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Merge pull request #20 from climate-resource/add-cubic
Add basic cubic interpolator
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‎changelog/20.docs.md‎

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+ convert `scratch.py` into how-to-guide and add it into the navigation
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+ add docstring to functions in `add_cubic.py` module

‎docs/NAVIGATION.md‎

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- [Installation](installation.md)
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- [How-to guides](how-to-guides/index.md)
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- [Do a basic calculation](how-to-guides/basic-calculation.md)
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- [Use a cubic spline for harmonisation](how-to-guides/cubic_spline.py)
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- [Tutorials](tutorials/index.md)
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- [Getting Started](tutorials/tutorial.py)
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- [Further background](further-background/index.md)

‎docs/assets/images/cubic_spline.png‎

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‎docs/how-to-guides/cubic_spline.py‎

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# ---
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# jupyter:
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# jupytext:
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# text_representation:
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# extension: .py
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# format_name: percent
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# format_version: '1.3'
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# jupytext_version: 1.16.6
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# kernelspec:
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# display_name: Python 3 (ipykernel)
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# language: python
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# name: python3
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# ---
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# %% [markdown]
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# # How to use a cubic-spline as harmonisation of two functions?
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# In this tutorial, we present use cases for applying a cubic-spline
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# to harmonise two functions which we will call in the following
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# `diverge_from` and `harmonisee`.
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# The `cubic-spline` interpolates between `diverge_from` and `harmonisee`.
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# %%
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# import relevant libraries
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from __future__ import annotations
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import matplotlib.pyplot as plt
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import numpy as np
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import scipy.interpolate
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from gradient_aware_harmonisation.add_cubic import (
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harmonise_splines_add_cubic,
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)
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from gradient_aware_harmonisation.spline import SplineScipy
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# %% [markdown]
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# We start by defining the spline `diverge_from` as a linear
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# function with intercept=1.0 and slope=2.5.
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# %%
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diverge_from_gradient = 2.5
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diverge_from_y_intercept = 1.0
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diverge_from = SplineScipy(
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scipy.interpolate.PPoly(
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c=[[diverge_from_gradient], [diverge_from_y_intercept]],
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x=[0, 1e8],
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)
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)
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# %% [markdown]
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# ## Scenarios
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# ### Harmonisation time < convergence time
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# In the following, we consider nine scenarios in which the
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# `harmonisee` spline differs from the `diverge_from` spline
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# due to varying shifts in the intercept (`[0.0, -1.2, 1.2]`)
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# and slope (`[1.0, 0.7, 1.4]`).
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# In all of these scenarios we consider harmonisation time
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# (`=0`) < convergence time (`=3.2`).
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# %%
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harmonisation_time = 0.0
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convergence_time = 3.2
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# %%
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def plot_spline(spline, x, ax, label, gradient=False): # noqa: D103
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ax.plot(
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x,
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spline(x),
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label=label,
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)
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if gradient:
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ax.set_title("Gradient")
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else:
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ax.set_title("Function")
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# %%
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i = 0
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for y_intercept_shift in [0.0, -1.2, 1.2]:
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for gradient_factor in [1.0, 0.7, 1.4]:
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harmonisee = SplineScipy(
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scipy.interpolate.PPoly(
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c=[
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[diverge_from_gradient * gradient_factor],
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[diverge_from_y_intercept + y_intercept_shift],
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],
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x=[0, 1e8],
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)
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)
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res = harmonise_splines_add_cubic(
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diverge_from=diverge_from,
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harmonisee=harmonisee,
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harmonisation_time=harmonisation_time,
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convergence_time=convergence_time,
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)
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fig, axes = plt.subplots(ncols=2, figsize=(12, 4))
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plot_spline(
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diverge_from, np.linspace(-1.0, 3.0, 101), ax=axes[0], label="diverge_from"
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)
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plot_spline(
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harmonisee,
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[0],
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label="harmonisee",
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)
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plot_spline(
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res,
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[0],
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label="res",
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)
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plot_spline(
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diverge_from.derivative(),
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np.linspace(-1.0, 3.0, 101),
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ax=axes[1],
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label="diverge_from",
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gradient=True,
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)
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plot_spline(
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harmonisee.derivative(),
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[1],
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label="harmonisee",
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gradient=True,
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)
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plot_spline(
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res.derivative(),
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[1],
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label="cubic-spline",
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gradient=True,
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)
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for ax in axes:
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ax.axvline(
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harmonisation_time,
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label="harmonisation_time",
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color="gray",
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linestyle=":",
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)
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ax.axvline(
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convergence_time, label="convergence_time", color="gray", linestyle="--"
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)
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for ax in axes[1::2]:
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ax.legend(handlelength=1.1, loc="center right", fontsize="small")
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fig.suptitle(
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f"Scenario {i+1} (intercept shift: {y_intercept_shift},"
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+ f" slope factor: {gradient_factor})"
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)
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plt.show()
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i = i + 1
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# %% [markdown]
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# ### Harmonisation time > convergence time
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# In the following, we consider the same nine scenarios as
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# above in which the `harmonisee` spline differs
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# from the `diverge_from` spline due to varying shifts in the
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# intercept (`[0.0, -1.2, 1.2]`) and slope (`[1.0, 0.7, 1.4]`).
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# However, this time we consider
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# harmonisation time (`=1.0`) > convergence time (`=-1.0`).
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# %%
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diverge_from_gradient = 2.5
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diverge_from_y_intercept = 1.0
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# TODO: from left-edge or something here
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diverge_from = SplineScipy(
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scipy.interpolate.PPoly(
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c=[
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[diverge_from_gradient],
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[diverge_from_y_intercept - 10.0 * diverge_from_gradient],
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],
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x=[-10.0, 10.0],
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)
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)
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# %%
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harmonisation_time = 1.0
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convergence_time = -1.0
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# %%
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# Backwards along x harmonisation
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i = 0
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for y_intercept_shift in [0.0, -1.2, 1.2]:
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for gradient_factor in [1.0, 0.7, 1.4]:
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harmonisee = SplineScipy(
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scipy.interpolate.PPoly(
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c=[
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[diverge_from_gradient * gradient_factor],
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[
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diverge_from_y_intercept
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- 10.0 * diverge_from_gradient
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+ y_intercept_shift
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],
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],
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x=[-10.0, 10.0],
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)
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)
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res = harmonise_splines_add_cubic(
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diverge_from=diverge_from,
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harmonisee=harmonisee,
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harmonisation_time=harmonisation_time,
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convergence_time=convergence_time,
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)
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fig, axes = plt.subplots(ncols=2, figsize=(12, 4))
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plot_spline(
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diverge_from, np.linspace(-1.0, 3.0, 101), ax=axes[0], label="diverge_from"
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)
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plot_spline(
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harmonisee,
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[0],
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label="harmonisee",
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)
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plot_spline(
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res,
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[0],
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label="res",
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)
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plot_spline(
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diverge_from.derivative(),
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np.linspace(-1.0, 3.0, 101),
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ax=axes[1],
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label="diverge_from",
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gradient=True,
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)
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plot_spline(
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harmonisee.derivative(),
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[1],
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label="harmonisee",
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gradient=True,
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)
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plot_spline(
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res.derivative(),
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np.linspace(harmonisation_time, 2 * convergence_time, 101),
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ax=axes[1],
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label="cubic-spline",
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gradient=True,
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)
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for ax in axes:
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ax.axvline(
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harmonisation_time,
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label="harmonisation_time",
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color="gray",
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linestyle=":",
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)
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ax.axvline(
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convergence_time, label="convergence_time", color="gray", linestyle="--"
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)
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for ax in axes[1::2]:
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ax.legend(handlelength=1.1, loc="center right", fontsize="small")
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fig.suptitle(
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f"Scenario {i+1} (intercept shift: {y_intercept_shift},"
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+ f" slope factor: {gradient_factor})"
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)
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plt.show()
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i = i + 1

‎docs/how-to-guides/index.md‎

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focuses on a **problem-oriented** approach.
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We'll go over how to solve common tasks.
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## How can I do a basic calculation?
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<!---
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You will probably want to remove this bit.
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It is included to demonstrate how to include sub-sections
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and cross-reference them.
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-->
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+ [How can I use a cubic spline for harmonisation?](cubic_spline)

‎mkdocs.yml‎

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- http://xarray.pydata.org/en/stable/objects.inv
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options:
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docstring_style: numpy
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relative_crossrefs: yes
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relative_crossrefs: true
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separate_signature: true
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show_root_heading: false
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show_signature_annotations: true
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show_docstring_examples: true
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show_source: true
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signature_crossrefs: true
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summary:

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