Added method for integrating across whole interval in Chebychev

discretization

Author: brownbaerchen

pySDC/helpers/spectral_helper.py

@@ -161,6 +161,10 @@ def get_differentiation_matrix(self):
     def get_integration_matrix(self):
         raise NotImplementedError()
 
+    def get_integration_weights(self):
+        """Weights for integration across entire domain"""
+        raise NotImplementedError()
+
     def get_wavenumbers(self):
         """
         Get the grid in spectral space
@@ -379,6 +383,15 @@ def get_integration_matrix(self, lbnd=0):
             raise NotImplementedError(f'This function allows to integrate only from x=0, you attempted from x={lbnd}.')
         return S
 
+    def get_integration_weights(self):
+        n = self.xp.arange(self.N, dtype=float)
+
+        weights = (-1) ** n + 1
+        weights[2:] /= 1 - (n**2)[2:]
+
+        weights /= 2 / self.L
+        return weights
+
     def get_differentiation_matrix(self, p=1):
         '''
         Keep in mind that the T2T differentiation matrix is dense.

pySDC/tests/test_helpers/test_spectral_helper_1d_chebychev.py

@@ -139,6 +139,35 @@ def test_integration_matrix(N):
     assert np.allclose(exact.coef[:-1], du)
 
 
+@pytest.mark.base
+@pytest.mark.parametrize('x0', [-1, 0])
+@pytest.mark.parametrize('x1', [0.789, 1])
+@pytest.mark.parametrize('N', [4, 7])
+def test_integral_whole_interval(x0, x1, N):
+    import numpy as np
+    from pySDC.helpers.spectral_helper import ChebychevHelper
+    from qmat.lagrange import LagrangeApproximation
+
+    cheby = ChebychevHelper(N, x0=x0, x1=x1)
+    x = cheby.get_1dgrid()
+
+    coeffs = np.random.random(N)
+    coeffs[-1] = 0
+
+    u_hat = coeffs
+    u = cheby.itransform(u_hat)
+
+    weights = cheby.get_integration_weights()
+    integral = weights @ u_hat
+
+    # generate a reference solution with qmat
+    lag = LagrangeApproximation(points=x)
+    Q = lag.getIntegrationMatrix(intervals=[(x0, x1)])
+    integral_ref = (Q @ u)[0]
+
+    assert np.isclose(integral, integral_ref)
+
+
 @pytest.mark.base
 @pytest.mark.parametrize('N', [4])
 @pytest.mark.parametrize('d', [1, 2, 3])