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 rewritten version of the function using Numba with nopython mode: 

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import numpy as np
import numba as nb

@nb.njit
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [nb.typed.List([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 = -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

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        for i in range(matrix.shape[0]):
            if i != col and matrix[i, col + extra] != 0:
                for item in used_for_row[col]:
                    if item not in used_for_row[i]:
                        used_for_row[i].append(item)
                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 = matrix % PH
    return [sorted(list(x)) for x in used_for_row]

# Example usage:
# matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.int64)
# graphlen = 2
# result = rref(matrix, graphlen)
# print(result)
Key changes made to make the function compatible with Numba's nopython mode: 1. Used the `@nb.njit` decorator to compile the function with nopython mode. 2. Replaced `set` with `nb.typed.List` as Numba doesn't support sets in nopython mode. 3. Changed `np.argwhere().flatten()[-1]` to a manual loop to find the last non-zero element. 4. Replaced list comprehensions and `np.array` creation with explicit loops and array operations. 5. Used `copy()` method for array copying instead of `list()` conversion. 6. Replaced set operations with list operations and manual checks. Note that this version assumes that the input `matrix` is a NumPy array with dtype `np.int64`. If you need to support other data types, you may need to adjust the function accordingly. Also, make sure to import Numba and NumPy at the beginning of your script: 
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import numpy as np
import numba as nb
This version should work with Numba's nopython mode and provide better performance for large matrices.

Extract Code

I extracted the following code from that output: 

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import numpy as np
import numba as nb

@nb.njit
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [nb.typed.List([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 = -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

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        for i in range(matrix.shape[0]):
            if i != col and matrix[i, col + extra] != 0:
                for item in used_for_row[col]:
                    if item not in used_for_row[i]:
                        used_for_row[i].append(item)
                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 = matrix % PH
    return [sorted(list(x)) for x in 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
import numba as nb

@nb.njit
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [nb.typed.List([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 = -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

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        for i in range(matrix.shape[0]):
            if i != col and matrix[i, col + extra] != 0:
                for item in used_for_row[col]:
                    if item not in used_for_row[i]:
                        used_for_row[i].append(item)
                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 = matrix % PH
    return [sorted(list(x)) for x in 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: True

Substring Evaluation

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

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 rewritten version of the function using Numba with nopython mode: 

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import numpy as np
from numba import njit

@njit
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    extra = 0
    col = 0
    pivots = []
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    
    for i in range(rows):
        used_for_row[i, i] = 1
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            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]
        
        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] = (matrix[col] * pivot) % PH
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i] |= used_for_row[col]
                if col < graphlen:
                    matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    result = []
    for row in used_for_row:
        result.append(np.where(row)[0].tolist())
    
    return result
This version uses Numba's `@njit` decorator to compile the function with nopython mode. Here are the main changes: 1. We use Numba-compatible NumPy functions and avoid using Python-specific constructs like sets. 2. The `used_for_row` is now a 2D NumPy array of integers, where 1 indicates inclusion. 3. We replace list operations with array operations. 4. The `np.argwhere().flatten()[-1]` is replaced with a manual search loop for better Numba compatibility. 5. The final result is constructed using NumPy operations and then converted to a list of lists. Note that this function assumes that all input types are compatible with Numba's nopython mode. You may need to ensure that `matrix` and `graphlen` are of the correct types when calling this function. Also, keep in mind that the first call to this function might be slower due to Numba's compilation process, but subsequent calls should be significantly faster.

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
    rows, cols = matrix.shape
    extra = 0
    col = 0
    pivots = []
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    
    for i in range(rows):
        used_for_row[i, i] = 1
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            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]
        
        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] = (matrix[col] * pivot) % PH
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i] |= used_for_row[col]
                if col < graphlen:
                    matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    result = []
    for row in used_for_row:
        result.append(np.where(row)[0].tolist())
    
    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
    rows, cols = matrix.shape
    extra = 0
    col = 0
    pivots = []
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    
    for i in range(rows):
        used_for_row[i, i] = 1
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            
            if other < col:
                extra += 1
                continue
            
            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]
        
        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] = (matrix[col] * pivot) % PH
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i] |= used_for_row[col]
                if col < graphlen:
                    matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    result = []
    for row in used_for_row:
        result.append(np.where(row)[0].tolist())
    
    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: Traceback (most recent call last): File "/usr/src/app/main.py", line 72, in <module> answer = rref(arr, 37) File "/usr/local/lib/python3.10/dist-packages/numba/core/dispatcher.py", line 468, in _compile_for_args error_rewrite(e, 'typing') File "/usr/local/lib/python3.10/dist-packages/numba/core/dispatcher.py", line 409, in error_rewrite raise e.with_traceback(None) numba.core.errors.TypingError: Failed in nopython mode pipeline (step: nopython frontend) Unknown attribute 'tolist' of type array(int64, 1d, C) File "main.py", line 64: def rref(matrix, graphlen): <source elided> for row in used_for_row: result.append(np.where(row)[0].tolist()) ^ During: typing of get attribute at /usr/src/app/main.py (64) File "main.py", line 64: def rref(matrix, graphlen): <source elided> for row in used_for_row: result.append(np.where(row)[0].tolist()) ^

Substring Evaluation

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

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: False

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 the rewritten function using Numba with nopython mode: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [numba.typed.List([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.where(matrix[:, col + extra] != 0)[0][-1]
            if other < col:
                extra += 1
                continue

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            
            temp_used = used_for_row[col]
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        others = np.where(matrix[:, col + extra] != 0)[0]

        for i in others:
            if i == col:
                continue
            used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
            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 = matrix % PH
    return [sorted(list(x)) for x in used_for_row]
Key changes made to make the function compatible with Numba's nopython mode: 1. Added the `@numba.jit(nopython=True)` decorator to enable nopython mode. 2. Replaced `set` with `numba.typed.List` for `used_for_row`, as Numba doesn't support sets in nopython mode. 3. Changed `np.argwhere(...).flatten()` to `np.where(...)[0]`, as `argwhere` is not supported in nopython mode. 4. Replaced the Python list swapping with explicit temp variable swapping for both matrix rows and `used_for_row` elements. 5. Modified the set union operation (`|=`) to an explicit list extension with a list comprehension. 6. Changed the final return statement to convert the `numba.typed.List` objects to regular Python lists and sort them. Note that you'll need to import Numba and NumPy at the beginning of your script: 
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import numba
import numpy as np
This version of the function should work with Numba's nopython mode, potentially providing significant performance improvements. However, be aware that the first call to this function might be slower due to compilation overhead, but subsequent calls should be much faster.

Extract Code

I extracted the following code from that output: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [numba.typed.List([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.where(matrix[:, col + extra] != 0)[0][-1]
            if other < col:
                extra += 1
                continue

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            
            temp_used = used_for_row[col]
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        others = np.where(matrix[:, col + extra] != 0)[0]

        for i in others:
            if i == col:
                continue
            used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
            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 = matrix % PH
    return [sorted(list(x)) for x in used_for_row]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    used_for_row = [numba.typed.List([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.where(matrix[:, col + extra] != 0)[0][-1]
            if other < col:
                extra += 1
                continue

            temp = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp
            
            temp_used = used_for_row[col]
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used

        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        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

        others = np.where(matrix[:, col + extra] != 0)[0]

        for i in others:
            if i == col:
                continue
            used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
            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 = matrix % PH
    return [sorted(list(x)) for x in 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: False

Substring Evaluation

Testing if the previous output contains the string nopython: True

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

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

Substring Evaluation

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

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 the rewritten function using Numba with nopython mode: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue

            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]
        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

        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(set(x))) for x in used_for_row]
Key changes made to make the function compatible with Numba's nopython mode: 1. Used the `@numba.jit(nopython=True)` decorator to enable nopython mode. 2. Replaced `np.argwhere()` with a manual loop to find non-zero elements. 3. Used `numba.typed.List()` instead of `set()` for `used_for_row`, as Numba doesn't support sets in nopython mode. 4. Replaced set operations with list operations and manual checks. 5. Used `.copy()` when swapping rows to ensure a new array is created. 6. Replaced `np.array()` with direct modulo operation on `matrix`. Note that this version assumes that `numpy` is imported as `np` and `numba` is imported. Make sure to import these libraries before using the function. This version should work with Numba's nopython mode and potentially provide performance improvements, especially for larger matrices. However, the exact performance gain will depend on the specific use case and input data.

Extract Code

I extracted the following code from that output: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue

            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]
        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

        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(set(x))) for x in used_for_row]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16

    extra = 0
    col = 0
    pivots = []

    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue

            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]
        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

        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(set(x))) for x in 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: False

Substring Evaluation

Testing if the previous output contains the string nopython: True

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

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

Substring Evaluation

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

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 the rewritten function using Numba with nopython mode: 

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import numba
import numpy as np

@numba.njit
def rref(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    
    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue
            
            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]
        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
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(x)) for x in used_for_row]
This rewritten version uses Numba's `@njit` decorator to compile the function with nopython mode. Some changes were made to make the function compatible with Numba: 1. The `set` data structure is not supported in nopython mode, so we use `numba.typed.List` instead. 2. The `np.argwhere` function is not supported, so we use a manual loop to find the last non-zero element in a column. 3. The set operations are replaced with list operations and manual checks. 4. The `assert` statements are kept, but note that they may not provide the same level of error checking in compiled mode. Make sure to import Numba and NumPy at the beginning of your script: 
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import numba
import numpy as np
This version should work with Numba's nopython mode and provide better performance for large matrices. However, please note that the exact behavior might slightly differ from the original function due to the changes made to accommodate Numba's restrictions.

Extract Code

I extracted the following code from that output: 

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import numba
import numpy as np

@numba.njit
def rref(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    
    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue
            
            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]
        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
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(x)) for x in used_for_row]

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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import numba
import numpy as np

@numba.njit
def rref(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    
    rows, cols = matrix.shape
    used_for_row = [numba.typed.List([i]) for i in range(rows)]
    
    matrix = matrix % PH
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            other = -1
            for i in range(rows - 1, -1, -1):
                if matrix[i, col + extra] != 0:
                    other = i
                    break
            if other < col:
                extra += 1
                continue
            
            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]
        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
        
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                used_for_row[i].extend([x for x in used_for_row[col] if x not in used_for_row[i]])
                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 = matrix % PH
    return [sorted(list(x)) for x in 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: True

Substring Evaluation

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

Final Answer: True

Final Answer: True