unless coercion.is_a?(Array) && coercion.length == 2
@@ -1085,10 +1083,12 @@ class Matrix
end
private :apply_through_coercion
+ #
# Helper method to coerce a value into a specific class.
# Raises a TypeError if the coercion fails or the returned value
# is not of the right class.
# (from Rubinius)
+ #
def self.coerce_to(obj, cls, meth) # :nodoc:
return obj if obj.kind_of?(cls)
@@ -1227,17 +1227,19 @@ class Vector
include ExceptionForMatrix
include Enumerable
include Matrix::CoercionHelper
+ extend Matrix::ConversionHelper
#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)
+ new convert_to_array(array, copy = false)
end
#
@@ -1245,7 +1247,7 @@ class Vector
# whether the array itself or a copy is used internally.
#
def Vector.elements(array, copy = true)
- new Matrix.convert_to_array(array, copy)
+ new convert_to_array(array, copy)
end
#
@@ -1502,7 +1504,11 @@ class Vector
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)
case other
@@ -1531,6 +1537,3 @@ class Vector
str = "Vector"+@elements.inspect
end
end
-
-# Documentation comments:
-# - Matrix#coerce and Vector#coerce need to be documented