Judea Pearl

Judea Pearl is the newest winner of the Turing Award.
Judea Pearl's studies and advancements range from in artificial intelligence to philosophy
I recently listened to 1hr 41min interview by Stephen Ibaraki on behalf of ACM  here are the highlights

Education:



Counterfactuals:


Success:

3: First Order Recurrence Relations

Check out the project description here

First Order what?
First order recurrence is a type of a recursive equation that can be . The following equations have first order recurrence relations:

• The coefficients are constants and only to the first power
• The nth term depends only on term ( n - 1 )
• General Form: S(n) = cS( n - 1 ) + g(n)

Here is the equation to convert first order recursive equations into linear equations

• S(n) = C^n-1S(1) + ⁿΣ_i=2 [ C^n-i * g(n) ]

Quick example

• Original: S(n) = 2*S( n - 1 ) + 3
• Becomes: S(n) = 2^n-1 * S(1) + ⁿΣ_i=2 [ 2^n-i * 3 ]

Imagine inputing 5,000 for n. The second equation would have a significantly smaller big-O complexity

The Code
Due to the fact that my professor usually gives us read-in-files contain similar formats I decided to make a master parsing class that you can look at on github if you want.

• The code doesn't contain anything fancy.
• I love ruby's exponent operator **
• I love ruby's for loops

2: Second Order Recurrence Relations

Second Order What?
Second Order Recurrence Relations is a fancy way of saying, if recursive equation meets a specific criteria, it can be reduced to a no recursive equation.

Requirements:

• The nth term depends on the two previous terms
• Constant coefficients with exponents no greater than 1
• Must be homogeneous ( g(n) == 0 )
• General form: S(n) = C₁S( n - 1 ) + C₂S( n - 2 )

Process:

1. Find the roots of t² - C₁t - C₂ = 0
1. r₁ & r₂
2. Solve for p & q
1. S(1) = p + q
2. S(2) = p( r₁ ) + q( r₂ )
3. Plug answers in the solution formula
1. S(n) = p( r₁ )^{n - 1} + q( r₂ )^{n - 1}

Example:

   S(n) = 2S( n - 1 ) + 3S( n - 2 )
   S(1) = 3
   S(2) = 1

1.  t² - 2t - 3 = 0
• r₁ = 3
•  r₂  = -1
2. Solve for p & q
• 3 = q + p
• p( 3 ) + q( -1 ) = 1
• p = 1
• q = 2
3. Substitute
1. S(n) = 1( 3 )^n-1 + 2( -1 )^n-1

Code

• line 10: Love how you can simultaneously assign variables from an array
• Line 36: This isn't a true quadratic formula. It takes advantage of the fact that a == 1in all cases  
• I added a master parse file 
• I love the ||= assignment, this is amazing. It will only assign the variable if it doesn't exist

	# PROJECT: Second Order Recurrence Relations
	$LOAD_PATH << '../lib'
	require 'parseFile.rb'
	class Sorr
	def initialize(inputs)
	s1 = inputs["S(1)"]; s2 = inputs["S(2)"]
	c1 = inputs['C1']; c2 = inputs['C2']
	r1,r2 = quadratic(c1,c2)
	puts "r1 = #{r1}"
	puts "r2 = #{r2}"
	unless r1 == r2
	q = ((s2 - (s1 * r1) ) / ( ( -r1 ) + r2 ))
	p = s1 - q
	puts "p = #{p}"
	puts "q = #{q}"
	puts "S(n) = (#{p})(#{r1})^(n-1) + (#{q})(#{r2})^(n-1)"
	for i in 1..10 do
	puts "S(#{i}) = #{(p*r1**(i-1) + q*r2**(i-1))}"
	end
	else
	p = s1
	q = ( s2 - p*r1 ) / r1
	puts "p = #{p}"
	puts "q = #{q}"
	puts "S(n) = #{r1}^(n-1) + #{q}(n-1)*#{r1}^(n-1)"
	for i in 1..10 do
	puts "S(#{i}) = #{r1**(i-1) + q*(i-1)*r1**(i-1)}"
	end
	end #unless
	end #initialize
	def quadratic(b,c)
	[ ( b + Math.sqrt(b**2 + 4 * c) ) / 2,
	( b - Math.sqrt(b**2 + 4 * c) ) / 2 ]
	end #quadratic
	end #class Sorr
	begin
	parsed = Master::ParseFile.new(Hash)
	if parsed.getFile.instance_of?(Hash) then Sorr.new(parsed.getFile) end
	end

view raw SORR.rb hosted with ❤ by GitHub

Sync RVM with TextMate

I've been trying to sync TextMate with RVM found this tutorial extremely helpful.

Basic Process:

1. Print path to RVM-AUTO-RUBY ( the exec file that runs the default interpreter set by rvm )
• Unix command: $ which rvm-auto-ruby
2. Copy path to TextMate's preferences
• Under TextMate > Preferences > Advanced > Shell Variables create a new shell variable 
• Variable: TM_RUBY
• Value: ( path returned by which rvm-auto-ruby cmd )

Debugging Tips:

• Print out path to current ruby interpreter 

• 	# Print Interpreter path
  	require 'rbconfig'
  	puts RbConfig.ruby()

  view raw InterpreterPath.rb hosted with ❤ by GitHub

1: Programming Review

Project description.

Concerns

• line 21: I'm not sure if this is the best way to check the command line inputs and save them.
• line 27: I feel like there should be a way to combine this with line 24? like or die in perl 
• I can't believe the there aren't any Math.sum Math.average or Math.median functions but I do like the way you can easily insert methods into a core class ( line 1 - 11 )
• line 31 - 36: I swear I've heard of an cleaner way to parse in a file, but my solution works 
• line 40: I'm not really sure what ensure does
• line 2: inject(:+) ??? what the crap? this is cool, but not intuitive at all. Someone please explain
• I could make it a little more object oriented by making a print result method ... but meh

Let me know what you think. 

	# Add sum, mean, & median to Array class
	class Array; def sum; inject(:+) end end
	class Array; def mean; sum.to_f / size end end
	class Array
	def median(arry)
	sorted = arry.sort
	medpt = arry.length / 2
	medpt1 = ( ( arry.length - 1 ).to_f / 2 )
	(sorted[medpt] + sorted[medpt1]).to_f / 2
	end
	end
	def empty
	puts "Sum: 0.0"
	puts "Mean: 0.0"
	puts "Median 0.0"
	exit
	end
	begin
	# Get file from cmd :: Default file is input1.txt
	if ARGV[0] != nil; input = ARGV[0] else input = "input1.txt" end
	#Read in a file
	file = File.new(input, 'r')
	# check file size
	if File.size(input) <= 0; empty end
	#Parse file
	nums = Array.new
	while (line = file.gets)
	num = line.split(" ")
	num.length.times do |n|
	nums.push(Float(num[n]))
	end
	end
	rescue Errno::ENOENT
	puts "The file was not found: #{$!}"
	exit
	ensure
	file.close if file
	end
	#Print out sum,mean & median
	puts "Sum: #{sprintf("%.2f", nums.sum)}"
	puts "Mean: #{sprintf("%.2f",nums.mean)}"
	puts "Median: #{sprintf("%.2f",nums.median(nums) )}"

view raw Review.rb hosted with ❤ by GitHub

Blog init

Blog.what?
Here are some sample projects from my CIS 206 Discrete Mathematics class. The course is taught by Geoffrey Draper at BYU-Hawaii.  In our class, we are permitted to program in any language of our choice. I've decided to take advantage of that freedom to try and learn Ruby. I'm using Ruby 1.9.2

Blog.why? 
I've decided to blog my projects for the following reasons:

• My programs will be helpful to others who learn Ruby
• People's comments will help me learn Ruby faster
• It's a personal programming journal

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