The given code appears to initialize a dynamic programming (DP)...

September 1, 2025 at 01:13 PM

def initiate_global_dp(m,n):
    S = np.zeros((m+1, n+1))       # An (m+1)*(n+1) matrix, initiated with 0's
    # Careful! S and trace are shape (m+1)*(n+1). The sequences lengths are m and n. Remember that in the future!
    # For the trace matrix we use a three dimentional matrix of booleans
    # where 
    #   trace(x,y,0) indicates a match in x,y
    #   trace(x,y,1) indicates an insert in x,y (fix column)
    #   trace(x,y,2) indicates a delete in x,y (fix row)
    trace = np.zeros((m+1, n+1, 3), dtype=np.bool_) # An (m+1)*(n+1)*3 boolean matrix, initiated with (False,False,False)

    # HINT: try printing S and trace for debugging.
    # trace is difficult to 3D-visualize out of the box with numpy, so use the function pretty_trace(trace) for a better result!
    # you can also use the function pretty_trace_arrows(trace) for an even clearer (but less abstract) result

    # First initiate the origin of S (0,0) here:
    S[0,0] = 0

    # Now, fill in the first row and the first column of the matrices S and trace
    # The first column of S (S[i, 0]) is filled with values based on the gap penalty.
    # Initiate the first column of S and trace here:
    for i in range (1,m+1):
        S[i,0] = i * gap_penalty()
        trace[i,0,2] = (-1,0,1)
        
    # Initiate the first row of S and trace here:
    for j in range(1,n+1):
        S[0,j] = j * gap_penalty()
        trace[0,j,1] = (0,-1,2)

The given code appears to initialize a dynamic programming (DP) data structure for use in sequence alignment, such as in bioinformatics (e.g., Needleman-Wunsch or Smith-Waterman algorithms). Let's break it down:

Code Purpose:

Input Parameters:
- m and n: Lengths of two sequences being aligned.
- These sequences are likely to be aligned using a scoring method based on matches, mismatches, and gaps.
Output Structures:
- S: A 2D matrix ((m+1)x(n+1)), initialized to zeros. It will store alignment scores (dynamic programming table of cumulative scores).
- trace: A 3D boolean matrix ((m+1)x(n+1)x3), where each cell tracks the alignment direction:
  - trace(x, y, 0): Indicates a match (diagonal move in DP table).
  - trace(x, y, 1): Indicates an insertion (move left in DP table; fixing a column).
  - trace(x, y, 2): Indicates a deletion (move up in DP table; fixing a row).

Description of Major Steps:

Zero Initialization:
- Both matrices, S and trace, are initialized with zeros. This sets up the base conditions for DP.
- S: The score matrix starts with 0s.
- trace: The boolean matrix starts with False in all cells.
Setting the Origin:
- S[0,0] is initialized to 0, reflecting the origin of the alignment process (no alignment penalties yet).
Filling the First Column of S and trace:
- Each cell in the first column (S[i, 0]) is filled with a cumulative gap penalty (i * gap_penalty()). This represents the cost of aligning a prefix of one sequence (length i) with gaps in the other sequence.
- Correspondingly, trace[i, 0, 2] is marked for deletions (up moves), since only gaps are involved.
Filling the First Row of S and trace:
- Similarly, each cell in the first row (S[0, j]) is filled with a cumulative gap penalty (j * gap_penalty()).
- Correspondingly, trace[0, j, 1] is marked for insertions (left moves), since only gaps are involved.

Gaps in the Code:

gap_penalty(): This function is likely defined elsewhere and should return the penalty score for a single gap.
Trace Initialization Errors:
- The assignments like trace[i,0,2] = (-1,0,1) and trace[0,j,1] = (0,-1,2) do not seem correct, as they attempt to assign tuples where boolean values are expected (since trace is a boolean matrix).

Overall Function:

This code initializes the DP structures (S and trace) required for aligning two sequences. It sets up:

A scoring matrix (S) starting from the basic cases of aligning a sequence to gaps.
A trace matrix that will later encode the direction of moves (for backtracking the optimal alignment).

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