From 8aac5f48fc96c4aa76d4758d8c873f3e2cb6de90 Mon Sep 17 00:00:00 2001
From: marcandre <marcandre@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Mon, 10 Dec 2012 16:53:57 +0000
Subject: * lib/matrix: alias {row|column}_size to {row|column}_count and use
 the latter.   [Bug #7369] [ruby-core:49409]

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@38300 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 lib/matrix.rb                          | 176 +++++++++++++++++----------------
 lib/matrix/eigenvalue_decomposition.rb |   2 +-
 lib/matrix/lup_decomposition.rb        |  56 +++++------
 3 files changed, 118 insertions(+), 116 deletions(-)

(limited to 'lib')

diff --git a/lib/matrix.rb b/lib/matrix.rb
index 3ffd0ddc78..3e61157c3f 100644
--- a/lib/matrix.rb
+++ b/lib/matrix.rb
@@ -36,7 +36,7 @@ end
 # * Matrix.[](*rows)
 # * Matrix.rows(rows, copy = true)
 # * Matrix.columns(columns)
-# * Matrix.build(row_size, column_size, &block)
+# * Matrix.build(row_count, column_count, &block)
 # * Matrix.diagonal(*values)
 # * Matrix.scalar(n, value)
 # * Matrix.identity(n)
@@ -48,8 +48,8 @@ end
 #
 # To access Matrix elements/columns/rows/submatrices/properties:
 # * #[](i, j)
-# * #row_size
-# * #column_size
+# * #row_count (row_size)
+# * #column_count (column_size)
 # * #row(i)
 # * #column(j)
 # * #collect
@@ -172,7 +172,7 @@ class Matrix
   end
 
   #
-  # Creates a matrix of size +row_size+ x +column_size+.
+  # Creates a matrix of size +row_count+ x +column_count+.
   # It fills the values by calling the given block,
   # passing the current row and column.
   # Returns an enumerator if no block is given.
@@ -182,17 +182,17 @@ class Matrix
   #   m = Matrix.build(3) { rand }
   #     => a 3x3 matrix with random elements
   #
-  def Matrix.build(row_size, column_size = row_size)
-    row_size = CoercionHelper.coerce_to_int(row_size)
-    column_size = CoercionHelper.coerce_to_int(column_size)
-    raise ArgumentError if row_size < 0 || column_size < 0
-    return to_enum :build, row_size, column_size unless block_given?
-    rows = Array.new(row_size) do |i|
-      Array.new(column_size) do |j|
+  def Matrix.build(row_count, column_count = row_count)
+    row_count = CoercionHelper.coerce_to_int(row_count)
+    column_count = CoercionHelper.coerce_to_int(column_count)
+    raise ArgumentError if row_count < 0 || column_count < 0
+    return to_enum :build, row_count, column_count unless block_given?
+    rows = Array.new(row_count) do |i|
+      Array.new(column_count) do |j|
         yield i, j
       end
     end
-    new rows, column_size
+    new rows, column_count
   end
 
   #
@@ -243,9 +243,9 @@ class Matrix
   #     => 0 0
   #        0 0
   #
-  def Matrix.zero(row_size, column_size = row_size)
-    rows = Array.new(row_size){Array.new(column_size, 0)}
-    new rows, column_size
+  def Matrix.zero(row_count, column_count = row_count)
+    rows = Array.new(row_count){Array.new(column_count, 0)}
+    new rows, column_count
   end
 
   #
@@ -273,8 +273,8 @@ class Matrix
   end
 
   #
-  # Creates a empty matrix of +row_size+ x +column_size+.
-  # At least one of +row_size+ or +column_size+ must be 0.
+  # Creates a empty matrix of +row_count+ x +column_count+.
+  # At least one of +row_count+ or +column_count+ must be 0.
   #
   #   m = Matrix.empty(2, 0)
   #   m == Matrix[ [], [] ]
@@ -285,26 +285,26 @@ class Matrix
   #   m * n
   #     => Matrix[[0, 0, 0], [0, 0, 0]]
   #
-  def Matrix.empty(row_size = 0, column_size = 0)
-    Matrix.Raise ArgumentError, "One size must be 0" if column_size != 0 && row_size != 0
-    Matrix.Raise ArgumentError, "Negative size" if column_size < 0 || row_size < 0
+  def Matrix.empty(row_count = 0, column_count = 0)
+    Matrix.Raise ArgumentError, "One size must be 0" if column_count != 0 && row_count != 0
+    Matrix.Raise ArgumentError, "Negative size" if column_count < 0 || row_count < 0
 
-    new([[]]*row_size, column_size)
+    new([[]]*row_count, column_count)
   end
 
   #
   # Matrix.new is private; use Matrix.rows, columns, [], etc... to create.
   #
-  def initialize(rows, column_size = rows[0].size)
+  def initialize(rows, column_count = 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,
+    # column_count 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
+    @column_count = column_count
   end
 
-  def new_matrix(rows, column_size = rows[0].size) # :nodoc:
-    self.class.send(:new, rows, column_size) # bypass privacy of Matrix.new
+  def new_matrix(rows, column_count = rows[0].size) # :nodoc:
+    self.class.send(:new, rows, column_count) # bypass privacy of Matrix.new
   end
   private :new_matrix
 
@@ -327,14 +327,16 @@ class Matrix
   #
   # Returns the number of rows.
   #
-  def row_size
+  def row_count
     @rows.size
   end
 
+  alias_method :row_size, :row_count
   #
   # Returns the number of columns.
   #
-  attr_reader :column_size
+  attr_reader :column_count
+  alias_method :column_size, :column_count
 
   #
   # Returns row vector number +i+ of the matrix as a Vector (starting at 0 like
@@ -356,14 +358,14 @@ class Matrix
   #
   def column(j) # :yield: e
     if block_given?
-      return self if j >= column_size || j < -column_size
-      row_size.times do |i|
+      return self if j >= column_count || j < -column_count
+      row_count.times do |i|
         yield @rows[i][j]
       end
       self
     else
-      return nil if j >= column_size || j < -column_size
-      col = Array.new(row_size) {|i|
+      return nil if j >= column_count || j < -column_count
+      col = Array.new(row_count) {|i|
         @rows[i][j]
       }
       Vector.elements(col, false)
@@ -380,7 +382,7 @@ class Matrix
   def collect(&block) # :yield: e
     return to_enum(:collect) unless block_given?
     rows = @rows.collect{|row| row.collect(&block)}
-    new_matrix rows, column_size
+    new_matrix rows, column_count
   end
   alias map collect
 
@@ -402,7 +404,7 @@ class Matrix
   #
   def each(which = :all) # :yield: e
     return to_enum :each, which unless block_given?
-    last = column_size - 1
+    last = column_count - 1
     case which
     when :all
       block = Proc.new
@@ -415,7 +417,7 @@ class Matrix
       end
     when :off_diagonal
       @rows.each_with_index do |row, row_index|
-        column_size.times do |col_index|
+        column_count.times do |col_index|
           yield row[col_index] unless row_index == col_index
         end
       end
@@ -427,7 +429,7 @@ class Matrix
       end
     when :strict_lower
       @rows.each_with_index do |row, row_index|
-        [row_index, column_size].min.times do |col_index|
+        [row_index, column_count].min.times do |col_index|
           yield row[col_index]
         end
       end
@@ -463,7 +465,7 @@ class Matrix
   #
   def each_with_index(which = :all) # :yield: e, row, column
     return to_enum :each_with_index, which unless block_given?
-    last = column_size - 1
+    last = column_count - 1
     case which
     when :all
       @rows.each_with_index do |row, row_index|
@@ -477,7 +479,7 @@ class Matrix
       end
     when :off_diagonal
       @rows.each_with_index do |row, row_index|
-        column_size.times do |col_index|
+        column_count.times do |col_index|
           yield row[col_index], row_index, col_index unless row_index == col_index
         end
       end
@@ -489,7 +491,7 @@ class Matrix
       end
     when :strict_lower
       @rows.each_with_index do |row, row_index|
-        [row_index, column_size].min.times do |col_index|
+        [row_index, column_count].min.times do |col_index|
           yield row[col_index], row_index, col_index
         end
       end
@@ -552,39 +554,39 @@ class Matrix
   #
   # 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.
+  # row or column is greater than row_count or column_count respectively.
   #
   def minor(*param)
     case param.size
     when 2
       row_range, col_range = param
       from_row = row_range.first
-      from_row += row_size if from_row < 0
+      from_row += row_count if from_row < 0
       to_row = row_range.end
-      to_row += row_size if to_row < 0
+      to_row += row_count if to_row < 0
       to_row += 1 unless row_range.exclude_end?
       size_row = to_row - from_row
 
       from_col = col_range.first
-      from_col += column_size if from_col < 0
+      from_col += column_count if from_col < 0
       to_col = col_range.end
-      to_col += column_size if to_col < 0
+      to_col += column_count if to_col < 0
       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
       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
+      from_row += row_count if from_row < 0
+      from_col += column_count 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
+    return nil if from_row > row_count || from_col > column_count || 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, size_col].min
+    new_matrix rows, [column_count - from_col, size_col].min
   end
 
   #--
@@ -605,7 +607,7 @@ class Matrix
   # or the number of columns is 0.
   #
   def empty?
-    column_size == 0 || row_size == 0
+    column_count == 0 || row_count == 0
   end
 
   #
@@ -651,9 +653,9 @@ class Matrix
   def orthogonal?
     Matrix.Raise ErrDimensionMismatch unless square?
     rows.each_with_index do |row, i|
-      column_size.times do |j|
+      column_count.times do |j|
         s = 0
-        row_size.times do |k|
+        row_count.times do |k|
           s += row[k] * rows[k][j]
         end
         return false unless s == (i == j ? 1 : 0)
@@ -668,7 +670,7 @@ class Matrix
   #
   def permutation?
     Matrix.Raise ErrDimensionMismatch unless square?
-    cols = Array.new(column_size)
+    cols = Array.new(column_count)
     rows.each_with_index do |row, i|
       found = false
       row.each_with_index do |e, j|
@@ -709,7 +711,7 @@ class Matrix
   # Returns +true+ is this is a square matrix.
   #
   def square?
-    column_size == row_size
+    column_count == row_count
   end
 
   #
@@ -731,9 +733,9 @@ class Matrix
   def unitary?
     Matrix.Raise ErrDimensionMismatch unless square?
     rows.each_with_index do |row, i|
-      column_size.times do |j|
+      column_count.times do |j|
         s = 0
-        row_size.times do |k|
+        row_count.times do |k|
           s += row[k].conj * rows[k][j]
         end
         return false unless s == (i == j ? 1 : 0)
@@ -765,13 +767,13 @@ class Matrix
   #
   def ==(other)
     return false unless Matrix === other &&
-                        column_size == other.column_size # necessary for empty matrices
+                        column_count == other.column_count # necessary for empty matrices
     rows == other.rows
   end
 
   def eql?(other)
     return false unless Matrix === other &&
-                        column_size == other.column_size # necessary for empty matrices
+                        column_count == other.column_count # necessary for empty matrices
     rows.eql? other.rows
   end
 
@@ -781,7 +783,7 @@ class Matrix
   # There should be no good reason to do this since Matrices are immutable.
   #
   def clone
-    new_matrix @rows.map(&:dup), column_size
+    new_matrix @rows.map(&:dup), column_count
   end
 
   #
@@ -807,22 +809,22 @@ class Matrix
       rows = @rows.collect {|row|
         row.collect {|e| e * m }
       }
-      return new_matrix rows, column_size
+      return new_matrix rows, column_count
     when Vector
       m = self.class.column_vector(m)
       r = self * m
       return r.column(0)
     when Matrix
-      Matrix.Raise ErrDimensionMismatch if column_size != m.row_size
+      Matrix.Raise ErrDimensionMismatch if column_count != m.row_count
 
-      rows = Array.new(row_size) {|i|
-        Array.new(m.column_size) {|j|
-          (0 ... column_size).inject(0) do |vij, k|
+      rows = Array.new(row_count) {|i|
+        Array.new(m.column_count) {|j|
+          (0 ... column_count).inject(0) do |vij, k|
             vij + self[i, k] * m[k, j]
           end
         }
       }
-      return new_matrix rows, m.column_size
+      return new_matrix rows, m.column_count
     else
       return apply_through_coercion(m, __method__)
     end
@@ -845,14 +847,14 @@ class Matrix
       return apply_through_coercion(m, __method__)
     end
 
-    Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size
+    Matrix.Raise ErrDimensionMismatch unless row_count == m.row_count and column_count == m.column_count
 
-    rows = Array.new(row_size) {|i|
-      Array.new(column_size) {|j|
+    rows = Array.new(row_count) {|i|
+      Array.new(column_count) {|j|
         self[i, j] + m[i, j]
       }
     }
-    new_matrix rows, column_size
+    new_matrix rows, column_count
   end
 
   #
@@ -872,14 +874,14 @@ class Matrix
       return apply_through_coercion(m, __method__)
     end
 
-    Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size
+    Matrix.Raise ErrDimensionMismatch unless row_count == m.row_count and column_count == m.column_count
 
-    rows = Array.new(row_size) {|i|
-      Array.new(column_size) {|j|
+    rows = Array.new(row_count) {|i|
+      Array.new(column_count) {|j|
         self[i, j] - m[i, j]
       }
     }
-    new_matrix rows, column_size
+    new_matrix rows, column_count
   end
 
   #
@@ -894,7 +896,7 @@ class Matrix
       rows = @rows.collect {|row|
         row.collect {|e| e / other }
       }
-      return new_matrix rows, column_size
+      return new_matrix rows, column_count
     when Matrix
       return self * other.inverse
     else
@@ -910,12 +912,12 @@ class Matrix
   #
   def inverse
     Matrix.Raise ErrDimensionMismatch unless square?
-    self.class.I(row_size).send(:inverse_from, self)
+    self.class.I(row_count).send(:inverse_from, self)
   end
   alias inv inverse
 
   def inverse_from(src) # :nodoc:
-    last = row_size - 1
+    last = row_count - 1
     a = src.to_a
 
     0.upto(last) do |k|
@@ -974,7 +976,7 @@ class Matrix
       x = self
       if other <= 0
         x = self.inverse
-        return self.class.identity(self.column_size) if other == 0
+        return self.class.identity(self.column_count) if other == 0
         other = -other
       end
       z = nil
@@ -1008,7 +1010,7 @@ class Matrix
   def determinant
     Matrix.Raise ErrDimensionMismatch unless square?
     m = @rows
-    case row_size
+    case row_count
       # Up to 4x4, give result using Laplacian expansion by minors.
       # This will typically be faster, as well as giving good results
       # in case of Floats
@@ -1057,7 +1059,7 @@ class Matrix
   # intermediate results with better precision.
   #
   def determinant_bareiss
-    size = row_size
+    size = row_count
     last = size - 1
     a = to_a
     no_pivot = Proc.new{ return 0 }
@@ -1106,8 +1108,8 @@ class Matrix
     # We currently use Bareiss' multistep integer-preserving gaussian elimination
     # (see comments on determinant)
     a = to_a
-    last_column = column_size - 1
-    last_row = row_size - 1
+    last_column = column_count - 1
+    last_row = row_count - 1
     pivot_row = 0
     previous_pivot = 1
     0.upto(last_column) do |k|
@@ -1152,7 +1154,7 @@ class Matrix
   #
   def trace
     Matrix.Raise ErrDimensionMismatch unless square?
-    (0...column_size).inject(0) do |tr, i|
+    (0...column_count).inject(0) do |tr, i|
       tr + @rows[i][i]
     end
   end
@@ -1169,8 +1171,8 @@ class Matrix
   #        2 4 6
   #
   def transpose
-    return self.class.empty(column_size, 0) if row_size.zero?
-    new_matrix @rows.transpose, row_size
+    return self.class.empty(column_count, 0) if row_count.zero?
+    new_matrix @rows.transpose, row_count
   end
   alias t transpose
 
@@ -1286,7 +1288,7 @@ class Matrix
   # Returns an array of the row vectors of the matrix.  See Vector.
   #
   def row_vectors
-    Array.new(row_size) {|i|
+    Array.new(row_count) {|i|
       row(i)
     }
   end
@@ -1295,7 +1297,7 @@ class Matrix
   # Returns an array of the column vectors of the matrix.  See Vector.
   #
   def column_vectors
-    Array.new(column_size) {|i|
+    Array.new(column_count) {|i|
       column(i)
     }
   end
@@ -1331,7 +1333,7 @@ class Matrix
   #
   def to_s
     if empty?
-      "#{self.class}.empty(#{row_size}, #{column_size})"
+      "#{self.class}.empty(#{row_count}, #{column_count})"
     else
       "#{self.class}[" + @rows.collect{|row|
         "[" + row.collect{|e| e.to_s}.join(", ") + "]"
@@ -1344,7 +1346,7 @@ class Matrix
   #
   def inspect
     if empty?
-      "#{self.class}.empty(#{row_size}, #{column_size})"
+      "#{self.class}.empty(#{row_count}, #{column_count})"
     else
       "#{self.class}#{@rows.inspect}"
     end
diff --git a/lib/matrix/eigenvalue_decomposition.rb b/lib/matrix/eigenvalue_decomposition.rb
index 55e41aaf7c..ab5888ff37 100644
--- a/lib/matrix/eigenvalue_decomposition.rb
+++ b/lib/matrix/eigenvalue_decomposition.rb
@@ -20,7 +20,7 @@ class Matrix
       # @v: Array for internal storage of eigenvectors.
       # @h: Array for internal storage of nonsymmetric Hessenberg form.
       raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix)
-      @size = a.row_size
+      @size = a.row_count
       @d = Array.new(@size, 0)
       @e = Array.new(@size, 0)
 
diff --git a/lib/matrix/lup_decomposition.rb b/lib/matrix/lup_decomposition.rb
index 8f5aac2e5a..cf3897e922 100644
--- a/lib/matrix/lup_decomposition.rb
+++ b/lib/matrix/lup_decomposition.rb
@@ -19,7 +19,7 @@ class Matrix
     include Matrix::ConversionHelper
 
     def l
-      Matrix.build(@row_size, @col_size) do |i, j|
+      Matrix.build(@row_count, @column_count) do |i, j|
         if (i > j)
           @lu[i][j]
         elsif (i == j)
@@ -33,7 +33,7 @@ class Matrix
     # Returns the upper triangular factor +U+
 
     def u
-      Matrix.build(@col_size, @col_size) do |i, j|
+      Matrix.build(@column_count, @column_count) do |i, j|
         if (i <= j)
           @lu[i][j]
         else
@@ -45,9 +45,9 @@ class Matrix
     # Returns the permutation matrix +P+
 
     def p
-      rows = Array.new(@row_size){Array.new(@col_size, 0)}
+      rows = Array.new(@row_count){Array.new(@column_count, 0)}
       @pivots.each_with_index{|p, i| rows[i][p] = 1}
-      Matrix.send :new, rows, @col_size
+      Matrix.send :new, rows, @column_count
     end
 
     # Returns +L+, +U+, +P+ in an array
@@ -64,7 +64,7 @@ class Matrix
     # Returns +true+ if +U+, and hence +A+, is singular.
 
     def singular? ()
-      @col_size.times do |j|
+      @column_count.times do |j|
         if (@lu[j][j] == 0)
           return true
         end
@@ -76,11 +76,11 @@ class Matrix
     # from the factorization.
 
     def det
-      if (@row_size != @col_size)
+      if (@row_count != @column_count)
         Matrix.Raise Matrix::ErrDimensionMismatch unless square?
       end
       d = @pivot_sign
-      @col_size.times do |j|
+      @column_count.times do |j|
         d *= @lu[j][j]
       end
       d
@@ -96,24 +96,24 @@ class Matrix
         Matrix.Raise Matrix::ErrNotRegular, "Matrix is singular."
       end
       if b.is_a? Matrix
-        if (b.row_size != @row_size)
+        if (b.row_count != @row_count)
           Matrix.Raise Matrix::ErrDimensionMismatch
         end
 
         # Copy right hand side with pivoting
-        nx = b.column_size
+        nx = b.column_count
         m = @pivots.map{|row| b.row(row).to_a}
 
         # Solve L*Y = P*b
-        @col_size.times do |k|
-          (k+1).upto(@col_size-1) do |i|
+        @column_count.times do |k|
+          (k+1).upto(@column_count-1) do |i|
             nx.times do |j|
               m[i][j] -= m[k][j]*@lu[i][k]
             end
           end
         end
         # Solve U*m = Y
-        (@col_size-1).downto(0) do |k|
+        (@column_count-1).downto(0) do |k|
           nx.times do |j|
             m[k][j] = m[k][j].quo(@lu[k][k])
           end
@@ -126,7 +126,7 @@ class Matrix
         Matrix.send :new, m, nx
       else # same algorithm, specialized for simpler case of a vector
         b = convert_to_array(b)
-        if (b.size != @row_size)
+        if (b.size != @row_count)
           Matrix.Raise Matrix::ErrDimensionMismatch
         end
 
@@ -134,13 +134,13 @@ class Matrix
         m = b.values_at(*@pivots)
 
         # Solve L*Y = P*b
-        @col_size.times do |k|
-          (k+1).upto(@col_size-1) do |i|
+        @column_count.times do |k|
+          (k+1).upto(@column_count-1) do |i|
             m[i] -= m[k]*@lu[i][k]
           end
         end
         # Solve U*m = Y
-        (@col_size-1).downto(0) do |k|
+        (@column_count-1).downto(0) do |k|
           m[k] = m[k].quo(@lu[k][k])
           k.times do |i|
             m[i] -= m[k]*@lu[i][k]
@@ -154,28 +154,28 @@ class Matrix
       raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix)
       # Use a "left-looking", dot-product, Crout/Doolittle algorithm.
       @lu = a.to_a
-      @row_size = a.row_size
-      @col_size = a.column_size
-      @pivots = Array.new(@row_size)
-      @row_size.times do |i|
+      @row_count = a.row_count
+      @column_count = a.column_count
+      @pivots = Array.new(@row_count)
+      @row_count.times do |i|
          @pivots[i] = i
       end
       @pivot_sign = 1
-      lu_col_j = Array.new(@row_size)
+      lu_col_j = Array.new(@row_count)
 
       # Outer loop.
 
-      @col_size.times do |j|
+      @column_count.times do |j|
 
         # Make a copy of the j-th column to localize references.
 
-        @row_size.times do |i|
+        @row_count.times do |i|
           lu_col_j[i] = @lu[i][j]
         end
 
         # Apply previous transformations.
 
-        @row_size.times do |i|
+        @row_count.times do |i|
           lu_row_i = @lu[i]
 
           # Most of the time is spent in the following dot product.
@@ -192,13 +192,13 @@ class Matrix
         # Find pivot and exchange if necessary.
 
         p = j
-        (j+1).upto(@row_size-1) do |i|
+        (j+1).upto(@row_count-1) do |i|
           if (lu_col_j[i].abs > lu_col_j[p].abs)
             p = i
           end
         end
         if (p != j)
-          @col_size.times do |k|
+          @column_count.times do |k|
             t = @lu[p][k]; @lu[p][k] = @lu[j][k]; @lu[j][k] = t
           end
           k = @pivots[p]; @pivots[p] = @pivots[j]; @pivots[j] = k
@@ -207,8 +207,8 @@ class Matrix
 
         # Compute multipliers.
 
-        if (j < @row_size && @lu[j][j] != 0)
-          (j+1).upto(@row_size-1) do |i|
+        if (j < @row_count && @lu[j][j] != 0)
+          (j+1).upto(@row_count-1) do |i|
             @lu[i][j] = @lu[i][j].quo(@lu[j][j])
           end
         end
-- 
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