import unittest import Tasmanian import os import numpy as np import testCommon ttc = testCommon.TestTasCommon() def batch_exp(x): aResult = np.zeros((x.shape[0], 1)) for i in range(x.shape[0]): aResult[i, 0] = np.exp(-np.sum(x[i,:])) return aResult class TestTasClass(unittest.TestCase): ''' Miscelaneous tests that don't quite fit in other categories. ''' def __init__(self): unittest.TestCase.__init__(self, "testNothing") def testNothing(self): pass def checkLoadNeeded(self): ''' Check the load needed construction procedure. ''' gridA = Tasmanian.SparseGrid() gridB = Tasmanian.SparseGrid() for i in range(4): if i < 2: gridA.makeGlobalGrid(2, 1, 3, 'level', 'fejer2') gridB.copyGrid(gridA) Tasmanian.loadNeededValues(lambda x, i : np.ones((1,)) * np.exp(-np.sum(x**2)), gridA, i) else: gridA.makeLocalPolynomialGrid(2, 1, 2, 2) gridB.copyGrid(gridA) gridA.printStats() gridA.loadNeededPoints(np.ones((gridA.getNumPoints(), 1))) Tasmanian.reloadLoadedPoints(lambda x, i : np.ones((1,)) * np.exp(-np.sum(x**2)), gridA, i - 2) ttc.loadExpN2(gridB) ttc.compareGrids(gridA, gridB) def checkConstruction(self): gridA = Tasmanian.SparseGrid() gridB = Tasmanian.SparseGrid() for i in range(12): if i < 2: gridA.makeGlobalGrid(2, 1, 3, 'level', 'fejer2') gridB.copyGrid(gridA) Tasmanian.constructAnisotropicSurrogate(lambda x, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i, 1, gridA, "hyperbolic", 0) elif i < 4: gridA.makeGlobalGrid(2, 1, 3, 'level', 'min-lebesgue') gridB.copyGrid(gridA) Tasmanian.constructAnisotropicSurrogate(lambda x, y, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i - 2, 1, gridA, "ipcurved", (6, 5, 1, 1), bUseInitialGuess = True, sCheckpointFilename = "cpf_addons") os.remove("cpf_addons") elif i < 6: gridA.makeGlobalGrid(2, 1, 3, 'level', 'min-delta', liLevelLimits = (5, 5)) gridB.copyGrid(gridA) gridA.clearLevelLimits() Tasmanian.constructAnisotropicSurrogate(lambda x, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i - 4, 1, gridA, "iplevel", (1, 2), liLevelLimits = (5, 5), bUseInitialGuess = False) elif i < 8: gridA.makeGlobalGrid(2, 1, 3, 'level', 'min-delta', liLevelLimits = (10, 10)) gridB.copyGrid(gridA) gridA.clearLevelLimits() Tasmanian.constructAnisotropicSurrogate(lambda x, y, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i - 6, 1, gridA, "iplevel", 0, liLevelLimits = (10, 10), bUseInitialGuess = True) elif i < 10: gridA.makeLocalPolynomialGrid(2, 1, 2, 2, liLevelLimits = (7, 7)) gridB.copyGrid(gridA) gridA.clearLevelLimits() Tasmanian.constructSurplusSurrogate(lambda x, y, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i - 8, 1, gridA, 1.E-5, "stable", -1, liLevelLimits = (7, 7), bUseInitialGuess = True) elif i < 12: gridA.makeLocalPolynomialGrid(2, 1, 2, 3) gridB.copyGrid(gridA) Tasmanian.constructSurplusSurrogate(lambda x, i : np.ones((1,1)) * np.exp(-np.sum(x**2)), gridA.getNumPoints(), i - 10, 1, gridA, 1.E-5, "fds", 0, bUseInitialGuess = False, sCheckpointFilename = "cpf_addons") os.remove("cpf_addons") ttc.loadExpN2(gridB) gridA.finishConstruction() ttc.compareGrids(gridA, gridB) def checkBatchConstruct(self): gridA = Tasmanian.SparseGrid() gridB = Tasmanian.SparseGrid() gridA.makeGlobalGrid(2, 1, 6, 'level', 'fejer2') gridB.copyGrid(gridA) Tasmanian.constructAnisotropicSurrogate(lambda x, i : batch_exp(x), gridA.getNumPoints(), 2, 1, gridA, "iptotal", 0) Tasmanian.constructAnisotropicSurrogate(lambda x, i : batch_exp(x), gridB.getNumPoints(), 2, 10, gridB, "iptotal", 0) ttc.compareGrids(gridA, gridB) gridA.makeLocalPolynomialGrid(2, 1, 3) gridB.copyGrid(gridA) Tasmanian.constructSurplusSurrogate(lambda x, i : batch_exp(x), gridA.getNumPoints(), 2, 1, gridA, 1.E-11, "classic") Tasmanian.constructSurplusSurrogate(lambda x, i : batch_exp(x), gridB.getNumPoints(), 2, 10, gridB, 1.E-11, "classic") ttc.compareGrids(gridA, gridB) def checkUnstructuredL2(self): grid = Tasmanian.makeLocalPolynomialGrid(2, 1, 5) if not grid.isAccelerationAvailable("cpu-blas"): return x = np.linspace(-0.9, 0.9, 40) xx, yy = np.meshgrid(x, x) points = np.column_stack([xx.reshape((xx.size,)), yy.reshape((yy.size,))]) model = np.exp(points[:,0] - points[:,1]).reshape((points.shape[0], 1)) Tasmanian.loadUnstructuredDataL2(points, model, 1.E-5, grid) x = np.linspace(-0.8, 0.8, 20) xx, yy = np.meshgrid(x, x) points = np.column_stack([xx.reshape((xx.size,)), yy.reshape((yy.size,))]) model = np.exp(points[:,0] - points[:,1]) surrogate = grid.evaluateBatch(points) self.assertLess(np.max(np.abs(model - surrogate[:,0])), 5.E-3, "Constructed from unstructured too inaccurate.") def checkExoticQuadrature(self): # Initialize some useful constants and utility functions. integrand = lambda x : np.exp(-np.linalg.norm(x) ** 2) sinc1s0 = lambda x : np.sinc(x / np.pi) sinc10s1 = lambda x : np.sinc(10 * (x - 1) / np.pi) max_level = 25 nref = 101 def create_surrogate(lambda_fn): grid = Tasmanian.makeGlobalGrid(1, 1, nref, "level", "gauss-legendre") grid.loadNeededValues(np.apply_along_axis(lambda_fn, 1, grid.getNeededPoints())) return grid def compute_integral(grid, integrand): return np.sum(np.apply_along_axis(integrand, 1, grid.getPoints()) * grid.getQuadratureWeights()) # Each pair below consists of a 1D integral value (first) and a CustomTabulated object (second) used to approximate this integral. testPairs = [ [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromFunction(max_level, 0.0, sinc1s0, nref, "Sinc1s0-shift0-Symm-byFn", True)], [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromFunction(max_level, 0.0, sinc1s0, nref, "Sinc1s0-shift0-nonSymm-byFn", False)], [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromFunction(max_level, 1.0, sinc1s0, nref, "Sinc1s0-shift1-Symm-byFn", True)], [6.4062055930705356E-02, Tasmanian.createExoticQuadratureFromFunction(max_level, 1.0, sinc10s1, nref, "Sinc10s1-shift1-nonSymm-byFn", False)], [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromGrid(max_level, 0.0, create_surrogate(sinc1s0), "Sinc1s0-shift0-Symm-byGrid", True)], [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromGrid(max_level, 0.0, create_surrogate(sinc1s0), "Sinc1s0-shift0-nonSymm-byGrid", False)], [1.4321357541271255E-00, Tasmanian.createExoticQuadratureFromGrid(max_level, 1.0, create_surrogate(sinc1s0), "Sinc1s0-shift1-Symm-byGrid", True)], [6.4062055930705356E-02, Tasmanian.createExoticQuadratureFromGrid(max_level, 1.0, create_surrogate(sinc10s1), "Sinc10s1-shift1-nonSymm-byGrid", False)], ] # Test the accuracy of exotic quadrature. for integral, ct in testPairs: self.assertEqual(max_level, ct.getNumLevels(), "Loaded number of levels does not match actual number of levels!") grid = Tasmanian.makeGlobalGridCustom(1, 0, max_level-1, "level", ct) np.testing.assert_almost_equal(compute_integral(grid, integrand), integral, 10, "Computed integral does not match exact integral in test instance " + ct.getDescription()) grid.makeGlobalGridCustom(2, 0, max_level-1, "level", ct) np.testing.assert_almost_equal(compute_integral(grid, integrand), integral ** 2, 10, "Computed integral does not match exact integral in test instance " + ct.getDescription()) def performAddonTests(self): self.checkLoadNeeded() self.checkConstruction() self.checkBatchConstruct() self.checkUnstructuredL2() self.checkExoticQuadrature()