def rank(self, grid, gp, alphas, *args, **kws):
gs = grid.getStorage()
x = DataVector(gs.getDimension())
gs.getCoordinates(gp, x)
opEval = createOperationEvalNaive(grid)
return abs(opEval.eval(alphas, x) - self.f(x))
def __init__(self, d, f):
self.f = f
self.d = d
self.grid = pysgpp.Grid.createBsplineClenshawCurtisGrid(d, 3)
self.gridStorage = self.grid.getStorage()
try :
self.hierarch = pysgpp.createOperationHierarchisation(self.grid)
except :
self.hierarch = pysgpp.createOperationMultipleHierarchisation(self.grid)
self.opeval = pysgpp.createOperationEvalNaive(self.grid)
self.alpha = pysgpp.DataVector(self.gridStorage.getSize())
def evalSGFunction(grid, alpha, p, isConsistent=True):
if grid.getSize() != len(alpha):
raise AttributeError(
"grid size differs from length of coefficient vector")
if len(p.shape) == 1:
if grid.getStorage().getDimension() != p.shape[0]:
raise AttributeError(
"grid dimension differs from dimension of sample")
evalNaiveGridTypes = [
GridType_Bspline, GridType_BsplineClenshawCurtis,
GridType_BsplineBoundary, GridType_ModBsplineClenshawCurtis,
GridType_ModBspline, GridType_LinearClenshawCurtis,
GridType_LinearClenshawCurtisBoundary,
GridType_ModLinearClenshawCurtis, GridType_PolyClenshawCurtis,
GridType_PolyClenshawCurtisBoundary, GridType_ModPolyClenshawCurtis
]
p_vec = DataVector(p)
alpha_vec = DataVector(alpha)
if isConsistent:
if grid.getType() in evalNaiveGridTypes:
opEval = createOperationEvalNaive(grid)
else:
opEval = createOperationEval(grid)
else:
opEval = createOperationEvalNaive(grid)
ans = opEval.eval(alpha_vec, p_vec)
del opEval
del alpha_vec
del p_vec
return ans
else:
if grid.getStorage().getDimension() != p.shape[1]:
raise AttributeError(
"grid dimension differs from dimension of samples")
return evalSGFunctionMulti(grid, alpha, p, isConsistent)
def checkInterpolation(grid, alpha, nodalValues, epsilon=1e-13):
# check if interpolation property is given
gs = grid.getStorage()
evalValues = np.ndarray(gs.getSize())
x = DataVector(gs.getDimension())
opEval = createOperationEvalNaive(grid)
alpha_vec = DataVector(alpha)
for i in range(gs.getSize()):
gs.getCoordinates(gs.getPoint(i), x)
evalValues[i] = opEval.eval(alpha_vec, x)
error = np.array([])
nodes = np.array([])
head = True
p = DataVector(gs.getDimension())
for i, (nodal, value) in enumerate(zip(nodalValues, evalValues)):
# compute the relative error
abs_error = np.abs(nodal - value)
rel_error = abs_error
if abs(nodal) > 1e-14:
rel_error = np.abs(abs_error / nodal)
if abs_error > epsilon:
spacing = 12
if head:
print()
print( "%s | %s | %s | %s | %s | %s | %s" % \
("index".rjust(spacing),
"levelsum".rjust(spacing),
"surplus".rjust(spacing),
"nodalValue".rjust(spacing),
"eval".rjust(spacing),
"rel err".rjust(spacing),
"abs err".rjust(spacing)))
head = False
gs.getCoordinates(gs.getPoint(i), p)
print( "%s | %s | %s | %s | %s | %s | %s" % \
(("%i" % i).rjust(spacing),
("%i" % gs.getPoint(i).getLevelSum()).rjust(spacing),
("%g" % alpha[i]).rjust(spacing),
("%g" % nodal).rjust(spacing),
("%g" % value).rjust(spacing),
("%g" % rel_error).rjust(spacing),
("%g" % abs_error).rjust(spacing)))
nodes = np.append(nodes, [i])
error = np.append(abs_error, [abs_error])
return error, nodes