New DiffMatOnDomain implementation of DiffMatrices

It linearly stretches and shift underlying DiffMatrices on an
arbitrary domain.

dmsuite/poly_diff.py

@@ -23,7 +23,7 @@
 
 from abc import ABC, abstractmethod
 from dataclasses import dataclass
-from functools import cached_property
+from functools import cached_property, lru_cache
 
 import numpy as np
 from numpy.typing import NDArray
@@ -335,3 +335,27 @@ def _dmat(self) -> GeneralPoly:
 
  def at_order(self, order: int) -> NDArray:
  return self.scale**order * self._dmat.at_order(order)
+
+
+@dataclass(frozen=True)
+class DiffMatOnDomain(DiffMatrices):
+ """Differentiation matrices stretched and shifted to a different domain.
+
+ The stretching and shifting is done linearly between xmin and xmax.
+ """
+
+ xmin: float
+ xmax: float
+ dmat: DiffMatrices
+
+ @cached_property
+ def stretching(self) -> NDArray:
+ return (self.dmat.nodes[-1] - self.dmat.nodes[0]) / (self.xmax - self.xmin)
+
+ @cached_property
+ def nodes(self) -> NDArray:
+ return (self.dmat.nodes - self.dmat.nodes[0]) / self.stretching + self.xmin
+
+ @lru_cache
+ def at_order(self, order: int) -> NDArray:
+ return self.stretching**order * self.dmat.at_order(order)

tests/test_chebdif.py

@@ -1,6 +1,6 @@
 import numpy as np
 
-from dmsuite.poly_diff import Chebyshev
+from dmsuite.poly_diff import Chebyshev, DiffMatOnDomain
 
 
 def test_chebdif4() -> None:
@@ -12,3 +12,19 @@ def test_chebdif4() -> None:
  computed[order - 1] = cheb.at_order(order)
  assert np.allclose(cheb.nodes, expected[0])
  assert np.allclose(computed, expected[1])
+
+
+def test_cheb_scaled() -> None:
+ dmat = DiffMatOnDomain(xmin=1.0, xmax=5.0, dmat=Chebyshev(degree=64))
+ nodes = dmat.nodes
+ assert np.allclose(nodes[0], dmat.xmin)
+ assert np.allclose(nodes[-1], dmat.xmax)
+ func = nodes**2
+ dfunc = 2 * nodes
+ d2func = 2.0
+ d1_cheb = dmat.at_order(1) @ func
+ d2_cheb = dmat.at_order(2) @ func
+ d3_cheb = dmat.at_order(3) @ func
+ assert np.allclose(d1_cheb, dfunc)
+ assert np.allclose(d2_cheb, d2func)
+ assert np.allclose(d3_cheb, 0.0, atol=1e-6)