Initial Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

LLM Generation

Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

Output

Here's a Numba implementation of the `rref` function using `@njit` decorator for nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    extra = 0
    col = 0
    
    # Pre-allocate pivots list (max size will be min of rows and columns)
    pivots = np.zeros(min(matrix.shape[0], matrix.shape[1]), dtype=np.int64)
    pivots_count = 0
    
    # Create used_for_row as a 2D list equivalent
    used_for_row = np.zeros((matrix.shape[0], matrix.shape[0]), dtype=np.bool_)
    for i in range(matrix.shape[0]):
        used_for_row[i, i] = True
    
    # Ensure matrix is modulo PH
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            matrix[i, j] %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current column is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row
            other = -1
            for i in range(matrix.shape[0] - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            for j in range(matrix.shape[1]):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(matrix.shape[0]):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivots_count] = col + extra
        pivots_count += 1
        
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        for j in range(matrix.shape[1]):
            matrix[col, j] *= pivot
            matrix[col, j] %= PH
        
        # Find rows with non-zero entries in the current column
        for i in range(matrix.shape[0]):
            if i == col or matrix[i, col + extra] == 0:
                continue
            
            # Update used_for_row
            for j in range(matrix.shape[0]):
                if used_for_row[col, j]:
                    used_for_row[i, j] = True
            
            # Eliminate entries
            if col < graphlen:
                factor = matrix[i, col + extra]
                for j in range(matrix.shape[1]):
                    matrix[i, j] -= matrix[col, j] * factor
            else:
                while matrix[i, col + extra] != 0:
                    for j in range(matrix.shape[1]):
                        matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
            
            # Ensure row is modulo PH
            for j in range(matrix.shape[1]):
                matrix[i, j] %= PH
        
        col += 1
    
    # Convert used_for_row to list of lists with sorted indices
    result = []
    for i in range(matrix.shape[0]):
        row_indices = []
        for j in range(matrix.shape[0]):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result
Key changes from the original implementation: 1. Used `@njit` decorator for nopython mode 2. Replaced list comprehensions and NumPy methods with explicit loops 3. Pre-allocated arrays instead of dynamic lists 4. Implemented equivalent logic using pure numerical operations 5. Converted used_for_row to a 2D boolean array 6. Converted final result generation to use explicit loops Note that this implementation assumes: - Input matrix is a NumPy array - Input types are compatible with Numba's nopython mode - No external library functions are used You would use this function similarly to the original: 
1
result = rref(matrix, graphlen)
The core algorithm remains the same, but it's now optimized for performance using Numba.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    extra = 0
    col = 0
    
    # Pre-allocate pivots list (max size will be min of rows and columns)
    pivots = np.zeros(min(matrix.shape[0], matrix.shape[1]), dtype=np.int64)
    pivots_count = 0
    
    # Create used_for_row as a 2D list equivalent
    used_for_row = np.zeros((matrix.shape[0], matrix.shape[0]), dtype=np.bool_)
    for i in range(matrix.shape[0]):
        used_for_row[i, i] = True
    
    # Ensure matrix is modulo PH
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            matrix[i, j] %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current column is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row
            other = -1
            for i in range(matrix.shape[0] - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            for j in range(matrix.shape[1]):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(matrix.shape[0]):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivots_count] = col + extra
        pivots_count += 1
        
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        for j in range(matrix.shape[1]):
            matrix[col, j] *= pivot
            matrix[col, j] %= PH
        
        # Find rows with non-zero entries in the current column
        for i in range(matrix.shape[0]):
            if i == col or matrix[i, col + extra] == 0:
                continue
            
            # Update used_for_row
            for j in range(matrix.shape[0]):
                if used_for_row[col, j]:
                    used_for_row[i, j] = True
            
            # Eliminate entries
            if col < graphlen:
                factor = matrix[i, col + extra]
                for j in range(matrix.shape[1]):
                    matrix[i, j] -= matrix[col, j] * factor
            else:
                while matrix[i, col + extra] != 0:
                    for j in range(matrix.shape[1]):
                        matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
            
            # Ensure row is modulo PH
            for j in range(matrix.shape[1]):
                matrix[i, j] %= PH
        
        col += 1
    
    # Convert used_for_row to list of lists with sorted indices
    result = []
    for i in range(matrix.shape[0]):
        row_indices = []
        for j in range(matrix.shape[0]):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    extra = 0
    col = 0
    
    # Pre-allocate pivots list (max size will be min of rows and columns)
    pivots = np.zeros(min(matrix.shape[0], matrix.shape[1]), dtype=np.int64)
    pivots_count = 0
    
    # Create used_for_row as a 2D list equivalent
    used_for_row = np.zeros((matrix.shape[0], matrix.shape[0]), dtype=np.bool_)
    for i in range(matrix.shape[0]):
        used_for_row[i, i] = True
    
    # Ensure matrix is modulo PH
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            matrix[i, j] %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current column is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row
            other = -1
            for i in range(matrix.shape[0] - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            for j in range(matrix.shape[1]):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(matrix.shape[0]):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivots_count] = col + extra
        pivots_count += 1
        
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        for j in range(matrix.shape[1]):
            matrix[col, j] *= pivot
            matrix[col, j] %= PH
        
        # Find rows with non-zero entries in the current column
        for i in range(matrix.shape[0]):
            if i == col or matrix[i, col + extra] == 0:
                continue
            
            # Update used_for_row
            for j in range(matrix.shape[0]):
                if used_for_row[col, j]:
                    used_for_row[i, j] = True
            
            # Eliminate entries
            if col < graphlen:
                factor = matrix[i, col + extra]
                for j in range(matrix.shape[1]):
                    matrix[i, j] -= matrix[col, j] * factor
            else:
                while matrix[i, col + extra] != 0:
                    for j in range(matrix.shape[1]):
                        matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
            
            # Ensure row is modulo PH
            for j in range(matrix.shape[1]):
                matrix[i, j] %= PH
        
        col += 1
    
    # Convert used_for_row to list of lists with sorted indices
    result = []
    for i in range(matrix.shape[0]):
        row_indices = []
        for j in range(matrix.shape[0]):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result



arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = rref(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

LLM Generation

Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

Output

Here's a Numba-optimized version of the `rref` function using `@njit` decorator and nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to modify
    matrix = matrix.copy()
    
    # Preallocate used_for_row 
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Modulo operation
    matrix %= PH
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if the current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find the last non-zero row in the column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validation and scaling of the pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero elements in the current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Update used_for_row
            temp_set = set(used_for_row[i])
            temp_set.update(used_for_row[col])
            used_for_row[i] = list(temp_set)
            
            # Elimination process
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    result = []
    for row in used_for_row:
        result.append(sorted(row))
    
    return result
Key changes and considerations: 1. Used `@njit` decorator from Numba to enable nopython mode compilation 2. Replaced NumPy specific operations with explicit loops where necessary 3. Made manual copies of lists and arrays to ensure Numba compatibility 4. Replaced set operations with manual list manipulation 5. Removed NumPy-specific assertions and replaced with standard Python assertions 6. Manually implemented column and row operations Note: This version assumes you'll pass a NumPy array as input. The function will work with both integer and floating-point inputs but will convert everything to the same type during compilation. When using this function, make sure to import NumPy and Numba: 
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import numpy as np
from numba import njit
The performance should be significantly improved compared to the original implementation, especially for larger matrices.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to modify
    matrix = matrix.copy()
    
    # Preallocate used_for_row 
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Modulo operation
    matrix %= PH
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if the current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find the last non-zero row in the column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validation and scaling of the pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero elements in the current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Update used_for_row
            temp_set = set(used_for_row[i])
            temp_set.update(used_for_row[col])
            used_for_row[i] = list(temp_set)
            
            # Elimination process
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    result = []
    for row in used_for_row:
        result.append(sorted(row))
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to modify
    matrix = matrix.copy()
    
    # Preallocate used_for_row 
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Modulo operation
    matrix %= PH
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if the current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find the last non-zero row in the column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validation and scaling of the pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero elements in the current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Update used_for_row
            temp_set = set(used_for_row[i])
            temp_set.update(used_for_row[col])
            used_for_row[i] = list(temp_set)
            
            # Elimination process
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    result = []
    for row in used_for_row:
        result.append(sorted(row))
    
    return result



arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = rref(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

LLM Generation

Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

Output

Here's a version of the function rewritten using Numba with nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    matrix = matrix % PH
    matrix_shape_0 = matrix.shape[0]
    matrix_shape_1 = matrix.shape[1]
    
    # Initialize used_for_row as a list of lists
    used_for_row = [[i] for i in range(matrix_shape_0)]
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix_shape_1 - 1 and col < matrix_shape_0:
        # Check if pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row in the column
            other = -1
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row entries
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other].copy()
            used_for_row[other] = temp_used
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Pivot validation
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Eliminate other rows
        for i in range(matrix_shape_0):
            if i == col:
                continue
            
            if matrix[i, col + extra] != 0:
                # Merge used_for_row
                for used_val in used_for_row[col]:
                    if used_val not in used_for_row[i]:
                        used_for_row[i].append(used_val)
                
                # Row reduction
                if col < graphlen:
                    matrix[i] -= matrix[col] * matrix[i, col + extra]
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                
                matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row
Key changes to make it compatible with Numba: 1. Replaced NumPy-specific methods with explicit loops 2. Used `.copy()` to create copies of arrays and lists 3. Implemented custom logic for `np.all()`, `np.argwhere()`, and other NumPy functions 4. Removed list comprehensions and replaced with explicit list creation 5. Added `@njit` decorator to enable nopython mode This version should work with Numba's nopython mode and provide similar functionality to the original function. Note that you'll need to have Numba installed (`pip install numba`) to use this function. The function expects the same inputs as the original: a matrix and a `graphlen` parameter. It returns a list of lists representing the rows used for each row in the reduced row echelon form.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    matrix = matrix % PH
    matrix_shape_0 = matrix.shape[0]
    matrix_shape_1 = matrix.shape[1]
    
    # Initialize used_for_row as a list of lists
    used_for_row = [[i] for i in range(matrix_shape_0)]
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix_shape_1 - 1 and col < matrix_shape_0:
        # Check if pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row in the column
            other = -1
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row entries
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other].copy()
            used_for_row[other] = temp_used
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Pivot validation
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Eliminate other rows
        for i in range(matrix_shape_0):
            if i == col:
                continue
            
            if matrix[i, col + extra] != 0:
                # Merge used_for_row
                for used_val in used_for_row[col]:
                    if used_val not in used_for_row[i]:
                        used_for_row[i].append(used_val)
                
                # Row reduction
                if col < graphlen:
                    matrix[i] -= matrix[col] * matrix[i, col + extra]
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                
                matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    matrix = matrix % PH
    matrix_shape_0 = matrix.shape[0]
    matrix_shape_1 = matrix.shape[1]
    
    # Initialize used_for_row as a list of lists
    used_for_row = [[i] for i in range(matrix_shape_0)]
    
    extra = 0
    col = 0
    pivots = []
    
    while col + extra < matrix_shape_1 - 1 and col < matrix_shape_0:
        # Check if pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero row in the column
            other = -1
            for i in range(matrix_shape_0):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row entries
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other].copy()
            used_for_row[other] = temp_used
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Pivot validation
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Eliminate other rows
        for i in range(matrix_shape_0):
            if i == col:
                continue
            
            if matrix[i, col + extra] != 0:
                # Merge used_for_row
                for used_val in used_for_row[col]:
                    if used_val not in used_for_row[i]:
                        used_for_row[i].append(used_val)
                
                # Row reduction
                if col < graphlen:
                    matrix[i] -= matrix[col] * matrix[i, col + extra]
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                
                matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row



arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = rref(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

LLM Generation

Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

Output

Here's a Numba-optimized version of the `rref` function using `@njit` decorator and nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    m, n = matrix.shape
    extra = 0
    col = 0
    pivots = []

    # Initialize used_for_row as a list of sets
    used_for_row = [set([i]) for i in range(m)]
    
    # Mod matrix by PH
    matrix %= PH
    
    while col + extra < n - 1 and col < m:
        # Check if current pivot is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero entry in column
            other = -1
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero entries in the column
        others = []
        for i in range(m):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate entries in other rows
        for i in others:
            if i == col:
                continue
            
            # Update used rows
            used_for_row[i] = set(list(used_for_row[i]) + list(used_for_row[col]))
            
            # Eliminate entry
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert sets to sorted lists
    used_for_row_list = []
    for row_set in used_for_row:
        used_for_row_list.append(sorted(list(row_set)))
    
    return used_for_row_list
Key changes for Numba compatibility: 1. Added `@njit` decorator to enable nopython mode 2. Replaced NumPy-specific operations with explicit loops 3. Used `.copy()` for row swapping to avoid reference issues 4. Converted set operations to list-based operations 5. Manually converted sets to sorted lists at the end Note that this implementation requires the input `matrix` to be a NumPy array. The function will now compile to machine code and run much faster for large matrices. Make sure to import Numba and NumPy before using this function: 
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import numpy as np
from numba import njit
Usage remains the same: 
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result = rref(matrix, graphlen)

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    m, n = matrix.shape
    extra = 0
    col = 0
    pivots = []

    # Initialize used_for_row as a list of sets
    used_for_row = [set([i]) for i in range(m)]
    
    # Mod matrix by PH
    matrix %= PH
    
    while col + extra < n - 1 and col < m:
        # Check if current pivot is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero entry in column
            other = -1
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero entries in the column
        others = []
        for i in range(m):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate entries in other rows
        for i in others:
            if i == col:
                continue
            
            # Update used rows
            used_for_row[i] = set(list(used_for_row[i]) + list(used_for_row[col]))
            
            # Eliminate entry
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert sets to sorted lists
    used_for_row_list = []
    for row_set in used_for_row:
        used_for_row_list.append(sorted(list(row_set)))
    
    return used_for_row_list

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    m, n = matrix.shape
    extra = 0
    col = 0
    pivots = []

    # Initialize used_for_row as a list of sets
    used_for_row = [set([i]) for i in range(m)]
    
    # Mod matrix by PH
    matrix %= PH
    
    while col + extra < n - 1 and col < m:
        # Check if current pivot is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero entry in column
            other = -1
            for i in range(m):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find rows with non-zero entries in the column
        others = []
        for i in range(m):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate entries in other rows
        for i in others:
            if i == col:
                continue
            
            # Update used rows
            used_for_row[i] = set(list(used_for_row[i]) + list(used_for_row[col]))
            
            # Eliminate entry
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    matrix %= PH
    
    # Convert sets to sorted lists
    used_for_row_list = []
    for row_set in used_for_row:
        used_for_row_list.append(sorted(list(row_set)))
    
    return used_for_row_list



arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = rref(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True

Initial Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

LLM Generation

Query

Rewrite this function to use numba and nopython mode. You can assume that the input is a 2d matrix correctly formatted. Call it rref still. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]

Output

Here's a Numba-optimized version of the function using nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to avoid modifying the original
    matrix = matrix.copy()
    
    extra = 0
    col = 0
    pivots = []
    
    # Initialize used_for_row as a list of sets
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Perform modulo operation on entire matrix
    matrix %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero element in column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot based on graphlen
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row by pivot
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find indices of non-zero elements in current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Combine used columns
            used_for_row[i] = list(set(used_for_row[i] + used_for_row[col]))
            
            # Reduce row
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    # Final modulo operation
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row
Key changes for Numba compatibility: 1. Used `@njit` decorator for nopython mode 2. Replaced NumPy-specific operations with explicit loops 3. Used `.copy()` for creating copies of lists and arrays 4. Used explicit `set()` conversion for merging lists 5. Simplified some NumPy-specific operations 6. Handled type conversions and list modifications Note that this version assumes the input `matrix` is a NumPy array. The function will now compile to machine code and should provide significant performance improvements for large matrices. To use this function, you would call it like: 
1
result = rref(np.array(matrix), graphlen)
Make sure to import NumPy and use NumPy arrays as input.

Extract Code

I extracted the following code from that output: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to avoid modifying the original
    matrix = matrix.copy()
    
    extra = 0
    col = 0
    pivots = []
    
    # Initialize used_for_row as a list of sets
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Perform modulo operation on entire matrix
    matrix %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero element in column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot based on graphlen
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row by pivot
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find indices of non-zero elements in current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Combine used columns
            used_for_row[i] = list(set(used_for_row[i] + used_for_row[col]))
            
            # Reduce row
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    # Final modulo operation
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    
    # Create a copy of the matrix to avoid modifying the original
    matrix = matrix.copy()
    
    extra = 0
    col = 0
    pivots = []
    
    # Initialize used_for_row as a list of sets
    used_for_row = [[i] for i in range(matrix.shape[0])]
    
    # Perform modulo operation on entire matrix
    matrix %= PH
    
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # Check if current pivot element is zero
        if matrix[col, col + extra] == 0:
            # Check if entire column is zero
            all_zero = True
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    all_zero = False
                    break
            
            if all_zero:
                extra += 1
                continue
            
            # Find last non-zero element in column
            other = -1
            for i in range(matrix.shape[0]):
                if matrix[i, col + extra] != 0:
                    other = i
            
            if other < col:
                extra += 1
                continue
            
            # Swap rows
            matrix[col], matrix[other] = matrix[other].copy(), matrix[col].copy()
            used_for_row[col], used_for_row[other] = used_for_row[other].copy(), used_for_row[col].copy()
        
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Validate pivot based on graphlen
        if col + extra < graphlen:
            assert abs(pivot) == 1 or abs(pivot) == PH - 1
        else:
            assert abs(pivot) == 2 or abs(pivot) == PH - 2
            pivot //= 2
        
        # Scale row by pivot
        matrix[col] *= pivot
        matrix[col] %= PH
        
        # Find indices of non-zero elements in current column
        others = []
        for i in range(matrix.shape[0]):
            if matrix[i, col + extra] != 0:
                others.append(i)
        
        # Eliminate other rows
        for i in others:
            if i == col:
                continue
            
            # Combine used columns
            used_for_row[i] = list(set(used_for_row[i] + used_for_row[col]))
            
            # Reduce row
            if col < graphlen:
                matrix[i] -= matrix[col] * matrix[i, col + extra]
            else:
                while matrix[i, col + extra] != 0:
                    matrix[i] = (matrix[i] - matrix[col]) % PH
            
            matrix[i] %= PH
        
        col += 1
    
    # Final modulo operation
    matrix %= PH
    
    # Convert used_for_row to sorted lists
    sorted_used_for_row = [sorted(x) for x in used_for_row]
    
    return sorted_used_for_row



arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = rref(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string import numba: False

Substring Evaluation

Testing if the previous output contains the string from numba: True

Final Answer: True

Final Answer: True