From 70bb0c99d174e66375b3c3b5129e7c9d95c276b9 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Tue, 31 Oct 2017 05:26:38 +0000
Subject: [PATCH 01/37] add benchmark/ips: 460 ips

---
 Rakefile              | 13 ++++++
 metrics/bench         |  5 +++
 test/bench/simplex.rb | 98 +++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 116 insertions(+)
 create mode 100644 metrics/bench
 create mode 100644 test/bench/simplex.rb

diff --git a/Rakefile b/Rakefile
index cb70dcb..0aba59a 100644
--- a/Rakefile
+++ b/Rakefile
@@ -5,3 +5,16 @@ task :default => :test
 Rake::TestTask.new do |t|
   t.test_files = FileList['test/**/*_test.rb']
 end
+
+Rake::TestTask.new(bench: :loadavg) do |t|
+  t.pattern = ['test/bench/*.rb']
+  t.warning = true
+  t.description = "Run benchmarks"
+end
+
+desc "Show current system load"
+task :loadavg do
+  puts "/proc/loadavg %s" % (File.read("/proc/loadavg") rescue "Unavailable")
+end
+
+task :default => :test
diff --git a/metrics/bench b/metrics/bench
new file mode 100644
index 0000000..09b8955
--- /dev/null
+++ b/metrics/bench
@@ -0,0 +1,5 @@
+/proc/loadavg 0.08 0.02 0.01 1/79 1931
+Warming up --------------------------------------
+      Simplex Vector    46.000  i/100ms
+Calculating -------------------------------------
+      Simplex Vector    460.019  (± 0.9%) i/s -      1.380k in   3.000113s
diff --git a/test/bench/simplex.rb b/test/bench/simplex.rb
new file mode 100644
index 0000000..60c0695
--- /dev/null
+++ b/test/bench/simplex.rb
@@ -0,0 +1,98 @@
+require 'simplex'
+require 'benchmark/ips'
+
+Benchmark.ips do |b|
+  b.config time: 3, warmup: 0.5
+
+  b.report("Simplex Vector") {
+    Simplex.new([1, 1],
+                [[2,  1],
+                 [1,  2]],
+                [4, 3]).solution
+
+    Simplex.new([3, 4],
+                [[1, 1],
+                 [2, 1]],
+                [4, 5]).solution
+
+    Simplex.new([2, -1],
+                [[1, 2],
+                 [3, 2],],
+                [6, 12]).solution
+
+    Simplex.new([60, 90, 300],
+                [[1, 1, 1],
+                 [1, 3, 0],
+                 [2, 0, 1]],
+                [600, 600, 900]).solution
+
+    Simplex.new([70, 210, 140],
+                [[1, 1, 1],
+                 [5, 4, 4],
+                 [40, 20, 30]],
+                [100, 480, 3200]).solution
+
+    Simplex.new([2, -1, 2],
+                [[2, 1, 0],
+                 [1, 2, -2],
+                 [0, 1, 2]],
+                [10, 20, 5]).solution
+
+    Simplex.new([11, 16, 15],
+                [[1, 2, Rational(3, 2)],
+                 [Rational(2, 3), Rational(2, 3), 1],
+                 [Rational(1, 2), Rational(1, 3), Rational(1, 2)]],
+                [12_000, 4_600, 2_400]).solution
+
+    Simplex.new([5, 4, 3],
+                [[2, 3, 1],
+                 [4, 1, 2],
+                 [3, 4, 2]],
+                [5, 11, 8]).solution
+
+    Simplex.new([3, 2, -4],
+                [[1, 4, 0],
+                 [2, 4,-2],
+                 [1, 1,-2]],
+                [5, 6, 2]).solution
+
+    Simplex.new([2, -1, 8],
+                [[2, -4, 6],
+                 [-1, 3, 4],
+                 [0, 0, 2]],
+                [3, 2, 1]).solution
+
+    Simplex.new([100_000, 40_000, 18_000],
+                [[20, 6, 3],
+                 [0, 1, 0],
+                 [-1,-1, 1],
+                 [-9, 1, 1]],
+                [182, 10, 0, 0]).solution
+
+    Simplex.new([1, 2, 1, 2],
+                [[1, 0, 1, 0],
+                 [0, 1, 0, 1],
+                 [1, 1, 0, 0],
+                 [0, 0, 1, 1]],
+                [1, 4, 2, 2]).solution
+
+    Simplex.new([10, -57, -9, -24],
+                [[0.5, -5.5, -2.5, 9],
+                 [0.5, -1.5, -0.5, 1],
+                 [ 1,    0,    0, 0]],
+                [0, 0, 1]).solution
+
+    Simplex.new([25, 20],
+                [[20, 12],
+                 [1, 1]],
+                [1800, 8*15]).solution
+  }
+
+#b.report("Simplex Array") {
+#}
+
+#b.report("Simplex Matrix") {
+#}
+
+#  b.compare!
+end

From e48c7ec08e25268bc14aa054f3f2d59882ad006f Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:26:57 +0000
Subject: [PATCH 02/37] use t.pattern and enable warnings

---
 Rakefile | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Rakefile b/Rakefile
index 0aba59a..9014442 100644
--- a/Rakefile
+++ b/Rakefile
@@ -1,9 +1,8 @@
 require 'rake/testtask'
 
-task :default => :test
-
 Rake::TestTask.new do |t|
-  t.test_files = FileList['test/**/*_test.rb']
+  t.pattern = ['test/*.rb']
+  t.warning = true
 end
 
 Rake::TestTask.new(bench: :loadavg) do |t|

From 15c85ce24917f90131661aade940a4a6a962065c Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:27:40 +0000
Subject: [PATCH 03/37] stop manipulating load path in code

---
 test/simplex_test.rb | 1 -
 1 file changed, 1 deletion(-)

diff --git a/test/simplex_test.rb b/test/simplex_test.rb
index 6b406e8..ed00878 100644
--- a/test/simplex_test.rb
+++ b/test/simplex_test.rb
@@ -1,5 +1,4 @@
 require 'test/unit'
-$:.push(File.expand_path("../../lib", __FILE__))
 require 'simplex'
 
 class SimplexTest < Test::Unit::TestCase

From d53f7d95cd90a2a581b9bd99e46c165163ec2513 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:28:36 +0000
Subject: [PATCH 04/37] fix warnings about unused locals

---
 test/simplex_test.rb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/simplex_test.rb b/test/simplex_test.rb
index ed00878..8001597 100644
--- a/test/simplex_test.rb
+++ b/test/simplex_test.rb
@@ -186,7 +186,7 @@ def test_cycle2
 
   def test_error_mismatched_dimensions
     assert_raise ArgumentError do
-      result = Simplex.new(
+      Simplex.new(
         [10, -57, -9],
         [
           [0.5, -5.5, -2.5, 9],
@@ -198,7 +198,7 @@ def test_error_mismatched_dimensions
     end
 
     assert_raise ArgumentError do
-      result = Simplex.new(
+      Simplex.new(
         [10, -57, -9, 2],
         [
           [0.5, -5.5, 9, 4],
@@ -210,7 +210,7 @@ def test_error_mismatched_dimensions
     end
 
     assert_raise ArgumentError do
-      result = Simplex.new(
+      Simplex.new(
         [10, -57, -9, 2],
         [
           [0.5, -5.5, 9, 4],

From b88eab0c78fc1949ea917233b40752422ce4e733 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:29:53 +0000
Subject: [PATCH 05/37] fix warnings about unused or shadow local vars

---
 lib/simplex.rb | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 98c893f..79ebbe1 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -26,8 +26,9 @@ def initialize(c, a, b)
     @a = a.map {|a1| Vector[*(a1.clone + [0]*@num_constraints)]}
     @b = Vector[*b.clone]
 
-    unless @a.all? {|a| a.size == @c.size } and @b.size == @a.length
-      raise ArgumentError, "Input arrays have mismatched dimensions" 
+    # unless @a.all? {|a| a.size == @c.size } and @b.size == @a.length
+    unless @a.all? {|a1| a1.size == @c.size } and @b.size == @a.length
+      raise ArgumentError, "Input arrays have mismatched dimensions"
     end
 
     0.upto(@num_constraints - 1) {|i| @a[i][@num_non_slack_vars + i] = 1 }
@@ -147,7 +148,7 @@ def formatted_tableau
     else
       pivot_row = nil
     end
-    num_cols = @c.size + 1
+    # num_cols = @c.size + 1
     c = formatted_values(@c.to_a)
     b = formatted_values(@b.to_a)
     a = @a.to_a.map {|ar| formatted_values(ar.to_a) }
@@ -156,12 +157,15 @@ def formatted_tableau
     end
     max = (c + b + a + ["1234567"]).flatten.map(&:size).max
     result = []
-    result << c.map {|c| c.rjust(max, " ") }
+    # result << c.map {|c| c.rjust(max, " ") }
+    result << c.map {|c1| c1.rjust(max, " ") }
     a.zip(b) do |arow, brow|
-      result << (arow + [brow]).map {|a| a.rjust(max, " ") }
+      # result << (arow + [brow]).map {|a| a.rjust(max, " ") }
+      result << (arow + [brow]).map {|a1| a1.rjust(max, " ") }
       result.last.insert(arow.length, "|")
     end
-    lines = result.map {|b| b.join("  ") }
+    # lines = result.map {|b| b.join("  ") }
+    lines = result.map {|b1| b1.join("  ") }
     max_line_length = lines.map(&:length).max
     lines.insert(1, "-"*max_line_length)
     lines.join("\n")

From 60b2edf70402fd7522e8020c2ca5df2b651ca0e2 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:30:12 +0000
Subject: [PATCH 06/37] remove trailing whitespace

---
 lib/simplex.rb       | 5 ++---
 test/simplex_test.rb | 6 +++---
 2 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 79ebbe1..acc0093 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -62,7 +62,7 @@ def update_solution
   def solve
     while can_improve?
       @pivot_count += 1
-      raise "Too many pivots" if @pivot_count > max_pivots 
+      raise "Too many pivots" if @pivot_count > max_pivots
       pivot
     end
   end
@@ -175,7 +175,7 @@ def formatted_values(array)
     array.map {|c| "%2.3f" % c }
   end
 
-  # like Enumerable#min_by except if multiple values are minimum 
+  # like Enumerable#min_by except if multiple values are minimum
   # it returns the last
   def last_min_by(array)
     best_element, best_value = nil, nil
@@ -193,4 +193,3 @@ def assert(boolean)
   end
 
 end
-
diff --git a/test/simplex_test.rb b/test/simplex_test.rb
index 8001597..f5d3964 100644
--- a/test/simplex_test.rb
+++ b/test/simplex_test.rb
@@ -262,16 +262,16 @@ def test_cup_factory
   #    [1, -2]
   #  )
   #  while simplex.can_improve?
-  #    puts 
+  #    puts
   #    puts simplex.formatted_tableau
   #    simplex.pivot
   #  end
   #  p :done
-  #  puts 
+  #  puts
   #  puts simplex.formatted_tableau
 
   #end
-  
+
   def test_unbounded
     simplex = Simplex.new(
       [1, 1, 1],

From 7ee8a0d8240263d37c3cac92c523623cf018d456 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 04:00:09 +0000
Subject: [PATCH 07/37] convert from test/unit to minitest/test

---
 test/simplex_test.rb | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/test/simplex_test.rb b/test/simplex_test.rb
index f5d3964..125e67c 100644
--- a/test/simplex_test.rb
+++ b/test/simplex_test.rb
@@ -1,7 +1,7 @@
-require 'test/unit'
+require 'minitest/autorun'
 require 'simplex'
 
-class SimplexTest < Test::Unit::TestCase
+class SimplexTest < Minitest::Test
   def test_2x2
     result = Simplex.new(
       [1, 1],
@@ -179,13 +179,13 @@ def test_cycle2
       ],
       [0, 0]
     )
-    assert_raise Simplex::UnboundedProblem do
+    assert_raises Simplex::UnboundedProblem do
       simplex.solution
     end
   end
 
   def test_error_mismatched_dimensions
-    assert_raise ArgumentError do
+    assert_raises ArgumentError do
       Simplex.new(
         [10, -57, -9],
         [
@@ -197,7 +197,7 @@ def test_error_mismatched_dimensions
       )
     end
 
-    assert_raise ArgumentError do
+    assert_raises ArgumentError do
       Simplex.new(
         [10, -57, -9, 2],
         [
@@ -209,7 +209,7 @@ def test_error_mismatched_dimensions
       )
     end
 
-    assert_raise ArgumentError do
+    assert_raises ArgumentError do
       Simplex.new(
         [10, -57, -9, 2],
         [
@@ -281,7 +281,7 @@ def test_unbounded
       ],
       [5, 7]
     )
-    assert_raise Simplex::UnboundedProblem do
+    assert_raises Simplex::UnboundedProblem do
       simplex.solution
     end
   end

From 38b20c42714142a66ddf056b56e69e7b6c2e366f Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 05:10:46 +0000
Subject: [PATCH 08/37] remove unused Simplex#assert; add comments

---
 lib/simplex.rb | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index acc0093..35629f2 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -12,6 +12,9 @@ class UnboundedProblem < StandardError
 
   attr_accessor :max_pivots
 
+  # c - coefficients of objective function
+  # a - inequality lhs coefficients
+  # b - inequality rhs constants
   def initialize(c, a, b)
     @pivot_count = 0
     @max_pivots = DEFAULT_MAX_PIVOTS
@@ -187,9 +190,4 @@ def last_min_by(array)
     end
     best_element
   end
-
-  def assert(boolean)
-    raise unless boolean
-  end
-
 end

From 5dfc7952d67ed2f371eb57cfb43f4974f76800c8 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 05:12:28 +0000
Subject: [PATCH 09/37] drop @pivot_count

---
 lib/simplex.rb | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 35629f2..2b585e3 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -16,7 +16,6 @@ class UnboundedProblem < StandardError
   # a - inequality lhs coefficients
   # b - inequality rhs constants
   def initialize(c, a, b)
-    @pivot_count = 0
     @max_pivots = DEFAULT_MAX_PIVOTS
 
     # Problem dimensions
@@ -63,10 +62,11 @@ def update_solution
   end
 
   def solve
+    count = 0
     while can_improve?
-      @pivot_count += 1
-      raise "Too many pivots" if @pivot_count > max_pivots
-      pivot
+      count += 1
+      raise "too many pivots: #{count}" unless count < @max_pivots
+      self.pivot
     end
   end
 

From 7c35aa3b2d59977063875e463d5d3e8f45347842 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 05:49:16 +0000
Subject: [PATCH 10/37] simplify initalize; make @x an Array rather than Vector

---
 lib/simplex.rb | 44 ++++++++++++++++++++++++++++----------------
 1 file changed, 28 insertions(+), 16 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 2b585e3..540a29d 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -12,31 +12,43 @@ class UnboundedProblem < StandardError
 
   attr_accessor :max_pivots
 
-  # c - coefficients of objective function
-  # a - inequality lhs coefficients
-  # b - inequality rhs constants
+  def self.new_vector(ary, num_constraints)
+    Vector[*(ary + Array.new(num_constraints, 0))]
+  end
+
+  # X = num vars
+  # Y = num inequalities
+
+  # c - coefficients of objective function (size X)
+  # a - inequality lhs coefficients, 2dim  (size Y, size X)
+  # b - inequality rhs constants           (size Y)
   def initialize(c, a, b)
+    num_vars = c.size
+    num_inequalities = b.size
+    raise(ArgumentError, "a doesn't match b") unless a.size == num_inequalities
+    raise(ArgumentError, "a doesn't match c") unless a.first.size == num_vars
+
     @max_pivots = DEFAULT_MAX_PIVOTS
 
     # Problem dimensions
-    @num_non_slack_vars = a.first.length
-    @num_constraints    = b.length
+    @num_non_slack_vars = num_vars
+    @num_constraints    = num_inequalities
     @num_vars           = @num_non_slack_vars + @num_constraints
 
     # Set up initial matrix A and vectors b, c
-    @c = Vector[*c.map {|c1| -1*c1 } + [0]*@num_constraints]
-    @a = a.map {|a1| Vector[*(a1.clone + [0]*@num_constraints)]}
-    @b = Vector[*b.clone]
-
-    # unless @a.all? {|a| a.size == @c.size } and @b.size == @a.length
-    unless @a.all? {|a1| a1.size == @c.size } and @b.size == @a.length
-      raise ArgumentError, "Input arrays have mismatched dimensions"
-    end
+    @c = self.class.new_vector(c.map { |flt| -1 * flt }, @num_constraints)
+    @a = a.map { |ary|
+      if ary.size != @num_non_slack_vars
+        raise ArgumentError, "a is inconsistent"
+      end
+      self.class.new_vector(ary, @num_constraints)
+    }
+    @b = self.class.new_vector(b, 0)
 
-    0.upto(@num_constraints - 1) {|i| @a[i][@num_non_slack_vars + i] = 1 }
+    @num_constraints.times { |i| @a[i][@num_non_slack_vars + i] = 1 }
 
     # set initial solution: all non-slack variables = 0
-    @x          = Vector[*([0]*@num_vars)]
+    @x = Array.new(@num_vars, 0)
     @basic_vars = (@num_non_slack_vars...@num_vars).to_a
     update_solution
   end
@@ -47,7 +59,7 @@ def solution
   end
 
   def current_solution
-    @x.to_a[0...@num_non_slack_vars]
+    @x[0...@num_non_slack_vars]
   end
 
   def update_solution

From e6db1c5513ac368811c742f6d32c461f3de8453d Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 06:13:17 +0000
Subject: [PATCH 11/37] cleanup

---
 lib/simplex.rb | 26 +++++++++-----------------
 1 file changed, 9 insertions(+), 17 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 540a29d..6ca3578 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -12,16 +12,9 @@ class UnboundedProblem < StandardError
 
   attr_accessor :max_pivots
 
-  def self.new_vector(ary, num_constraints)
-    Vector[*(ary + Array.new(num_constraints, 0))]
-  end
-
-  # X = num vars
-  # Y = num inequalities
-
-  # c - coefficients of objective function (size X)
-  # a - inequality lhs coefficients, 2dim  (size Y, size X)
-  # b - inequality rhs constants           (size Y)
+  # c - coefficients of objective function; size: num_vars
+  # a - inequality lhs coefficients;   2dim size: num_inequalities, num_vars
+  # b - inequality rhs constants            size: num_inequalities
   def initialize(c, a, b)
     num_vars = c.size
     num_inequalities = b.size
@@ -36,16 +29,15 @@ def initialize(c, a, b)
     @num_vars           = @num_non_slack_vars + @num_constraints
 
     # Set up initial matrix A and vectors b, c
-    @c = self.class.new_vector(c.map { |flt| -1 * flt }, @num_constraints)
-    @a = a.map { |ary|
+    @c = Vector[*(c.map { |flt| -1 * flt } + Array.new(@num_constraints, 0))]
+    @a = a.map.with_index { |ary, i|
       if ary.size != @num_non_slack_vars
         raise ArgumentError, "a is inconsistent"
       end
-      self.class.new_vector(ary, @num_constraints)
+      constraints = Array.new(@num_constraints) { |ci| ci == i ? 1 : 0 }
+      Vector[*(ary + constraints)]
     }
-    @b = self.class.new_vector(b, 0)
-
-    @num_constraints.times { |i| @a[i][@num_non_slack_vars + i] = 1 }
+    @b = Vector.elements(b, true)
 
     # set initial solution: all non-slack variables = 0
     @x = Array.new(@num_vars, 0)
@@ -63,7 +55,7 @@ def current_solution
   end
 
   def update_solution
-    0.upto(@num_vars - 1) {|i| @x[i] = 0 }
+    @x = Array.new(@num_vars, 0)
 
     @basic_vars.each do |basic_var|
       row_with_1 = row_indices.detect do |row_ix|

From f5cb8ebca3e1f087e2e6971be0dae45cf49ff7a1 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 06:43:53 +0000
Subject: [PATCH 12/37] drop Simplex#variables and #replace_basic_variable

---
 lib/simplex.rb | 23 +++++++----------------
 1 file changed, 7 insertions(+), 16 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 6ca3578..960829e 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -23,7 +23,7 @@ def initialize(c, a, b)
 
     @max_pivots = DEFAULT_MAX_PIVOTS
 
-    # Problem dimensions
+    # Problem dimensions; these never change
     @num_non_slack_vars = num_vars
     @num_constraints    = num_inequalities
     @num_vars           = @num_non_slack_vars + @num_constraints
@@ -40,7 +40,6 @@ def initialize(c, a, b)
     @b = Vector.elements(b, true)
 
     # set initial solution: all non-slack variables = 0
-    @x = Array.new(@num_vars, 0)
     @basic_vars = (@num_non_slack_vars...@num_vars).to_a
     update_solution
   end
@@ -78,13 +77,10 @@ def can_improve?
     !!entering_variable
   end
 
-  def variables
-    (0...@c.size).to_a
-  end
-
   def entering_variable
-    variables.select { |var| @c[var] < 0 }.
-              min_by { |var| @c[var] }
+    (0...@c.size).to_a.select { |var|
+      @c[var] < 0
+    }.min_by { |var| @c[var] }
   end
 
   def pivot
@@ -92,7 +88,9 @@ def pivot
     pivot_row    = pivot_row(pivot_column)
     raise UnboundedProblem unless pivot_row
     leaving_var  = basic_variable_in_row(pivot_row)
-    replace_basic_variable(leaving_var => pivot_column)
+    @basic_vars.delete(leaving_var)
+    @basic_vars.push(pivot_column)
+    @basic_vars.sort!
 
     pivot_ratio = Rational(1, @a[pivot_row][pivot_column])
 
@@ -113,13 +111,6 @@ def pivot
     update_solution
   end
 
-  def replace_basic_variable(hash)
-    from, to = hash.keys.first, hash.values.first
-    @basic_vars.delete(from)
-    @basic_vars << to
-    @basic_vars.sort!
-  end
-
   def pivot_row(column_ix)
     row_ix_a_and_b = row_indices.map { |row_ix|
       [row_ix, @a[row_ix][column_ix], @b[row_ix]]

From 2449f2284dac04f38e8003d1675f08a20317756c Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 06:57:57 +0000
Subject: [PATCH 13/37] drop Gemfile and update travis

---
 .travis.yml  | 11 ++++++++---
 Gemfile      |  6 ------
 Gemfile.lock | 12 ------------
 3 files changed, 8 insertions(+), 21 deletions(-)
 delete mode 100644 Gemfile
 delete mode 100644 Gemfile.lock

diff --git a/.travis.yml b/.travis.yml
index d250ed9..a582fbd 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,10 @@
 language: ruby
 rvm:
-  - 1.9.3
-  - 2.0.0
-  - jruby
+  - 2.2
+  - 2.3
+  - 2.4
+  - ruby
+  - ruby-head
+  - jruby-9.1.9
+install: gem install minitest
+script: rake
diff --git a/Gemfile b/Gemfile
deleted file mode 100644
index 75db47d..0000000
--- a/Gemfile
+++ /dev/null
@@ -1,6 +0,0 @@
-source "https://rubygems.org"
-gem "rake"
-
-group :test do
-  gem "test-unit"
-end
diff --git a/Gemfile.lock b/Gemfile.lock
deleted file mode 100644
index 9b744b9..0000000
--- a/Gemfile.lock
+++ /dev/null
@@ -1,12 +0,0 @@
-GEM
-  remote: https://rubygems.org/
-  specs:
-    rake (10.1.0)
-    test-unit (2.0.0.0)
-
-PLATFORMS
-  ruby
-
-DEPENDENCIES
-  rake
-  test-unit

From 919d78492f5d166a0edda2fccc92180976281386 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:05:58 +0000
Subject: [PATCH 14/37] rename to test/simplex.rb

---
 test/{simplex_test.rb => simplex.rb} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename test/{simplex_test.rb => simplex.rb} (100%)

diff --git a/test/simplex_test.rb b/test/simplex.rb
similarity index 100%
rename from test/simplex_test.rb
rename to test/simplex.rb

From 20a948438bcd8b999cd8f09b299e0554de00ba67 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:21:10 +0000
Subject: [PATCH 15/37] drop #basic_variable_in_row

---
 lib/simplex.rb | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 960829e..911ab8c 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -87,7 +87,10 @@ def pivot
     pivot_column = entering_variable
     pivot_row    = pivot_row(pivot_column)
     raise UnboundedProblem unless pivot_row
-    leaving_var  = basic_variable_in_row(pivot_row)
+    leaving_var = self.column_indices.detect { |idx|
+      @a[pivot_row][idx] == 1 and @basic_vars.include?(idx)
+    }
+
     @basic_vars.delete(leaving_var)
     @basic_vars.push(pivot_column)
     @basic_vars.sort!
@@ -125,12 +128,6 @@ def pivot_row(column_ix)
     row_ix
   end
 
-  def basic_variable_in_row(pivot_row)
-    column_indices.detect do |column_ix|
-      @a[pivot_row][column_ix] == 1 and @basic_vars.include?(column_ix)
-    end
-  end
-
   def row_indices
     (0...@a.length).to_a
   end

From 9f5f9a57f1948d0cee158660d9fc76f2bcb00d96 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:24:24 +0000
Subject: [PATCH 16/37] use self.instance_method when calling instance methods

---
 lib/simplex.rb | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 911ab8c..aeca588 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -41,12 +41,12 @@ def initialize(c, a, b)
 
     # set initial solution: all non-slack variables = 0
     @basic_vars = (@num_non_slack_vars...@num_vars).to_a
-    update_solution
+    self.update_solution
   end
 
   def solution
-    solve
-    current_solution
+    self.solve
+    self.current_solution
   end
 
   def current_solution
@@ -66,7 +66,7 @@ def update_solution
 
   def solve
     count = 0
-    while can_improve?
+    while self.can_improve?
       count += 1
       raise "too many pivots: #{count}" unless count < @max_pivots
       self.pivot
@@ -74,7 +74,7 @@ def solve
   end
 
   def can_improve?
-    !!entering_variable
+    !!self.entering_variable
   end
 
   def entering_variable
@@ -84,8 +84,8 @@ def entering_variable
   end
 
   def pivot
-    pivot_column = entering_variable
-    pivot_row    = pivot_row(pivot_column)
+    pivot_column = self.entering_variable
+    pivot_row    = self.pivot_row(pivot_column)
     raise UnboundedProblem unless pivot_row
     leaving_var = self.column_indices.detect { |idx|
       @a[pivot_row][idx] == 1 and @basic_vars.include?(idx)

From cadb517db47e3f25ff10474f3f81ccaa6eab4471 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:43:01 +0000
Subject: [PATCH 17/37] add comments

---
 lib/simplex.rb | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index aeca588..dd9bbb9 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -53,6 +53,7 @@ def current_solution
     @x[0...@num_non_slack_vars]
   end
 
+  # does not modify vector / matrix
   def update_solution
     @x = Array.new(@num_vars, 0)
 
@@ -77,6 +78,9 @@ def can_improve?
     !!self.entering_variable
   end
 
+  # idx of @c's minimum negative value
+  # nil when no improvement is possible
+  #
   def entering_variable
     (0...@c.size).to_a.select { |var|
       @c[var] < 0

From e6c420c5077cae4274c889afb339f06cc54abc0a Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:44:11 +0000
Subject: [PATCH 18/37] cleanup; check for non-nil self.entering_variable

---
 lib/simplex.rb | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index dd9bbb9..7a6f952 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -75,22 +75,19 @@ def solve
   end
 
   def can_improve?
-    !!self.entering_variable
+    !self.entering_variable.nil?
   end
 
   # idx of @c's minimum negative value
   # nil when no improvement is possible
   #
   def entering_variable
-    (0...@c.size).to_a.select { |var|
-      @c[var] < 0
-    }.min_by { |var| @c[var] }
+    (0...@c.size).select { |i| @c[i] < 0 }.min_by { |i| @c[i] }
   end
 
   def pivot
-    pivot_column = self.entering_variable
-    pivot_row    = self.pivot_row(pivot_column)
-    raise UnboundedProblem unless pivot_row
+    pivot_column = self.entering_variable or return nil
+    pivot_row = self.pivot_row(pivot_column) or raise UnboundedProblem
     leaving_var = self.column_indices.detect { |idx|
       @a[pivot_row][idx] == 1 and @basic_vars.include?(idx)
     }

From 3c3c2e70af4892e00d4d1e886a36bd5efd7bbe2e Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:51:49 +0000
Subject: [PATCH 19/37] use self.instance method and fix some block parameters

---
 lib/simplex.rb | 29 +++++++++++++----------------
 1 file changed, 13 insertions(+), 16 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 7a6f952..b491b27 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -106,24 +106,24 @@ def pivot
     @c -= @c[pivot_column] * @a[pivot_row]
 
     # update A and B
-    (row_indices - [pivot_row]).each do |row_ix|
+    (self.row_indices - [pivot_row]).each do |row_ix|
       r = @a[row_ix][pivot_column]
       @a[row_ix] -= r * @a[pivot_row]
       @b[row_ix] -= r * @b[pivot_row]
     end
 
-    update_solution
+    self.update_solution
   end
 
   def pivot_row(column_ix)
-    row_ix_a_and_b = row_indices.map { |row_ix|
+    row_ix_a_and_b = self.row_indices.map { |row_ix|
       [row_ix, @a[row_ix][column_ix], @b[row_ix]]
     }.reject { |_, a, b|
       a == 0
     }.reject { |_, a, b|
       (b < 0) ^ (a < 0) # negative sign check
     }
-    row_ix, _, _ = *last_min_by(row_ix_a_and_b) { |_, a, b|
+    row_ix, _, _ = *self.last_min_by(row_ix_a_and_b) { |_, a, b|
       Rational(b, a)
     }
     row_ix
@@ -138,30 +138,27 @@ def column_indices
   end
 
   def formatted_tableau
-    if can_improve?
-      pivot_column = entering_variable
-      pivot_row    = pivot_row(pivot_column)
+    if self.can_improve?
+      pivot_column = self.entering_variable
+      pivot_row    = self.pivot_row(pivot_column)
     else
       pivot_row = nil
     end
     # num_cols = @c.size + 1
-    c = formatted_values(@c.to_a)
-    b = formatted_values(@b.to_a)
-    a = @a.to_a.map {|ar| formatted_values(ar.to_a) }
+    c = self.formatted_values(@c.to_a)
+    b = self.formatted_values(@b.to_a)
+    a = @a.to_a.map {|ar| self.formatted_values(ar.to_a) }
     if pivot_row
       a[pivot_row][pivot_column] = "*" + a[pivot_row][pivot_column]
     end
     max = (c + b + a + ["1234567"]).flatten.map(&:size).max
     result = []
-    # result << c.map {|c| c.rjust(max, " ") }
-    result << c.map {|c1| c1.rjust(max, " ") }
+    result << c.map { |flt| flt.rjust(max, " ") }
     a.zip(b) do |arow, brow|
-      # result << (arow + [brow]).map {|a| a.rjust(max, " ") }
-      result << (arow + [brow]).map {|a1| a1.rjust(max, " ") }
+      result << (arow + [brow]).map { |val| val.rjust(max, " ") }
       result.last.insert(arow.length, "|")
     end
-    # lines = result.map {|b| b.join("  ") }
-    lines = result.map {|b1| b1.join("  ") }
+    lines = result.map {|ary| ary.join("  ") }
     max_line_length = lines.map(&:length).max
     lines.insert(1, "-"*max_line_length)
     lines.join("\n")

From 3516aae1e99f60041b85260736829b9e54d39c64 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 07:52:04 +0000
Subject: [PATCH 20/37] TODO: investigate conditional

---
 lib/simplex.rb | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index b491b27..05d42ac 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -174,6 +174,7 @@ def last_min_by(array)
     best_element, best_value = nil, nil
     array.each do |element|
       value = yield element
+      # TODO: uh oh
       if !best_element || value <= best_value
         best_element, best_value = element, value
       end

From 7950c49c8d478ecc64c55adcb6d6259234588a21 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:04:06 +0000
Subject: [PATCH 21/37] drop #formatted_values

---
 lib/simplex.rb | 15 +++++----------
 1 file changed, 5 insertions(+), 10 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 05d42ac..267b66d 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -144,30 +144,25 @@ def formatted_tableau
     else
       pivot_row = nil
     end
-    # num_cols = @c.size + 1
-    c = self.formatted_values(@c.to_a)
-    b = self.formatted_values(@b.to_a)
-    a = @a.to_a.map {|ar| self.formatted_values(ar.to_a) }
+    c = @c.to_a.map { |flt| "%2.3f" % flt }
+    b = @b.to_a.map { |flt| "%2.3f" % flt }
+    a = @a.to_a.map { |vec| vec.to_a.map { |flt| "%2.3f" % flt } }
     if pivot_row
       a[pivot_row][pivot_column] = "*" + a[pivot_row][pivot_column]
     end
     max = (c + b + a + ["1234567"]).flatten.map(&:size).max
     result = []
-    result << c.map { |flt| flt.rjust(max, " ") }
+    result << c.map { |str| str.rjust(max, " ") }
     a.zip(b) do |arow, brow|
       result << (arow + [brow]).map { |val| val.rjust(max, " ") }
       result.last.insert(arow.length, "|")
     end
-    lines = result.map {|ary| ary.join("  ") }
+    lines = result.map { |ary| ary.join("  ") }
     max_line_length = lines.map(&:length).max
     lines.insert(1, "-"*max_line_length)
     lines.join("\n")
   end
 
-  def formatted_values(array)
-    array.map {|c| "%2.3f" % c }
-  end
-
   # like Enumerable#min_by except if multiple values are minimum
   # it returns the last
   def last_min_by(array)

From 19ab1aeb7e5b9368ba33b025bd0f00f81bc5de12 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:14:12 +0000
Subject: [PATCH 22/37] make last_min_by a class method

---
 lib/simplex.rb | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 267b66d..0f578ae 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -10,6 +10,20 @@ class Simplex
   class UnboundedProblem < StandardError
   end
 
+  # like Enumerable#min_by except if multiple values are minimum
+  # it returns the last
+  def self.last_min_by array, &blk
+    best_element, best_value = nil, nil
+    array.each do |element|
+      value = yield element
+      # TODO: uh oh
+      if !best_element || value <= best_value
+        best_element, best_value = element, value
+      end
+    end
+    best_element
+  end
+
   attr_accessor :max_pivots
 
   # c - coefficients of objective function; size: num_vars
@@ -123,7 +137,7 @@ def pivot_row(column_ix)
     }.reject { |_, a, b|
       (b < 0) ^ (a < 0) # negative sign check
     }
-    row_ix, _, _ = *self.last_min_by(row_ix_a_and_b) { |_, a, b|
+    row_ix, _, _ = *self.class.last_min_by(row_ix_a_and_b) { |_, a, b|
       Rational(b, a)
     }
     row_ix
@@ -162,18 +176,4 @@ def formatted_tableau
     lines.insert(1, "-"*max_line_length)
     lines.join("\n")
   end
-
-  # like Enumerable#min_by except if multiple values are minimum
-  # it returns the last
-  def last_min_by(array)
-    best_element, best_value = nil, nil
-    array.each do |element|
-      value = yield element
-      # TODO: uh oh
-      if !best_element || value <= best_value
-        best_element, best_value = element, value
-      end
-    end
-    best_element
-  end
 end

From 58b2f89047e35bddc63987f92a7cf18919724f58 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:15:03 +0000
Subject: [PATCH 23/37] just call reject once

---
 lib/simplex.rb | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 0f578ae..d068520 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -133,9 +133,7 @@ def pivot_row(column_ix)
     row_ix_a_and_b = self.row_indices.map { |row_ix|
       [row_ix, @a[row_ix][column_ix], @b[row_ix]]
     }.reject { |_, a, b|
-      a == 0
-    }.reject { |_, a, b|
-      (b < 0) ^ (a < 0) # negative sign check
+      a == 0 or (b < 0) ^ (a < 0) # negative sign check
     }
     row_ix, _, _ = *self.class.last_min_by(row_ix_a_and_b) { |_, a, b|
       Rational(b, a)

From 59b2ae940e2523d79182bd4994c5f3f7ed11e9fd Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:27:13 +0000
Subject: [PATCH 24/37] drop last_min_by

---
 lib/simplex.rb | 30 ++++++++----------------------
 1 file changed, 8 insertions(+), 22 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index d068520..4e2695e 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -10,20 +10,6 @@ class Simplex
   class UnboundedProblem < StandardError
   end
 
-  # like Enumerable#min_by except if multiple values are minimum
-  # it returns the last
-  def self.last_min_by array, &blk
-    best_element, best_value = nil, nil
-    array.each do |element|
-      value = yield element
-      # TODO: uh oh
-      if !best_element || value <= best_value
-        best_element, best_value = element, value
-      end
-    end
-    best_element
-  end
-
   attr_accessor :max_pivots
 
   # c - coefficients of objective function; size: num_vars
@@ -130,15 +116,15 @@ def pivot
   end
 
   def pivot_row(column_ix)
-    row_ix_a_and_b = self.row_indices.map { |row_ix|
-      [row_ix, @a[row_ix][column_ix], @b[row_ix]]
-    }.reject { |_, a, b|
-      a == 0 or (b < 0) ^ (a < 0) # negative sign check
-    }
-    row_ix, _, _ = *self.class.last_min_by(row_ix_a_and_b) { |_, a, b|
-      Rational(b, a)
+    min_ratio = nil
+    idx = nil
+    self.row_indices.each { |i|
+      a, b = @a[i][column_ix], @b[i]
+      next if a == 0 or (b < 0) ^ (a < 0)
+      ratio = Rational(b, a)
+      idx, min_ratio = i, ratio if min_ratio.nil? or ratio <= min_ratio
     }
-    row_ix
+    idx
   end
 
   def row_indices

From 11d7239c361705e341aee60fefcf628a622abaa7 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:37:51 +0000
Subject: [PATCH 25/37] drop #row_indices

---
 lib/simplex.rb | 30 ++++++++++++++++--------------
 1 file changed, 16 insertions(+), 14 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 4e2695e..4e53408 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -58,10 +58,15 @@ def update_solution
     @x = Array.new(@num_vars, 0)
 
     @basic_vars.each do |basic_var|
-      row_with_1 = row_indices.detect do |row_ix|
-        @a[row_ix][basic_var] == 1
-      end
-      @x[basic_var] = @b[row_with_1]
+      idx = nil
+      @a.size.times { |i|
+        if @a[i][basic_var] == 1
+          idx = i
+          break
+        end
+      }
+      raise "no idx found for basic_var #{basic_var} in a" unless idx
+      @x[basic_var] = @b[idx]
     end
   end
 
@@ -106,11 +111,12 @@ def pivot
     @c -= @c[pivot_column] * @a[pivot_row]
 
     # update A and B
-    (self.row_indices - [pivot_row]).each do |row_ix|
-      r = @a[row_ix][pivot_column]
-      @a[row_ix] -= r * @a[pivot_row]
-      @b[row_ix] -= r * @b[pivot_row]
-    end
+    @a.size.times { |i|
+      next if i == pivot_row
+      r = @a[i][pivot_column]
+      @a[i] -= r * @a[pivot_row]
+      @b[i] -= r * @b[pivot_row]
+    }
 
     self.update_solution
   end
@@ -118,7 +124,7 @@ def pivot
   def pivot_row(column_ix)
     min_ratio = nil
     idx = nil
-    self.row_indices.each { |i|
+    @a.size.times { |i|
       a, b = @a[i][column_ix], @b[i]
       next if a == 0 or (b < 0) ^ (a < 0)
       ratio = Rational(b, a)
@@ -127,10 +133,6 @@ def pivot_row(column_ix)
     idx
   end
 
-  def row_indices
-    (0...@a.length).to_a
-  end
-
   def column_indices
     (0...@a.first.size).to_a
   end

From a24525b194ec681a10dd320760dd68a9285636e8 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:38:45 +0000
Subject: [PATCH 26/37] prefer @num_constraints to @a.size

---
 lib/simplex.rb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 4e53408..f48cdbd 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -59,7 +59,7 @@ def update_solution
 
     @basic_vars.each do |basic_var|
       idx = nil
-      @a.size.times { |i|
+      @num_constraints.times { |i|
         if @a[i][basic_var] == 1
           idx = i
           break
@@ -111,7 +111,7 @@ def pivot
     @c -= @c[pivot_column] * @a[pivot_row]
 
     # update A and B
-    @a.size.times { |i|
+    @num_constraints.times { |i|
       next if i == pivot_row
       r = @a[i][pivot_column]
       @a[i] -= r * @a[pivot_row]
@@ -124,7 +124,7 @@ def pivot
   def pivot_row(column_ix)
     min_ratio = nil
     idx = nil
-    @a.size.times { |i|
+    @num_constraints.times { |i|
       a, b = @a[i][column_ix], @b[i]
       next if a == 0 or (b < 0) ^ (a < 0)
       ratio = Rational(b, a)

From 6f0e0a24c169139b223704bdc103a8e146bfae22 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:45:35 +0000
Subject: [PATCH 27/37] drop #column_indices

---
 lib/simplex.rb | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index f48cdbd..2a21392 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -93,8 +93,12 @@ def entering_variable
   def pivot
     pivot_column = self.entering_variable or return nil
     pivot_row = self.pivot_row(pivot_column) or raise UnboundedProblem
-    leaving_var = self.column_indices.detect { |idx|
-      @a[pivot_row][idx] == 1 and @basic_vars.include?(idx)
+    leaving_var = nil
+    @a[pivot_row].each_with_index { |a, i|
+      if a == 1 and @basic_vars.include?(i)
+        leaving_var = i
+        break
+      end
     }
 
     @basic_vars.delete(leaving_var)
@@ -133,10 +137,6 @@ def pivot_row(column_ix)
     idx
   end
 
-  def column_indices
-    (0...@a.first.size).to_a
-  end
-
   def formatted_tableau
     if self.can_improve?
       pivot_column = self.entering_variable

From 20e81aa54a422d00aa07e3daa9ccd9803ff7af6d Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:49:28 +0000
Subject: [PATCH 28/37] reorder some method definitions

---
 lib/simplex.rb | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 2a21392..876f2b3 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -44,15 +44,6 @@ def initialize(c, a, b)
     self.update_solution
   end
 
-  def solution
-    self.solve
-    self.current_solution
-  end
-
-  def current_solution
-    @x[0...@num_non_slack_vars]
-  end
-
   # does not modify vector / matrix
   def update_solution
     @x = Array.new(@num_vars, 0)
@@ -70,6 +61,11 @@ def update_solution
     end
   end
 
+  def solution
+    self.solve
+    self.current_solution
+  end
+
   def solve
     count = 0
     while self.can_improve?
@@ -79,6 +75,10 @@ def solve
     end
   end
 
+  def current_solution
+    @x[0...@num_non_slack_vars]
+  end
+
   def can_improve?
     !self.entering_variable.nil?
   end

From 433c05c8fbd2f152540d583a073e4d74becada7b Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 08:57:56 +0000
Subject: [PATCH 29/37] Exceptions: add SanityCheck and TooManyPivots; inherit
 from RuntimeError

---
 lib/simplex.rb | 16 +++++++++-------
 1 file changed, 9 insertions(+), 7 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 876f2b3..8ab0909 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -7,8 +7,9 @@ class Vector
 class Simplex
   DEFAULT_MAX_PIVOTS = 10_000
 
-  class UnboundedProblem < StandardError
-  end
+  class UnboundedProblem < RuntimeError; end
+  class SanityCheck < RuntimeError; end
+  class TooManyPivots < RuntimeError; end
 
   attr_accessor :max_pivots
 
@@ -48,17 +49,17 @@ def initialize(c, a, b)
   def update_solution
     @x = Array.new(@num_vars, 0)
 
-    @basic_vars.each do |basic_var|
+    @basic_vars.each { |basic_var|
       idx = nil
       @num_constraints.times { |i|
         if @a[i][basic_var] == 1
-          idx = i
+          idx =i
           break
         end
       }
-      raise "no idx found for basic_var #{basic_var} in a" unless idx
+      raise(SanityCheck, "no idx for basic_var #{basic_var} in a") unless idx
       @x[basic_var] = @b[idx]
-    end
+    }
   end
 
   def solution
@@ -70,7 +71,7 @@ def solve
     count = 0
     while self.can_improve?
       count += 1
-      raise "too many pivots: #{count}" unless count < @max_pivots
+      raise(TooManyPivots, count.to_s) unless count < @max_pivots
       self.pivot
     end
   end
@@ -100,6 +101,7 @@ def pivot
         break
       end
     }
+    raise(SanityCheck, "no leaving_var") if leaving_var.nil?
 
     @basic_vars.delete(leaving_var)
     @basic_vars.push(pivot_column)

From e1617c8cea8cf85b5226d88339147bf03a184285 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 09:09:13 +0000
Subject: [PATCH 30/37] introduce Simplex::Error and inherit from it

---
 lib/simplex.rb | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 8ab0909..53ae3b8 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -7,9 +7,10 @@ class Vector
 class Simplex
   DEFAULT_MAX_PIVOTS = 10_000
 
-  class UnboundedProblem < RuntimeError; end
-  class SanityCheck < RuntimeError; end
-  class TooManyPivots < RuntimeError; end
+  class Error < RuntimeError; end
+  class UnboundedProblem < Error; end
+  class SanityCheck < Error; end
+  class TooManyPivots < Error; end
 
   attr_accessor :max_pivots
 

From 97ffa3d771259b9da0387470b3be4daa4d0d2db5 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Tue, 31 Oct 2017 05:34:42 +0000
Subject: [PATCH 31/37] benchmark/ips: 546 ips (was 460)

---
 metrics/bench | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/metrics/bench b/metrics/bench
index 09b8955..e0ab388 100644
--- a/metrics/bench
+++ b/metrics/bench
@@ -1,5 +1,5 @@
-/proc/loadavg 0.08 0.02 0.01 1/79 1931
+/proc/loadavg 0.01 0.01 0.00 1/79 3023
 Warming up --------------------------------------
-      Simplex Vector    46.000  i/100ms
+      Simplex Vector    54.000  i/100ms
 Calculating -------------------------------------
-      Simplex Vector    460.019  (± 0.9%) i/s -      1.380k in   3.000113s
+      Simplex Vector    546.614  (± 1.3%) i/s -      1.674k in   3.063034s

From f58fe51eae0e0345e054c7407bec5c41140f3831 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Tue, 31 Oct 2017 04:56:57 +0000
Subject: [PATCH 32/37] s/Vector/Array/g

---
 lib/simplex.rb        | 26 +++++++++++---------------
 metrics/bench         |  6 +++---
 test/bench/simplex.rb |  2 +-
 3 files changed, 15 insertions(+), 19 deletions(-)

diff --git a/lib/simplex.rb b/lib/simplex.rb
index 53ae3b8..573b678 100644
--- a/lib/simplex.rb
+++ b/lib/simplex.rb
@@ -1,9 +1,3 @@
-require 'matrix'
-
-class Vector
-  public :[]=
-end
-
 class Simplex
   DEFAULT_MAX_PIVOTS = 10_000
 
@@ -31,15 +25,14 @@ def initialize(c, a, b)
     @num_vars           = @num_non_slack_vars + @num_constraints
 
     # Set up initial matrix A and vectors b, c
-    @c = Vector[*(c.map { |flt| -1 * flt } + Array.new(@num_constraints, 0))]
+    @c = c.map { |flt| -1 * flt } + Array.new(@num_constraints, 0)
     @a = a.map.with_index { |ary, i|
       if ary.size != @num_non_slack_vars
         raise ArgumentError, "a is inconsistent"
       end
-      constraints = Array.new(@num_constraints) { |ci| ci == i ? 1 : 0 }
-      Vector[*(ary + constraints)]
+      ary + Array.new(@num_constraints) { |ci| ci == i ? 1 : 0 }
     }
-    @b = Vector.elements(b, true)
+    @b = b
 
     # set initial solution: all non-slack variables = 0
     @basic_vars = (@num_non_slack_vars...@num_vars).to_a
@@ -111,18 +104,21 @@ def pivot
     pivot_ratio = Rational(1, @a[pivot_row][pivot_column])
 
     # update pivot row
-    @a[pivot_row] *= pivot_ratio
-    @b[pivot_row] = pivot_ratio * @b[pivot_row]
+    @a[pivot_row] = @a[pivot_row].map { |val| val * pivot_ratio }
+    @b[pivot_row] = @b[pivot_row] * pivot_ratio
 
     # update objective
-    @c -= @c[pivot_column] * @a[pivot_row]
+    # @c -= @c[pivot_column] * @a[pivot_row]
+    @c = @c.map.with_index { |val, i|
+      val - @c[pivot_column] * @a[pivot_row][i]
+    }
 
     # update A and B
     @num_constraints.times { |i|
       next if i == pivot_row
       r = @a[i][pivot_column]
-      @a[i] -= r * @a[pivot_row]
-      @b[i] -= r * @b[pivot_row]
+      @a[i] = @a[i].map.with_index { |val, j| val - r * @a[pivot_row][j] }
+      @b[i] = @b[i] - r * @b[pivot_row]
     }
 
     self.update_solution
diff --git a/metrics/bench b/metrics/bench
index e0ab388..32918eb 100644
--- a/metrics/bench
+++ b/metrics/bench
@@ -1,5 +1,5 @@
-/proc/loadavg 0.01 0.01 0.00 1/79 3023
+/proc/loadavg 0.01 0.01 0.00 1/77 1173
 Warming up --------------------------------------
-      Simplex Vector    54.000  i/100ms
+       Simplex Array    84.000  i/100ms
 Calculating -------------------------------------
-      Simplex Vector    546.614  (± 1.3%) i/s -      1.674k in   3.063034s
+       Simplex Array    849.092  (± 1.3%) i/s -      2.604k in   3.067337s
diff --git a/test/bench/simplex.rb b/test/bench/simplex.rb
index 60c0695..10728e0 100644
--- a/test/bench/simplex.rb
+++ b/test/bench/simplex.rb
@@ -4,7 +4,7 @@
 Benchmark.ips do |b|
   b.config time: 3, warmup: 0.5
 
-  b.report("Simplex Vector") {
+  b.report("Simplex Array") {
     Simplex.new([1, 1],
                 [[2,  1],
                  [1,  2]],

From daf4e2554bc88e3e05e2b71092c3b1129e17d2e2 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 03:55:59 +0000
Subject: [PATCH 33/37] add Simplex::Parse module

---
 lib/simplex/parse.rb | 51 ++++++++++++++++++++++++++++++++++++++++++++
 test/parse.rb        | 38 +++++++++++++++++++++++++++++++++
 2 files changed, 89 insertions(+)
 create mode 100644 lib/simplex/parse.rb
 create mode 100644 test/parse.rb

diff --git a/lib/simplex/parse.rb b/lib/simplex/parse.rb
new file mode 100644
index 0000000..1acb462
--- /dev/null
+++ b/lib/simplex/parse.rb
@@ -0,0 +1,51 @@
+class Simplex
+  module Parse
+    TERM_RGX = %r{
+      \A                  # starts with
+        (-)?              # possible negative sign
+        (\d+\.?\d*)?      # possible float (optional)
+        ([a-zA-Z])        # single letter variable
+      \z                  # end str
+    }x
+
+    # rules: variables are a single letter
+    #        may have a coefficient (default: 1.0)
+    #        only sum and difference operations allowed
+    #        normalize to all sums with possibly negative coefficients
+    # valid inputs:
+    #   'x + y'          => [1.0, 1.0],         [:x, :y]
+    #   '2x - 5y'        => [2.0, -5.0],        [:x, :y]
+    #   '-2x - 3y + -4z' => [-2.0, -3.0, -4.0], [:x, :y, :z]
+    def self.objective(str)
+      terms = str.split(/\s+/)
+      negative = false
+      coefficients = []
+      variables = []
+      while !terms.empty?
+        # consume plus and minus operations
+        term = terms.shift
+        if term == '-'
+          negative = true
+          term = terms.shift
+        elsif term == '+'
+          negative = false
+          term = terms.shift
+        end
+
+        coefficient, variable = self.term(term)
+        coefficient *= -1 if negative
+        coefficients << coefficient
+        variables << variable
+      end
+      return coefficients, variables
+    end
+
+    def self.term(term_str)
+      matches = term_str.match TERM_RGX
+      raise "bad term: #{term_str}" unless matches
+      flt = (matches[2] || 1).to_f * (matches[1] ? -1 : 1)
+      sym = matches[3].to_sym # consider matches[3].downcase.to_sym
+      return flt, sym
+    end
+  end
+end
diff --git a/test/parse.rb b/test/parse.rb
new file mode 100644
index 0000000..84111d3
--- /dev/null
+++ b/test/parse.rb
@@ -0,0 +1,38 @@
+require 'simplex/parse'
+require 'minitest/autorun'
+
+describe Simplex::Parse do
+  describe "Parse.term" do
+    it "must parse valid terms" do
+      { "-1.2A" => [-1.2, :A],
+        "99x" => [99.0, :x],
+        "z" => [1.0, :z],
+        "-b" => [-1.0, :b] }.each { |valid, expected|
+        Simplex::Parse.term(valid).must_equal expected
+      }
+    end
+
+    it "must reject invalid terms" do
+      ["3xy", "24/7x", "x17", "2*x"].each { |invalid|
+        proc { Simplex::Parse.term(invalid) }.must_raise RuntimeError
+      }
+    end
+  end
+
+  describe "Parse.objective" do
+    it "must parse valid expressions" do
+      { "x + y" => [[1.0, 1.0], [:x, :y]],
+        "2x - 5y" => [[2.0, -5.0], [:x, :y]],
+        "-2x - 3y + -42.7z" => [[-2.0, -3.0, -42.7], [:x, :y, :z]],
+      }.each { |valid, expected|
+        Simplex::Parse.objective(valid).must_equal expected
+      }
+    end
+
+    it "must reject invalid expressions" do
+      ["a2 + b2 = c2", "x + xy", "x * 2"].each { |invalid|
+        proc { Simplex::Parse.objective(invalid) }.must_raise RuntimeError
+      }
+    end
+  end
+end

From d59592b450d64c4b6fa780dd5526069aa43d2f71 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 04:47:12 +0000
Subject: [PATCH 34/37] add tokenizing, expression and inequality parsing, and
 some regexen

---
 lib/simplex/parse.rb | 37 +++++++++++++++++++++++++++------
 test/parse.rb        | 49 ++++++++++++++++++++++++++++++++++++++------
 2 files changed, 74 insertions(+), 12 deletions(-)

diff --git a/lib/simplex/parse.rb b/lib/simplex/parse.rb
index 1acb462..62bc520 100644
--- a/lib/simplex/parse.rb
+++ b/lib/simplex/parse.rb
@@ -1,13 +1,38 @@
 class Simplex
   module Parse
+    # coefficient concatenated with a single letter variable, e.g. "-1.23x"
     TERM_RGX = %r{
       \A                  # starts with
         (-)?              # possible negative sign
-        (\d+\.?\d*)?      # possible float (optional)
+        (\d+(?:\.\d*)?)?  # possible float (optional)
         ([a-zA-Z])        # single letter variable
       \z                  # end str
     }x
 
+    # a float or integer, possibly negative
+    CONSTANT_RGX = %r{
+      \A           # starts with
+        -?         # possible negative sign
+        \d+        # integer portion
+        (?:\.\d*)? # possible decimal portion
+      \z           # end str
+    }x
+
+    def self.inequality(str)
+      lhs, rhs = str.split('<=')
+      lhco, lhvar = self.expression(lhs)
+      rht = self.tokenize(rhs)
+      raise "bad inequality: #{str}; bad rhs: #{rhs}" unless rht.size == 1
+      raise "bad rhs: #{rhs}" if !rht.first.match CONSTANT_RGX
+      return lhco, lhvar, rht.first.to_f
+    end
+
+    # ignore leading and trailing spaces
+    # ignore multiple spaces
+    def self.tokenize(str)
+      str.strip.split(/\s+/)
+    end
+
     # rules: variables are a single letter
     #        may have a coefficient (default: 1.0)
     #        only sum and difference operations allowed
@@ -16,8 +41,8 @@ module Parse
     #   'x + y'          => [1.0, 1.0],         [:x, :y]
     #   '2x - 5y'        => [2.0, -5.0],        [:x, :y]
     #   '-2x - 3y + -4z' => [-2.0, -3.0, -4.0], [:x, :y, :z]
-    def self.objective(str)
-      terms = str.split(/\s+/)
+    def self.expression(str)
+      terms = self.tokenize(str)
       negative = false
       coefficients = []
       variables = []
@@ -40,9 +65,9 @@ def self.objective(str)
       return coefficients, variables
     end
 
-    def self.term(term_str)
-      matches = term_str.match TERM_RGX
-      raise "bad term: #{term_str}" unless matches
+    def self.term(str)
+      matches = str.match TERM_RGX
+      raise "bad term: #{str}" unless matches
       flt = (matches[2] || 1).to_f * (matches[1] ? -1 : 1)
       sym = matches[3].to_sym # consider matches[3].downcase.to_sym
       return flt, sym
diff --git a/test/parse.rb b/test/parse.rb
index 84111d3..43a0045 100644
--- a/test/parse.rb
+++ b/test/parse.rb
@@ -2,36 +2,73 @@
 require 'minitest/autorun'
 
 describe Simplex::Parse do
+  P = Simplex::Parse
+
   describe "Parse.term" do
     it "must parse valid terms" do
       { "-1.2A" => [-1.2, :A],
         "99x" => [99.0, :x],
         "z" => [1.0, :z],
         "-b" => [-1.0, :b] }.each { |valid, expected|
-        Simplex::Parse.term(valid).must_equal expected
+        P.term(valid).must_equal expected
       }
     end
 
     it "must reject invalid terms" do
       ["3xy", "24/7x", "x17", "2*x"].each { |invalid|
-        proc { Simplex::Parse.term(invalid) }.must_raise RuntimeError
+        proc { P.term(invalid) }.must_raise RuntimeError
       }
     end
   end
 
-  describe "Parse.objective" do
+  describe "Parse.expression" do
     it "must parse valid expressions" do
       { "x + y" => [[1.0, 1.0], [:x, :y]],
         "2x - 5y" => [[2.0, -5.0], [:x, :y]],
         "-2x - 3y + -42.7z" => [[-2.0, -3.0, -42.7], [:x, :y, :z]],
+        " -5y + -x  " => [[-5.0, -1.0], [:y, :x]],
+        "a - -b" => [[1.0, 1.0], [:a, :b]],
+        "a b c" => [[1.0, 1.0, 1.0], [:a, :b, :c]],
       }.each { |valid, expected|
-        Simplex::Parse.objective(valid).must_equal expected
+        P.expression(valid).must_equal expected
       }
     end
 
     it "must reject invalid expressions" do
-      ["a2 + b2 = c2", "x + xy", "x * 2"].each { |invalid|
-        proc { Simplex::Parse.objective(invalid) }.must_raise RuntimeError
+      ["a2 + b2 = c2",
+       "x + xy",
+       "x * 2"].each { |invalid|
+        proc { P.expression(invalid) }.must_raise RuntimeError
+      }
+    end
+  end
+
+  describe "Parse.tokenize" do
+    it "ignores leading or trailing whitespace" do
+      P.tokenize("  5x + 2.9y ").must_equal ["5x", "+", "2.9y"]
+    end
+
+    it "ignores multiple spaces" do
+      P.tokenize("5x   +   2.9y").must_equal ["5x", "+", "2.9y"]
+    end
+  end
+
+  describe "Parse.inequality" do
+    it "must parse valid inequalities" do
+      { "x + y <= 4" => [[1.0, 1.0], [:x, :y], 4.0],
+        "0.94a - 22.1b <= -14.67" => [[0.94, -22.1], [:a, :b], -14.67],
+        "x <= 0" => [[1.0], [:x], 0],
+      }.each { |valid, expected|
+        P.inequality(valid).must_equal expected
+      }
+    end
+
+    it "must reject invalid inequalities" do
+      ["x + y >= 4",
+       "0.94a - 22.1b <= -14.67c",
+       "x < 0",
+      ].each { |invalid|
+        proc { P.inequality(invalid) }.must_raise RuntimeError
       }
     end
   end

From 6808fe458810a2170cccec899590c73c61e06884 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 09:07:03 +0000
Subject: [PATCH 35/37] introduce Parse::Error and use it

---
 lib/simplex/parse.rb | 14 ++++++++++----
 test/parse.rb        |  4 ++--
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/lib/simplex/parse.rb b/lib/simplex/parse.rb
index 62bc520..54e605a 100644
--- a/lib/simplex/parse.rb
+++ b/lib/simplex/parse.rb
@@ -1,5 +1,10 @@
 class Simplex
   module Parse
+    class Error < RuntimeError; end
+    class InvalidExpression < Error; end
+    class InvalidInequality < Error; end
+    class InvalidTerm < Error; end
+
     # coefficient concatenated with a single letter variable, e.g. "-1.23x"
     TERM_RGX = %r{
       \A                  # starts with
@@ -22,9 +27,10 @@ def self.inequality(str)
       lhs, rhs = str.split('<=')
       lhco, lhvar = self.expression(lhs)
       rht = self.tokenize(rhs)
-      raise "bad inequality: #{str}; bad rhs: #{rhs}" unless rht.size == 1
-      raise "bad rhs: #{rhs}" if !rht.first.match CONSTANT_RGX
-      return lhco, lhvar, rht.first.to_f
+      raise(InvalidInequality, "#{str}; bad rhs: #{rhs}") unless rht.size == 1
+      c = rht.first
+      raise(InvalidInequality, "bad rhs: #{rhs}") if !c.match CONSTANT_RGX
+      return lhco, lhvar, c.to_f
     end
 
     # ignore leading and trailing spaces
@@ -67,7 +73,7 @@ def self.expression(str)
 
     def self.term(str)
       matches = str.match TERM_RGX
-      raise "bad term: #{str}" unless matches
+      raise(InvalidTerm, str) unless matches
       flt = (matches[2] || 1).to_f * (matches[1] ? -1 : 1)
       sym = matches[3].to_sym # consider matches[3].downcase.to_sym
       return flt, sym
diff --git a/test/parse.rb b/test/parse.rb
index 43a0045..1bdf355 100644
--- a/test/parse.rb
+++ b/test/parse.rb
@@ -38,7 +38,7 @@
       ["a2 + b2 = c2",
        "x + xy",
        "x * 2"].each { |invalid|
-        proc { P.expression(invalid) }.must_raise RuntimeError
+        proc { P.expression(invalid) }.must_raise P::Error
       }
     end
   end
@@ -68,7 +68,7 @@
        "0.94a - 22.1b <= -14.67c",
        "x < 0",
       ].each { |invalid|
-        proc { P.inequality(invalid) }.must_raise RuntimeError
+        proc { P.inequality(invalid) }.must_raise P::Error
       }
     end
   end

From 35bc7d7368c362debad16ece43e35c8999dc75d7 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Mon, 30 Oct 2017 09:24:27 +0000
Subject: [PATCH 36/37] reformat for readability

---
 test/parse.rb | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/test/parse.rb b/test/parse.rb
index 1bdf355..84e2cf3 100644
--- a/test/parse.rb
+++ b/test/parse.rb
@@ -7,9 +7,9 @@
   describe "Parse.term" do
     it "must parse valid terms" do
       { "-1.2A" => [-1.2, :A],
-        "99x" => [99.0, :x],
-        "z" => [1.0, :z],
-        "-b" => [-1.0, :b] }.each { |valid, expected|
+        "99x"   => [99.0, :x],
+        "z"     => [1.0,  :z],
+        "-b"    => [-1.0, :b] }.each { |valid, expected|
         P.term(valid).must_equal expected
       }
     end
@@ -23,12 +23,12 @@
 
   describe "Parse.expression" do
     it "must parse valid expressions" do
-      { "x + y" => [[1.0, 1.0], [:x, :y]],
-        "2x - 5y" => [[2.0, -5.0], [:x, :y]],
+      { "x + y"             => [[1.0, 1.0],          [:x, :y]],
+        "2x - 5y"           => [[2.0, -5.0],         [:x, :y]],
         "-2x - 3y + -42.7z" => [[-2.0, -3.0, -42.7], [:x, :y, :z]],
-        " -5y + -x  " => [[-5.0, -1.0], [:y, :x]],
-        "a - -b" => [[1.0, 1.0], [:a, :b]],
-        "a b c" => [[1.0, 1.0, 1.0], [:a, :b, :c]],
+        " -5y + -x  "       => [[-5.0, -1.0],        [:y, :x]],
+        "a - -b"            => [[1.0, 1.0],          [:a, :b]],
+        "a A b"             => [[1.0, 1.0, 1.0],     [:a, :A, :b]],
       }.each { |valid, expected|
         P.expression(valid).must_equal expected
       }
@@ -55,9 +55,9 @@
 
   describe "Parse.inequality" do
     it "must parse valid inequalities" do
-      { "x + y <= 4" => [[1.0, 1.0], [:x, :y], 4.0],
+      { "x + y <= 4"              => [[1.0, 1.0],    [:x, :y], 4.0],
         "0.94a - 22.1b <= -14.67" => [[0.94, -22.1], [:a, :b], -14.67],
-        "x <= 0" => [[1.0], [:x], 0],
+        "x <= 0"                  => [[1.0],         [:x],     0],
       }.each { |valid, expected|
         P.inequality(valid).must_equal expected
       }

From f75d70b277575d840058cdcee0b504ff9b53e551 Mon Sep 17 00:00:00 2001
From: Rick Hull <rick.hull@gmail.com>
Date: Tue, 31 Oct 2017 07:24:38 +0000
Subject: [PATCH 37/37] add Simplex.maximize

- based on Simplex.problem
- which required changing Parse.expression's return type to a hash
  with variable keys and coefficient values
---
 lib/simplex/parse.rb | 57 +++++++++++++++++++++++++++++++++++++-------
 test/parse.rb        | 37 ++++++++++++++++++++--------
 2 files changed, 76 insertions(+), 18 deletions(-)

diff --git a/lib/simplex/parse.rb b/lib/simplex/parse.rb
index 54e605a..00f360e 100644
--- a/lib/simplex/parse.rb
+++ b/lib/simplex/parse.rb
@@ -25,12 +25,14 @@ class InvalidTerm < Error; end
 
     def self.inequality(str)
       lhs, rhs = str.split('<=')
-      lhco, lhvar = self.expression(lhs)
+      if lhs.nil? or lhs.empty? or rhs.nil? or rhs.empty?
+        raise(InvalidInequality, "#{str}")
+      end
       rht = self.tokenize(rhs)
       raise(InvalidInequality, "#{str}; bad rhs: #{rhs}") unless rht.size == 1
       c = rht.first
       raise(InvalidInequality, "bad rhs: #{rhs}") if !c.match CONSTANT_RGX
-      return lhco, lhvar, c.to_f
+      return self.expression(lhs), c.to_f
     end
 
     # ignore leading and trailing spaces
@@ -50,8 +52,7 @@ def self.tokenize(str)
     def self.expression(str)
       terms = self.tokenize(str)
       negative = false
-      coefficients = []
-      variables = []
+      coefficients = {}
       while !terms.empty?
         # consume plus and minus operations
         term = terms.shift
@@ -64,11 +65,10 @@ def self.expression(str)
         end
 
         coefficient, variable = self.term(term)
-        coefficient *= -1 if negative
-        coefficients << coefficient
-        variables << variable
+        raise("double variable: #{str}") if coefficients.key?(variable)
+        coefficients[variable] = negative ? coefficient * -1 : coefficient
       end
-      return coefficients, variables
+      coefficients
     end
 
     def self.term(str)
@@ -79,4 +79,45 @@ def self.term(str)
       return flt, sym
     end
   end
+
+  def self.problem(maximize: nil, constraints: [], **kwargs)
+    if maximize
+      obj, maximize = maximize, true
+    elsif kwargs[:minimize]
+      obj, maximize = kwargs[:minimize], false
+    else
+      raise(ArgumentError, "one of maximize/minimize expected")
+    end
+    unless obj.is_a?(String)
+      raise(ArgumentError, "bad expr: #{expr} (#{expr.class})")
+    end
+    obj_cof = Parse.expression(obj)
+
+    c = [] # coefficients of objective expression
+    a = [] # array (per constraint) of the inequality's lhs coefficients
+    b = [] # rhs (constant) for the inequalities / constraints
+
+    # this determines the order of coefficients
+    letter_vars = obj_cof.keys
+    letter_vars.each { |v| c << obj_cof[v] }
+
+    constraints.each { |str|
+      unless str.is_a?(String)
+        raise(ArgumentError, "bad constraint: #{str} (#{str.class})")
+      end
+      cofs = []
+      ineq_cofs, rhs = Parse.inequality(str)
+      letter_vars.each { |v|
+        raise("constraint #{str} is missing var #{v}") unless ineq_cofs.key?(v)
+        cofs << ineq_cofs[v]
+      }
+      a.push cofs
+      b.push rhs
+    }
+    self.new(c, a, b)
+  end
+
+  def self.maximize(expression, *ineqs)
+    self.problem(maximize: expression, constraints: ineqs).solution
+  end
 end
diff --git a/test/parse.rb b/test/parse.rb
index 84e2cf3..73f816b 100644
--- a/test/parse.rb
+++ b/test/parse.rb
@@ -8,7 +8,7 @@
     it "must parse valid terms" do
       { "-1.2A" => [-1.2, :A],
         "99x"   => [99.0, :x],
-        "z"     => [1.0,  :z],
+        "z"     => [ 1.0, :z],
         "-b"    => [-1.0, :b] }.each { |valid, expected|
         P.term(valid).must_equal expected
       }
@@ -23,12 +23,12 @@
 
   describe "Parse.expression" do
     it "must parse valid expressions" do
-      { "x + y"             => [[1.0, 1.0],          [:x, :y]],
-        "2x - 5y"           => [[2.0, -5.0],         [:x, :y]],
-        "-2x - 3y + -42.7z" => [[-2.0, -3.0, -42.7], [:x, :y, :z]],
-        " -5y + -x  "       => [[-5.0, -1.0],        [:y, :x]],
-        "a - -b"            => [[1.0, 1.0],          [:a, :b]],
-        "a A b"             => [[1.0, 1.0, 1.0],     [:a, :A, :b]],
+      { "x + y"             => { x:  1.0, y:  1.0 },
+        "2x - 5y"           => { x:  2.0, y: -5.0 },
+        "-2x - 3y + -42.7z" => { x: -2.0, y: -3.0, z: -42.7 },
+        " -5y + -x  "       => { y: -5.0, x: -1.0 },
+        "a - -b"            => { a:  1.0, b:  1.0 },
+        "a A b"             => { a:  1.0, :A => 1.0, b: 1.0 },
       }.each { |valid, expected|
         P.expression(valid).must_equal expected
       }
@@ -55,9 +55,9 @@
 
   describe "Parse.inequality" do
     it "must parse valid inequalities" do
-      { "x + y <= 4"              => [[1.0, 1.0],    [:x, :y], 4.0],
-        "0.94a - 22.1b <= -14.67" => [[0.94, -22.1], [:a, :b], -14.67],
-        "x <= 0"                  => [[1.0],         [:x],     0],
+      { "x + y <= 4"              => [{ x: 1.0, y: 1.0 }, 4.0],
+        "0.94a - 22.1b <= -14.67" => [{ a: 0.94, b: -22.1 }, -14.67],
+        "x <= 0"                  => [{ x: 1.0 }, 0],
       }.each { |valid, expected|
         P.inequality(valid).must_equal expected
       }
@@ -73,3 +73,20 @@
     end
   end
 end
+
+describe "Simplex.maximize" do
+  it "must problem stuff" do
+    prob = Simplex.problem(maximize: 'x + y',
+                           constraints: ['2x + y <= 4',
+                                         'x + 2y <= 3'])
+    sol = prob.solution
+    sol.must_equal [Rational(5, 3), Rational(2, 3)]
+  end
+
+  it "must maximize stuff" do
+    Simplex.maximize('x + y',
+                     '2x + y <= 4',
+                     'x + 2y <= 3').must_equal [Rational(5, 3),
+                                                Rational(2, 3)]
+  end
+end