1. Generating Data#

The idea of xyzpy is to ease the some of the pain generating data with a large parameter space. The central aim being that, once you know what a single run of a function looks like, it should be as easy as saying, “run these combinations of parameters, now run these particular cases” with everything automatically aggregated into a fully self-described dataset.

%matplotlib inline
%config InlineBackend.figure_formats = ['svg']

from xyzpy import *
import numpy as np

1.1. Combos & Cases#

The main backend function is combo_runner(), which in its simplest form takes a function, say:

def foo(a, b, c):
    return f"{a}-{b}-{c}", np.sin(a)

and combos of the form:

combos = [
    ('a', [1, 2, 3]),
    ('b', ['x', 'y', 'z']),
    ('c', [True, False]),

and generates a nested (here 3 dimensional) array of all the outputs of foo with the 3 * 3 * 2 = 18 combinations of input arguments:

combo_runner(foo, combos)
100%|##########| 18/18 [00:00<00:00, 114563.69it/s]
(((('1-x-True', 0.8414709848078965), ('1-x-False', 0.8414709848078965)),
  (('1-y-True', 0.8414709848078965), ('1-y-False', 0.8414709848078965)),
  (('1-z-True', 0.8414709848078965), ('1-z-False', 0.8414709848078965))),
 ((('2-x-True', 0.9092974268256817), ('2-x-False', 0.9092974268256817)),
  (('2-y-True', 0.9092974268256817), ('2-y-False', 0.9092974268256817)),
  (('2-z-True', 0.9092974268256817), ('2-z-False', 0.9092974268256817))),
 ((('3-x-True', 0.1411200080598672), ('3-x-False', 0.1411200080598672)),
  (('3-y-True', 0.1411200080598672), ('3-y-False', 0.1411200080598672)),
  (('3-z-True', 0.1411200080598672), ('3-z-False', 0.1411200080598672))))

Note the progress bar shown. If the function was slower (generally the target case for xyzpy), this would show the remaining time before completion.

There is also case_runner() for running isolated cases:

cases = [(4, 'z', False), (5, 'y', True)]
case_runner(foo, fn_args=('a', 'b', 'c'), cases=cases)
100%|##########| 2/2 [00:00<00:00, 18236.10it/s]
(('4-z-False', -0.7568024953079282), ('5-y-True', -0.9589242746631385))

You can also mix the two, supplying some function arguments as cases and some as combos. In this situation, for each case, all sub combinations are run:

        {'a': 1, 'c': True},
        {'a': 2, 'c': False},
        {'a': 3, 'c': True},
        'b': ['x', 'y', 'z'],
100%|##########| 9/9 [00:00<00:00, 85019.68it/s]
((((array(nan), array(nan)),
   (array(nan), array(nan)),
   (array(nan), array(nan))),
  (('1-x-True', 0.8414709848078965),
   ('1-y-True', 0.8414709848078965),
   ('1-z-True', 0.8414709848078965))),
 ((('2-x-False', 0.9092974268256817),
   ('2-y-False', 0.9092974268256817),
   ('2-z-False', 0.9092974268256817)),
  ((array(nan), array(nan)),
   (array(nan), array(nan)),
   (array(nan), array(nan)))),
 (((array(nan), array(nan)),
   (array(nan), array(nan)),
   (array(nan), array(nan))),
  (('3-x-True', 0.1411200080598672),
   ('3-y-True', 0.1411200080598672),
   ('3-z-True', 0.1411200080598672))))

Note now that for the combo_runner missing results are automatically filled with nan, (or possibly None depending on shape and dtype). Note we also avoided specifying the specific function argument order by supplying a list of dicts. You can supply both combos and cases to either combo_runner(), or case_runner(), the main difference is

  1. combo_runner() outputs a nested tuple suitable to be turned into an array

  2. case_runner() outputs a flat tuple of results suitable to be put into a table

You will likely not use these functions in their raw form, but they illustrate the concept of combos and cases and underly most other functionality.

1.2. Describing the function - Runner#

To automatically put the generated data into a labelled xarray.Dataset you need to describe your function using the Runner class. In the simplest case this is just a matter of naming the outputs:

runner = Runner(foo, var_names=['a_out', 'b_out'])
100%|##########| 18/18 [00:00<00:00, 135786.82it/s]
Dimensions:  (a: 3, b: 3, c: 2)
  * a        (a) int64 1 2 3
  * b        (b) <U1 'x' 'y' 'z'
  * c        (c) bool True False
Data variables:
    a_out    (a, b, c) <U9 '1-x-True' '1-x-False' ... '3-z-True' '3-z-False'
    b_out    (a, b, c) float64 0.8415 0.8415 0.8415 ... 0.1411 0.1411 0.1411

The output dataset is also stored in runner.last_ds and, as can be seen, is completely labelled - see xarray for details of the myriad functionality this allows. See also the Basic Output Example for a more complete example.


As a convenience, label() can be used to decorate a function, turning it directly into a Runner like so:

@label(var_names=['sum', 'diff'])
def foo(x, y):
    return x + y, x - y

Various other arguments to Runner allow: 1) constant arguments to be specified, 2) for each variable to have its own dimensions and 3) to specify the coordinates of those dimensions. For example, imagine we have a function bar with signature:

"bar(i, j, k, t) -> (A, B[x], C[x, t])"

Maybe i, j, k index a location and t is a (constant) series of times to compute. There are 3 outputs: (i) the scalar A, (ii) the vector B which has a dimension x with known coordinates, say [10, 20, 30], and (iii) the 2D-array C, which shares the x dimension but also depends on t. The arguments to Runner to describe this situation would be:

var_names = ['A', 'B', 'C']
var_dims = {'B': ['x'], 'C': ['x', 't']}
var_coords = {'x': [10, 20, 30]}
constants = {'t': np.linspace(0, 1, 101)}

Note that 't' doesn’t need to be specified in var_coords as it can be found in constants. Let’s explicitly mock a function with this signature and some combos to run:

def bar(i, j, k, t):
    A = np.random.rand()
    B = np.random.rand(3)  # 'B[x]'
    C = np.random.rand(3, len(t))  # 'C[x, t]'
    return A, B, C

# if we are using a runner, combos can be supplied as a dict
combos = {
    'i': [5, 6, 7],
    'j': [0.5, 0.6, 0.7],
    'k': [0.05, 0.06, 0.07],

We can then run the combos:

r = Runner(bar, constants=constants,
100%|##########| 27/27 [00:00<00:00, 62291.64it/s]
Dimensions:  (i: 3, j: 3, k: 3, x: 3, t: 101)
  * i        (i) int64 5 6 7
  * j        (j) float64 0.5 0.6 0.7
  * k        (k) float64 0.05 0.06 0.07
  * x        (x) int64 10 20 30
  * t        (t) float64 0.0 0.01 0.02 0.03 0.04 ... 0.96 0.97 0.98 0.99 1.0
Data variables:
    A        (i, j, k) float64 0.09133 0.001715 0.5488 ... 0.4148 0.8277 0.07938
    B        (i, j, k, x) float64 0.8565 0.492 0.9438 ... 0.2236 0.9373 0.6762
    C        (i, j, k, x, t) float64 0.6665 0.5983 0.1811 ... 0.1725 0.5512

We can see the dimensions 'i', 'j' and 'k' have been generated by the combos for all variables, as well as the ‘internal’ dimensions 'x' and 't' only for 'B' and 'C'. See also the Structured Output with Julia Set Example for a fuller demonstration.

Finally, if the function itself returns a xarray.Dataset, then just use var_names=None and all the outputs will be concatenated together automatically. The overhead this incurs is often negligible for anything but very fast functions.

1.3. Aggregating data - Harvester#

A common scenario when running simulations is the following:

  1. Generate some data

  2. Save it to disk

  3. Generate a different set of data (maybe after analysis of the first set)

  4. Load the old data

  5. Merge the new data with the old data

  6. Save the new combined data

  7. Repeat

The aim of the Harvester is to automate that process. A Harvester is instantiated with a Runner instance and, optionally, a data_name. If a data_name is given, then every time a round of combos/cases is generated, it will be automatically synced with a on-disk dataset of that name. Either way, the harvester will aggregate all runs into the full_ds attribute.

combos = [
    ('a', [1, 2, 3]),
    ('b', ['x', 'y', 'z']),
    ('c', [True, False]),

harvester = Harvester(runner, data_name='foo.h5')
100%|##########| 18/18 [00:00<00:00, 114217.05it/s]

Which, because it didn’t exist yet, created the file data_name:

ls *.h5

xyzpy.Harvester.harvest_combos() calls xyzpy.Runner.run_combos() itself - this doesn’t need to be done seperately.

Now we can run a second set of different combos:

combos2 = {
    'a': [4, 5, 6],
    'b': ['w', 'v'],
    'c': [True, False],
100%|##########| 12/12 [00:00<00:00, 42762.66it/s]

Now we can check the total dataset containing all combos and cases run so far:

Dimensions:  (a: 6, b: 5, c: 2)
  * a        (a) int64 1 2 3 4 5 6
  * b        (b) object 'v' 'w' 'x' 'y' 'z'
  * c        (c) bool True False
Data variables:
    a_out    (a, b, c) object nan nan nan nan '1-x-True' ... nan nan nan nan nan
    b_out    (a, b, c) float64 nan nan nan nan 0.8415 ... nan nan nan nan nan
@label(var_names=['sum', 'diff'], harvester='foo.h5')
def foo(x, y):
    return x + y, x - y

Runner: <xyzpy.Runner>
    fn: <function foo at 0x7f72b035a3a0>
    fn_args: ('x', 'y')
    var_names: ('sum', 'diff')
    var_dims: {'sum': (), 'diff': ()}
Sync file -->
    foo.h5    [h5netcdf]

Note that, since the different runs were disjoint, missing values have automatically been filled in with nan values - see xarray.merge(). The on-disk dataset now contains both runs.


As a convenience, label() can also be used to decorate a function as a xyzpy.Harvester by supplying the harvester kwarg. If True a harvester will be instantiated with data_name=None. If a string, it is used as the data_name.

>>> @label(var_names=['sum', 'diff'], harvester='foo.h5')
... def foo(x, y):
...     return x + y, x - y
>>> foo
Runner: <xyzpy.Runner>
    fn: <function foo at 0x7f6217a2b550>
    fn_args: ('x', 'y')
    var_names: ('sum', 'diff')
    var_dims: {'sum': (), 'diff': ()}
Sync file -->
    foo.h5    [h5netcdf]

1.4. Aggregating Random samples of data - Sampler#

Occasionally, exhaustively iterating through all combinations of arguments is unneccesary. If instead you just want to sample the parameter space sparsely then the Sampler object allows this with much the same interface as a Harvester. The main difference is that, since the parameters are no longer gridded, the data is stored as a table in a pandas.DataFrame.

import math
import random

def trig(amp, fn, x, phase):
    return amp * getattr(math, fn)(x - phase)

# these are the default combos/distributions to sample from
default_combos = {
    'amp': [1, 2, 3],
    'fn': ['cos', 'sin'],
    # for distributions we can supply callables
    'x': lambda: 2 * math.pi * random.random(),
    'phase': lambda: random.gauss(0.0, 0.1),

sampler = Sampler(trig, 'trig.pkl', default_combos)
Runner: <xyzpy.Runner>
    fn: <function trig at 0x7f72b035a9d0>
    fn_args: ('amp', 'fn', 'x', 'phase')
    var_names: ('out',)
    var_dims: {'out': ()}
Sync file -->
    trig.pkl    [pickle]

Now we can run the sampler many times (and supply any of the usual arguments such as parallel=True etc). This generates a pandas.DataFrame:

100%|##########| 10000/10000 [00:00<00:00, 305687.24it/s]

This has also synced the data with the on-disk file:

!ls *.pkl

You can specify Sampler(..., engine='csv') etc to use formats other than pickle.

As with the Harvester, next time we run combinations, the data is automatically aggregated into the full set:

# here we will override some of the default sampling choices
combos = {
    'fn': ['tan'],
    'x': lambda: random.random() * math.pi / 4

sampler.sample_combos(5000, combos);
100%|##########| 5000/5000 [00:00<00:00, 299970.25it/s]

We can then use tools such as seaborn to visualize the full data:

import seaborn as sns

sns.relplot(x='x', y='out', hue='fn', size='amp', data=sampler.full_df)
<seaborn.axisgrid.FacetGrid at 0x7f72b029f8e0>


As a convenience, label() can also be used to decorate a function as a xyzpy.Sampler by supplying the sampler kwarg. If True a sampler will be instantiated with data_name=None. If a string, it is used as the data_name.

1.5. Summary#

  1. combo_runner() is the core function which outputs a nested tuple and contains the parallelization logic and progress display etc.

  2. Runner and xyzpy.Runner.run_combos() are used to describe the function’s output and perform a single set of runs yielding a Dataset. These internally call combo_runner().

  3. Harvester and xyzpy.Harvester.harvest_combos() are used to perform many sets of runs, continuously merging the results into one larger Dataset - Harvester.full_ds, probably synced to disk. These internally call xyzpy.Runner.run_combos().

  4. Sampler and xyzpy.Sampler.sample_combos() are used to sparsely sample from parameter combinations. Unlike a normal Harvester, the data is aggregated automatically into a pandas.DataFrame.

In general, you would only generate data with one of these methods at once - see the full demonstrations in Examples.

# some cleanup