Consensus string

docs/src/rosalind/10-cons.md

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+# Consensus and Profile
+
+🤔 [Problem link](https://rosalind.info/problems/cons/)
+
+!!! warning "The Problem". 
+
+    A matrix is a rectangular table of values divided into rows and columns.   
+    An m×n matrix has m rows and n columns.   
+    Given a matrix A, we write Ai,j.  
+    to indicate the value found at the intersection of row i and column j.  
+
+    Say that we have a collection of DNA strings,   
+    all having the same length n.   
+    Their profile matrix is a 4×n matrix P in which P1,    
+    j represents the number of times that 'A' occurs in the jth position of one of the strings,   
+    P2,j represents the number of times that C occurs in the jth position,   
+    and so on (see below).
+
+    A consensus string c is a string of length n
+    formed from our collection by taking the most common symbol at each position;   
+    the jth symbol of c therefore corresponds to the symbol having the maximum value 
+    in the j-th column of the profile matrix.     
+    Of course, there may be more than one most common symbol, 
+    leading to multiple possible consensus strings.  
+
+    ### DNA Strings
+    A T C C A G C T
+    G G G C A A C T
+    A T G G A T C T
+    A A G C A A C C
+    T T G G A A C T
+    A T G C C A T T
+    A T G G C A C T
+
+    ### Profile
+
+    A   5 1 0 0 5 5 0 0
+	C   0 0 1 4 2 0 6 1
+    G   1 1 6 3 0 1 0 0
+    T   1 5 0 0 0 1 1 6
+
+    Consensus	A T G C A A C T
+
+    Given:     
+    A collection of at most 10 DNA strings of equal length (at most 1 kbp) in FASTA format.
+
+    Return:   
+    A consensus string and profile matrix for the collection. 
+    (If several possible consensus strings exist,   
+    then you may return any one of them.)
+
+    Sample Dataset
+    >Rosalind_1
+    ATCCAGCT
+    >Rosalind_2
+    GGGCAACT
+    >Rosalind_3
+    ATGGATCT
+    >Rosalind_4
+    AAGCAACC
+    >Rosalind_5
+    TTGGAACT
+    >Rosalind_6
+    ATGCCATT
+    >Rosalind_7
+    ATGGCACT
+
+    Sample Output
+    ATGCAACT
+    A: 5 1 0 0 5 5 0 0
+    C: 0 0 1 4 2 0 6 1
+    G: 1 1 6 3 0 1 0 0
+    T: 1 5 0 0 0 1 1 6
+
+
+The first thing we will need to do is read in the input fasta.  
+In this case, we will not be reading in an actual fasta file,   
+but a set of strings in fasta format.
+If we were reading in an actual fasta file,  
+we could use the [FASTX.jl](https://github.com/BioJulia/FASTX.jl) package to help us with that.  
+
+Since the task required here is something that was already demonstrated in the [GC-content tutorial](./05-gc.md),  
+we can borrow the function from that tutorial.
+
+```julia
+
+fake_file = IOBuffer("""
+    >Rosalind_1
+    ATCCAGCT
+    >Rosalind_2
+    GGGCAACT
+    >Rosalind_3
+    ATGGATCT
+    >Rosalind_4
+    AAGCAACC
+    >Rosalind_5
+    TTGGAACT
+    >Rosalind_6
+    ATGCCATT
+    >Rosalind_7
+    ATGGCACT
+    """
+)
+
+function parse_fasta(buffer)
+    records = [] # this is a Vector of type `Any`
+    record_name = ""
+    sequence = ""
+    for line in eachline(buffer)
+        if startswith(line, ">")
+            !isempty(record_name) && push!(records, (record_name, sequence))
+            record_name = lstrip(line, '>')
+            sequence = ""
+        else
+            sequence *= line
+        end
+    end
+    push!(records, (record_name, sequence))
+    return records
+end
+
+records = parse_fasta(fake_file)
+```
+
+Once the fasta is read in, we can iterate over each read and store its nucleotide sequence in a data matrix.
+
+From there, we can generate the profile matrix.  
+We'll need to sum the number of times each nucleotide appears at a particular row of the data matrix.  
+
+Then, we can identify the most common nucleotide at each column of the data matrix,   
+which represents each index of the consensus string.  
+After we have done this for all columns of the data matrix,   
+we can generate the consensus string.  
+
+
+```julia
+using DataFrames
+
+function consensus(fasta_string)
+
+    # extract strings from fasta
+    records = parse_fasta(fasta_string)
+
+    # make a vector of just strings
+    data_vector = last.(records)
+
+    # convert data_vector to matrix where each column is a char and each row is a string
+    data_matrix = reduce(vcat, permutedims.(collect.(data_vector)))
+
+    # make profile matrix
+    consensus_matrix_list = Vector{Int64}[] 
+    for nuc in ['A', 'C', 'G', 'T']
+        nuc_count = vec(sum(x->x==nuc, data_matrix, dims=1))
+        push!(consensus_matrix_list, nuc_count)
+    end
+
+    consensus_matrix = vcat(consensus_matrix_list)
+
+    # convert matrix to DF and add row names for nucleotides
+    consensus_df = DataFrame(consensus_matrix, ["A", "C", "G", "T"])
+
+
+    # make column with nucleotide with max value 
+    # argmax returns the index or key of the first one encountered
+    nuc_max_df = transform(consensus_df, AsTable(:) => ByRow(argmax) => :MaxColName)
+
+    # return consensus string
+    return join(nuc_max_df.MaxColName)
+
+end
+
+consensus(fake_file)
+```
+
+As mentioned in the problem description above,   
+it is possible that there can be multiple consensus strings,    
+as some nucleotides may appear the same number of times  
+in each column of the data matrix. 
+
+If this is the case,   
+the function we are using (`argmax`) returns the nucleotide with the most occurences that it first encounters. 
+
+The way our function is written,  
+we first scan for 'A', 'C', then 'G' and 'T',   
+so the final consensus string will be biased towards more A's, then C's, G's and T's.  
+This simply based on which nucleotide counts it will encounter first in the profile matrix.
+