Matrix views

These are views of the matrix object (i.e they don’t replicate the matrix data), kinda like how .keys() and .values() are to dict.

Note that these objects “expire” (become invalid) if the matrix is resized i.e if you create a matrix view object and then resize the matrix by any means, the previously created matrix view object becomes invalid and any operation on it raises an error.

Rows, Columns RowsSlice, ColumnsSlice instances.

These objects provide a view over multiple rows or columns of a matrix.

• Rows and Columns instances cover all rows and columns respectively.
  • They can be retrieved using the matrix attributes rows and columns respectively.
  • Every matrix has only one each of these instances.
• RowsSlice and ColumnsSlice instances cover a slice (selection) of the rows or columns respectively.
  • They can be gotten by slicing the Rows or Columns instance of a matrix.

These objects support the following operations:

• Subscription
  • Single row/column Indexing.
  • Slicing.
    • A slice of a RowsSlice instance returns another RowsSlice instance that is a view over the matrix rows selected from the former slice. Similarly for ColumnSlice.
• Row/column assignment and deletion (RowsSlice and ColumnsSlice DO NOT support these yet).
  • Can only modify single rows, not a slice of rows but can delete a slice of rows.
  • Assigned object can be any iterable of real numbers.
  • Augmented assigment counterparts of operations supported by Row and Column also work and update the row/column of the matrix.
  • Deleting a row/column changes the size of the matrix.
  • Emptying a matrix is not allowed.
• Length (number of rows/columns “in” the view) via len().
• Iteration through rows/columns.

Row and Column instances

These objects provide a view over a single row or column of a matrix.

• They can be gotten by indexing a Rows, Columns, RowsSlice, or ColumnsSlice instance of a matrix.

They support the following operations:

• String representation
• Subscription
  • Single element indexing
  • Multiple element slicing (returns a list)
  • The subscriptions can also be assignment targets to change the element or elements of the matrix.
  • Also, augmented assignment counterparts of operators supported by the matrix elements, update the elements of the matrix.
  • Augmented assignments won’t work with Row/Column slices due to the fact that they return list objects.
  • Elements cannot be deleted.
• Equality comparison
• Arithmetic operations (Also supports augmented assignment counterparts of these operations):
  • Addition and subtraction of rows and/or columns (Element-wise)
  • Multiplication and Division by scalar
  • Multiplication and Division by row/column (i.e inter-operation of two rows/columns element-by-element)
• Row/column length with len()
• Membership tests
• Iteration through elements

Row objects have one property:

• pivot_index -> Pivot index.
  • gets the 1-based index of the leading non-zero (pivot) element on that row.
  • returns 0 (zero) for a zero-row.

NOTE on Row/Column arithmetic operations:

• Each binary operation returns a list containing the result of the operation.
• Augmented assignments counterparts of these operations perform in-place operations i.e affect the matrix itself.
• Due to this difference, if row = m.rows[1], then row += row is very different from row = row + row.
  • In the former, the corresponding row (row 1) of the matrix m is modified and row references a Row instance after the operation.
  • While in the latter, the matrix row remains unchanged and row references a list instance after the operation.
  • The only exception to this behaviour is when using subscripts of the Rows or Columns instance directly e.g m.rows[1] = m.rows[1] * 2 is equivalent to m.rows[1] *= 2, in terms of end results.
  • Same applies to Column.