Initial Query

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

LLM Generation

Query

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

Output

Here's a numba-compatible version of the function using `@njit` (nopython mode). Note that some modifications were necessary since numba doesn't support Python sets or certain NumPy operations: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
from numba import njit
import numpy as np

@njit
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    # Work with a copy of the matrix
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            for j in range(cols):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(rows):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Process other rows
        for i in range(rows):
            if i == col:
                continue
                
            if matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_indices.append(j)
        result.append(row_indices)
    
    return result
Key changes made to make the function numba-compatible: 1. Replaced Python sets with a boolean matrix (used_for_row) 2. Replaced NumPy operations with explicit loops where necessary 3. Changed list operations to array operations 4. Implemented manual row swapping instead of using Python list assignments 5. Removed assert statements (replaced with if/raise) 6. Used explicit type operations that numba supports 7. Changed the return format to work with numba's limitations To use this function: 
1
2
3
4
5
6
7
import numpy as np
from numba import njit

# Example usage:
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.int64)
graphlen = 2
result = rref(matrix, graphlen)
Note that this version should be significantly faster for large matrices due to the JIT compilation, while maintaining the same functionality as the original function. The main trade-off is that the code is more verbose and less Pythonic due to numba's restrictions. Make sure your input matrix is of type np.int64 for best compatibility with numba.

Extract Code

I extracted the following code from that output: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
from numba import njit
import numpy as np

@njit
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    # Work with a copy of the matrix
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            for j in range(cols):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(rows):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Process other rows
        for i in range(rows):
            if i == col:
                continue
                
            if matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_indices.append(j)
        result.append(row_indices)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
from numba import njit
import numpy as np

@njit
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    # Work with a copy of the matrix
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            for j in range(cols):
                temp = matrix[col, j]
                matrix[col, j] = matrix[other, j]
                matrix[other, j] = temp
            
            # Swap used_for_row
            for j in range(rows):
                temp = used_for_row[col, j]
                used_for_row[col, j] = used_for_row[other, j]
                used_for_row[other, j] = temp
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Process other rows
        for i in range(rows):
            if i == col:
                continue
                
            if matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_indices.append(j)
        result.append(row_indices)
    
    return result



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

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

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: False

Final Answer: True

Check if any of the following conditions are true:

Substring Evaluation

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

Substring Evaluation

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

Final Answer: True

Final Answer: True

Initial Query

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

LLM Generation

Query

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

Output

Here's the numba-optimized version of the function using nopython mode. Note that we need to make some adjustments since numba doesn't support certain Python operations like sets: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize tracking arrays
    extra = 0
    col = 0
    
    # Create array to track used rows (instead of sets)
    # Using a 2D boolean array where each row represents what rows were used
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row tracking
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivot = matrix[col, col + extra]
        
        # Multiply row by inverse of pivot
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                        
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row to list of sorted indices
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result
Key changes made to make the function numba-compatible: 1. Replaced Python sets with a boolean 2D array to track used rows 2. Removed numpy functions like `np.all` and `np.argwhere` in favor of explicit loops 3. Modified the row swapping to use temporary variables 4. Changed the assertion statements to raise ValueError (as assertions aren't supported in nopython mode) 5. Used explicit loops instead of numpy broadcasting operations where necessary 6. Created the result list at the end using explicit loops instead of set operations This version should run significantly faster than the original Python version while producing the same results. The function still takes a 2D numpy array as input and returns a list of lists containing the indices of used rows. Note that you'll need to have numba installed (`pip install numba`) to use this function. The first time you run it, there will be a compilation overhead, but subsequent calls will be much faster.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize tracking arrays
    extra = 0
    col = 0
    
    # Create array to track used rows (instead of sets)
    # Using a 2D boolean array where each row represents what rows were used
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row tracking
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivot = matrix[col, col + extra]
        
        # Multiply row by inverse of pivot
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                        
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row to list of sorted indices
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize tracking arrays
    extra = 0
    col = 0
    
    # Create array to track used rows (instead of sets)
    # Using a 2D boolean array where each row represents what rows were used
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            # Swap used_for_row tracking
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivot = matrix[col, col + extra]
        
        # Multiply row by inverse of pivot
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                        
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row to list of sorted indices
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result



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

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

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: 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 numba version of the function using nopython mode. Note that since numba doesn't support Python sets, I've modified the function to use arrays instead: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize arrays instead of sets for tracking used rows
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    extra = 0
    col = 0
    pivots = []
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
            
        # Find other rows to reduce
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_list = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_list.append(j)
        result.append(row_list)
    
    return result
Key changes made to make the function compatible with numba: 1. Replaced sets with boolean/integer arrays 2. Removed numpy operations that aren't supported in nopython mode 3. Replaced list operations with array operations 4. Added explicit type handling 5. Replaced assertions with if-raise statements 6. Used explicit loops instead of numpy vectorized operations The function should provide the same results as the original but with better performance due to the JIT compilation. Note that the first run of the function will be slower due to the compilation overhead, but subsequent runs will be faster. To use this function, you'll need to have numba installed (`pip install numba`) and import both numba and numpy. The input matrix should be a numpy array with dtype=np.int64 for best performance.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize arrays instead of sets for tracking used rows
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    extra = 0
    col = 0
    pivots = []
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
            
        # Find other rows to reduce
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_list = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_list.append(j)
        result.append(row_list)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize arrays instead of sets for tracking used rows
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, i] = 1
    
    extra = 0
    col = 0
    pivots = []
    
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
            
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
            
        # Find other rows to reduce
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for k in range(rows):
                    if used_for_row[col, k] == 1:
                        used_for_row[i, k] = 1
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_list = []
        for j in range(rows):
            if used_for_row[i, j] == 1:
                row_list.append(j)
        result.append(row_list)
    
    return result



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

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

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: 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 numba-optimized version of the function using nopython mode. Note that we need to make some adjustments since numba doesn't support certain Python operations like sets directly: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
import numba
import numpy as np
from numba import jit

@jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = []
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    # Work with a copy of the matrix
    matrix = matrix.copy() % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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]
        
        # Verify pivot value
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result
Key changes made to make the function work with numba: 1. Replaced sets with a boolean matrix for `used_for_row` 2. Removed numpy functions like `np.all` and `np.argwhere` in favor of explicit loops 3. Modified the array operations to be more explicit 4. Changed the set operations to boolean matrix operations 5. Used explicit array copying instead of list conversion 6. Modified the return format to work with numba's restrictions To use this function: 
1
2
3
4
5
6
7
import numpy as np
from numba import jit

# Example usage:
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.int64)
graphlen = 2
result = rref(matrix, graphlen)
Note that the first time you call this function, it will compile, which might take a moment. Subsequent calls will be much faster. Also, make sure your input matrix is of a compatible numeric dtype (like np.int64). The function maintains the same logic as the original but is optimized for numba execution. The main difference is in how we handle the tracking of used rows, which is now done with a boolean matrix instead of sets.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
import numba
import numpy as np
from numba import jit

@jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = []
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    # Work with a copy of the matrix
    matrix = matrix.copy() % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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]
        
        # Verify pivot value
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
import numba
import numpy as np
from numba import jit

@jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = []
    
    # Create used_for_row as a boolean matrix instead of sets
    used_for_row = np.zeros((rows, rows), dtype=np.bool_)
    for i in range(rows):
        used_for_row[i, i] = True
    
    # Work with a copy of the matrix
    matrix = matrix.copy() % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col + extra] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            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]
        
        # Verify pivot value
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        matrix[col] = (matrix[col] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Update used_for_row
                for j in range(rows):
                    if used_for_row[col, j]:
                        used_for_row[i, j] = True
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    matrix[i] = (matrix[i] - matrix[col] * mult) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        matrix[i] = (matrix[i] - matrix[col]) % PH
                        
        col += 1
    
    matrix = matrix % PH
    
    # Convert used_for_row back to list format
    result = []
    for i in range(rows):
        row_indices = []
        for j in range(rows):
            if used_for_row[i, j]:
                row_indices.append(j)
        result.append(row_indices)
    
    return result



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

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

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: 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: True

Final Answer: True

Final Answer: True

Initial Query

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

LLM Generation

Query

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

Output

Here's the numba-optimized version of the function using nopython mode. Note that sets aren't supported in numba, so I've modified the function to use arrays instead: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a 2D array instead of list of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, 0] = i
        used_for_row[i, 1:] = -1  # Use -1 to mark unused entries
    
    # Convert matrix to modulo PH
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Merge used_for_row entries
                temp_used = np.zeros(rows, dtype=np.int64) - 1
                idx = 0
                
                # Add entries from both rows
                for k in range(rows):
                    if used_for_row[i, k] != -1:
                        temp_used[idx] = used_for_row[i, k]
                        idx += 1
                for k in range(rows):
                    if used_for_row[col, k] != -1:
                        val = used_for_row[col, k]
                        if val not in temp_used:
                            temp_used[idx] = val
                            idx += 1
                            
                used_for_row[i] = temp_used
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    # Convert used_for_row to sorted lists
    result = []
    for i in range(rows):
        row = []
        for j in range(rows):
            if used_for_row[i, j] != -1:
                row.append(used_for_row[i, j])
        row.sort()
        result.append(row)
    
    return result
Key changes made to make the function numba-compatible: 1. Replaced sets with arrays (sets aren't supported in numba) 2. Used arrays instead of Python lists where possible 3. Implemented set operations manually using arrays 4. Added explicit type declarations where needed 5. Removed numpy functions that aren't supported in nopython mode 6. Implemented row operations explicitly The function maintains the same logic as the original but is optimized for numba execution. The main difference is in how we track the used_for_row information, which is now done using 2D arrays with -1 as a sentinel value for unused entries. To use this function: 
1
2
3
4
import numpy as np
matrix = np.array([[...]])  # Your input matrix
graphlen = ...  # Your graphlen value
result = rref(matrix, graphlen)
The function will return the same type of output as the original function (a list of sorted lists representing the used rows), but it will execute much faster due to numba's just-in-time compilation.

Extract Code

I extracted the following code from that output: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a 2D array instead of list of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, 0] = i
        used_for_row[i, 1:] = -1  # Use -1 to mark unused entries
    
    # Convert matrix to modulo PH
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Merge used_for_row entries
                temp_used = np.zeros(rows, dtype=np.int64) - 1
                idx = 0
                
                # Add entries from both rows
                for k in range(rows):
                    if used_for_row[i, k] != -1:
                        temp_used[idx] = used_for_row[i, k]
                        idx += 1
                for k in range(rows):
                    if used_for_row[col, k] != -1:
                        val = used_for_row[col, k]
                        if val not in temp_used:
                            temp_used[idx] = val
                            idx += 1
                            
                used_for_row[i] = temp_used
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    # Convert used_for_row to sorted lists
    result = []
    for i in range(rows):
        row = []
        for j in range(rows):
            if used_for_row[i, j] != -1:
                row.append(used_for_row[i, j])
        row.sort()
        result.append(row)
    
    return result

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
import numba
import numpy as np

@numba.jit(nopython=True)
def rref(matrix, graphlen):
    PH = 16
    rows, cols = matrix.shape
    
    # Initialize variables
    extra = 0
    col = 0
    pivots = np.zeros(cols, dtype=np.int64)
    pivot_count = 0
    
    # Create used_for_row as a 2D array instead of list of sets
    used_for_row = np.zeros((rows, rows), dtype=np.int64)
    for i in range(rows):
        used_for_row[i, 0] = i
        used_for_row[i, 1:] = -1  # Use -1 to mark unused entries
    
    # Convert matrix to modulo PH
    matrix = matrix % PH
    
    while col + extra < cols - 1 and col < rows:
        if matrix[col, col + extra] == 0:
            # Check if column is all zeros
            all_zeros = True
            for i in range(rows):
                if matrix[i, col] != 0:
                    all_zeros = False
                    break
                    
            if all_zeros:
                extra += 1
                continue
                
            # Find last non-zero entry
            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
                
            # Swap rows
            temp_row = matrix[col].copy()
            matrix[col] = matrix[other]
            matrix[other] = temp_row
            
            temp_used = used_for_row[col].copy()
            used_for_row[col] = used_for_row[other]
            used_for_row[other] = temp_used
        
        pivots[pivot_count] = col + extra
        pivot_count += 1
        
        pivot = matrix[col, col + extra]
        if col + extra < graphlen:
            if not (abs(pivot) == 1 or abs(pivot) == PH-1):
                raise ValueError("Invalid pivot value")
        else:
            if not (abs(pivot) == 2 or abs(pivot) == PH-2):
                raise ValueError("Invalid pivot value")
            pivot //= 2
            
        # Multiply row by pivot inverse
        for j in range(cols):
            matrix[col, j] = (matrix[col, j] * pivot) % PH
        
        # Eliminate in other rows
        for i in range(rows):
            if i != col and matrix[i, col + extra] != 0:
                # Merge used_for_row entries
                temp_used = np.zeros(rows, dtype=np.int64) - 1
                idx = 0
                
                # Add entries from both rows
                for k in range(rows):
                    if used_for_row[i, k] != -1:
                        temp_used[idx] = used_for_row[i, k]
                        idx += 1
                for k in range(rows):
                    if used_for_row[col, k] != -1:
                        val = used_for_row[col, k]
                        if val not in temp_used:
                            temp_used[idx] = val
                            idx += 1
                            
                used_for_row[i] = temp_used
                
                if col < graphlen:
                    mult = matrix[i, col + extra]
                    for j in range(cols):
                        matrix[i, j] = (matrix[i, j] - mult * matrix[col, j]) % PH
                else:
                    while matrix[i, col + extra] != 0:
                        for j in range(cols):
                            matrix[i, j] = (matrix[i, j] - matrix[col, j]) % PH
                            
        col += 1
    
    # Convert used_for_row to sorted lists
    result = []
    for i in range(rows):
        row = []
        for j in range(rows):
            if used_for_row[i, j] != -1:
                row.append(used_for_row[i, j])
        row.sort()
        result.append(row)
    
    return result



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

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

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: 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