Initial revisionv1_0_r2r2

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@2 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

1 files changed, 777 insertions, 0 deletions

diff --git a/lib/matrix.rb b/lib/matrix.rb
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+#!/usr/local/bin/ruby
+#
+#   matrix.rb - 
+#   	$Release Version: 1.0$
+#   	$Revision: 1.0 $
+#   	$Date: 97/05/23 11:35:28 $
+#       Original Version from Smalltalk-80 version
+#	   on July 23, 1985 at 8:37:17 am
+#   	by Keiju ISHITSUKA
+#
+# --
+#
+#   Matrix[[1,2,3],
+#	      :
+#	   [3,4,5]]
+#   Matrix[row0,
+#          row1,
+#	    :
+#          rown]
+#
+#   column: Îó
+#   row:    ¹Ô
+#
+
+require "e2mmap.rb"
+
+module ExceptionForMatrix
+  Exception2MessageMapper.extend_to(binding)
+  
+  def_e2message(TypeError, "wrong argument type %s (expected %s)")
+  def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)")
+  
+  def_exception("ErrDimensionMismatch", "\#{self.type} dimemsion mismatch")
+  def_exception("ErrNotRegular", "Not Regular Matrix")
+  def_exception("ErrOperationNotDefined", "This operation(%s) can\\'t defined")
+end
+
+class Matrix
+  RCS_ID='-$Header: ruby-mode,v 1.2 91/04/20 17:24:57 keiju Locked $-'
+  
+  include ExceptionForMatrix
+  
+  # instance creations
+  private_class_method :new
+  
+  def Matrix.[](*rows)
+    new(:init_rows, rows, FALSE)
+  end
+  
+  def Matrix.rows(rows, copy = TRUE)
+    new(:init_rows, rows, copy)
+  end
+  
+  def Matrix.columns(columns)
+    rows = (0 .. columns[0].size - 1).collect {
+      |i|
+      (0 .. columns.size - 1).collect {
+	|j|
+	columns[j][i]
+      }
+    }
+    Matrix.rows(rows, FALSE)
+  end
+  
+  def Matrix.diagonal(*values)
+    size = values.size
+    rows = (0 .. size  - 1).collect {
+      |j|
+      row = Array.new(size).fill(0, 0, size)
+      row[j] = values[j]
+      row
+    }
+    self
+    rows(rows, FALSE)
+  end
+  
+  def Matrix.scalar(n, value)
+    Matrix.diagonal(*Array.new(n).fill(value, 0, n))
+  end
+
+  def Matrix.identity(n)
+    Matrix.scalar(n, 1)
+  end
+  class << Matrix 
+    alias unit identity
+    alias I identity
+  end
+  
+  def Matrix.zero(n)
+    Matrix.scalar(n, 0)
+  end
+  
+  def Matrix.row_vector(row)
+    case row
+    when Vector
+      Matrix.rows([row.to_a], FALSE)
+    when Array
+      Matrix.rows([row.dup], FALSE)
+    else
+      Matrix.row([[row]], FALSE)
+    end
+  end
+  
+  def Matrix.column_vector(column)
+    case column
+    when Vector
+      Matrix.columns([column.to_a])
+    when Array
+      Matrix.columns([column])
+    else
+      Matrix.columns([[column]])
+    end
+  end
+
+  # initializing
+  def initialize(init_method, *argv)
+    self.send(init_method, *argv)
+  end
+  
+  def init_rows(rows, copy)
+    if copy
+      @rows = rows.collect{|row| row.dup}
+    else
+      @rows = rows
+    end
+    self
+  end
+  private :init_rows
+  
+  #accessing
+  def [](i, j)
+    @rows[i][j]
+  end
+
+  def row_size
+    @rows.size
+  end
+  
+  def column_size
+    @rows[0].size
+  end
+
+  def row(i)
+    if iterator?
+      for e in @rows[i]
+	yield e
+      end
+    else
+      Vector.elements(@rows[i])
+    end
+  end
+
+  def column(j)
+    if iterator?
+      0.upto(row_size - 1) do
+	|i|
+	yield @rows[i][j]
+      end
+    else
+      col = (0 .. row_size - 1).collect {
+	|i|
+	@rows[i][j]
+      }
+      Vector.elements(col, FALSE)
+    end
+  end
+  
+  def collect
+    rows = @rows.collect{|row| row.collect{|e| yield e}}
+    Matrix.rows(rows, FALSE)
+  end
+  alias map collect
+  
+  #
+  # param:  (from_row, row_size, from_col, size_col)
+  #	    (from_row..to_row, from_col..to_col)
+  #
+  def minor(*param)
+    case param.size
+    when 2
+      from_row = param[0].first
+      size_row = param[0].size
+      from_col = param[1].first
+      size_col = param[1].size
+    when 4
+      from_row = param[0]
+      size_row = param[1]
+      from_col = param[2]
+      size_col = param[3]
+    else
+      Matrix.fail ArgumentError, param.inspect
+    end
+    
+    rows = @rows[from_row, size_row].collect{
+      |row|
+      row[from_col, size_col]
+    }
+    Matrix.rows(rows, FALSE)
+  end
+  
+  # TESTING
+  def regular?
+    square? and rank == column_size
+  end
+  
+  def singular?
+    not regular?
+  end
+
+  def square?
+    column_size == row_size
+  end
+  
+  # ARITHMETIC
+  
+  def *(m) #is matrix or vector or number"
+    case(m)
+    when Numeric
+      rows = @rows.collect {
+	|row|
+	row.collect {
+	  |e|
+	  e * m
+	}
+      }
+      return Matrix.rows(rows, FALSE)
+    when Vector
+      m = Matrix.column_vector(m)
+      r = self * m
+      return r.column(0)
+    when Matrix
+      Matrix.fail ErrDimensionMismatch if column_size != m.row_size
+    
+      rows = (0 .. row_size - 1).collect {
+	|i|
+	(0 .. m.column_size - 1).collect {
+	  |j|
+	  vij = 0
+	  0.upto(column_size - 1) do
+	    |k|
+	    vij += self[i, k] * m[k, j]
+	  end
+	  vij
+	}
+      }
+      return Matrix.rows(rows, FALSE)
+    else
+      x, y = m.coerce(self)
+      return x * y
+    end
+  end
+  
+  def +(m)
+    case m
+    when Numeric
+      Matrix.fail ErrOperationNotDefined, "+"
+    when Vector
+      m = Matrix.column_vector(m)
+    when Matrix
+    else
+      x, y = m.coerce(self)
+      return x + y
+    end
+    
+    Matrix.fail 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]
+      }
+    }
+    Matrix.rows(rows, FALSE)
+  end
+
+  def -(m)
+    case m
+    when Numeric
+      Matrix.fail ErrOperationNotDefined, "-"
+    when Vector
+      m = Matrix.column_vector(m)
+    when Matrix
+    else
+      x, y = m.coerce(self)
+      return x - y
+    end
+    
+    Matrix.fail 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]
+      }
+    }
+    Matrix.rows(rows, FALSE)
+  end
+
+  def inverse
+    Matrix.fail ErrDimensionMismatch unless square?
+    Matrix.I(row_size).inverse_from(self)
+  end
+  alias inv inverse
+  
+  def inverse_from(src)
+    size = row_size - 1
+    a = src.to_a
+    
+    for k in 0..size
+      if (akk = a[k][k]) == 0
+	i = k
+	begin
+	  fail ErrNotRegular if (i += 1) > size
+	end while a[i][k] == 0
+	a[i], a[k] = a[k], a[i]
+	@rows[i], @rows[k] = @rows[k], @rows[i]
+	akk = a[k][k]
+      end
+      
+      for i in 0 .. size
+	next if i == k
+	q = a[i][k] / akk
+	a[i][k] = 0
+	
+	(k + 1).upto(size) do	
+	  |j|
+	  a[i][j] -= a[k][j] * q
+	end
+	0.upto(size) do
+	  |j|
+	  @rows[i][j] -= @rows[k][j] * q
+	end
+      end
+      
+      (k + 1).upto(size) do
+	|j|
+	a[k][j] /= akk
+      end
+      0.upto(size) do
+	|j|
+	@rows[k][j] /= akk
+      end
+    end
+    self
+  end
+  #alias reciprocal inverse
+  
+  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 = x
+      n = other  - 1
+      while n != 0
+	while (div, mod = n.divmod(2)
+	       mod == 0)
+	  x = x * x
+	  n = div
+	end
+	z *= x
+	n -= 1
+      end
+      z
+    elsif other.kind_of?(Float) || defined?(Rational) && other.kind_of?(Rational)
+      fail ErrOperationNotDefined, "**"
+    else
+      fail ErrOperationNotDefined, "**"
+    end
+  end
+  
+  # Matrix functions
+  
+  def determinant
+    return 0 unless square?
+    
+    size = row_size - 1
+    a = to_a
+    
+    det = 1
+    k = 0
+    begin 
+      if (akk = a[k][k]) == 0
+	i = k
+	begin
+	  return 0 if (i += 1) > size
+	end while a[i][k] == 0
+	a[i], a[k] = a[k], a[i]
+	akk = a[k][k]
+      end
+      (k + 1).upto(size) do
+	|i|
+	q = a[i][k] / akk
+	(k + 1).upto(size) do
+	  |j|
+	  a[i][j] -= a[k][j] * q
+	end
+      end
+      det *= akk
+    end while (k += 1) <= size
+    det
+  end
+  alias det determinant
+	
+  def rank
+    if column_size > row_size
+      a = transpose.to_a
+    else
+      a = to_a
+    end
+    rank = 0
+    k = 0
+    begin
+      if (akk = a[k][k]) == 0
+	i = -1
+	nothing = FALSE
+	begin
+	  if (i += 1) > column_size - 1
+	    nothing = TRUE
+	    break
+	  end
+	end while a[i][k] == 0
+	next if nothing
+	a[i], a[k] = a[k], a[i]
+	akk = a[k][k]
+      end
+      (k + 1).upto(row_size - 1) do
+	|i|
+	q = a[i][k] / akk
+	(k + 1).upto(column_size - 1) do
+	  |j|
+	  a[i][j] -= a[k][j] * q
+	end
+      end
+      rank += 1
+    end while (k += 1) <= column_size - 1
+    return rank
+  end
+
+  def trace
+    tr = 0
+    0.upto(column_size - 1) do
+      |i|
+      tr += @rows[i][i]
+    end
+    tr
+  end
+  alias tr trace
+  
+  def transpose
+    Matrix.columns(@rows)
+  end
+  alias t transpose
+  
+  # CONVERTING
+  
+  def coerce(other)
+    case other
+    when Numeric
+      return Scalar.new(other), self
+    end
+  end
+
+  def row_vectors
+    rows = (0 .. column_size - 1).collect {
+      |i|
+      row(i)
+    }
+    rows
+  end
+  
+  def column_vectors
+    columns = (0 .. row_size - 1).collect {
+      |i|
+      column(i)
+    }
+    columns
+  end
+  
+  def to_a
+    @rows.collect{|row| row.collect{|e| e}}
+  end
+  
+  def to_f
+    collect{|e| e.to_f}
+  end
+  
+  def to_i
+    collect{|e| e.to_i}
+  end
+  
+  def to_r
+    collect{|e| e.to_r}
+  end
+  
+  # PRINTING
+  def to_s
+    "Matrix[" + @rows.collect{
+      |row|
+      "[" + row.collect{|e| e.to_s}.join(", ") + "]"
+    }.join(", ")+"]"
+  end
+  
+  def inspect
+    "Matrix"+@rows.inspect
+  end
+  
+  # Private CLASS
+  
+  class Scalar < Numeric
+    include ExceptionForMatrix
+    
+    def initialize(value)
+      @value = value
+    end
+    
+    # ARITHMETIC
+    def +(other)
+      case other
+      when Numeric
+	Scalar.new(@value + other)
+      when Vector, Matrix
+	Scalar.fail WrongArgType, other.type, "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.fail WrongArgType, other.type, "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.fail WrongArgType, other.type, "Numeric or Scalar or Matrix"
+      when Matrix
+	self * _M.inverse
+      else
+	x, y = other.coerce(self)
+	x / y
+      end
+    end
+    
+    def ** (other)
+      case other
+      when Numeric
+	Scalar.new(@value ** other)
+      when Vector
+	Scalar.fail WrongArgType, other.type, "Numeric or Scalar or Matrix"
+      when Matrix
+	other.powered_by(self)
+      else
+	x, y = other.coerce(self)
+	x ** y
+      end
+    end
+  end
+end
+
+#----------------------------------------------------------------------
+#
+#    - 
+#
+#----------------------------------------------------------------------
+class Vector
+  include ExceptionForMatrix
+
+  
+  #INSTANCE CREATION
+  
+  private_class_method :new
+  def Vector.[](*array)
+    new(:init_elements, array, copy = FALSE)
+  end
+  
+  def Vector.elements(array, copy = TRUE)
+    new(:init_elements, array, copy)
+  end
+  
+  def initialize(method, array, copy)
+    self.send(method, array, copy)
+  end
+  
+  def init_elements(array, copy)
+    if copy
+      @elements = array.dup
+    else
+      @elements = array
+    end
+  end
+  
+  # ACCSESSING
+	 
+  def [](i)
+    @elements[i]
+  end
+  
+  def size
+    @elements.size
+  end
+  
+  # ENUMRATIONS
+  def each2(v)
+    Vector.fail ErrDimensionMismatch if size != v.size
+    0.upto(size - 1) do
+      |i|
+      yield @elements[i], v[i]
+    end
+  end
+  
+  def collect2(v)
+    Vector.fail ErrDimensionMismatch if size != v.size
+    (0 .. size - 1).collect do
+      |i|
+      yield @elements[i], v[i]
+    end
+  end
+
+  # ARITHMETIC
+  
+  def *(x) "is matrix or number"
+    case x
+    when Numeric
+      els = @elements.collect{|e| e * x}
+      Vector.elements(els, FALSE)
+    when Matrix
+      self.covector * x
+    else
+      s, x = X.corece(self)
+      s * x
+    end
+  end
+
+  def +(v)
+    case v
+    when Vector
+      Vector.fail 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.corece(self)
+      s + x
+    end
+  end
+
+  def -(v)
+    case v
+    when Vector
+      Vector.fail 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.corece(self)
+      s - x
+    end
+  end
+  
+  # VECTOR FUNCTIONS
+  
+  def inner_product(v)
+    Vector.fail ErrDimensionMismatch if size != v.size
+    
+    p = 0
+    each2(v) {
+      |v1, v2|
+      p += v1 * v2
+    }
+    p
+  end
+  
+  def collect
+    els = @elements.collect {
+      |v|
+      yield v
+    }
+    Vector.elements(els, FALSE)
+  end
+  alias map collect
+  
+  def map2(v)
+    els = collect2(v) {
+      |v1, v2|
+      yield v1, v2
+    }
+    Vector.elements(els, FALSE)
+  end
+  
+  def r
+    v = 0
+    for e in @elements
+      v += e*e
+    end
+    return v.sqrt
+  end
+  
+  # CONVERTING
+  def covector
+    Matrix.row_vector(self)
+  end
+  
+  def to_a
+    @elements.dup
+  end
+  
+  def to_f
+    collect{|e| e.to_f}
+  end
+  
+  def to_i
+    collect{|e| e.to_i}
+  end
+  
+  def to_r
+    collect{|e| e.to_r}
+  end
+  
+  def coerce(other)
+    case other
+    when Numeric
+      return Scalar.new(other), self
+    end
+  end
+  
+  # PRINTING
+  
+  def to_s
+    "Vector[" + @elements.join(", ") + "]"
+  end
+  
+  def inspect
+    str = "Vector"+@elements.inspect
+  end
+end
+