DTW Windows¶

class darts.dataprocessing.dtw.window.CRWindow(n, m, ranges=None)[source]¶

Bases: Window

Compressed row representation window. Stores the range of active grid cells in each column. Any window with contiguous columns can be expressed as a CRWindow. Supports efficient iterative construction and updates.

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1
m (int) – The height of the window, must be equal to the length of series2
ranges (Optional[ndarray]) – The ranges of active cells within a column [[start_column0, end_column0], …] with shape (n, 2) and where start >= 0 and end <= m.

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

add(elem)[source]¶

Marks a grid cell as active.

Parameters: elem (Tuple[int, int]) – Tuple of grid cell index (column, row)

add_range(column, start, end)[source]¶

Extends the active cells in the column by the range (start,end). Ranges smaller than the current one are ignored. Note (1, m+1), not (0,m) corresponds to an entire column.

Parameters

column (int) – Column int index
start (int) – Row element int index where start >= 1 and start <= end
end (int) – Row element int index where end >= 1 and end <= m+1

column_index(elem)[source]¶

Gives the number of active grid cells before row element j, in column i.

Parameters: elem (Tuple[int, int]) – (i,j) index, where i indexes columns and j rows
Returns: The number of active grid cells before row element j, in column i, If (i,j) is not an active grid cell returns -1
Return type: int

column_length(column)[source]¶

Gives the number of active grid cells in a column.

Parameters: column (int) – A column in the window, must be within 0 < column < n+1
Returns: The number of active grid cells in a column.
Return type: int

column_lengths()[source]¶

Gives the number of activate grid cells in each column.

Returns: The number of active grid cells in each column.
Return type: np.ndarray of shape (n+1,)

column_ranges: array¶

init_size(n, m)¶

Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1 used for DTW
m (int) – The height of the window, must be equal to the length of series2 used for DTW

length: int¶

m: int¶

n: int¶

class darts.dataprocessing.dtw.window.Itakura(max_slope)[source]¶

Bases: CRWindow

Forms the Itakura parallelogram, where max_slope determines the slope of the steeper side.

Examples

>>>                                      x
>>>                                  xxxx
>>>                   B           xxxxxx
>>>                         xxxxxxxxxxx
>>>                     xxxxxxxxxxxxxx
>>>                 xxxxxxxxxxxxxxxxx
>>>              xxxxxxxxxxxxxxxxxxxx     C
>>>            xxxxxxxxxxxxxxxxxxxxx
>>>           xxxxxxxxxxxxxxxxxxxxx
>>>          xxxxxxxxxxxxxxxxxxxxx
>>>     A   xxxxxxxxxxxxxxxxxxxxx
>>>        xxxxxxxxxxxxxxxxxxxxx
>>>       xxxxxxxxxxxxxxxxxxxxx
>>>      xxxxxxxxxxxxxxxxxxxx
>>>     xxxxxxxxxxxxxxxx       D
>>>     xxxxxxxxxxxx
>>>    xxxxxxxxx
>>>   xxxxxx
>>>  xxx
>>> x

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

Parameters: max_slope (float) – The slope of the steeper parallelogram side.

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

add(elem)¶

Marks a grid cell as active.

Parameters: elem (Tuple[int, int]) – Tuple of grid cell index (column, row)

add_range(column, start, end)¶

Extends the active cells in the column by the range (start,end). Ranges smaller than the current one are ignored. Note (1, m+1), not (0,m) corresponds to an entire column.

Parameters

column (int) – Column int index
start (int) – Row element int index where start >= 1 and start <= end
end (int) – Row element int index where end >= 1 and end <= m+1

column_index(elem)¶

Gives the number of active grid cells before row element j, in column i.

Parameters: elem (Tuple[int, int]) – (i,j) index, where i indexes columns and j rows
Returns: The number of active grid cells before row element j, in column i, If (i,j) is not an active grid cell returns -1
Return type: int

column_length(column)¶

Gives the number of active grid cells in a column.

Parameters: column (int) – A column in the window, must be within 0 < column < n+1
Returns: The number of active grid cells in a column.
Return type: int

column_lengths()¶

Gives the number of activate grid cells in each column.

Returns: The number of active grid cells in each column.
Return type: np.ndarray of shape (n+1,)

column_ranges: array¶

init_size(n, m)[source]¶

Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1 used for DTW
m (int) – The height of the window, must be equal to the length of series2 used for DTW

length: int¶

m: int¶

n: int¶

class darts.dataprocessing.dtw.window.NoWindow[source]¶

Bases: Window

Window covers the entire grid, meaning every possible alignment between series1 and series2 is considered.

Methods

`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

column_index(elem)[source]¶

Gives the number of active grid cells before row element j, in column i.

Parameters: elem (Tuple[int, int]) – (i,j) index, where i indexes columns and j rows
Returns: The number of active grid cells before row element j, in column i, If (i,j) is not an active grid cell returns -1
Return type: int

column_length(column)[source]¶

Gives the number of active grid cells in a column.

Parameters: column (int) – A column in the window, must be within 0 < column < n+1
Returns: The number of active grid cells in a column.
Return type: int

column_lengths()[source]¶

Gives the number of activate grid cells in each column.

Returns: The number of active grid cells in each column.
Return type: np.ndarray of shape (n+1,)

init_size(n, m)¶

Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1 used for DTW
m (int) – The height of the window, must be equal to the length of series2 used for DTW

m: int¶

n: int¶

class darts.dataprocessing.dtw.window.SakoeChiba(window_size)[source]¶

Bases: CRWindow

Forms a diagonal window where window_size controls the maximum allowed shift between the two series. If both time-series have the same time axis, window_size corresponds to the maximum number of time periods

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

Parameters: window_size (int) – The maximum allowed shift between the two series used in DTW.

Methods

`add`(elem)	Marks a grid cell as active.
`add_range`(column, start, end)	Extends the active cells in the column by the range (start,end).
`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

add(elem)¶

Marks a grid cell as active.

Parameters: elem (Tuple[int, int]) – Tuple of grid cell index (column, row)

add_range(column, start, end)¶

Extends the active cells in the column by the range (start,end). Ranges smaller than the current one are ignored. Note (1, m+1), not (0,m) corresponds to an entire column.

Parameters

column (int) – Column int index
start (int) – Row element int index where start >= 1 and start <= end
end (int) – Row element int index where end >= 1 and end <= m+1

column_index(elem)¶

Gives the number of active grid cells before row element j, in column i.

Parameters: elem (Tuple[int, int]) – (i,j) index, where i indexes columns and j rows
Returns: The number of active grid cells before row element j, in column i, If (i,j) is not an active grid cell returns -1
Return type: int

column_length(column)¶

Gives the number of active grid cells in a column.

Parameters: column (int) – A column in the window, must be within 0 < column < n+1
Returns: The number of active grid cells in a column.
Return type: int

column_lengths()¶

Gives the number of activate grid cells in each column.

Returns: The number of active grid cells in each column.
Return type: np.ndarray of shape (n+1,)

column_ranges: array¶

init_size(n, m)[source]¶

Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1 used for DTW
m (int) – The height of the window, must be equal to the length of series2 used for DTW

length: int¶

m: int¶

n: int¶

class darts.dataprocessing.dtw.window.Window[source]¶

Bases: ABC

Methods

`column_index`(elem)	Gives the number of active grid cells before row element j, in column i.
`column_length`(column)	Gives the number of active grid cells in a column.
`column_lengths`()	Gives the number of activate grid cells in each column.
`init_size`(n, m)	Called by dtw to initialize the window to a certain size.

abstract column_index(elem)[source]¶

Gives the number of active grid cells before row element j, in column i.

Parameters: elem (Tuple[int, int]) – (i,j) index, where i indexes columns and j rows
Returns: The number of active grid cells before row element j, in column i, If (i,j) is not an active grid cell returns -1
Return type: int

abstract column_length(column)[source]¶

Gives the number of active grid cells in a column.

Parameters: column (int) – A column in the window, must be within 0 < column < n+1
Returns: The number of active grid cells in a column.
Return type: int

column_lengths()[source]¶

Gives the number of activate grid cells in each column.

Returns: The number of active grid cells in each column.
Return type: np.ndarray of shape (n+1,)

init_size(n, m)[source]¶

Called by dtw to initialize the window to a certain size.

Parameters

n (int) – The width of the window, must be equal to the length of series1 used for DTW
m (int) – The height of the window, must be equal to the length of series2 used for DTW

m: int¶

n: int¶

darts.dataprocessing.dtw.window.gtz(value)[source]¶

Dynamic Time Warping (DTW)

Time Axis Encoders