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Welcome to lecture 4: An introduction to modular PERL IGERT – Sponsored Bioinformatics Workshop Series Michael Janis and Max Kopelevich, Ph.D. Dept. of Chemistry & Biochemistry, UCLA

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Last time… We covered a bit of material… Try to keep up with the reading – it’s all in there! We’ve covered variables, control structures, data structures, functions… –Now we’ll cover modular programming –We’ll create libraries of our own to use –We’ll take an example of a biological problem that incorporates everything we’ve learned and used so far…

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Gene Finding (A very simplified example)

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How to find a gene given a sequence? Conversely, what is the likelihood that a given region of sequence is a coding region? Note that we used the term ‘likelihood’: –A simplified statistical approach Codon usage throughout an organisms genome is non-uniform Non-coding regions differ from coding regions in their codon usage We can use this information to test putative ORFs –A more traditional approach Makes use of homology of putative regions to other known protein sequences Does not require prior information regarding codon bias Suffers from problems inherit in homology – based analysis

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How to find a gene given a sequence? We don’t have to choose. We can use both (heuristics)? We’ll be dealing with sometimes complex and contradicting information Genes are non-linear linear: –There may be many methionine codons present –There are different reading frames possible –There are intron / exon combinations (alt. splicing) ATG possible start codons possible stop codons In-frame start to stop putative ORF

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Note that we used the term ‘likelihood’: We need to introduce, briefly, some Probability and statistics Just a little Evil…

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Permutations Groups of Ordered arrangements of things How many 3 letter permutations of the letters a, b, & c are there? abc, acb, bac, bca, cba, cab 6 total – General Formula: – n = total number of things – k = size of the groups your taking k < n 3!/(3-3)! = 6 – Can use Basic Principle of Counting: 3*2*1 = 6

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IQR What if some of the things are identical? How many permutations of the letters a, a, b, c, c & c are there? Permutations 6! / (3!2!) = 60 Where n 1, n 2, … n r are the number of objects that are alike

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IQR Combinations Groups of things (Order doesn’t matter) How many 3 letter combinations of the letters a, b, & c are there? 1: abc How many 2 letter combinations of the letters a, b, & c are there? 3: ab, ac, bc ab = ba; ac = ca; bc = cb* Order doesn’t matter – General Formula: – n = total number of things – k = size of the groups your taking k < n “n choose k”

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IQR E = {a, b, c, d}F = {b, c, d, e, f, g} E SF S E c = {e, f, g, h, i, j}F c = {a, h, i, j} E F = {a, b, c, d, e, f, g} E F = EF = {b, c, d} Set Theory Sample Space of an experiment is the set of all possible values/outcomes of the experiment S = {a, b, c, d, e, f, g, h, i, j}S = {Heads, Tails} S = {1, 2, 3, 4, 5, 6}

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IQR S Venn Diagrams E F G

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Simple Probability Frequent assumption: All Outcomes Equally likely to occur The probability of an event E, is simply: Number of possible outcomes in E Number of Total possible outcomes S = {a, b, c, d, e, f, g, h, i, j} E = {a, b, c, d}F = {b, c, d, e, f, g} P(E) = 4/10P(F) = 6/10 P(S) = 1 0 < P(E) < 1P(E c ) = 1 – P(E) P(E F) = P(E) + P(F) – P(EF)

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IQR Independence Two events, E & F are independent if neither of their outcomes depends on the outcomes of others. So if E & F are independent, then: P(EF) = P(E)*P(F) If E, F & G are independent, then: P(EFG) = P(E)*P(F)*P(G)

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IQR Conditional Probability Given E, the probability of F is: S E F EF Similarly:

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ASSUME Here’s a simple question. I come from a family of two children (prior information states: I am a male). What’s the probability that my sibling is a sister? Outcome (sex of offspring) is equally likely Is it 0.5? Something else? What is the question really asking?

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Assumptions Here’s a simple question. I come from a family of two children. What’s the probability that my sibling is a sister? Sample space is actually four pairs of possible siblings (in order of birth): {(B,B),(B,G),(G,B),(G,G)} Let U be the event “one child is a girl” Let V be the event “one child is Mike” We want to calculate P(U|V)

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IQR Assumptions… Here’s a simple question. I come from a family of two children. What’s the probability that my sibling is a sister? P(U|V)=P(U V)/P(V) = P(one child is B, one is G)/P(one is B) = 2/4 / ¾=2/3 biologists cringe now…

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IQR Conditional Probability Given E, the probability of F is: S E F EF Similarly:

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IQR Random Variables Definition: A variable that can have different values Each value has its own probability X = Result of coin toss Heads 50%, Tails 50% Y = Result of die roll 1, 2, 3, 4, 5, 6 each 1/6

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IQR Discrete vs. Continuous Discrete random variables can only take a finite set of different values. Die roll, coin flip Continuous random variables can take on an infinite number (real) of values Time of day of event, height of a person

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Probability Density Function Many problems don’t have simple probabilities. For those the probabilities are expressed as a function… aka “pdf” Plug a into some function i.e. 2a 2 – a 3

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Some Useful pdf’s Simple cases (like fair/loaded coin/dice, etc…) Uniform random variable (“equally likely”) For a = Heads For a = Tails

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IQR pdf of a Binomial Very useful function! Where p = P(success) & q = P(failure) P(success) + P(failure) = 1 n choose k is the total number of possible ways to get k successes in n attempts

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IQR Hypergeometric distribution Tends towards the binomial distribution when N is large We can use combinatorics to test for enrichment; i.e. is the number found greater than expected by chance?

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IQR Hypergeometric distribution Our microarray of 9300 probesets (genes with some duplication) yields 200 upregulated genes in response to substance X. We use gene ontology to cluster these genes into 4 biological process clusters: 160 genes in mitosis, 80 in oncogenesis, 60 in cell proliferation, and 40 in glucose transport. Is substance X related to cancer? Need to account for total number of genes queried by microarray in each category… An enrichment problem (obs genes M, total number of genes N, the number of categorical genes x on the array, and the number of regulated genes K). Source: Data Analysis Tools for DNA Microarrays. Sorin Draghici, 2003.

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Hypergeometric distribution We may find that the inferred effect of substance X is very different from our initial response… Glucose transport 4x more than expected by chance; oncogenesis not better than chance… Maybe correlation is with diabetes instead?

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IQR Using the p.d.f. What is the Probability of getting 3 Heads in 5 coin tosses? (Same as 2T in 5 tosses) n = 5 tossesk = 3 Heads p = P(H) =.5q = P(T) =.5 P(3H in 5 tosses) = p 3 q 2 = 10p 3 q 2 = 10*P(H) 3 *P(T) 2 = 10(.5) 3 (.5) 2 = 0.3125

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IQR Notice how these are Binomials… What is the probability of winning the lottery in 2 of your next 3 tries? n = 3 triesk = 2 wins Assume P(win) = 10 -7 P(lose) = 1-10 -7 P(win 2 of 3 lotto) = P(win) 2 P(lose) = 3(10 -7 ) 2 (1-10 -7 ) = ~ 3*10 -14 That’s about a 3 in 100 trillion chance. Good Luck!

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IQR Expectation of a Discrete Random Variable Weighted average of a random variable …Of a function

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IQR Measures of central tendency Sample mean: the sum of measurements divided by the number of subjects. Sample median: the measurement that falls at the middle of the ordered sample.

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IQR Variance Variation, or spread of the values of a random variable Where μ = E[X]

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IQR Variance and standard deviation: measures of variation in statistics: Variance (s 2 ): the mean of the squared deviations for a sample. standard deviation (s ): the square root of the variance, or the root mean squared deviation, labelled

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IQR Statistics of populations The equations so far are for sample statistics a statistic is a single number estimated from a sample We use the sample to make inferences about the population. a parameter is a single number that summarizes some quality of a variable in a population. the term for the population mean is (mu), and Y bar is a sample estimator of . the term for the population standard deviation is (sigma), and s is a sample estimator of . Note that and are both elements of the normal probability curve. Source: http://www.bsos.umd.edu/socy/smartin/601/

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IQR Measuring probabilities under the normal curve We can make transformations by scaling everything with respect to the mean and standard deviation. Let z = the number of standard deviations above or below the population mean. z = 0y = z = 1y = +/- (p=0.68) z = 2y = +/- 2 (p=0.95) z = 3y = +/- 3 (p=0.997)

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Did rounding occur? Ordered Array (radix sort) yields stem and leaf plots

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Difficult to integrate… But probabilities have been Mapped out to this curve. Transformations from other Curves possible…

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Box plots (box and whiskers plots, Tukey, 1977) Outliers Fence / whiskers IQR Q3 Q1 Median Fence / whiskers min((Q3+1.5(IQR)),largest X) max((Q1+1.5(IQR)),smallest X)

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IQR

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Statistics of populations The equations so far are for sample statistics a statistic is a single number estimated from a sample We use the sample to make inferences about the population. a parameter is a single number that summarizes some quality of a variable in a population. the term for the population mean is (mu), and Y bar is a sample estimator of . the term for the population standard deviation is (sigma), and s is a sample estimator of . Note that and are both elements of the normal probability curve. Source: http://www.bsos.umd.edu/socy/smartin/601/

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IQR Measuring probabilities under the normal curve We can make transformations by scaling everything with respect to the mean and standard deviation. Let z = the number of standard deviations above or below the population mean. z = 0y = z = 1y = +/- (p=0.68) z = 2y = +/- 2 (p=0.95) z = 3y = +/- 3 (p=0.997)

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IQR

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Back to our task – gene finding Let’s start with a simple model that utilizes codon bias What we need: –A routine for reading and accessing the data –A statistical construct for evaluating all possible codons within the data –A way to reuse segments of our code when appropriate ATG possible start codons possible stop codons In-frame start to stop putative ORF

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IQR Codon bias assumptions Codons are independent of each other So if E & F are independent, then: P(EF) = P(E)*P(F) Codon frequencies are not uniform across the genome

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Conditional Probability Given E, the probability of F is: (this is the likelihood) S E F EF We can evaluate competing likehoods Through a ratio; called log-odds ratio, Or LOD

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Conditional Probability Our LOD is culled from the following information: S E F EF

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Our model To get our codon model, we need a TRAINING SET of data for known coding regions… We then simply count the frequencies of each codon occurrence S E F EF We can often get this information from genomic databases in the form of ORF- only FASTA files…

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Our model To get our random model, it is typical to model noncoding sequences as random DNA (uniform distribution) S E F EF

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We need to deal with the sequence It’s in a FASTA file: we need to build a ‘reader’ of sorts to load the data into useful data structures –Recall that our grep search of FASTA had problems –Sequence read is across many lines –Only one strand present –WE CAN SOLVE THIS BY USING A HASH #!/usr/bin/perl –w Use strict; open(IN, “chr.fsa”); while ( ) { chomp; # load the fasta file into a hash # the header will be the key # the sequence will be the value } close(IN); >one CTAAACAAAGTGCTGCCAC CCCGAATTGCCAATATAAT… (fasta file looks like this)

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There are multiple FASTA files Each chromosomal sequence has it’s own FASTA file We need a training set of data to get our LODs for evaluation We can build a complex data structure (HoH or AoH) My approach: HoH (Major, minor; or outer, inner hashes) foreach my $file(@chrFiles) { chomp($file); # get rid of metacharacters, newlines from filenames %fastaSeqs=(); $header=''; open (IN,"$file"); # create a file handle for the file being processed $file=~s/\.fsa//; while ( ) { chomp; # INSERT YOUR CODE TO READ IN A FASTA FILE HERE # # (Hint: use the hash function you learned about) } close IN; # close that file, filehandle. we'll need to use it for the next file ### you'll need to update the hash... }

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We can build up our program piecemeal First, let’s write a fasta file reader On the first pass, write it for one small file –Then build it for multiple files We’ll also need some functions… –This is a good time to introduce modular programming –At the very least, we should incorporate subroutines We might need functions to: –Reverse complement a sequence (you did this already!!! Now we’ll just make it a function so we can call is whenever we want – it’s like a control structure that’s ALWAYS AVAILABLE!) –Translate a sequence to amino acids (much like the revcom) –Calculate LOD scores for codons –Count and get frequencies of nucleotides in the sequence –We may add more… such as creating a random sequence that preserves the nucleotide composition of the original sequence… This will come in handy later

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Let’s begin First, let’s write a fasta file reader On the first pass, write it for one small file –We’ll build it for our test file, which contains two sequences We’ll evaluate these sequences for the propensity of ORFs using our statistical model We’ll revisit this problem with a more traditional homology search problem –We’ll write our own aligner!!!!!!! –The starting code and sequences are available for you http://www.chem.ucla.edu/~mjanis/biohackers2005.html Remember you can use wget!!!

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Where to start? I’ve written an outline for you to follow –#!/usr/bin/perl -w –use strict; –# this is straight out of your reading: –# a simple hash to map codons to their –# corresponding amino acids –my %geneticCode = ( – 'TCA'=>'S', # Serine – 'TCC'=>'S', – 'TCG'=>'S', – 'TCT'=>'S', – 'TTC'=>'F', # Phenylalanine – 'TTT'=>'F', – 'TTA'=>'L', # Leucine – 'TTG'=>'L', – 'TAC'=>'Y', # Tyrosine – 'TAT'=>'Y', – 'TAA'=>'-', # STOP CODON – 'TAG'=>'-', # STOP CODON – 'TGA'=>'-', # STOP CODON – 'TGC'=>'C', # Cysteine – 'TGT'=>'C',

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My fasta file loader my %fastaSeqs; # declaration of the minor hash to (re)used to hold the fasta data files my $header; # declaration of scalar to hold the fasta header for each instance my %chrList; # declaration of master hash, a hash of hashes, for every file my @chrFiles=`ls -1 *.fsa`; # a way to use wildcards to load all fasta files in the CWD foreach my $file(@chrFiles) { # process each file in turn; here we populate each minor hash, # then pass that hash to the master hash chomp($file); # get rid of metacharacters, newlines from filenames %fastaSeqs=(); # clear out the minor hash from the last instance $header=''; # clear out the header scalar open (IN,"$file"); # create a file handle for the file being processed $file=~s/\.fsa//; # we've used the filename to create the filehandle; # we don't need the filename any longer, so we'll # remove the.fsa extension and use the filename as # the major hash key while ( ) { # use a while loop to go through the file one line at a time chomp; # remove newlines/metacharacters if ($_=~/^\s*$/) { # let's ignore blank lines in the file that may exist next; } elsif ($_=~/^>/) { # here we grad the header; note that the key - value pair # is empty at this point in the minor hash $header=$_; # just take the whole header $header=~s/>//; # strip out the leading > from the header } else { # here's where we grab the sequence; # (if it's not a header, it's sequence in our fasta) $fastaSeqs{$header}.= $_; # we simply concatenate all the sequence lines together # into a cohesive sequence. } close IN; # close that file, filehandle! we'll need to use it for # next file $chrList{$file}={%fastaSeqs}; # finally, for each minor hash created, we append it to # major hash (called chrList). }

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Hopefully your fasta file reader makes sense… Now let’s build some functionality for the sequences we’ve loaded… First steps in modular programming

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An analogy for programmers - procedural C++

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A bit about the C language family C is the basis of most OS C is a compiled language C is portable C extends functionality of many programs well (especially if they are slow)

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C++ is C, ++ C++ is the OOC ANSI C/C++ is handled by gcc/g++ compiler Of course emacs has edit/compile/debug functions for both! C/C++ are modular, based on libraries – this is the hardest part of learning C, remembering all the libraries!

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Procedural C++ We’ll look at procedural C++, and leave the OOP for later… C++ is a great language to start with –grammer similar to PERL (although syntax isn’t) –forces the programmer to declare variables and clean memory these are good programming basics to learn!

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A simple C++ program #include using namespace std; int main() { int numberGenes; cout << “Enter number of genes\”; cin >> numberGenes; Return 0; }

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C works by function calls #include using namespace std; int main() { int numberGenes; cout << “Enter number of genes\”; cin >> numberGenes; Return 0; }

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C uses arrays in functions No matrices; arrays of arrays are used instead Double a[10]=(1.2,3.3,4.4); Char b[3]={‘a’,’b’,’c’,}; For (int b=0; b<10; b++) { cout << a[b] << endl; }

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An example function Write a function, which accept an integer array and return the sum of the array. int sumOfArray(int a[], int size) { int sum = 0; for(int j = 0; j < size; j++) sum = sum + a[j]; return (sum); }

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Perl functions Perl has functions as well… subroutines and Modules. This is the basis of modern bioinformatics programming – modularity The environment gives C or PERL the language references it should use – kind of like locality or accent for a language

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Functions We can access these functions by a call: –functionName(); Likewise we can pass parameters to these functions: –functionName(x) or functionName(int x); And we can return results from these functions: –return(y);

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First steps - subroutines We have been using a form of subroutines all along. Perl functions are basically built in subroutines. You call them (or "invoke") a function by typing its name, and giving it one or more arguments.

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Subroutines Perl gives you the opportunity to define your own functions, called "subroutines". In the simplest sense, subroutines are named blocks of code that can be reused as many times as you wish.

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Subroutines sub hypotenuse { my ($a,$b) = @_; return sqrt($a**2 + $b**2); } sub E { return 2.71828182845905; }

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Calling subroutines $y = 3; $x = hypotenuse($y,4); # $x now contains 5 $x = hypotenuse((3*$y),12); # $x now contains 15 $value_e = E(); # $value_e now contains 2.71828182845905

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Subroutines This way of using subroutines makes them look suspiciously like functions. Note: Unlike a function, you must use parentheses when calling a subroutine in this manner, even if you are giving it no arguments.

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The Magic Array @_ Perhaps the most important concept to understand is that values are passed to the subroutine in the default array @_. This array springs magically into existence (like the scalar $_ we learned about earlier), and contains the list of values that you gave to subroutine (within the parentheses).

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The Magic Array @_ sub Add_two_numbers { my ($number1) = shift; # get first argument from @_ # and put it in $number1 my ($number2) = shift; # get second argument from @_ # and put it in $number2 my $sum = $number1 + $number2; return $sum; }

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"my" Variables (scoping, strict) Variables that you use in a subroutine should be made private to that subroutine with the my operator. –This avoids accidentally overwriting similarly-named variables in the main program. If you already included use strict at the top of your program, perl will check that all variables are introduced with my.

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Introducing References Sometimes you need a more complex data structure! (we’ll be using a HoH!) Examples: * An array of arrays (can do the job of a 2-dimensional matrix). DATA: Spot_numCh1-BKGDCH1Ch2-BKGDCh2 0000.12443.20.10280.4 0010.11360.70.09122.6 0020.084112.20.14435.3 my @spotarray = ([0.124, 43.2, 0.102, 80.4], [0.113, 60.7, 0.091, 22.6], [0.084, 112.2, 0.144, 35.3]);

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What Is A Reference? Well, first, what is a variable? Think of a variable as a (named) box that holds a value. The name of the box is the name of the variable. After $x = 1; we have +---+ $x: | 1 | +---+ After @y = (1, 'a', 23); we have +---------------+ @y: | (1, 'a', 23) | +---------------+

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Making References To Variables' Values $list_ref = \@array; $map_ref = \%hash; $c_ref = \$count; Refs to subroutines: $sub_ref = \&subroutine; A reference is an additional, rather different way, to name the variable. Ex: from $ref_to_y = \@y we have +---------------+ +-> @y: | (1, 'a', 23) | | +---------------+ | +-|- + $ref_to_y: | * | +---+ $ref_to_y contains a reference (pointer) to @y. print @y yields 1a23 and print $ref_to_y yields ARRAY(0x80cd6ac).

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Getting At The Value ('de- referencing') @{array_reference} %{hash_reference} ${scalar_reference} print @{$ref_to_y} yields 1a23.

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Scripting Example: Hash of Hashes #!/usr/bin/perl -w use strict; @ARGV = '/home/mako/DATA/sequences.txt' unless @ARGV; $/ = ">"; my %DATA; while (<>) { chomp; my ($id_line,@rest) = split "\n"; $id_line =~ /^(\S+)/ or next; my $id = $1; my $sequence = join '',@rest; my $length = length $sequence; my $gc_count = $sequence =~ tr/gcGC/gcGC/; my $gc_content = $gc_count/$length; $DATA{$id} = { sequence => $sequence, length => $length, gc_content => sprintf("%3.2f",$gc_content) }; } my @ids = sort { $DATA{$a}->{gc_content} $DATA{$b}->{gc_content} } keys %DATA; foreach my $id (@ids) { print "$id\n"; print "\tgc content = $DATA{$id}->{gc_content}\n"; print "\tlength = $DATA{$id}->{length}\n"; print "\n"; }

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Using a Module After writing some of our functions, we can see that they might be really useful to other programs as well –Handling sequence pattern matching for example –Cleans up the main portion of our program’s code A module is a package of useful subroutines and variables that someone (you?) has put together. –Modules extend the ability of Perl.subroutine in this manner, even if you are giving it no arguments.

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File::Basename Module The File::Basename module is a standard module that is distributed with Perl. When you load the File::Basename module, you get two new functions, basename and dirname. basename takes a long UNIX path name and returns the file name at the end. dirname takes a long UNIX path name and returns the directory part. The File::Basename is the syntax for accessing any module you create But you might have to tell perl where you put it…

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File::Basename Module #!/usr/bin/perl # file: basename.pl use strict; use File::Basename; my $path = '/home/mako/DATA/chrT.fsa'; my $base = basename($path); my $dir = dirname($path); print "The base is $base and the directory is $dir.\n";

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Using a Module Each module will automatically import a different set of variables and subroutines when you use it. You can control what gets imported by providing use with a list of what to import.

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Finding out What Modules are Installed To find out what modules come with perl, look in Appendix A of Perl 5 Pocket Reference. From the command line, use the perldoc command from the UNIX shell. All the Perl documentation is available with this command: % perldoc perlmodlib To learn more about a module, run perldoc with the module's name: % perldoc File::Basename

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Installing Modules You can find thousands of Perl Modules on CPAN, the Comprehensive Perl Archive Network: http://www.cpan.org

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Installing Modules Using the CPAN Shell Perl has a CPAN module installer built into it. You run it like this: % perl -MCPAN -e shell cpan shell -- CPAN exploration and modules installation (v1.59_54) ReadLine support enabled cpan> cpan> install Text::Wrap

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Object-Oriented Modules Some modules are object-oriented. Instead of importing a series of subroutines that are called directly, these modules define a series of object types that you can create and use. We’ll see what OOP is and why we want to use it next time…

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Chapter 4 Probability and Probability Distributions

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