TL: added padding for Butcher tables

Author: tlunet

docs/notebooks/21_lagrange.ipynb

@@ -8,9 +8,9 @@
     "# Tutorial 1 : using the `qmat.lagrange` module\n",
     "\n",
     "📜 _The_ `LagrangeApproximation` _class from the_ `qmat.lagrange` _module is a multi-purpose class to perform interpolation, integration or derivative approximation from a given set of 1D points._\n",
-    "_It is based on the Barycentric Lagrange interpolation theory, originally developed by Joseph-Louis Lagrange around 1795, and widely popularized by the paper of Jean-Paul Berrut ahd Llyod N. Trefethen : [\"Barycentric Lagrange interpolation\"](https://doi.org/10.1137/S0036144502417715)._\n",
+    "_It is based on the Barycentric Lagrange interpolation theory, originally developed by Joseph-Louis Lagrange around 1795, and widely popularized by the paper of Jean-Paul Berrut ahd Llyod N. Trefethen: [\"Barycentric Lagrange interpolation\"](https://doi.org/10.1137/S0036144502417715)._\n",
     "\n",
-    "The main concept behind the `LagrangeApproximation` class is to precompute the barycentric weights for any provided set of points, then use them to generate value-independent matrices used later to compute approximations (interpolation, integration or derivative) from values vectors."
+    "The main concept behind this class is to precompute the barycentric weights for any provided set of points, then use them to generate value-independent matrices used later to compute approximations (interpolation, integration or derivative) from values vectors."
    ]
   },
   {
@@ -375,7 +375,7 @@
    "source": [
     "## Handling duplicated points\n",
     "\n",
-    "📜 _While the base theory behind Barycentric Interpolation required all points to be unique, the `LagrangeApproximation` class can also take interpolation points with duplicates._\n",
+    "📜 _While the base theory behind Barycentric Interpolation required all points to be unique, the_ `LagrangeApproximation` _class can also take interpolation points with duplicates._\n",
     "\n",
     "Let's consider the following example :"
    ]

qmat/qcoeff/butcher.py

@@ -20,7 +20,20 @@
 
 
 class RK(QGenerator):
-    """Base class for Runge-Kutta generators"""
+    """
+    Base class for Runge-Kutta generators
+
+    Parameters
+    ----------
+    padding : str, optional
+        Eventually add padding to the Butcher table. Can be
+
+        - LEFT : add padding corresponding to an additional node at t=0
+        - RIGHT : add padding corresponding to an additional node at t=1
+        - BOTH : add both LEFT and RIGHT padding
+
+        The default is None.
+    """
 
     A = None
     """:math:`A` matrix of the Butcher table"""
@@ -31,6 +44,29 @@ class RK(QGenerator):
     b2 = None
     """:math:`b_2` coefficients for the embedded methods"""
 
+    def __init__(self, padding=None):
+        if padding:
+            assert padding in ["LEFT", "RIGHT", "BOTH"], "padding choices can only be LEFT, RIGHT or BOTH"
+
+            if padding in ["LEFT", "BOTH"]:
+                self.c = np.array([0] + self.c.tolist())
+                self.b = np.array([0] + self.b.tolist())
+
+                newA = np.zeros((self.nNodes, self.nNodes))
+                newA[1:, 1:] = self.A
+                self.A = newA
+
+            if padding in ["RIGHT", "BOTH"]:
+                self.c = np.array(self.c.tolist() + [1])
+                self.b = np.array(self.b.tolist() + [0])
+
+                newA = np.zeros((self.nNodes, self.nNodes))
+                newA[:-1, :-1] = self.A
+                newA[-1] = self.b
+                self.A = newA
+
+            self.padding = padding
+
     @property
     def nodes(self)->np.ndarray: return self.c
 

tests/test_qcoeff/test_butcher.py

@@ -0,0 +1,12 @@
+import pytest
+import numpy as np
+
+from qmat.qcoeff.butcher import RK_SCHEMES
+
+@pytest.mark.parametrize("lam", [-1, 1j, -0.5+0.5j])
+@pytest.mark.parametrize("scheme", RK_SCHEMES.keys())
+@pytest.mark.parametrize("which", ["LEFT", "RIGHT", "BOTH"])
+def testPadding(which, scheme, lam):
+    ref = RK_SCHEMES[scheme]().solveDahlquist(lam, 1, 1, 1)
+    pad = RK_SCHEMES[scheme](padding=which).solveDahlquist(lam, 1, 1, 1)
+    assert np.allclose(ref, pad), f"{which} padded Butcher table produces inconsistent result for {scheme}"