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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()
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