import unittest import TasmanianSG import numpy as np import testCommon # needed to compare grids after merge refinement ttc = testCommon.TestTasCommon() class TestTasClass(unittest.TestCase): ''' Test methods for directly setting hierarchical matrices and coeffs, useful to build grids from unstructured/random data. ''' def __init__(self): unittest.TestCase.__init__(self, "testNothing") def testNothing(self): pass def checkAgainstKnown(self): ''' Check hierarchical functions against known (pen-and-paper) solutions. ''' grid = TasmanianSG.TasmanianSparseGrid() # evalHierarchicalBasis (all done in batch), dense mode grid.makeLocalPolynomialGrid(2, 2, 1, 1, 'localp') aT = np.empty([0,2], np.float64) np.testing.assert_equal(aT, grid.getHierarchicalCoefficients(), "coeff mismatch", True) grid.makeLocalPolynomialGrid(2, 0, 1, 1, 'localp') aT = np.empty([0,0], np.float64) np.testing.assert_equal(aT, grid.getHierarchicalCoefficients(), "coeff mismatch", True) grid.makeLocalPolynomialGrid(2, 2, 1, 1, 'localp') aPoints = grid.getPoints() aV = np.column_stack([np.exp(2.0 * aPoints[:,0] + aPoints[:,1]), np.sin(3.0 * aPoints[:,0] + aPoints[:,1])]) grid.loadNeededPoints(aV) aS = grid.getHierarchicalCoefficients() aT = np.array([[1.0, 0.0], [np.exp(-1.0)-1.0, np.sin(-1.0)], [np.exp(1.0)-1.0, np.sin(1.0)], [np.exp(-2.0)-1.0, np.sin(-3.0)], [np.exp(2.0)-1.0, np.sin(3.0)]]) np.testing.assert_almost_equal(aS, aT, 14, "Surplusses equal", True) grid.makeGlobalGrid(3, 1, 4, 'level', 'fejer2') aPoints = grid.getPoints() aVan = grid.evaluateHierarchicalFunctions(aPoints) aIdentity = np.zeros([grid.getNumPoints(), grid.getNumPoints()], np.float64) for iI in range(grid.getNumPoints()): aIdentity[iI,iI] = 1.0 np.testing.assert_almost_equal(aVan, aIdentity, 14, "evaluateHierarchicalFunctions", True) grid.makeGlobalGrid(2, 1, 1, 'level', 'clenshaw-curtis') aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) f0 = (1.0 - aPoints[:,0]**2) + (1.0 - aPoints[:,1]**2) - 1.0 f1 = 0.5 * aPoints[:,1] * (aPoints[:,1] - 1.0) f2 = 0.5 * aPoints[:,1] * (aPoints[:,1] + 1.0) f3 = 0.5 * aPoints[:,0] * (aPoints[:,0] - 1.0) f4 = 0.5 * aPoints[:,0] * (aPoints[:,0] + 1.0) aResult = np.column_stack([f0, f1, f2, f3, f4]) aVan = grid.evaluateHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aVan, aResult, 14, "evaluateHierarchicalFunctions", True) grid.makeSequenceGrid(2, 1, 2, 'level', 'leja') aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) f0 = np.ones([aPoints.shape[0],]) f1 = aPoints[:,1] f2 = 0.5 * aPoints[:,1] * (aPoints[:,1] - 1.0) f3 = aPoints[:,0] f4 = aPoints[:,0] * aPoints[:,1] f5 = 0.5 * aPoints[:,0] * (aPoints[:,0] - 1.0) aResult = np.column_stack([f0, f1, f2, f3, f4, f5]) aVan = grid.evaluateHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aVan, aResult, 14, "evaluateHierarchicalFunctions", True) grid.makeLocalPolynomialGrid(2, 1, 1, 1, 'localp') aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) f0 = np.ones([aPoints.shape[0],]) f1 = -aPoints[:,1] f2 = np.copy(aPoints[:,1]) f3 = -aPoints[:,0] f4 = np.copy(aPoints[:,0]) for iI in range(aPoints.shape[0]): if (aPoints[iI,1] > 0.0): f1[iI] = 0.0 if (aPoints[iI,1] < 0.0): f2[iI] = 0.0 if (aPoints[iI,0] > 0.0): f3[iI] = 0.0 if (aPoints[iI,0] < 0.0): f4[iI] = 0.0 aResult = np.column_stack([f0, f1, f2, f3, f4]) aVan = grid.evaluateHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aVan, aResult, 14, "evaluateHierarchicalFunctions", True) grid.makeFourierGrid(2, 1, 1, "level") aPoints = np.array([[0.25, 0.5]]); aResult = np.array([[1.0 + 0.0 * 1j, -1.0 + 0.0 * 1j, -1.0 + 0.0 * 1j, 0.0 - 1.0 * 1j, 0.0 + 1.0 * 1j]]) aVan = grid.evaluateHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aVan, aResult, 14, "evaluateHierarchicalFunctions", True) # sparse hierarchical functions pSparse = TasmanianSG.TasmanianSimpleSparseMatrix() np.testing.assert_almost_equal(np.empty([0,0], np.float64), pSparse.getDenseForm(), 14, "TasmanianSimpleSparseMatrix.getDense()", True) grid.makeLocalPolynomialGrid(2, 1, 4, 1, 'localp') aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) aDense = grid.evaluateHierarchicalFunctions(aPoints) pSparse = grid.evaluateSparseHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aDense, pSparse.getDenseForm(), 14, "evaluateSparseHierarchicalFunctions", True) grid.makeWaveletGrid(2, 1, 4, 1) aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) aDense = grid.evaluateHierarchicalFunctions(aPoints) pSparse = grid.evaluateSparseHierarchicalFunctions(aPoints) np.testing.assert_almost_equal(aDense, pSparse.getDenseForm(), 14, "evaluateSparseHierarchicalFunctions", True) def checkSetCoeffsMergeRefine(self): ''' Set the coefficients and use mergeRefinement() ''' aPoints = np.array([[0.33, 0.25], [-0.27, 0.39], [0.97, -0.76], [-0.44, 0.21], [-0.813, 0.03], [-0.666, 0.666]]) # set hierarchical coeffs/merge refinement gridA = TasmanianSG.TasmanianSparseGrid() gridB = TasmanianSG.TasmanianSparseGrid() gridA.makeGlobalGrid(2, 1, 4, 'level', 'chebyshev') gridB.makeGlobalGrid(2, 1, 4, 'level', 'chebyshev') ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA = TasmanianSG.TasmanianSparseGrid() gridB = TasmanianSG.TasmanianSparseGrid() gridA.makeGlobalGrid(2, 1, 4, 'level', 'fejer2') gridB.makeGlobalGrid(2, 1, 4, 'level', 'fejer2') ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.setAnisotropicRefinement('iptotal', 10, 0) gridB.setAnisotropicRefinement('iptotal', 10, 0) ttc.loadExpN2(gridA) gridB.mergeRefinement() self.assertEqual(gridA.getNumPoints(), gridB.getNumPoints(), 'different number of points after merge refinement') aRes = gridB.evaluateBatch(aPoints) np.testing.assert_almost_equal(aRes, np.zeros(aRes.shape), 14, "not zero after merged refinement", True) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.makeSequenceGrid(2, 1, 5, 'ipcurved', 'min-delta') gridB.makeSequenceGrid(2, 1, 5, 'ipcurved', 'min-delta') ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.setAnisotropicRefinement('iptotal', 30, 0) gridB.setAnisotropicRefinement('iptotal', 30, 0) ttc.loadExpN2(gridA) gridB.mergeRefinement() self.assertEqual(gridA.getNumPoints(), gridB.getNumPoints(), 'different number of points after merge refinement') aRes = gridB.evaluateBatch(aPoints) np.testing.assert_almost_equal(aRes, np.zeros(aRes.shape), 14, "not zero after merged refinement", True) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.makeLocalPolynomialGrid(2, 1, 4, 2, 'semi-localp') gridB.makeLocalPolynomialGrid(2, 1, 4, 2, 'semi-localp') ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.setSurplusRefinement(1.E-4, 0, 'classic') gridB.setSurplusRefinement(1.E-4, 0, 'classic') ttc.loadExpN2(gridA) gridB.mergeRefinement() self.assertEqual(gridA.getNumPoints(), gridB.getNumPoints(), 'different number of points after merge refinement') aRes = gridB.evaluateBatch(aPoints) np.testing.assert_almost_equal(aRes, np.zeros(aRes.shape), 14, "not zero after merged refinement", True) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.makeWaveletGrid(2, 1, 2, 1) gridB.makeWaveletGrid(2, 1, 2, 1) ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.setSurplusRefinement(1.E-3, 0, 'classic') gridB.setSurplusRefinement(1.E-3, 0, 'classic') ttc.loadExpN2(gridA) gridB.mergeRefinement() self.assertEqual(gridA.getNumPoints(), gridB.getNumPoints(), 'different number of points after merge refinement') aRes = gridB.evaluateBatch(aPoints) np.testing.assert_almost_equal(aRes, np.zeros(aRes.shape), 14, "not zero after merged refinement", True) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) gridA.makeFourierGrid(2, 1, 3, 'level') gridB.makeFourierGrid(2, 1, 3, 'level') ttc.loadExpN2(gridA) gridB.setHierarchicalCoefficients(gridA.getHierarchicalCoefficients()) ttc.compareGrids(gridA, gridB) def checkIntegrals(self): grid = TasmanianSG.TasmanianSparseGrid() lTests = ['grid.makeGlobalGrid(2, 1, 4, "level", "clenshaw-curtis")', 'grid.makeSequenceGrid(2, 1, 4, "level", "rleja")', 'grid.makeFourierGrid(2, 1, 3, "level")', 'grid.makeLocalPolynomialGrid(2, 1, 4)', 'grid.makeWaveletGrid(2, 1, 2)'] for t in lTests: exec(t) grid.setDomainTransform(np.array([[-3.0, 5.0], [-4.0, 2.0]])) ttc.loadExpN2(grid) aIntegrals = grid.integrateHierarchicalFunctions() aSurps = grid.getHierarchicalCoefficients() fResult = np.real(np.sum(aIntegrals * aSurps.reshape((aSurps.shape[0],)))) fExpected = grid.integrate() np.testing.assert_almost_equal(fResult, fExpected[0], 12, 'integrals different by too much') # check support grid.makeLocalPolynomialGrid(1, 1, 3) aSup = grid.getHierarchicalSupport() aResult = (1.0, 1.0, 1.0, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25) np.testing.assert_almost_equal(aSup, np.array(aResult).reshape((9, 1)), 12, 'support different by too much') def checkValues(self): lTests = ['grid.makeGlobalGrid(2, 2, 3, "level", "clenshaw-curtis")', 'grid.makeSequenceGrid(2, 2, 3, "level", "rleja")', 'grid.makeFourierGrid(2, 2, 2, "level")', 'grid.makeLocalPolynomialGrid(2, 2, 2)', 'grid.makeWaveletGrid(2, 2, 2)'] for t in lTests: grid = TasmanianSG.TasmanianSparseGrid() aResult = grid.getLoadedValues() self.assertTrue(len(aResult) == 0, "failed to return a empty array") exec(t) iNP = grid.getNumNeeded() iOuts = 2 aReferece = np.array([float(i) for i in range(iNP * iOuts)]).reshape(iNP, iOuts) grid.loadNeededPoints(aReferece) aResult = grid.getLoadedValues() np.testing.assert_almost_equal(aResult, aReferece, 14, 'values in getLoadedValues() differ by too much') def performUnstructuredDataTests(self): self.checkAgainstKnown() self.checkSetCoeffsMergeRefine() self.checkIntegrals() self.checkValues()