tc_multiarray.rb

# multiarray - Lazy multi-dimensional arrays for Ruby
# Copyright (C) 2010 Jan Wedekind
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

require 'test/unit'
begin
  require 'rubygems'
rescue LoadError
end
Kernel::require 'multiarray'

class TC_MultiArray < Test::Unit::TestCase

  O = Hornetseye::OBJECT
  B = Hornetseye::BOOL
  I = Hornetseye::INT
  C = Hornetseye::INTRGB
  X = Hornetseye::DCOMPLEX
  S = Hornetseye::Sequence
  M = Hornetseye::MultiArray
  Malloc = Hornetseye::Malloc

  def C( *args )
    Hornetseye::RGB *args
  end

  def X( *args )
    Complex *args
  end
  
  def S( *args )
    Hornetseye::Sequence *args
  end

  def M( *args )
    Hornetseye::MultiArray *args
  end

  def sum( *args, &action )
    Hornetseye::sum *args, &action
  end

  def argmin( *args, &action )
    Hornetseye::argmin *args, &action
  end

  def argmax( *args, &action )
    Hornetseye::argmax *args, &action
  end

  def finalise( *args, &action )
    Hornetseye::finalise *args, &action
  end

  def setup
  end

  def teardown
  end

  def test_multiarray_inspect
    assert_equal 'MultiArray(OBJECT,2)', M(O,2).inspect
    assert_equal 'MultiArray(OBJECT,2)', S(S(O)).inspect
  end

  def test_multiarray_to_s
    assert_equal 'MultiArray(OBJECT,2)', M(O,2).to_s
    assert_equal 'MultiArray(OBJECT,2)', S(S(O)).to_s
  end

  def test_multiarray_at
    assert_equal [ [ 1, 2, 3 ], [ 4, 5, 6 ] ],
                 M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].to_a
    assert_equal [ [ 1, 2, 3 ], [ 4, 5, 6 ] ],
                 M(O, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].to_a
    assert_equal O, M[ [ :a ] ].typecode
    assert_equal B, M[ [ false ], [ true ] ].typecode
    assert_equal I, M[ [ -2 ** 31, 2 ** 31 - 1 ] ].typecode
  end

  def test_multiarray_indgen
    assert_equal M(I, 2)[ [ 0, 1, 2 ], [ 3, 4, 5 ] ],
                 M(I, 2).indgen(3, 2)
    assert_equal M(I, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ],
                 M(I, 2).indgen(3, 2, 1)
    assert_equal M(I, 2)[ [ 0, 2, 4 ], [ 6, 8, 10 ] ],
                 M(I, 2).indgen(3, 2, 0, 2)
    assert_equal M(I, 2)[ [ 1, 3, 5 ], [ 7, 9, 11 ] ],
                 M(I, 2).indgen(3, 2, 1, 2)
    assert_equal M(C, 2)[ [ C( 1, 2, 3 ), C( 2, 2, 2 ) ],
                          [ C( 3, 2, 1 ), C( 4, 2, 0 ) ] ],
                 M(C, 2).indgen(2, 2, C( 1, 2, 3 ), C( 1, 0, -1 ))
  end

  def test_inspect
    assert_equal "MultiArray(OBJECT,2):\n[ [ :a, 2, 3 ],\n  [ 4, 5, 6 ] ]",
                 M[ [ :a, 2, 3 ], [ 4, 5, 6 ] ].inspect
    assert_equal "MultiArray(UBYTE,3):\n" +
                 "[ [ [ 0, 1, 2, 3 ],\n" +
                 "    [ 4, 5, 6, 7 ],\n" +
                 "    [ 8, 9, 10, 11 ] ],\n" +
                 "  [ [ 12, 13, 14, 15 ],\n" +
                 "    [ 16, 17, 18, 19 ],\n" +
                 "    [ 20, 21, 22, 23 ] ] ]",
                 M[ [ [ 0, 1, 2, 3 ],
                      [ 4, 5, 6, 7 ],
                      [ 8, 9, 10, 11 ] ],
                    [ [ 12, 13, 14, 15 ],
                      [ 16, 17, 18, 19 ],
                      [ 20, 21, 22, 23 ] ] ].inspect
  end

  def test_dup
    m = M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    v = m.dup
    v[ 2, 1 ] = 0
    assert_equal M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ], m
  end

  def test_typecode
    assert_equal O, M(O, 2).new(3, 2).typecode
    assert_equal I, M(I, 2).new(3, 2).typecode
    assert_equal C, M(C, 2).new(3, 2).typecode
  end

  def test_dimension
    assert_equal 2, M(O, 2).new(3, 2).dimension
    assert_equal 2, M(I, 2).new(3, 2).dimension
    assert_equal 2, M(C, 2).new(3, 2).dimension
  end

  def test_shape
    assert_equal [ 3, 2 ], M(O, 2).new(3, 2).shape
  end

  def test_size
    assert_equal 6, M(O, 2).new(3, 2).size
  end

  def test_import
    str = "\001\000\000\000\002\000\000\000\003\000\000\000" +
          "\004\000\000\000\005\000\000\000\006\000\000\000"
    assert_equal [ [ 1, 2, 3 ], [ 4, 5, 6 ] ], M.import( I, str, 3, 2 ).to_a
    m = Malloc.new str.bytesize
    m.write str
    assert_equal [ [ 1, 2, 3 ], [ 4, 5, 6 ] ], M.import( I, m, 3, 2 ).to_a
  end

  def test_at_assign
    [ M(O, 2), M(I, 2) ].each do |t|
      m = t.new 3, 2
      for j in 0 ... 2
        for i in 0 ... 3
          assert_equal j * 3 + i + 1, m[ j ][ i ] = j * 3 + i + 1
          assert_equal j * 3 + i + 1, m[ i, j ] = j * 3 + i + 1
        end
      end
      for j in 0 ... 2
        for i in 0 ... 3
          assert_equal j * 3 + i + 1, m[ j ][ i ]
          assert_equal j * 3 + i + 1, m[ i, j ]
        end
      end
      assert_raise(RuntimeError) { m[ -1 ] }
      assert_raise(RuntimeError) { m[ 2 ] }
      assert_nothing_raised { m[ 0 ] }
      assert_nothing_raised { m[ 1 ] }
      assert_raise(RuntimeError) { m[ -1 ] = 0 }
      assert_raise(RuntimeError) { m[ 2 ] = 0 }
      assert_raise(RuntimeError) { m[ 3, 1 ] }
      assert_raise(RuntimeError) { m[ 3, 1 ]  = 0 }
      assert_raise(RuntimeError) { m[ -1, 1 ] }
      assert_raise(RuntimeError) { m[ -1, 1 ]  = 0 }
      assert_raise(RuntimeError) { m[ 2, -1 ] }
      assert_raise(RuntimeError) { m[ 2, -1 ]  = 0 }
      assert_raise(RuntimeError) { m[ 2, 2 ] }
      assert_raise(RuntimeError) { m[ 2, 2 ]  = 0 }
      assert_nothing_raised { m[ 0, 0 ] }
      assert_nothing_raised { m[ 2, 1 ] }
      assert_raise(RuntimeError) { m[ 0 ] = m }
      assert_raise(RuntimeError) { m[ 0 ] = S[ 0, 1 ] }
      assert_nothing_raised { m[ 0 ] = 0 }
      assert_nothing_raised { m[ 1 ] = 0 }
      assert_nothing_raised { m[ 0 ] = m[ 1 ] }
    end
  end

  def test_slice
    [ M(O, 2), M(I, 2) ].each do |t|
      m = t.indgen(5, 4)[]
      assert_equal [ [ 5, 10 ], [ 6, 11 ], [ 7, 12 ], [ 8, 13 ], [ 9, 14 ] ],
                   m[ 1 .. 2 ].to_a
      assert_equal [ [ 6, 7, 8 ], [ 11, 12, 13 ] ],
                   m[ 1 .. 2 ][ 1 .. 3 ].to_a
      assert_equal [ [ 6, 7, 8 ], [ 11, 12, 13 ] ],
                   m[ 1 .. 3, 1 .. 2 ].to_a
      m[ 1 .. 2 ] = 0
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 0, 0, 0, 0, 0 ],
                     [ 0, 0, 0, 0, 0 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      m[ 1 ... 3 ] = 1
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 1, 1, 1, 1, 1 ],
                     [ 1, 1, 1, 1, 1 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      m[ 1 .. 2 ] = S[ 2, 3, 4, 5, 6 ]
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 2, 3, 4, 5, 6 ],
                     [ 2, 3, 4, 5, 6 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      m[ 1 ... 3 ] = S[ 3, 4, 5, 6, 7 ]
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 3, 4, 5, 6, 7 ],
                     [ 3, 4, 5, 6, 7 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      m[ 1 .. 3, 1 .. 2 ] = 0
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 3, 0, 0, 0, 7 ],
                     [ 3, 0, 0, 0, 7 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      m[ 1 ... 4, 1 ... 3 ] = 1
      assert_equal [ [ 0, 1, 2, 3, 4 ], [ 3, 1, 1, 1, 7 ],
                     [ 3, 1, 1, 1, 7 ], [ 15, 16, 17, 18, 19 ] ], m.to_a
      assert_raise(RuntimeError) { m[ 2 .. 4 ] }
      assert_raise(RuntimeError) { m[ 2 .. 4 ] = 0 }
      assert_raise(RuntimeError) { m[ 2 .. 4 ] = m[ 1 .. 3 ] }
      assert_raise(RuntimeError) { m[ 2 .. 3 ] = m[ 1 .. 3 ] }
      assert_raise(RuntimeError) { m[ 2 ... 5 ] }
      assert_raise(RuntimeError) { m[ 2 ... 5 ] = 0 }
      assert_raise(RuntimeError) { m[ 2 ... 5 ] = m[ 1 ... 4 ] }
      assert_raise(RuntimeError) { m[ 2 ... 4 ] = m[ 1 ... 4 ] }
      assert_raise(RuntimeError) { m[ -1 .. 0 ] }
      assert_raise(RuntimeError) { m[ -1 .. 0 ] = 0 }
      assert_raise(RuntimeError) { m[ -1 .. 0 ] = m[ 0 .. 1 ] }
      assert_raise(RuntimeError) { m[ -1 ... 1 ] }
      assert_raise(RuntimeError) { m[ -1 ... 1 ] = 0 }
      assert_raise(RuntimeError) { m[ -1 ... 1 ] = m[ 0 ... 2 ] }
      assert_nothing_raised { m[ 0 .. 3 ] }
      assert_nothing_raised { m[ 0 .. 3 ] = 0 }
      assert_nothing_raised { m[ 0 .. 3 ] = m[ 0 .. 3 ] }
      assert_nothing_raised { m[ 0 ... 4 ] }
      assert_nothing_raised { m[ 0 ... 4 ] = 0 }
      assert_nothing_raised { m[ 0 ... 4 ] = m[ 0 ... 4 ] }
      assert_raise(RuntimeError) { m[ 1 .. 5, 1 ] }
      assert_raise(RuntimeError) { m[ 1 .. 5, 1 ] = 0 }
      assert_raise(RuntimeError) { m[ 1 .. 5, 1 ] = m[ 0 .. 4, 1 ] }
      assert_raise(RuntimeError) { m[ 1 .. 4, 1 ] = m[ 0 .. 4, 1 ] }
      assert_raise(RuntimeError) { m[ 1 ... 6, 1 ] }
      assert_raise(RuntimeError) { m[ 1 ... 6, 1 ] = 0 }
      assert_raise(RuntimeError) { m[ 1 ... 6, 1 ] = m[ 0 ... 5, 1 ] }
      assert_raise(RuntimeError) { m[ 1 ... 5, 1 ] = m[ 0 ... 5, 1 ] }
      assert_raise(RuntimeError) { m[ -1 .. 3, 1 ] }
      assert_raise(RuntimeError) { m[ -1 .. 3, 1 ] = 0 }
      assert_raise(RuntimeError) { m[ -1 .. 3, 1 ] = m[ 0 .. 4, 1 ] }
      assert_raise(RuntimeError) { m[ -1 ... 3, 1 ] }
      assert_raise(RuntimeError) { m[ -1 ... 3, 1 ] = 0 }
      assert_raise(RuntimeError) { m[ -1 ... 3, 1 ] = m[ 0 ... 4, 1 ] }
      assert_nothing_raised { m[ 0 .. 4, 1 ] }
      assert_nothing_raised { m[ 0 .. 4, 1 ] = 0 }
      assert_nothing_raised { m[ 0 .. 4, 1 ] = m[ 0 .. 4, 0 ] }
      assert_nothing_raised { m[ 0 ... 5, 1 ] }
      assert_nothing_raised { m[ 0 ... 5, 1 ] = 0 }
      assert_nothing_raised { m[ 0 ... 5, 1 ] = m[ 0 ... 5, 0 ] }
      assert_raise(RuntimeError) { m[ 1, 1 .. 4 ] }
      assert_raise(RuntimeError) { m[ 1, 1 .. 4 ] = 0 }
      assert_raise(RuntimeError) { m[ 1, 1 .. 4 ] = m[ 1, 0 .. 3 ] }
      assert_raise(RuntimeError) { m[ 1, 1 .. 3 ] = m[ 1, 0 .. 3 ] }
      assert_raise(RuntimeError) { m[ 1, 1 ... 5 ] }
      assert_raise(RuntimeError) { m[ 1, 1 ... 5 ] = 0 }
      assert_raise(RuntimeError) { m[ 1, 1 ... 5 ] = m[ 1, 0 ... 4 ] }
      assert_raise(RuntimeError) { m[ 1, 1 ... 4 ] = m[ 1, 0 ... 4 ] }
      assert_raise(RuntimeError) { m[ 1, -1 .. 2 ] }
      assert_raise(RuntimeError) { m[ 1, -1 .. 2 ] = 0 }
      assert_raise(RuntimeError) { m[ 1, -1 .. 2 ] = m[ 1, 0 .. 3 ] }
      assert_raise(RuntimeError) { m[ 1, -1 ... 2 ] }
      assert_raise(RuntimeError) { m[ 1, -1 ... 2 ] = 0 }
      assert_raise(RuntimeError) { m[ 1, -1 ... 2 ] = m[ 1, 0 ... 3 ] }
      assert_nothing_raised { m[ 1, 0 .. 3 ] }
      assert_nothing_raised { m[ 1, 0 .. 3 ] = 0 }
      assert_nothing_raised { m[ 1, 0 .. 3 ] = m[ 0, 0 .. 3 ] }
      assert_nothing_raised { m[ 1, 0 ... 4 ] }
      assert_nothing_raised { m[ 1, 0 ... 4 ] = 0 }
      assert_nothing_raised { m[ 1, 0 ... 4 ] = m[ 0, 0 ... 4 ] }
    end
  end

   def test_view
    [ M(O, 2), M(I, 2) ].each do |t|
      m = t[[1, 2, 3], [4, 5, 6]]
      v = m[1, 0 ... 2]
      v[] = 0
      assert_equal [[1, 0, 3], [4, 0, 6]], m.to_a
    end
   end

   def test_transpose
    assert_equal [ [ 1, 4 ], [ 2, 5 ], [ 3, 6 ] ],
                 M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].transpose(1, 0).to_a
    assert_equal [ [ [ 0, 3 ], [ 1, 4 ], [ 2, 5 ] ] ],
                 M(I, 3).indgen(3, 2, 1).transpose(1, 0, 2).to_a
    assert_raise(RuntimeError) { M[[1, 2], [3, 4]].transpose }
    assert_raise(RuntimeError) { M[[1, 2], [3, 4]].transpose 1, 2 }
    assert_raise(RuntimeError) { M[[1, 2], [3, 4]].transpose 0, 0 }
   end

  def test_roll_unroll
    assert_equal [ [ [ 0 ], [ 1 ], [ 2 ] ], [ [ 3 ], [ 4 ], [ 5 ] ] ],
                 M(I, 3).indgen(3, 2, 1).unroll.to_a
    assert_equal [ [ [ 0, 3 ] ], [ [ 1, 4 ] ], [ [ 2, 5 ] ] ],
                 M(I, 3).indgen(3, 2, 1).roll.to_a
  end

  def test_equal
    assert_equal M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ], M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    assert_not_equal M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ],
                     M[ [ 1, 2, 3 ], [ 4, 6, 5 ] ]
    # !!!
    assert_not_equal M[ [ 1, 1 ], [ 1, 1 ] ], 1
    assert_not_equal M[ [ 1, 1 ], [ 1, 1 ] ], S[ 1, 1 ]
  end

  def test_r_g_b
    assert_equal M[ [ 1, 4 ], [ 5, 6 ] ], M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].r
    assert_equal M[ [ 2, 4 ], [ 5, 6 ] ], M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].g
    assert_equal M[ [ 3, 4 ], [ 5, 6 ] ], M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].b
    assert_equal M[ [ C( 3, 2, 1 ), 4 ], [ 5, 6 ] ],
                 M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].swap_rgb
    assert_equal M[ [ 1, 4 ], [ 5, 6 ] ],
                 M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].collect { |x| x.r }
    assert_equal M[ [ 2, 4 ], [ 5, 6 ] ],
                 M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].collect { |x| x.g }
    assert_equal M[ [ 3, 4 ], [ 5, 6 ] ],
                 M[ [ C( 1, 2, 3 ), 4 ], [ 5, 6 ] ].collect { |x| x.b }
  end

  def test_real_imag
    assert_equal M[ [ 1, 3 ], [ 4, 5 ] ], M[ [ X( 1, 2 ), 3 ], [ 4, 5 ] ].real
    assert_equal M[ [ 2, 0 ], [ 0, 0 ] ], M[ [ X( 1, 2 ), 3 ], [ 4, 5 ] ].imag
    assert_equal M[ [ 1, 3 ], [ 4, 5 ] ],
                 M[ [ X( 1, 2 ), 3 ], [ 4, 5 ] ].collect { |x| x.real }
    assert_equal M[ [ 2, 0 ], [ 0, 0 ] ],
                 M[ [ X( 1, 2 ), 3 ], [ 4, 5 ] ].collect { |x| x.imag }
  end

  def test_inject
    assert_equal 21, M[[1, 2, 3], [4, 5, 6]].inject { |a,b| a + b }
    assert_equal 21, M[[1, 2, 3], [4, 5, 6]].inject(:+)
    assert_equal 28, M[[1, 2, 3], [4, 5, 6]].inject(7) { |a,b| a + b }
    assert_equal 28, M[[1, 2, 3], [4, 5, 6]].inject(7, :+)
  end

  def test_collect
    assert_equal M[ [ 2, 3, 4 ], [ 5, 6, 7 ] ], 
                 M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].collect { |x| x + 1 }
    assert_equal M[ [ 6 ] ], M[ [ C( 1, 2, 3 ) ] ].collect { |x| x.r + x.g + x.b }
  end

  def test_each
    a = []
    M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].each { |x| a << x }
    assert_equal [ 1, 2, 3, 4, 5, 6 ], a
  end

  def test_sum
    m = M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    assert_equal 21, sum { |i,j| m[ i, j ] }
    assert_equal [ 5, 7, 9 ], sum { |i| m[ i ] }.to_a
    assert_equal [ 6, 15 ], finalise { |j| sum { |i| m[ i, j ] } }.to_a
    assert_equal [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ], sum { || m }.to_a
  end

  def test_argmax
    assert_equal [[1, 1, 0]],
                 argmax { |i| M[[1, 2, 3], [4, 3, 2]][i] }.collect { |x| x.to_a }
    assert_equal [0, 1], argmax { |i,j| M[[1, 2, 3], [4, 3, 0]][i,j] }
    m = M[[[1,0,3,4],[5,4,3,2],[1,2,1,0]],[[3,2,4,1],[7,4,8,2],[2,1,9,1]]]
    assert_equal [[[1, 1, 1, 0], [1, 0, 1, 0], [1, 0, 1, 1]]],
                 argmax { |i| m[i] }.collect { |x| x.to_a }
    assert_equal [[1, 1, 2, 0], [1, 0, 1, 0]],
                 argmax { |i,j| m[i,j] }.collect { |x| x.to_a }
    assert_equal [2, 2, 1], argmax { |i,j,k| m[i,j,k] }
  end

  def test_min
    assert_equal 1, M[ [ 5, 3, 7 ], [ 2, 1, 6 ] ].min
  end

  def test_max
    assert_equal 7, M[ [ 5, 3, 7 ], [ 2, 1, 6 ] ].max
  end

  def test_sum
    assert_equal 24, M[ [ 5, 3, 7 ], [ 2, 1, 6 ] ].sum
  end

  def test_range
    assert_equal 1 .. 7, M[ [ 5, 3, 7 ], [ 2, 1, 6 ] ].range
  end

  def test_diagonal
    assert_equal S[ 'b1a2', 'c1b2a3', 'c2b3' ],
                 M[ [ 'a1', 'a2', 'a3' ],
                    [ 'b1', 'b2', 'b3' ],
                    [ 'c1', 'c2', 'c3' ] ].diagonal { |a,b| a + b }
    assert_equal S[ 'c1b2a3', 'c2b3a4', 'c3b4' ],
                 M[ [ 'a1', 'a2', 'a3', 'a4' ],
                    [ 'b1', 'b2', 'b3', 'b4' ],
                    [ 'c1', 'c2', 'c3', 'c4' ] ].diagonal { |a,b| a + b }
    assert_equal S[ 'xb1a2', 'xc1b2a3', 'xd1c2b3', 'xd2c3' ],
                 M[ [ 'a1', 'a2', 'a3' ],
                    [ 'b1', 'b2', 'b3' ],
                    [ 'c1', 'c2', 'c3' ],
                    [ 'd1', 'd2', 'd3' ] ].diagonal( 'x' ) { |a,b| a + b }
    assert_equal S(I)[ 4, 12, 21, 18 ],
                 M(I, 2).indgen(3, 4).diagonal { |a,b| a + b }
    assert_equal S(I)[ 4, 12, 12 ],
                 M(I, 2).indgen(3, 3).diagonal { |a,b| a + b }
    assert_equal S(I)[ 4, 6 ],
                 M(I, 2).indgen(3, 2).diagonal { |a,b| a + b }
  end

  def test_convolve
    f = M[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
    s = S[ 1, 2, 3 ]
    assert_equal M[ [ 5, 6, 0 ], [ 8, 9, 0 ], [ 0, 0, 0 ] ],
                 M[ [ 1, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ].convolve( f )
    assert_equal M[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ],
                 M[ [ 0, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 0 ] ].convolve( f )
    assert_equal M[ [ 0, 0, 0 ], [ 1, 2, 3 ], [ 4, 5, 6 ] ],
                 M[ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 1, 0 ] ].convolve( f )
    assert_equal M[ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 1, 2, 3 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ],
                 M[ [ 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0 ] ].
                 convolve( s )
    assert_raise(RuntimeError) { S[ 1, 2, 3 ].convolve f }
  end

  def test_erode
    assert_equal [ [ 0, 0, 0 ], [ 0, -1, -1 ], [ 0, -1, -1 ] ],
                 M[ [ 1, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -1 ] ].erode.to_a
  end

  def test_dilate
    assert_equal [ [ 1, 1, 0 ], [ 1, 1, 0 ], [ 0, 0, 0 ] ],
                 M[ [ 1, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -1 ] ].dilate.to_a
  end

  def test_sobel
    m = M[ [ 0, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 0 ] ]
    assert_equal [ [ 1, 0, -1, 0 ], [ 2, 0, -2, 0 ], [ 1, 0, -1, 0 ] ],
                 m.sobel( 0 ).to_a
    assert_equal [ [ 1, 2, 1, 0 ], [ 0, 0, 0, 0 ], [ -1, -2, -1, 0 ] ],
                 m.sobel( 1 ).to_a
  end

  def test_histogram
    assert_equal [ 0, 1, 1, 2, 0 ],
                 M[ [ 1, 2 ], [ 3, 3 ] ].histogram( 5, :weight => 1 ).to_a
    assert_equal [ [ 1, 0 ], [ 1, 1 ] ],
                 M[ [ 0, 0 ], [ 0, 1 ], [ 1, 1 ] ].
                 histogram( 2, 2, :weight => 1 ).to_a
    assert_equal [ [ 1, 0 ], [ 1, 1 ] ],
                 [ S[ 0, 0, 1 ], S[ 0, 1, 1 ] ].
                 histogram( 2, 2, :weight => 1 ).to_a
    assert_equal [ [ [ 0, 1 ], [ 1, 0 ] ] ],
                 S[ C( 1, 0, 0 ), C( 0, 1, 0 ) ].
                 histogram( 2, 2, 1, :weight => 1 ).to_a
    assert_raise(RuntimeError) { S[ 1, 2, 3 ].histogram 4, 4 }
    assert_raise(RuntimeError) { M[ [ -1, 0 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { M[ [ 0, -1 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { M[ [ 3, 0 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { M[ [ 0, 2 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { [ S[ -1, 0 ], S[ 0, 1 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { [ S[ 0, 3 ], S[ 0, 1 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { [ S[ 0, 0, 1 ], S[ 0, 1 ] ].histogram 3, 2 }
    assert_raise(RuntimeError) { [ S[ 0, 1 ], S[ 0, 1 ] ].histogram 3 }
  end

  def test_lut
    assert_equal M[ [ 1, 2 ], [ 3, 1 ] ],
                 M[ [ 0, 1 ], [ 2, 0 ] ].lut( S[ 1, 2, 3, 4 ] )
    assert_equal M[ 1, 3, 4 ],
                 M[ [ 0, 0 ], [ 0, 1 ], [ 1, 1 ] ].lut( M[ [ 1, 2 ], [ 3, 4 ] ] )
    assert_equal M[ 1, 3, 4 ],
                 [ S[ 0, 0, 1 ], S[ 0, 1, 1 ] ].lut( M[ [ 1, 2 ], [ 3, 4 ] ] )
    assert_equal M[ [ 3, 4 ], [ 1, 2 ] ],
                 M[ [ 1 ], [ 0 ] ].lut( M[ [ 1, 2 ], [ 3, 4 ] ] )
    assert_equal S[ 2, 3 ], S[ C( 1, 0, 0 ), C( 0, 1, 0 ) ].
                 lut( M[ [ [ 1, 2 ], [ 3, 4 ] ] ] )
    assert_raise(RuntimeError) { S[ 0, 1, 2 ].lut M[ [ 1, 2 ], [ 3, 4 ] ] }
    assert_raise(RuntimeError) { M[ [ -1, 0 ] ].lut M[ [ 1, 2 ] ] }
    assert_raise(RuntimeError) { M[ [ 0, -1 ] ].lut M[ [ 1, 2 ] ] }
    assert_raise(RuntimeError) { M[ [ 2, 0 ] ].lut M[ [ 1, 2 ] ] }
    assert_raise(RuntimeError) { M[ [ 0, 1 ] ].lut M[ [ 1, 2 ] ] }
    assert_raise(RuntimeError) { M[ [ 1 ], [ 2 ] ].lut M[ [ 1, 2 ], [ 3, 4 ] ] }
    assert_raise(RuntimeError) { [ S[ -1, 0 ], S[ 0, 1 ] ].
                                   lut M[ [ 1, 2 ], [ 3, 4 ] ] }
    assert_raise(RuntimeError) { [ S[ 0, 0 ], S[ 0, 2 ] ].
                                   lut M[ [ 1, 2 ], [ 3, 4 ] ] }
    assert_raise(RuntimeError) { [ S[ 0, 0, 1 ], S[ 0, 1 ] ].
                                   lut M[ [ 1, 2 ], [ 3, 4 ] ] }
    assert_raise(RuntimeError) { [ S[ 0, 1 ], S[ 0, 1 ] ].lut S[ 1, 2 ] }
  end

  def test_warp
    [O, I].each do |t1|
      [O, I].each do |t2|
        z = t1.default
        assert_equal M(t1, 2)[ [ 1, 2, z ], [ 3, 4, z ], [ z, z, z ] ],
                     M(t1, 2)[ [ 1, 2 ], [ 3, 4 ] ].
                     warp( M(t2, 2)[ [ 0, 1, 2 ], [ 0, 1, 2 ], [ 0, 1, 2 ] ],
                           M(t2, 2)[ [ 0, 0, 0 ], [ 1, 1, 1 ], [ 2, 2, 2 ] ] )
      end
    end
  end

  def test_flip
    [ O, I ].each do |t|
      assert_equal M(t, 2)[ [ 3, 2, 1 ], [ 6, 5, 4 ] ],
                   M(t, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].flip( 0 )
      assert_equal M(t, 2)[ [ 4, 5, 6 ], [ 1, 2, 3 ] ],
                   M(t, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].flip( 1 )
      assert_equal M(t, 2)[ [ 6, 5, 4 ], [ 3, 2, 1 ] ],
                   M(t, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ].flip( 0, 1 )
    end
  end

  def test_shift
    [ O, I ].each do |t|
      assert_equal M(t, 2)[ [ 4, 3 ], [ 2, 1 ] ],
                   M(t, 2)[ [ 1, 2 ], [ 3, 4 ] ].shift( 1, 1 )
    end
  end

  def test_downsample
    [ O, I ].each do |t|
      assert_equal M(t, 2)[ [ 2 ], [ 6 ] ],
                   M(t, 2)[ [ 1, 2, 3 ], [ 5, 6, 7 ] ].downsample( 2, 1 )
      assert_equal M(t, 2)[ [ 1, 3 ], [ 5, 7 ] ],
                   M(t, 2)[ [ 1, 2, 3 ], [ 5, 6, 7 ] ].
                   downsample( 2, 1, :offset => [ 0, 0 ] )
    end
  end

  def test_zero
    assert_equal M[ [ false, true ], [ true, false ] ],
                 M[ [ -1, 0 ], [ 0, 1 ] ].zero?
  end

  def test_nonzero
    assert_equal M[ [ true, false ], [ false, true ] ],
                 M[ [ -1, 0 ], [ 0, 1 ] ].nonzero?
  end

  def test_not
    assert_equal [ [ true, false ], [ false, true ] ],
                 M[ [ false, true ], [ true, false ] ].not.to_a
    assert_equal [ [ true, false ], [ false, true ] ],
                 M[ [ 0, 1 ], [ 2, 0 ] ].not.to_a
  end

  def test_and
    assert_equal [ [ false, false ] ], M[ [ false, true ] ].and( false ).to_a
    assert_equal [ [ false, false ] ], false.and( M[ [ false, true ] ] ).to_a
    assert_equal [ [ false, true ] ], M[ [ false, true ] ].and( true ).to_a
    assert_equal [ [ false, true ] ], true.and( M[ [ false, true ] ] ).to_a
    assert_equal [ [ false, false ], [ false, true ] ],
                 M[ [ false, true ], [ false, true ] ].
                 and( M[ [ false, false ], [ true, true ] ] ).to_a
    assert_equal [ [ false, false ], [ true, false ] ],
                 M[ [ false, true ], [ true, false ] ].
                 and( S[ false, true ] ).to_a
  end

  def test_or
    assert_equal [ [ false, true ] ], M[ [ false, true ] ].or( false ).to_a
    assert_equal [ [ false, true ] ], false.or( M[ [ false, true ] ] ).to_a
    assert_equal [ [ true, true ] ], M[ [ false, true ] ].or( true ).to_a
    assert_equal [ [ true, true ] ], true.or( M[ [ false, true ] ] ).to_a
    assert_equal [ [ false, true ], [ true, true ] ],
                 M[ [ false, true ], [ false, true ] ].
                 or( M[ [ false, false ], [ true, true ] ] ).to_a
    assert_equal [ [ false, true ], [ true, true ] ],
                 M[ [ false, true ], [ true, false ] ].
                 or( S[ false, true ] ).to_a
  end

  def test_bitwise_not
    assert_equal [ [ 255, 254 ], [ 253, 252 ] ],
                 ( ~M[ [ 0, 1 ], [ 2, 3 ] ] ).to_a
    assert_equal [ [ 0, -1 ], [ -2, -3 ] ],
                 ( ~M[ [ -1, 0 ], [ 1, 2 ] ] ).to_a
  end

  def test_bitwise_and
    assert_equal [ [ 0, 1 ], [ 0, 1 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] & 1 ).to_a
    assert_equal [ [ 0, 1 ], [ 0, 1 ] ], ( 1 & M[ [ 0, 1 ], [ 2, 3 ] ] ).to_a
    assert_equal [ [ 0, 1 ], [ 0, 2 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] &
                                           M[ [ 4, 3 ], [ 1, 2 ] ] ).to_a
  end

  def test_bitwise_or
    assert_equal [ [ 1, 1 ], [ 3, 3 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] | 1 ).to_a
    assert_equal [ [ 1, 1 ], [ 3, 3 ] ], ( 1 | M[ [ 0, 1 ], [ 2, 3 ] ] ).to_a
    assert_equal [ [ 4, 3 ], [ 3, 3 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] |
                                           M[ [ 4, 3 ], [ 1, 2 ] ] ).to_a
  end

  def test_bitwise_xor
    assert_equal [ [ 1, 0 ], [ 3, 2 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] ^ 1 ).to_a
    assert_equal [ [ 1, 0 ], [ 3, 2 ] ], ( 1 ^ M[ [ 0, 1 ], [ 2, 3 ] ] ).to_a
    assert_equal [ [ 4, 2 ], [ 3, 1 ] ], ( M[ [ 0, 1 ], [ 2, 3 ] ] ^
                                           M[ [ 4, 3 ], [ 1, 2 ] ] ).to_a
  end

  def test_shl
    assert_equal [ [ 2, 4 ], [ 6, 8 ] ], ( M[ [ 1, 2 ], [ 3, 4 ] ] << 1 ).to_a
    assert_equal [ [ 6, 12 ], [ 24, 48 ] ],
                 ( 3 << M[ [ 1, 2 ], [ 3, 4 ] ] ).to_a
    assert_equal [ [ 8, 8 ], [ 6, 4 ] ],
                 ( M[ [ 1, 2 ], [ 3, 4 ] ] << M[ [ 3, 2 ], [ 1, 0 ] ] ).to_a
  end

  def test_shr
    assert_equal [ [ 1, 2 ], [ 3, 4 ] ], ( M[ [ 2, 4 ], [ 6, 8 ] ] >> 1 ).to_a
    assert_equal [ [ 24, 12 ], [ 6, 3 ] ],
                 ( 48 >> M[ [ 1, 2 ], [ 3, 4 ] ] ).to_a
    assert_equal [ [ 2, 1 ], [ 3, 2 ] ],
                 ( M[ [ 16, 4 ], [ 6, 2 ] ] >> M[ [ 3, 2 ], [ 1, 0 ] ] ).to_a
  end

  def test_negate
    assert_equal M[ [ -1, 2, -3 ], [ 4, -5, 6 ] ],
                 -M[ [ 1, -2, 3 ], [ -4, 5, -6 ] ]
  end

  def test_plus
    assert_equal M[ [ 2, 3, 5 ], [ 3, 5, 7 ] ],
                 M[ [ 1, 2, 4 ], [ 2, 4, 6 ] ] + 1
    assert_equal M[ [ 2, 3, 5 ], [ 3, 5, 7 ] ],
                 1 + M[ [ 1, 2, 4 ], [ 2, 4, 6 ] ]
    assert_equal M[ [ -1, 2, 3 ], [ 4, 5, 6 ] ],
                 M[ [ -3, 2, 1 ], [ 8, 6, 4 ] ] +
                 M[ [ 2, 0, 2 ], [ -4, -1, 2 ] ]
    assert_equal M[ [ 2, 3, 4 ], [ 6, 7, 8 ] ],
                 M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ] + S[ 1, 2 ]
    assert_equal M[ [ 2, 3, 4 ], [ 6, 7, 8 ] ],
                 S[ 1, 2 ] + M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    assert_raise(RuntimeError) do
      M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ] + M[ [ 1, 2 ], [ 3, 4 ] ]
    end
    assert_raise(RuntimeError) do
      M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ] + M[ [ 1, 2, 3 ] ]
    end
    assert_raise(RuntimeError) do
      M[ [ 1, 2 ], [ 3, 4 ] ] + M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ] 
    end
    assert_raise(RuntimeError) do
      M[ [ 1, 2, 3 ] ] + M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    end
    assert_raise(RuntimeError) do
      M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ] + S[ 1, 2, 3 ]
    end
    assert_raise(RuntimeError) do
      S[ 1, 2, 3 ] + M[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    end
  end

  def test_major
    assert_equal M[ [ 4, 2 ], [ 3, 4 ] ],
                 M[ [ 1, 2 ], [ 3, 4 ] ].major( M[ [ 4, 1 ], [ 3, 2 ] ] )
  end

  def test_minor
    assert_equal M[ [ 1, 1 ], [ 3, 2 ] ],
                 M[ [ 1, 2 ], [ 3, 4 ] ].minor( M[ [ 4, 1 ], [ 3, 2 ] ] )
  end

  def test_cond
    assert_equal M[ [ -1, 2 ], [ 3, -4 ] ],
                 M[ [ false, true ], [ true, false ] ].
                 conditional( M[ [ 1, 2 ], [ 3, 4 ] ],
                              M[ [ -1, -2 ], [ -3, -4 ] ] )
    assert_equal M[ [ -1, -2 ], [ 3, 4 ] ],
                 S[ false, true ].
                 conditional( M[ [ 1, 2 ], [ 3, 4 ] ],
                              M[ [ -1, -2 ], [ -3, -4 ] ] )
    assert_equal M[ [ -1, -1 ], [ 3, 4 ] ],
                 S[ false, true ].
                 conditional( M[ [ 1, 2 ], [ 3, 4 ] ], -1 )
    assert_equal M[ [ -1, -1 ], [ 3, 4 ] ],
                 S[ false, true ].
                 conditional( M[ [ 1, 2 ], [ 3, 4 ] ], S[ -1, -2 ] )
  end

  def test_cmp
    assert_equal M[ [ -1, -1 ], [ 0, 1 ] ], M[ [ 1, 2 ], [ 3, 4 ] ] <=> 3
    assert_equal M[ [ 1, 1 ], [ 0, -1 ] ], 3 <=> M[ [ 1, 2 ], [ 3, 4 ] ]
  end

  def test_fill
    m = M(I, 2)[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
    assert_equal M(I, 2)[ [ 1, 1, 1 ], [ 1, 1, 1 ] ], m.fill!( 1 )
    assert_equal M(I, 2)[ [ 1, 1, 1 ], [ 1, 1, 1 ] ], m
  end

  def test_to_type
    assert_equal M(C, 2)[ [ 1, 2 ], [ 3, 4 ] ],
                 M(I, 2)[ [ 1, 2 ], [ 3, 4 ] ].to_intrgb
  end

  def test_reshape
    [O, I].each do |t|
      assert_equal M(t, 2)[[1, 2, 3], [4, 5, 6]],
                   S(t)[1, 2, 3, 4, 5, 6].reshape(3, 2)
      assert_equal S(t)[1, 2, 3, 4, 5, 6],
                   M(t, 2)[[1, 2, 3], [4, 5, 6]].reshape(6)
      assert_equal M(t, 2)[[1, 2], [3, 4], [5, 6]],
                   M(t, 2)[[1, 2, 3], [4, 5, 6]].reshape(2, 3)
      assert_raise(RuntimeError) { M(t, 2)[[1, 2], [3, 4]].reshape 3 }
    end
  end

  def test_integral
    assert_equal M(O, 2)[[1, 3, 6], [5, 12, 21]],
                 M(O, 2)[[1, 2, 3], [4, 5, 6]].integral
    assert_equal M(I, 2)[[1, 3, 6], [5, 12, 21]],
                 M(I, 2)[[1, 2, 3], [4, 5, 6]].integral
  end

  def test_components
    assert_equal [ [ 1, 0, 2 ], [ 0, 0, 2 ], [ 2, 2, 2 ] ],
                 M[ [ 1, 0, 1 ], [ 0, 0, 1 ], [ 1, 1, 1 ] ].components.to_a
  end

  def test_mask
    [O, I].each do |t|
      assert_equal M(t, 2)[[1, 2], [5, 7]],
                   M(t, 2)[[1, 2], [3, 4], [5, 7]].
                   mask(S[true, false, true])
      assert_equal S(t)[2, 5, 7], M(t, 2)[[1, 2, 3], [4, 5, 7]].
                   mask( M[[false, true, false], [false, true, true]])
      assert_raise(RuntimeError) do
        M(t, 2)[[1, 2], [3, 4], [5, 7]].mask S[false, true]
      end
    end
  end

  def test_unmask
    [ O, I ].each do |t|
      assert_equal M(t, 2)[[1, 2], [4, 4], [5, 7]],
                   M(t, 2)[[1, 2], [5, 7]].
                   unmask( S[true, false, true], :default => S[3, 4, 5] )
      assert_equal M(t, 2)[[0, 2, 0], [0, 5, 7]],
                   S(t)[2, 5, 7].
                   unmask( M[[false, true, false], [false, true, true]],
                           :default => 0 )
      assert_raise(RuntimeError) { S(t)[1].unmask M[[true, true]] }
    end
  end

end