diff options
Diffstat (limited to 'lib/matrix.rb')
| -rw-r--r-- | lib/matrix.rb | 210 |
1 files changed, 105 insertions, 105 deletions
diff --git a/lib/matrix.rb b/lib/matrix.rb index ec03c730fa..4bc000588b 100644 --- a/lib/matrix.rb +++ b/lib/matrix.rb @@ -1,6 +1,6 @@ #!/usr/local/bin/ruby #-- -# matrix.rb - +# matrix.rb - # $Release Version: 1.0$ # $Revision: 1.13 $ # Original Version from Smalltalk-80 version @@ -13,9 +13,9 @@ # An implementation of Matrix and Vector classes. # # Author:: Keiju ISHITSUKA -# Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly)) +# 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. # require "e2mmap.rb" @@ -24,7 +24,7 @@ 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") @@ -59,7 +59,7 @@ end # * <tt> Matrix.row_vector(row) </tt> # * <tt> Matrix.column_vector(column) </tt> # -# To access Matrix elements/columns/rows/submatrices/properties: +# To access Matrix elements/columns/rows/submatrices/properties: # * <tt> [](i, j) </tt> # * <tt> #row_size </tt> # * <tt> #column_size </tt> @@ -104,13 +104,13 @@ end # 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 - + # # Creates a matrix where each argument is a row. # Matrix[ [25, 93], [-1, 66] ] @@ -120,7 +120,7 @@ class Matrix def Matrix.[](*rows) new(:init_rows, rows, false) end - + # # Creates a matrix where +rows+ is an array of arrays, each of which is a row # to the matrix. If the optional argument +copy+ is false, use the given @@ -131,7 +131,7 @@ class Matrix def Matrix.rows(rows, copy = true) new(:init_rows, rows, copy) end - + # # Creates a matrix using +columns+ as an array of column vectors. # Matrix.columns([[25, 93], [-1, 66]]) @@ -147,7 +147,7 @@ class Matrix } Matrix.rows(rows, false) end - + # # Creates a matrix where the diagonal elements are composed of +values+. # Matrix.diagonal(9, 5, -3) @@ -164,7 +164,7 @@ class Matrix } rows(rows, false) end - + # # Creates an +n+ by +n+ diagonal matrix where each diagonal element is # +value+. @@ -185,11 +185,11 @@ class Matrix def Matrix.identity(n) Matrix.scalar(n, 1) end - class << Matrix + class << Matrix alias unit identity alias I identity end - + # # Creates an +n+ by +n+ zero matrix. # Matrix.zero(2) @@ -199,7 +199,7 @@ class Matrix 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+. @@ -216,7 +216,7 @@ class Matrix Matrix.rows([[row]], false) end end - + # # Creates a single-column matrix where the values of that column are as given # in +column+. @@ -243,7 +243,7 @@ class Matrix def initialize(init_method, *argv) self.send(init_method, *argv) end - + def init_rows(rows, copy) if copy @rows = rows.collect{|row| row.dup} @@ -253,7 +253,7 @@ class Matrix self end private :init_rows - + # # Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+. # @@ -276,7 +276,7 @@ class Matrix def row_size @rows.size end - + # # Returns the number of columns. Note that it is possible to construct a # matrix with uneven columns (e.g. Matrix[ [1,2,3], [4,5] ]), but this is @@ -318,7 +318,7 @@ class Matrix 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. @@ -331,7 +331,7 @@ class Matrix Matrix.rows(rows, false) end alias map collect - + # # Returns a section of the matrix. The parameters are either: # * start_row, nrows, start_col, ncols; OR @@ -358,13 +358,13 @@ class Matrix else Matrix.Raise ArgumentError, param.inspect end - + rows = @rows[from_row, size_row].collect{|row| row[from_col, size_col] } Matrix.rows(rows, false) end - + #-- # TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- #++ @@ -375,7 +375,7 @@ class Matrix def regular? square? and rank == column_size end - + # # Returns +true+ is this is a singular (i.e. non-regular) matrix. # @@ -390,7 +390,7 @@ class Matrix def square? column_size == row_size end - + #-- # OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- #++ @@ -400,27 +400,27 @@ class Matrix # def ==(other) return false unless Matrix === other - + other.compare_by_row_vectors(@rows) end def eql?(other) return false unless Matrix === other - + other.compare_by_row_vectors(@rows, :eql?) end - + # # Not really intended for general consumption. # def compare_by_row_vectors(rows, comparison = :==) return false unless @rows.size == rows.size - + 0.upto(@rows.size - 1) 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. @@ -428,7 +428,7 @@ class Matrix def clone Matrix.rows(@rows) end - + # # Returns a hash-code for the matrix. # @@ -441,11 +441,11 @@ class Matrix end return value end - + #-- # ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- #++ - + # # Matrix multiplication. # Matrix[[2,4], [6,8]] * Matrix.identity(2) @@ -467,7 +467,7 @@ class Matrix return r.column(0) when Matrix Matrix.Raise ErrDimensionMismatch if column_size != m.row_size - + rows = (0 .. row_size - 1).collect {|i| (0 .. m.column_size - 1).collect {|j| vij = 0 @@ -483,7 +483,7 @@ class Matrix return x * y end end - + # # Matrix addition. # Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]] @@ -501,9 +501,9 @@ class Matrix 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 - 1).collect {|i| (0 .. column_size - 1).collect {|j| self[i, j] + m[i, j] @@ -529,9 +529,9 @@ class Matrix 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 - 1).collect {|i| (0 .. column_size - 1).collect {|j| self[i, j] - m[i, j] @@ -539,7 +539,7 @@ class Matrix } Matrix.rows(rows, false) end - + # # Matrix division (multiplication by the inverse). # Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]] @@ -581,7 +581,7 @@ class Matrix def inverse_from(src) size = row_size - 1 a = src.to_a - + for k in 0..size i = k akk = a[k][k].abs @@ -598,12 +598,12 @@ class Matrix @rows[i], @rows[k] = @rows[k], @rows[i] end akk = a[k][k] - + for i in 0 .. size next if i == k q = a[i][k].quo(akk) a[i][k] = 0 - + for j in (k + 1).. size a[i][j] -= a[k][j] * q end @@ -611,7 +611,7 @@ class Matrix @rows[i][j] -= @rows[k][j] * q end end - + for j in (k + 1).. size a[k][j] = a[k][j].quo(akk) end @@ -622,7 +622,7 @@ class Matrix self end #alias reciprocal inverse - + # # Matrix exponentiation. Defined for integer powers only. Equivalent to # multiplying the matrix by itself N times. @@ -656,11 +656,11 @@ class Matrix 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 algorism is Gaussian elimination method @@ -673,10 +673,10 @@ class Matrix # def determinant return 0 unless square? - + size = row_size - 1 a = to_a - + det = 1 k = 0 loop do @@ -706,20 +706,20 @@ class Matrix # # Returns the determinant of the matrix. If the matrix is not square, the - # result is 0. This method's algorism is Gaussian elimination method. + # result is 0. This method's algorism is Gaussian elimination method. # This method uses Euclidean algorism. If all elements are integer, # really exact value. But, if an element is a float, can't return - # exact value. + # exact value. # # Matrix[[7,6], [3,9]].determinant # => 63 # def determinant_e return 0 unless square? - + size = row_size - 1 a = to_a - + det = 1 k = 0 loop do @@ -821,7 +821,7 @@ class Matrix # # Returns the rank of the matrix. This method uses Euclidean # algorism. If all elements are integer, really exact value. But, if - # an element is a float, can't return exact value. + # an element is a float, can't return exact value. # # Matrix[[7,6], [3,9]].rank # => 2 @@ -866,7 +866,7 @@ class Matrix tr end alias tr trace - + # # Returns the transpose of the matrix. # Matrix[[1,2], [3,4], [5,6]] @@ -881,11 +881,11 @@ class Matrix Matrix.columns(@rows) end alias t transpose - + #-- # CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- #++ - + # # FIXME: describe #coerce. # @@ -907,7 +907,7 @@ class Matrix } rows end - + # # Returns an array of the column vectors of the matrix. See Vector. # @@ -917,30 +917,30 @@ class Matrix } columns end - + # # Returns an array of arrays that describe the rows of the matrix. # def to_a @rows.collect{|row| row.collect{|e| e}} 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 # @@ -949,23 +949,23 @@ class Matrix "[" + row.collect{|e| e.to_s}.join(", ") + "]" }.join(", ")+"]" end - + # # Overrides Object#inspect # def inspect "Matrix"+@rows.inspect end - + # Private CLASS - + class Scalar < Numeric # :nodoc: include ExceptionForMatrix - + def initialize(value) @value = value end - + # ARITHMETIC def +(other) case other @@ -980,7 +980,7 @@ class Matrix x + y end end - + def -(other) case other when Numeric @@ -994,7 +994,7 @@ class Matrix x - y end end - + def *(other) case other when Numeric @@ -1006,7 +1006,7 @@ class Matrix x * y end end - + def / (other) case other when Numeric @@ -1020,7 +1020,7 @@ class Matrix x.quo(y) end end - + def ** (other) case other when Numeric @@ -1079,9 +1079,9 @@ end # class Vector include ExceptionForMatrix - + #INSTANCE CREATION - + private_class_method :new # @@ -1091,7 +1091,7 @@ class Vector def Vector.[](*array) new(:init_elements, 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. @@ -1099,14 +1099,14 @@ class Vector def Vector.elements(array, copy = true) new(:init_elements, array, copy) end - + # # For internal use. # def initialize(method, array, copy) self.send(method, array, copy) end - + # # For internal use. # @@ -1117,9 +1117,9 @@ class Vector @elements = array end end - + # ACCESSING - + # # Returns element number +i+ (starting at zero) of the vector. # @@ -1135,14 +1135,14 @@ class Vector 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 -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- #++ @@ -1156,7 +1156,7 @@ class Vector yield @elements[i], v[i] end end - + # # Collects (as in Enumerable#collect) over the elements of this vector and +v+ # in conjunction. @@ -1177,40 +1177,40 @@ class Vector # def ==(other) return false unless Vector === other - + other.compare_by(@elements) end def eql?(other) return false unless Vector === other - + other.compare_by(@elements, :eql?) end - + # # For internal use. # 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. # @@ -1264,25 +1264,25 @@ class Vector 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. # @@ -1293,7 +1293,7 @@ class Vector Vector.elements(els, false) end alias map collect - + # # Like Vector#collect2, but returns a Vector instead of an Array. # @@ -1303,7 +1303,7 @@ class Vector } Vector.elements(els, false) end - + # # Returns the modulus (Pythagorean distance) of the vector. # Vector[5,8,2].r => 9.643650761 @@ -1315,7 +1315,7 @@ class Vector end return Math.sqrt(v) end - + #-- # CONVERTING #++ @@ -1326,26 +1326,26 @@ class 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. # @@ -1357,18 +1357,18 @@ class Vector 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 # |