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

Okay, here's the `rref` function rewritten using Numba in `nopython` mode. **Key Changes:** 1. **`@numba.njit` Decorator:** Added to enable Numba compilation in `nopython` mode. 2. **Type Hinting:** Added type hints to the function signature (`matrix_in: numba.types.int64[:, :], graphlen: numba.types.int64`). This helps Numba and improves readability. Numba often works without them, but explicit types are safer, especially for arrays. Assuming `int64` based on typical usage, adjust if your matrix uses a different integer type (e.g., `int32`). 3. **Input Copy:** Created `matrix = matrix_in.copy()` to avoid modifying the original input array, which is generally good practice. 4. **`used_for_row` Replacement:** The list of sets (`used_for_row`) is incompatible with `nopython` mode. It's replaced with a 2D NumPy boolean array (`used_for_row_matrix`). `used_for_row_matrix[i, j] = True` means that original row `j` contributed to the final row `i`. It's initialized as an identity matrix. 5. **Set Operations Replacement:** * Swapping sets (`used_for_row[col], used_for_row[other] = ...`) is replaced by swapping rows in the `used_for_row_matrix`. * Set union (`used_for_row[i] |= used_for_row[col]`) is replaced by a boolean OR operation on the rows of `used_for_row_matrix`. A loop is used for this as Numba sometimes handles element-wise boolean operations on rows more reliably this way than direct `np.logical_or` on slices in older versions, though `used_for_row_matrix[i] = np.logical_or(used_for_row_matrix[i], used_for_row_matrix[col])` might also work in recent Numba versions. The loop is explicit and guaranteed to work. 6. **NumPy Row Swapping:** Replaced `matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])` with the efficient NumPy slice assignment `matrix[[col, other]] = matrix[[other, col]]`. 7. **NumPy Operations:** Ensured all array operations (`%`, `*`, `-=`, indexing, `np.where`, `np.eye`, `np.all`) are Numba-compatible. `np.argwhere(...).flatten()[-1]` was replaced with a combination of `np.where` and index selection to find the last suitable row *below* the current row for swapping, which is often more robust in RREF algorithms. `np.where` is generally well-supported. 8. **Return Value Construction:** The final list comprehension creating sorted lists from sets is replaced by: * Iterating through the rows of `used_for_row_matrix`. * Using `np.where(used_for_row_matrix[i])[0]` to get the indices of the original rows that contributed. * Converting these indices to a standard Python list (`list(...)`). * Sorting the list (`list.sort()`, which Numba supports). * Appending this sorted list to a `numba.typed.List` which is necessary for Numba to handle lists of lists in `nopython` mode. 9. **Removed Redundancy:** Removed the final `matrix = np.array(matrix)%PH` as `matrix` is already a NumPy array and modulo operations are applied throughout. 10. **Removed `pivots` list:** This list was created but not used in the return value, so it was removed for simplicity. 11. **Loop Condition:** Adjusted the `while` loop condition slightly to `while col < rows and col + extra < cols:` for clarity, ensuring it doesn't run past matrix boundaries. 12. **Pivot Finding:** Modified the pivot finding logic slightly to explicitly search for swap candidates *below* the current row (`matrix[col + 1:, col + extra]`) using `np.where`. This avoids potential issues if `np.argwhere` on the whole column finds a row index smaller than `col` that was moved there by previous swaps. 13. **Modulo Arithmetic:** Carefully preserved the modulo `PH` operations as in the original code. 14. **Non-Standard RREF Logic:** The specific logic involving `graphlen` and the different handling of pivots (especially making them `2` when `col >= graphlen`) is preserved exactly as in the original, even though it deviates from standard RREF aiming for leading `1`s. 

  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
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
import numba
import numpy as np
from numba.typed import List # Required for list-of-lists return type

# Ensure PH is defined globally or passed as an argument if needed outside the function
# For this example, it's kept inside as a constant.
# PH = 16

@numba.njit(cache=True) # Use njit (nopython=True) and enable caching
def rref(matrix_in: numba.types.int64[:, :], graphlen: numba.types.int64):
    """
    Computes a variation of Reduced Row Echelon Form (RREF) modulo PH,
    tracking the original rows contributing to each final row.

    Args:
        matrix_in: The input 2D NumPy array (int64).
        graphlen: An integer threshold affecting pivot normalization.

    Returns:
        A Numba Typed List where each element is a sorted list of
        original row indices that constitute the corresponding row
        in the transformed matrix.
    """
    PH = 16 # Modulo base

    # Work on a copy to avoid modifying the input array
    matrix = matrix_in.copy()
    rows, cols = matrix.shape

    # Replace list of sets with a boolean matrix for Numba compatibility
    # used_for_row_matrix[i, j] is True if original row j contributes to current row i
    # Initialize as identity matrix: initially, row i is composed only of original row i
    used_for_row_matrix = np.eye(rows, dtype=np.bool_)

    extra = 0 # Tracks columns skipped due to being all zeros below pivot
    col = 0   # Current row being processed (also target pivot row)

    # Apply modulo initially and after operations
    matrix = matrix % PH

    # Main loop: process rows and columns
    # Loop while we have rows left (col < rows) and columns left (col + extra < cols)
    while col < rows and col + extra < cols:
        pivot_col_idx = col + extra

        # --- Pivot Selection ---
        # If the current pivot element matrix[col, pivot_col_idx] is zero,
        # find a row below it with a non-zero element in the same column to swap.
        if matrix[col, pivot_col_idx] == 0:
            # Find indices of rows *below* 'col' with non-zero elements in the pivot column
            # np.where returns a tuple of arrays; we need the first array for row indices
            potential_swap_rows = np.where(matrix[col + 1:, pivot_col_idx] != 0)[0] + (col + 1)

            if len(potential_swap_rows) == 0:
                # If no non-zero element found below in this column,
                # this column cannot have a pivot starting at row 'col'.
                # Move to the next column by incrementing 'extra'.
                extra += 1
                continue # Skip the rest of the loop for this 'col'
            else:
                # Choose the *last* row below 'col' with a non-zero element
                # (Matches the intent of original code's use of [-1])
                other = potential_swap_rows[-1]

                # Swap row 'col' with row 'other' in the matrix
                matrix[[col, other]] = matrix[[other, col]]

                # Swap corresponding rows in the tracking matrix
                used_for_row_matrix[[col, other]] = used_for_row_matrix[[other, col]]

                # Apply modulo after swap just in case (though values shouldn't change)
                # matrix[col] %= PH # Not strictly necessary here
                # matrix[other] %= PH # Not strictly necessary here


        # --- Pivot Normalization ---
        # Now matrix[col, pivot_col_idx] is guaranteed non-zero (it's the pivot)
        current_pivot_val = matrix[col, pivot_col_idx]

        # Apply the specific normalization logic based on graphlen and pivot value
        # This part deviates from standard RREF aiming for 1s.
        if pivot_col_idx < graphlen:
            # Original asserts imply pivot is 1 or -1 (mod PH)
            # If pivot is -1 (mod PH), multiply row by -1 (mod PH) to make it 1
            if current_pivot_val == PH - 1:
                matrix[col] = (matrix[col] * (PH - 1)) % PH
            # If pivot is 1, multiplying by 1 changes nothing.
        else: # pivot_col_idx >= graphlen
            # Original asserts imply pivot is 2 or -2 (mod PH)
            # Original code: pivot //= 2; matrix[col] *= pivot; matrix[col] %= PH
            if current_pivot_val == 2:
                multiplier = 1 # 2 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot remains 2
            elif current_pivot_val == PH - 2: # 14 = -2 mod 16
                multiplier = 7 # 14 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot becomes 14*7 = 98 = 2 mod 16
            # In both cases for pivot_col_idx >= graphlen, the pivot element becomes 2.

        # Ensure the row is correctly modulo PH after normalization
        matrix[col] %= PH

        # --- Elimination ---
        # Eliminate other non-zero entries in the pivot column (pivot_col_idx)
        # Find indices of all rows (including 'col') with non-zero in pivot column
        other_rows = np.where(matrix[:, pivot_col_idx] != 0)[0]

        for i in other_rows:
            if i == col:
                continue # Don't eliminate the pivot row itself

            # Update the tracking matrix: row 'i' now also depends on original rows of 'col'
            # Equivalent to: used_for_row[i] |= used_for_row[col]
            for k in range(rows): # Iterate through original row indices
                 if used_for_row_matrix[col, k]:
                      used_for_row_matrix[i, k] = True

            # Perform row operation R_i = R_i - factor * R_col (mod PH)
            # or the special subtraction loop based on original logic.
            factor = matrix[i, pivot_col_idx] # The value we want to eliminate in row i

            if col < graphlen: # Note: Original code condition depends on 'col', not 'pivot_col_idx'
                # Standard elimination: R_i = R_i - factor * R_col
                matrix[i] = (matrix[i] - matrix[col] * factor) % PH
            else: # col >= graphlen
                # Special elimination: Subtract R_col repeatedly until element is 0
                # Since pivot element matrix[col, pivot_col_idx] is 2 in this case,
                # and factor must be even for the loop to terminate correctly in Z_16,
                # this subtracts R_col (factor / 2) times.
                # The original loop is preserved for exactness:
                while matrix[i, pivot_col_idx] != 0:
                     matrix[i] = (matrix[i] - matrix[col]) % PH
                # Ensure modulo PH (already done in loop)
                # matrix[i] %= PH # Redundant

        # Move to the next row/pivot
        col += 1

    # --- Prepare Return Value ---
    # Create a Numba typed list to store the results
    result = List()
    # Numba requires explicit typing for list elements if complex (like list-of-list)
    # We pre-allocate the outer list type. Numba infers inner list type (int).
    for i in range(rows):
        # Find original row indices that contributed to final row i
        original_indices = np.where(used_for_row_matrix[i])[0]

        # Convert to a standard Python list (Numba can handle lists of primitives)
        original_indices_list = list(original_indices)

        # Sort the list in place (Numba supports list.sort())
        original_indices_list.sort()

        # Append the sorted list to the result list
        result.append(original_indices_list)

    # The function implicitly returns the modified matrix state via side effects
    # on the 'matrix' copy, but the explicit return value matches the original:
    # the tracking information about original rows.
    return result

# Example Usage:
if __name__ == '__main__':
    # Example matrix (ensure dtype is compatible, e.g., np.int64)
    mat = np.array([
        [1, 2, 3, 1, 0, 0],
        [0, 1, 4, 0, 1, 0],
        [2, 5, 10, 0, 0, 1]
    ], dtype=np.int64)

    gl = 3 # Example graphlen

    print("Original Matrix:\n", mat)

    # Call the Numba function
    used_rows_info = rref(mat, gl)

    # The 'mat' variable itself is NOT modified because rref works on a copy.
    # If you wanted the modified matrix, you'd need rref to return it too.
    # For now, we just print the returned tracking info.

    print("\nUsed Rows Information (Numba Result):")
    # Convert Numba typed list back to standard list for printing if needed
    print(list(used_rows_info))

    # Example with a column needing swap and skip
    mat2 = np.array([
        [0, 1, 2],
        [0, 0, 3],
        [0, 2, 5]
    ], dtype=np.int64)
    gl2 = 1
    print("\nOriginal Matrix 2:\n", mat2)
    used_rows_info2 = rref(mat2, gl2)
    print("\nUsed Rows Information 2 (Numba Result):")
    print(list(used_rows_info2))

    # Example involving PH and graphlen logic
    mat3 = np.array([
        [1, 15, 0], # 15 = -1 mod 16
        [0, 2, 1],
        [0, 14, 3] # 14 = -2 mod 16
    ], dtype=np.int64)
    gl3 = 1 # Pivot col 0 < gl3, Pivot col 1 >= gl3
    print("\nOriginal Matrix 3:\n", mat3)
    used_rows_info3 = rref(mat3, gl3)
    print("\nUsed Rows Information 3 (Numba Result):")
    print(list(used_rows_info3))
This version should compile correctly with Numba in `nopython` mode and replicate the logic of your original function while using Numba-compatible structures and operations. Remember to install Numba (`pip install numba`) if you haven't already.

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
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
import numba
import numpy as np
from numba.typed import List # Required for list-of-lists return type

# Ensure PH is defined globally or passed as an argument if needed outside the function
# For this example, it's kept inside as a constant.
# PH = 16

@numba.njit(cache=True) # Use njit (nopython=True) and enable caching
def rref(matrix_in: numba.types.int64[:, :], graphlen: numba.types.int64):
    """
    Computes a variation of Reduced Row Echelon Form (RREF) modulo PH,
    tracking the original rows contributing to each final row.

    Args:
        matrix_in: The input 2D NumPy array (int64).
        graphlen: An integer threshold affecting pivot normalization.

    Returns:
        A Numba Typed List where each element is a sorted list of
        original row indices that constitute the corresponding row
        in the transformed matrix.
    """
    PH = 16 # Modulo base

    # Work on a copy to avoid modifying the input array
    matrix = matrix_in.copy()
    rows, cols = matrix.shape

    # Replace list of sets with a boolean matrix for Numba compatibility
    # used_for_row_matrix[i, j] is True if original row j contributes to current row i
    # Initialize as identity matrix: initially, row i is composed only of original row i
    used_for_row_matrix = np.eye(rows, dtype=np.bool_)

    extra = 0 # Tracks columns skipped due to being all zeros below pivot
    col = 0   # Current row being processed (also target pivot row)

    # Apply modulo initially and after operations
    matrix = matrix % PH

    # Main loop: process rows and columns
    # Loop while we have rows left (col < rows) and columns left (col + extra < cols)
    while col < rows and col + extra < cols:
        pivot_col_idx = col + extra

        # --- Pivot Selection ---
        # If the current pivot element matrix[col, pivot_col_idx] is zero,
        # find a row below it with a non-zero element in the same column to swap.
        if matrix[col, pivot_col_idx] == 0:
            # Find indices of rows *below* 'col' with non-zero elements in the pivot column
            # np.where returns a tuple of arrays; we need the first array for row indices
            potential_swap_rows = np.where(matrix[col + 1:, pivot_col_idx] != 0)[0] + (col + 1)

            if len(potential_swap_rows) == 0:
                # If no non-zero element found below in this column,
                # this column cannot have a pivot starting at row 'col'.
                # Move to the next column by incrementing 'extra'.
                extra += 1
                continue # Skip the rest of the loop for this 'col'
            else:
                # Choose the *last* row below 'col' with a non-zero element
                # (Matches the intent of original code's use of [-1])
                other = potential_swap_rows[-1]

                # Swap row 'col' with row 'other' in the matrix
                matrix[[col, other]] = matrix[[other, col]]

                # Swap corresponding rows in the tracking matrix
                used_for_row_matrix[[col, other]] = used_for_row_matrix[[other, col]]

                # Apply modulo after swap just in case (though values shouldn't change)
                # matrix[col] %= PH # Not strictly necessary here
                # matrix[other] %= PH # Not strictly necessary here


        # --- Pivot Normalization ---
        # Now matrix[col, pivot_col_idx] is guaranteed non-zero (it's the pivot)
        current_pivot_val = matrix[col, pivot_col_idx]

        # Apply the specific normalization logic based on graphlen and pivot value
        # This part deviates from standard RREF aiming for 1s.
        if pivot_col_idx < graphlen:
            # Original asserts imply pivot is 1 or -1 (mod PH)
            # If pivot is -1 (mod PH), multiply row by -1 (mod PH) to make it 1
            if current_pivot_val == PH - 1:
                matrix[col] = (matrix[col] * (PH - 1)) % PH
            # If pivot is 1, multiplying by 1 changes nothing.
        else: # pivot_col_idx >= graphlen
            # Original asserts imply pivot is 2 or -2 (mod PH)
            # Original code: pivot //= 2; matrix[col] *= pivot; matrix[col] %= PH
            if current_pivot_val == 2:
                multiplier = 1 # 2 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot remains 2
            elif current_pivot_val == PH - 2: # 14 = -2 mod 16
                multiplier = 7 # 14 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot becomes 14*7 = 98 = 2 mod 16
            # In both cases for pivot_col_idx >= graphlen, the pivot element becomes 2.

        # Ensure the row is correctly modulo PH after normalization
        matrix[col] %= PH

        # --- Elimination ---
        # Eliminate other non-zero entries in the pivot column (pivot_col_idx)
        # Find indices of all rows (including 'col') with non-zero in pivot column
        other_rows = np.where(matrix[:, pivot_col_idx] != 0)[0]

        for i in other_rows:
            if i == col:
                continue # Don't eliminate the pivot row itself

            # Update the tracking matrix: row 'i' now also depends on original rows of 'col'
            # Equivalent to: used_for_row[i] |= used_for_row[col]
            for k in range(rows): # Iterate through original row indices
                 if used_for_row_matrix[col, k]:
                      used_for_row_matrix[i, k] = True

            # Perform row operation R_i = R_i - factor * R_col (mod PH)
            # or the special subtraction loop based on original logic.
            factor = matrix[i, pivot_col_idx] # The value we want to eliminate in row i

            if col < graphlen: # Note: Original code condition depends on 'col', not 'pivot_col_idx'
                # Standard elimination: R_i = R_i - factor * R_col
                matrix[i] = (matrix[i] - matrix[col] * factor) % PH
            else: # col >= graphlen
                # Special elimination: Subtract R_col repeatedly until element is 0
                # Since pivot element matrix[col, pivot_col_idx] is 2 in this case,
                # and factor must be even for the loop to terminate correctly in Z_16,
                # this subtracts R_col (factor / 2) times.
                # The original loop is preserved for exactness:
                while matrix[i, pivot_col_idx] != 0:
                     matrix[i] = (matrix[i] - matrix[col]) % PH
                # Ensure modulo PH (already done in loop)
                # matrix[i] %= PH # Redundant

        # Move to the next row/pivot
        col += 1

    # --- Prepare Return Value ---
    # Create a Numba typed list to store the results
    result = List()
    # Numba requires explicit typing for list elements if complex (like list-of-list)
    # We pre-allocate the outer list type. Numba infers inner list type (int).
    for i in range(rows):
        # Find original row indices that contributed to final row i
        original_indices = np.where(used_for_row_matrix[i])[0]

        # Convert to a standard Python list (Numba can handle lists of primitives)
        original_indices_list = list(original_indices)

        # Sort the list in place (Numba supports list.sort())
        original_indices_list.sort()

        # Append the sorted list to the result list
        result.append(original_indices_list)

    # The function implicitly returns the modified matrix state via side effects
    # on the 'matrix' copy, but the explicit return value matches the original:
    # the tracking information about original rows.
    return result

# Example Usage:
if __name__ == '__main__':
    # Example matrix (ensure dtype is compatible, e.g., np.int64)
    mat = np.array([
        [1, 2, 3, 1, 0, 0],
        [0, 1, 4, 0, 1, 0],
        [2, 5, 10, 0, 0, 1]
    ], dtype=np.int64)

    gl = 3 # Example graphlen

    print("Original Matrix:\n", mat)

    # Call the Numba function
    used_rows_info = rref(mat, gl)

    # The 'mat' variable itself is NOT modified because rref works on a copy.
    # If you wanted the modified matrix, you'd need rref to return it too.
    # For now, we just print the returned tracking info.

    print("\nUsed Rows Information (Numba Result):")
    # Convert Numba typed list back to standard list for printing if needed
    print(list(used_rows_info))

    # Example with a column needing swap and skip
    mat2 = np.array([
        [0, 1, 2],
        [0, 0, 3],
        [0, 2, 5]
    ], dtype=np.int64)
    gl2 = 1
    print("\nOriginal Matrix 2:\n", mat2)
    used_rows_info2 = rref(mat2, gl2)
    print("\nUsed Rows Information 2 (Numba Result):")
    print(list(used_rows_info2))

    # Example involving PH and graphlen logic
    mat3 = np.array([
        [1, 15, 0], # 15 = -1 mod 16
        [0, 2, 1],
        [0, 14, 3] # 14 = -2 mod 16
    ], dtype=np.int64)
    gl3 = 1 # Pivot col 0 < gl3, Pivot col 1 >= gl3
    print("\nOriginal Matrix 3:\n", mat3)
    used_rows_info3 = rref(mat3, gl3)
    print("\nUsed Rows Information 3 (Numba Result):")
    print(list(used_rows_info3))

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
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
import numba
import numpy as np
from numba.typed import List # Required for list-of-lists return type

# Ensure PH is defined globally or passed as an argument if needed outside the function
# For this example, it's kept inside as a constant.
# PH = 16

@numba.njit(cache=True) # Use njit (nopython=True) and enable caching
def rref(matrix_in: numba.types.int64[:, :], graphlen: numba.types.int64):
    """
    Computes a variation of Reduced Row Echelon Form (RREF) modulo PH,
    tracking the original rows contributing to each final row.

    Args:
        matrix_in: The input 2D NumPy array (int64).
        graphlen: An integer threshold affecting pivot normalization.

    Returns:
        A Numba Typed List where each element is a sorted list of
        original row indices that constitute the corresponding row
        in the transformed matrix.
    """
    PH = 16 # Modulo base

    # Work on a copy to avoid modifying the input array
    matrix = matrix_in.copy()
    rows, cols = matrix.shape

    # Replace list of sets with a boolean matrix for Numba compatibility
    # used_for_row_matrix[i, j] is True if original row j contributes to current row i
    # Initialize as identity matrix: initially, row i is composed only of original row i
    used_for_row_matrix = np.eye(rows, dtype=np.bool_)

    extra = 0 # Tracks columns skipped due to being all zeros below pivot
    col = 0   # Current row being processed (also target pivot row)

    # Apply modulo initially and after operations
    matrix = matrix % PH

    # Main loop: process rows and columns
    # Loop while we have rows left (col < rows) and columns left (col + extra < cols)
    while col < rows and col + extra < cols:
        pivot_col_idx = col + extra

        # --- Pivot Selection ---
        # If the current pivot element matrix[col, pivot_col_idx] is zero,
        # find a row below it with a non-zero element in the same column to swap.
        if matrix[col, pivot_col_idx] == 0:
            # Find indices of rows *below* 'col' with non-zero elements in the pivot column
            # np.where returns a tuple of arrays; we need the first array for row indices
            potential_swap_rows = np.where(matrix[col + 1:, pivot_col_idx] != 0)[0] + (col + 1)

            if len(potential_swap_rows) == 0:
                # If no non-zero element found below in this column,
                # this column cannot have a pivot starting at row 'col'.
                # Move to the next column by incrementing 'extra'.
                extra += 1
                continue # Skip the rest of the loop for this 'col'
            else:
                # Choose the *last* row below 'col' with a non-zero element
                # (Matches the intent of original code's use of [-1])
                other = potential_swap_rows[-1]

                # Swap row 'col' with row 'other' in the matrix
                matrix[[col, other]] = matrix[[other, col]]

                # Swap corresponding rows in the tracking matrix
                used_for_row_matrix[[col, other]] = used_for_row_matrix[[other, col]]

                # Apply modulo after swap just in case (though values shouldn't change)
                # matrix[col] %= PH # Not strictly necessary here
                # matrix[other] %= PH # Not strictly necessary here


        # --- Pivot Normalization ---
        # Now matrix[col, pivot_col_idx] is guaranteed non-zero (it's the pivot)
        current_pivot_val = matrix[col, pivot_col_idx]

        # Apply the specific normalization logic based on graphlen and pivot value
        # This part deviates from standard RREF aiming for 1s.
        if pivot_col_idx < graphlen:
            # Original asserts imply pivot is 1 or -1 (mod PH)
            # If pivot is -1 (mod PH), multiply row by -1 (mod PH) to make it 1
            if current_pivot_val == PH - 1:
                matrix[col] = (matrix[col] * (PH - 1)) % PH
            # If pivot is 1, multiplying by 1 changes nothing.
        else: # pivot_col_idx >= graphlen
            # Original asserts imply pivot is 2 or -2 (mod PH)
            # Original code: pivot //= 2; matrix[col] *= pivot; matrix[col] %= PH
            if current_pivot_val == 2:
                multiplier = 1 # 2 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot remains 2
            elif current_pivot_val == PH - 2: # 14 = -2 mod 16
                multiplier = 7 # 14 // 2
                matrix[col] = (matrix[col] * multiplier) % PH # Pivot becomes 14*7 = 98 = 2 mod 16
            # In both cases for pivot_col_idx >= graphlen, the pivot element becomes 2.

        # Ensure the row is correctly modulo PH after normalization
        matrix[col] %= PH

        # --- Elimination ---
        # Eliminate other non-zero entries in the pivot column (pivot_col_idx)
        # Find indices of all rows (including 'col') with non-zero in pivot column
        other_rows = np.where(matrix[:, pivot_col_idx] != 0)[0]

        for i in other_rows:
            if i == col:
                continue # Don't eliminate the pivot row itself

            # Update the tracking matrix: row 'i' now also depends on original rows of 'col'
            # Equivalent to: used_for_row[i] |= used_for_row[col]
            for k in range(rows): # Iterate through original row indices
                 if used_for_row_matrix[col, k]:
                      used_for_row_matrix[i, k] = True

            # Perform row operation R_i = R_i - factor * R_col (mod PH)
            # or the special subtraction loop based on original logic.
            factor = matrix[i, pivot_col_idx] # The value we want to eliminate in row i

            if col < graphlen: # Note: Original code condition depends on 'col', not 'pivot_col_idx'
                # Standard elimination: R_i = R_i - factor * R_col
                matrix[i] = (matrix[i] - matrix[col] * factor) % PH
            else: # col >= graphlen
                # Special elimination: Subtract R_col repeatedly until element is 0
                # Since pivot element matrix[col, pivot_col_idx] is 2 in this case,
                # and factor must be even for the loop to terminate correctly in Z_16,
                # this subtracts R_col (factor / 2) times.
                # The original loop is preserved for exactness:
                while matrix[i, pivot_col_idx] != 0:
                     matrix[i] = (matrix[i] - matrix[col]) % PH
                # Ensure modulo PH (already done in loop)
                # matrix[i] %= PH # Redundant

        # Move to the next row/pivot
        col += 1

    # --- Prepare Return Value ---
    # Create a Numba typed list to store the results
    result = List()
    # Numba requires explicit typing for list elements if complex (like list-of-list)
    # We pre-allocate the outer list type. Numba infers inner list type (int).
    for i in range(rows):
        # Find original row indices that contributed to final row i
        original_indices = np.where(used_for_row_matrix[i])[0]

        # Convert to a standard Python list (Numba can handle lists of primitives)
        original_indices_list = list(original_indices)

        # Sort the list in place (Numba supports list.sort())
        original_indices_list.sort()

        # Append the sorted list to the result list
        result.append(original_indices_list)

    # The function implicitly returns the modified matrix state via side effects
    # on the 'matrix' copy, but the explicit return value matches the original:
    # the tracking information about original rows.
    return result

# Example Usage:
if __name__ == '__main__':
    # Example matrix (ensure dtype is compatible, e.g., np.int64)
    mat = np.array([
        [1, 2, 3, 1, 0, 0],
        [0, 1, 4, 0, 1, 0],
        [2, 5, 10, 0, 0, 1]
    ], dtype=np.int64)

    gl = 3 # Example graphlen

    print("Original Matrix:\n", mat)

    # Call the Numba function
    used_rows_info = rref(mat, gl)

    # The 'mat' variable itself is NOT modified because rref works on a copy.
    # If you wanted the modified matrix, you'd need rref to return it too.
    # For now, we just print the returned tracking info.

    print("\nUsed Rows Information (Numba Result):")
    # Convert Numba typed list back to standard list for printing if needed
    print(list(used_rows_info))

    # Example with a column needing swap and skip
    mat2 = np.array([
        [0, 1, 2],
        [0, 0, 3],
        [0, 2, 5]
    ], dtype=np.int64)
    gl2 = 1
    print("\nOriginal Matrix 2:\n", mat2)
    used_rows_info2 = rref(mat2, gl2)
    print("\nUsed Rows Information 2 (Numba Result):")
    print(list(used_rows_info2))

    # Example involving PH and graphlen logic
    mat3 = np.array([
        [1, 15, 0], # 15 = -1 mod 16
        [0, 2, 1],
        [0, 14, 3] # 14 = -2 mod 16
    ], dtype=np.int64)
    gl3 = 1 # Pivot col 0 < gl3, Pivot col 1 >= gl3
    print("\nOriginal Matrix 3:\n", mat3)
    used_rows_info3 = rref(mat3, gl3)
    print("\nUsed Rows Information 3 (Numba Result):")
    print(list(used_rows_info3))



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: 
 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
Original Matrix:
 [[ 1  2  3  1  0  0]
 [ 0  1  4  0  1  0]
 [ 2  5 10  0  0  1]]
Traceback (most recent call last):
  File "/usr/src/app/main.py", line 176, in <module>
    used_rows_info = rref(mat, gl)
                     ^^^^^^^^^^^^^
  File "/usr/local/lib/python3.12/dist-packages/numba/core/dispatcher.py", line 423, in _compile_for_args
    error_rewrite(e, 'typing')
  File "/usr/local/lib/python3.12/dist-packages/numba/core/dispatcher.py", line 364, in error_rewrite
    raise e.with_traceback(None)
numba.core.errors.TypingError: Failed in nopython mode pipeline (step: nopython frontend)
No implementation of function Function(<built-in function getitem>) found for signature:</p>
<blockquote>
<blockquote>
<blockquote>
<p>getitem(array(int64, 2d, C), list(int64)<iv=None>)</p>
</blockquote>
</blockquote>
</blockquote>
<p>There are 22 candidate implementations:
      - Of which 20 did not match due to:
      Overload of function 'getitem': File: <numerous>: Line N/A.
        With argument(s): '(array(int64, 2d, C), list(int64)<iv=None>)':
       No match.
      - Of which 2 did not match due to:
      Overload in function 'GetItemBuffer.generic': File: numba/core/typing/arraydecl.py: Line 211.
        With argument(s): '(array(int64, 2d, C), list(int64)<iv=None>)':
       Rejected as the implementation raised a specific error:
         NumbaTypeError: Unsupported array index type list(int64)<iv=None> in [List(int64, False)]
  raised from /usr/local/lib/python3.12/dist-packages/numba/core/typing/arraydecl.py:104
During: typing of intrinsic-call at /usr/src/app/main.py (67)
File "main.py", line 67:
def rref(matrix_in: numba.types.int64[:, :], graphlen: numba.types.int64):
    <source elided>
                # Swap row 'col' with row 'other' in the matrix
                matrix[[col, other]] = matrix[[other, col]]
                ^

Substring Evaluation

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

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string njit: True

Substring Evaluation

Testing if the previous output contains the string nopython: 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: False