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import param
import numpy as np
import holoviews as hv
hv.notebook_extension('bokeh', 'matplotlib')
HoloViews objects provide a convenient way of wrapping your data along with some metadata for exploration and visualization. For the simplest visualizations, you can simply declare a small collection of element which can then be composed or placed in an appropriate container. As soon as the task becomes more complex, it is natural to write a function of a class to output HoloViews objects.
In this tutorial, the concept of Operations are introduced which help structure such code, making it possible to write general code that can process HoloViews objects. This enables powerful new ways of specifying HoloViews objects computed from existing data, allowing flexible data processing pipelines to be constructed. Examples of such operations are histogram, rolling, datashade or decimate, which apply some computation on certain types of Element and return a new Element with the transformed data.
In this Tutorial we will discover how operations work, how to control their parameters and how to chain them. The Dynamic_Operations extends what we have learned to demonstrate how operations can be applied lazily by using the dynamic flag, letting us define deferred processing pipelines that can drive highly complex visualizations and dashboards.
Operations in HoloViews are subclasses of Operation, which transform one Element or Overlay of Elements by returning a new Element that may be a transformation of the original. All operations are parameterized using the param library which allows easy validation and documentation of the operation arguments. In particular, operations are instances of param.ParameterizedFunction which allows operations to be used in the same way as normal python functions.
This approach has several advantages, one of which is that we can manipulate the operations parameters at several different levels: at the class-level, at the instance-level or when we call it. Another advantage, is that using parameterizing operations allows them to be inspected just like any other HoloViews object using hv.help. We will now do this for the histogram operation:
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from holoviews.operation import histogram
hv.help(histogram)
Above we can see a listing of all the parameters of the operation, with their defaults, the expected types and detailed docstrings for each one. The histogram operation can be applied to any Element and will by default generate a histogram for the first value dimension defined on the object it is applied to. As a simple example we can create an BoxWhisker Element containing samples from a normal distribution, and then apply the histogram operation to those samples in two ways: 1) by creating an instance on which we will change the num_bins and 2) by passing bin_range directly when calling the operation:
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boxw = hv.BoxWhisker(np.random.randn(10000))
histop_instance = histogram.instance(num_bins=50)
boxw + histop_instance(boxw).relabel('num_bins=50') + histogram(boxw, bin_range=(0, 3)).relabel('bin_range=(0, 3)')
We can see that these two ways of using operations gives us convenient control over how the parameters are applied. An instance allows us to persist some defaults which will be used in all subsequent calls, while passing keyword argument to the operations applies the parameters for just that particular call.
The third way to manipulate parameters is to set them at the class level. If we always want to use num_bins=30 instead of the default of num_bins=20 shown in the help output above, we can simply set histogram.num_binds=30.
Operations in HoloViews are applied to individual elements, which means that when you apply an operation to a container object (such as NdLayout, GridSpace and HoloMap) the operation is once applied per element. For an operation to work, all the elements must be of the same type which means the operation effectively acts to map the operation over all the contained elements. As a simple example we can define a HoloMap of BoxWhisker Elements by varying the width of the distribution via the Sigma value and then apply the histogram operation to it:
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holomap = hv.HoloMap({(i*0.1+0.1): hv.BoxWhisker(np.random.randn(10000)*(i*0.1+0.1)) for i in range(5)},
kdims=['Sigma'])
holomap + histogram(holomap)
As you can see the operation has generated a Histogram for each value of Sigma in the HoloMap. In this way we can apply the operation to the entire parameter space defined by a HoloMap, GridSpace, and NdLayout.
Since operations take a HoloViews object as input and return another HoloViews object we can very easily chain and combine multiple operations to perform complex analyses quickly and easily, while instantly visualizing the output.
In this example we'll work with a timeseries, so we'll define a small function to generate a random, noisy timeseries:
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from holoviews.operation import timeseries
def time_series(T = 1, N = 100, mu = 0.1, sigma = 0.1, S0 = 20):
"""Parameterized noisy time series"""
dt = float(T)/N
t = np.linspace(0, T, N)
W = np.random.standard_normal(size = N)
W = np.cumsum(W)*np.sqrt(dt) # standard brownian motion
X = (mu-0.5*sigma**2)*t + sigma*W
S = S0*np.exp(X) # geometric brownian motion
return S
curve = hv.Curve(time_series(N=1000))
Now we will start applying some operations to this data. HoloViews ships with two ready-to-use timeseries operations: the rolling operation, which applies a function over a rolling window, and a rolling_outlier_std operation that computes outlier points in a timeseries by excluding points less than sigma standard deviation removed from the rolling mean:
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%%opts Scatter [width=600] (color='black')
smoothed = curve * timeseries.rolling(curve) * timeseries.rolling_outlier_std(curve)
smoothed
In the next section we will define a custom operation that will compose with the smoothed operation output above to form a short operation pipeline.
We can now define our own custom Operation which as you may recall can process either elements and overlays. This means we can define a simple operation that takes our smoothed overlay and computes a difference between the raw and smoothed curves that it contains. Such a subtraction will give us the residual between the smoothed and unsmoothed Curve elements, removing long-term trends and leaving the short-term variation.
Defining an operation is very simple. An Operation subclass should define a _process method, which simply accepts an element argument. Optionally we can also define parameters on the operation, which we can access using the self.p attribute on the operation. In this case we define a String parameter, which specifies the name of the subtracted value dimension on the returned Element.
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from holoviews.operation import Operation
class residual(Operation):
"""
Subtracts two curves from one another.
"""
label = param.String(default='Residual', doc="""
Defines the label of the returned Element.""")
def _process(self, element, key=None):
# Get first and second Element in overlay
el1, el2 = element.get(0), element.get(1)
# Get x-values and y-values of curves
xvals = el1.dimension_values(0)
yvals = el1.dimension_values(1)
yvals2 = el2.dimension_values(1)
# Return new Element with subtracted y-values
# and new label
return el1.clone((xvals, yvals-yvals2),
vdims=[self.p.label])
Having defined the residual operation let's try it out right away by applying it to our original and smoothed Curve. We'll place the two objects on top of each other so they can share an x-axis and we can compare them directly:
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%%opts Curve [width=600] Overlay [xaxis=None]
(smoothed + residual(smoothed)).cols(1)
In this view we can immediately see that only a very small residual is left when applying this level of smoothing. However we have only tried one particular rolling_window value, the default value of 10. To assess how this parameter affects the residual we can evaluate the operation over a number different parameter settongs, as we will now see in the next section.
When applying an operation there are often various parameters to vary. Using traditional plotting approaches it's often difficult to evaluate them interactively to get an detailed understanding of what they do. Here we will apply the rolling operations with varying rolling_window widths and window_types across a HoloMap:
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rolled = hv.HoloMap({(w, str(wt)): timeseries.rolling(curve, rolling_window=w, window_type=wt)
for w in [10, 25, 50, 100, 200] for wt in [None, 'hamming', 'triang']},
kdims=['Window', 'Window Type'])
rolled
This visualization is already useful as we can compare between various parameter values by moving the slider and trying different window options. However since we can also chain operations we can also easily compute the residual and view the two together.
To do this we simply overlay the HoloMap of smoothed curves on top of the original curve and pass it to our new residual function. Then we can combine the smoothed view with the original and see how the smoothing and residual curves vary across parameter values:
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%%opts Curve [width=600] Overlay [legend_position='top_left']
(curve(style=dict(color='black')) * rolled + residual(curve * rolled)).cols(1)
Using a few additional lines we have now evaluated the operation over a number of different parameters values, allowing us to process the data with different smoothing parameters. In addition, by interacting with this visualization we can gain a better understanding of the operation parameters as well as gain insights into the structure of the underlying data.
OperationNow that we have seen some operations in action we can get some appreciation of what makes them useful. When working with data interactively you often end up applying a lot of ad-hoc data transforms, which provides maximum flexibility but is neither reproducible nor maintainable. Operations allow you to encapsulate analysis code using a well defined interface that is well suited for building complex analysis pipelines:
Operation parameters are well defined by declaring parameters on the class. These parameters can be easily documented and automatically carry out validation on the types and ranges of the inputs. These parameters are documented using hv.help.
Both inputs and outputs of an operation are instantly visualizable, because the data is the visualization. This means you're not constantly context switching between data processing and visualization --- visualization comes for free as you build your data processing pipeline.
Operations understand HoloViews datastructures and can be immediately applied to any appropriate collection of elements, allowing you to evaluate the operation with permutations of parameter values. This flexibility makes it easy to assess the effect of operation parameters and their effect on your data.
As we will discover in the Dynamic Operation Tutorial, operations can be applied lazily to build up complex deferred data-processing pipelines, which can aid your data exploration and drive interactive visualizations and dashboards.
As we have seen Operation is defined at the level of processing HoloViews elements or overlays of elements. In some situations, you may want to compute a new HoloViews datastructure from a number of elements contained in a structure other than an overlay, such as a HoloMap or a Layout.
One such pattern is an operation that accepts and returns a HoloMap where each of the output element depends on all the data in the input HoloMap. For situations such as these, subclassing Operation is not appropriate and we recommend defining your own function. These custom operation types won't automatically gain support for lazy pipelines as described in the Dynamic Operation Tutorial and how these custom operations are pipelined is left as a design decision for the user. Note that as long as these functions return simple elements or containers, their output can be used by subclasses of Operation as normal.
What we do recommend is that you subclass from param.ParameterizedFunction so that you can declare well-documented and validated parameters, add a description of your operation with a class level docstring and gain automatic documentation support via hv.help.