logio.dynamic_time_warping package

Submodules

logio.dynamic_time_warping.DTW module

logio.dynamic_time_warping.DTW.dtw(x, y, dist='euclidean', window_type='none', window_size=None, step_pattern='symmetric2', dist_only=False, open_begin=False, open_end=False)

Perform dynamic time warping (dtw).

A Dynamic Programming algorithm to correlate well logs and to find the minimum-cost or “best” match.

Parameters

• x (1D or 2D array (sample * feature)) – Query log.

• y (1D or 2D array (sample * feature)) – Reference log.

• dist (string or callable) – Define how to calclulate pair-wise distance between x and y. If a string given, it will be interpreted as metric argument of scipy.spatial.distance. If callable that defines metric between two samples, it will be used to compute distance matrix.

• window_type (string) – Window type to use. If “sakoechiba” given, Sakoechiba window will be used. If “itakura” given, Itakura window will be used.

• window_size (int) – Window size to use for Sakoechiba window.

• step_pattern (string) – Step pattern to use.

• dist_only (bool) – Whether or not to obtain warping path. If true, only alignment distance will be calculated.

• open_begin (bool) – Whether or not perform open-ended alignment at the starting point of query log. If true, partial alignment will be performed.

• open_end (bool) – Whether or not perform open-ended alignment at the end point of query log. If true, partial alignment will be performed.

Returns

Result obj.

Return type

result.DtwResult

logio.dynamic_time_warping.DTW.dtw_from_distance_matrix(X, window_type='none', window_size=None, step_pattern='symmetric2', dist_only=False, open_begin=False, open_end=False)

Perform dtw based correlation using pre-computed pair-wise distance matrix.

Parameters

• X (2D array) – Pre-computed pair-wise distance matrix.

• others – see dtw() function.

Returns

Result obj.

Return type

result.DtwResult

logio.dynamic_time_warping.DTW.dtw_low(X, window, pattern, dist_only=False, open_begin=False, open_end=False)

Low-level dtw interface.

Parameters

• X (2D array) – Pair-wise distance matrix.

• window (window.BaseWindow object) – window object.

• pattern (step_pattern.BasePattern object) – step pattern object.

• others – see dtw() function.

Returns

Result obj.

Return type

result.DtwResult

logio.dynamic_time_warping.backtrack module

Backtracking implementation.

logio.dynamic_time_warping.cost module

Cost matrix computation.

logio.dynamic_time_warping.distance module

logio.dynamic_time_warping.dtwPlot module

DTW plotting functions

logio.dynamic_time_warping.dtwPlot.AlignmentPlot(alignment_vector, query_index='Query Log index', reference_index='Reference Log index', **kwargs)

Plotting of dynamic time warp results: annotated warping function

Details Display the query and reference well logs and their warping curve, arranged for visual inspection. The query log is plotted in the bottom panel, with indices growing rightwards and values upwards. Reference log is in the left panel, indices growing upwards and values leftwards.

Parameters

• alignment_vector (object) – an alignment result, object of class DtwResult

• query_index (str) – name of query_index label

• reference_index (str) – name of reference_index label

• ... – additional arguments, used for the warping curve

Returns

axes

Return type

figure axes

logio.dynamic_time_warping.dtwPlot.ThreeWayPlot(alignment_vector, query=None, reference=None, match_indices=None, match_col='gray', query_label='Query log index', reference_label='Reference log index', **kwargs)

Plotting of dynamic time warp results: annotated warping function

Details Display the query and reference well logs and their warping curve, arranged for visual inspection. The query log is plotted in the bottom panel, with indices growing rightwards and values upwards. Reference log is in the left panel, indices growing upwards and values leftwards.

Parameters

• alignment_vector (object) – an alignment result, object of class DtwResult

• query (Series) – query log (log of considerable interest)

• reference (Series) – log from another well, which we intend to correlate or align with the query log.

• query_label – label for the query axis

• reference_label – label for the reference axis

• match_indices – indices for which to draw a visual guide

• ... – additional arguments, used for the warping curve

Returns

axes

Return type

figure axes

logio.dynamic_time_warping.result module

class logio.dynamic_time_warping.result.DtwResult(cumsum_matrix, path, window, pattern)

Bases: object

Result of Dynamic time warping.

cumsum_matrix

Alignment matrix

Type

2d array

path

Alignment path.

• First column: query path array

• Second column: reference path array

Type

float

window

window constraints

Type

2d array

pattern

Alignment pattern

Type

2d array

get_warping_path(target="query"):

Get warping path.

plot_window():

visualize window

plot_cumsum_matrix():

plot heatmap of cumsum_matrix

plot_path(with_="cum"):

plot alignment path; warp function/curve

plot_pattern():

Plot alignment pattern

dtw_plot(query=None,reference=None, type=None,**kwargs):

Plot dynamic time warp results using specific type plot.

plot_aligned_logs(query=None,reference=None):

plot optimal aligment of both logs.

dtw_plot(query=None, reference=None, type=None, **kwargs)

Plot dynamic time warp results by displaying alignment contained in DtwResult object.

Details Various plotting styles are available, passing strings to the type argument (may be abbreviated):

• alignment plots the warping curve in alignment_vector;

• threeway vis-a-vis inspection of the timeseries and their warping curve;

  see [dtwPlot.ThreeWayPlot()]

Additional parameters are passed to the plotting functions: use with care.

Parameters

• query – log from another well, which we intend to correlate or align with the reference log

• reference – reference log (log of considerable interest)

• xlab (str) – label for the query axis

• ylab (str) – label for the reference axis

• type (str) – general style for the plot, see below

• ... – additional arguments, passed to plotting functions

get_warping_path(target='query')

Get warping path.

Parameters

target (string, "query" or "reference") – Specify the target to be warped.

Returns

warping_index – Warping index.

Return type

1D array

plot_aligned_logs(query=None, reference=None)

Plot query log such that it is locally stretched and/or compressed in order to achieve the best possible match to the reference.

Parameters

• query (array, DataFrame or Series) – log from another well, which we intend to correlate or align with the reference log.

• reference (array, DataFrame or Series) – well log used as reference point for correlation.

plot_cumsum_matrix()

Plot heatmap of cumsum matrix

plot_path(with_='cum')

Plot alignment path.

Parameters

with (string, "win" or "cum" or None) – If given, following will be plotted with alignment path: * “win” : window matrix * “cum” : cumsum matrix

plot_pattern()

plot step_pattern

plot_window()

Visualize window constraint

logio.dynamic_time_warping.step_pattern module

class logio.dynamic_time_warping.step_pattern.Asymmetric

Bases: BasePattern

label = 'asymmetric'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, 0), (0, 0)], 'weights': [1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.AsymmetricP0

Bases: BasePattern

label = 'asymmetricP0'

normalize_guide = 'N'

pattern_info = [{'indices': [(0, -1), (0, 0)], 'weights': [0]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, 0), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.AsymmetricP05

Bases: BasePattern

label = 'asymmetricP05'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, -3), (0, -2), (0, -1), (0, 0)], 'weights': [0.3333333333333333, 0.3333333333333333, 0.3333333333333333]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [0.5, 0.5]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-3, -1), (-2, 0), (-1, 0), (0, 0)], 'weights': [1, 1, 1]}]

class logio.dynamic_time_warping.step_pattern.AsymmetricP1

Bases: BasePattern

label = 'asymmetricP1'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [0.5, 0.5]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}]

class logio.dynamic_time_warping.step_pattern.AsymmetricP2

Bases: BasePattern

label = 'asymmetricP2'

normalize_guide = 'N'

pattern_info = [{'indices': [(-2, -3), (-1, -2), (0, -1), (0, 0)], 'weights': [0.6666666666666666, 0.6666666666666666, 0.6666666666666666]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-3, -2), (-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1, 1]}]

class logio.dynamic_time_warping.step_pattern.BasePattern

Bases: object

Step pattern base class. A BasePattern object lists the transitions allowed while searching for the minimum-distance path.

Methods Plot

_normalize

_get_array

__repr__ prints a user-readable description of the recurrence equation defined by the given pattern.

property is_normalizable

plot()

Visualize step pattern.

class logio.dynamic_time_warping.step_pattern.Mori2006

Bases: BasePattern

label = 'mori2006'

normalize_guide = 'M'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [2, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [3]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [3, 3]}]

class logio.dynamic_time_warping.step_pattern.Symmetric1

Bases: BasePattern

label = 'symmetric1'

normalize_guide = 'none'

pattern_info = [{'indices': [(-1, 0), (0, 0)], 'weights': [1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(0, -1), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.Symmetric2

Bases: BasePattern

label = 'symmetric2'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-1, 0), (0, 0)], 'weights': [1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(0, -1), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.SymmetricP0

Bases: Symmetric2

Same as symmetric2 pattern.

label = 'symmetricP05'

class logio.dynamic_time_warping.step_pattern.SymmetricP05

Bases: BasePattern

label = 'symmetricP05'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-1, -3), (0, -2), (0, -1), (0, 0)], 'weights': [2, 1, 1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [2, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [2, 1]}, {'indices': [(-3, -1), (-2, 0), (-1, 0), (0, 0)], 'weights': [2, 1, 1]}]

class logio.dynamic_time_warping.step_pattern.SymmetricP1

Bases: BasePattern

label = 'symmetricP1'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [2, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [2, 1]}]

class logio.dynamic_time_warping.step_pattern.SymmetricP2

Bases: BasePattern

label = 'symmetricP2'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-3, -2), (-2, -1), (-1, 0), (0, 0)], 'weights': [2, 2, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-2, -3), (-1, -2), (0, -1), (0, 0)], 'weights': [2, 2, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIIIc

Bases: BasePattern

label = 'typeIIIc'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, -2), (0, 0)], 'weights': [1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-2, -2), (-1, 0), (0, 0)], 'weights': [1, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIIa

Bases: BasePattern

label = 'typeIIa'

normalize_guide = 'none'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.TypeIIb

Bases: BasePattern

label = 'typeIIb'

normalize_guide = 'none'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, 0)], 'weights': [2]}, {'indices': [(-2, -1), (0, 0)], 'weights': [2]}]

class logio.dynamic_time_warping.step_pattern.TypeIIc

Bases: BasePattern

label = 'typeIIc'

normalize_guide = 'none'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (0, 0)], 'weights': [2]}]

class logio.dynamic_time_warping.step_pattern.TypeIId

Bases: BasePattern

label = 'typeIId'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-1, -2), (0, 0)], 'weights': [3]}, {'indices': [(-2, -1), (0, 0)], 'weights': [3]}]

class logio.dynamic_time_warping.step_pattern.TypeIVc

Bases: BasePattern

label = 'typeIVc'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, 0)], 'weights': [1]}, {'indices': [(-1, -3), (0, 0)], 'weights': [1]}, {'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-2, -2), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-2, -3), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-3, -1), (-2, 0), (-1, 0), (0, 0)], 'weights': [1, 1, 1]}, {'indices': [(-3, -2), (-2, 0), (-1, 0), (0, 0)], 'weights': [1, 1, 1]}, {'indices': [(-3, -3), (-2, 0), (-1, 0), (0, 0)], 'weights': [1, 1, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIa

Bases: BasePattern

label = 'typeIa'

normalize_guide = 'none'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 0]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [1, 0]}]

class logio.dynamic_time_warping.step_pattern.TypeIas

Bases: BasePattern

label = 'typeIas'

normalize_guide = 'none'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [0.5, 0.5]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [0.5, 0.5]}]

class logio.dynamic_time_warping.step_pattern.TypeIb

Bases: BasePattern

label = 'typeIb'

normalize_guide = 'none'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [1, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIbs

Bases: BasePattern

label = 'typeIbs'

normalize_guide = 'none'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [1, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIc

Bases: BasePattern

label = 'typeIc'

normalize_guide = 'N'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [1, 0]}]

class logio.dynamic_time_warping.step_pattern.TypeIcs

Bases: BasePattern

label = 'typeIcs'

normalize_guide = 'N'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [1]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [0.5, 0.5]}]

class logio.dynamic_time_warping.step_pattern.TypeId

Bases: BasePattern

label = 'typeId'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [2, 1]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [2, 1]}]

class logio.dynamic_time_warping.step_pattern.TypeIds

Bases: BasePattern

label = 'typeIds'

normalize_guide = 'N+M'

pattern_info = [{'indices': [(-2, -1), (-1, 0), (0, 0)], 'weights': [1.5, 1.5]}, {'indices': [(-1, -1), (0, 0)], 'weights': [2]}, {'indices': [(-1, -2), (0, -1), (0, 0)], 'weights': [1.5, 1.5]}]

class logio.dynamic_time_warping.step_pattern.Unitary

Bases: BasePattern

label = 'unitary'

normalize_guide = 'N'

pattern_info = [{'indices': [(-1, -1), (0, 0)], 'weights': [1]}]

class logio.dynamic_time_warping.step_pattern.UserStepPattern(pattern_info, normalize_guide)

Bases: BasePattern

label = 'user defined step pattern'

logio.dynamic_time_warping.window module

class logio.dynamic_time_warping.window.BaseWindow

Bases: object

Base class on which the desired window constraint is built upon. The warping window intuitively controls the amount of distortion allowed when comparing a pair of well logs.

Generally they are two types of wapring windows: 1. Sakoechiba’s Window implemented in SakoechibaWindow class. 2. Itakura’s Window implemented in ItakuraWindow class.

plot():

Visualize window (constraint)..

plot()

Visualize window (constraint).

class logio.dynamic_time_warping.window.ItakuraWindow(len_x, len_y)

Bases: BaseWindow

A class for the Itakura window warping constraint.

len_x

Length of query log.

Type

int

len_y

Length of reference log.

Type

int

_gen_window(len_x, len_y):

Generates the window constraint matrix.

label = 'itakura window'

class logio.dynamic_time_warping.window.NoWindow(len_x, len_y)

Bases: BaseWindow

No window class.

len_x

Length of query log.

Type

int

len_y

Length of reference log.

Type

int

_gen_window(len_x, len_y):

Generates the window constraint matrix.

label = 'no window'

class logio.dynamic_time_warping.window.SakoechibaWindow(len_x, len_y, size)

Bases: BaseWindow

Sakoechiba window warping constraint.

len_x

Length of query log.

Type

int

len_y

Length of reference log.

Type

int

size

Size of window width.

Type

int

_gen_window(len_x, len_y, size):

Generates the window constraint matrix.

label = 'sakoechiba window'

class logio.dynamic_time_warping.window.UserWindow(len_x, len_y, win_func, *args, **kwargs)

Bases: BaseWindow

A class for user defined window constraints.

Option for a user defined window is implemented in UserWindow class. The user window defined must be a function that returns a boolean.

len_x

Length of query log.

Type

int

len_y

Length of reference log.

Type

int

win_func

Any function which returns bool.

Type

callable

\*args, \*\*kwargs

Arguments for win_func

_gen_window(len_x, len_y, win_func, \*args, \*\*kwargs):

Generates the window constraint matrix.

label = 'user defined window'

Module contents