def __computeRanking(self, v, A, b):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | v (2 Av - vb) |
@param v: DataVector, coefficients of known grid points
@param A: DataMatrix, stiffness matrix
@param b: DataVector, squared expectation value contribution
@return: numpy array, contains the ranking for the given samples
"""
# update the ranking
av = DataVector(A.getNrows())
av.setAll(0.0)
# = Av
for i in xrange(A.getNrows()):
for j in xrange(A.getNcols()):
av[i] += A.get(i, j) * v[j]
av.mult(2.) # = 2 * Av
b.componentwise_mult(v) # = v * b
av.sub(b) # = 2 * Av - v * b
w = DataVector(v)
w.componentwise_mult(av) # = v * (2 * Av - v * b)
w.abs() # = | v * (2 * Av - v * b) |
return w.array()
def __computeRanking(self, v, A, b):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | v (2 Av - vb) |
@param v: DataVector, coefficients of known grid points
@param A: DataMatrix, stiffness matrix
@param b: DataVector, squared expectation value contribution
@return: numpy array, contains the ranking for the given samples
"""
# update the ranking
av = DataVector(A.getNrows())
av.setAll(0.0)
# = Av
for i in xrange(A.getNrows()):
for j in xrange(A.getNcols()):
av[i] += A.get(i, j) * v[j]
av.mult(2.) # = 2 * Av
b.componentwise_mult(v) # = v * b
av.sub(b) # = 2 * Av - v * b
w = DataVector(v)
w.componentwise_mult(av) # = v * (2 * Av - v * b)
w.abs() # = | v * (2 * Av - v * b) |
return w.array()
def testOps(self):
from pysgpp import DataVector
# sum
self.assertAlmostEqual(self.d_rand.sum(), sum(self.l_rand_total))
# sqr
d = DataVector(self.d_rand)
d.sqr()
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]**2, d[i])
# abs
d = DataVector(self.d_rand)
d.abs()
for i in xrange(self.N):
self.assertEqual(abs(self.d_rand[i]), d[i])
# componentwise_mult
d = DataVector(self.d_rand)
# d2 = DataVector(self.nrows, self.ncols)
d2 = DataVector(self.N)
for i in xrange(self.N):
d2[i] = i
d.componentwise_mult(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]*i, d[i])
# componentwise_div
d = DataVector(self.d_rand)
for i in xrange(self.N):
d2[i] = i+1
d.componentwise_div(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]/(i+1), d[i])
def testOps(self):
from pysgpp import DataVector
# sum
self.assertAlmostEqual(self.d_rand.sum(), sum(self.l_rand_total))
# sqr
d = DataVector(self.d_rand)
d.sqr()
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]**2, d[i])
# abs
d = DataVector(self.d_rand)
d.abs()
for i in xrange(self.N):
self.assertEqual(abs(self.d_rand[i]), d[i])
# componentwise_mult
d = DataVector(self.d_rand)
# d2 = DataVector(self.nrows, self.ncols)
d2 = DataVector(self.N)
for i in xrange(self.N):
d2[i] = i
d.componentwise_mult(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i] * i, d[i])
# componentwise_div
d = DataVector(self.d_rand)
for i in xrange(self.N):
d2[i] = i + 1
d.componentwise_div(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i] / (i + 1), d[i])
def computeErrors(jgrid, jalpha,
grid1, alpha1,
grid2, alpha2,
n=200):
"""
Compute some errors to estimate the quality of the
interpolation.
@param jgrid: Grid, new discretization
@param jalpha: DataVector, new surpluses
@param grid1: Grid, old discretization
@param alpha1: DataVector, old surpluses
@param grid2: Grid, old discretization
@param alpha2: DataVector, old surpluses
@return: tuple(<float>, <float>), maxdrift, l2norm
"""
jgs = jgrid.getStorage()
# create control samples
samples = DataMatrix(np.random.rand(n, jgs.getDimension()))
# evaluate the sparse grid functions
jnodalValues = evalSGFunctionMulti(jgrid, jalpha, samples)
# eval grids
nodalValues1 = evalSGFunctionMulti(grid1, alpha1, samples)
nodalValues2 = evalSGFunctionMulti(grid2, alpha2, samples)
# compute errors
p = DataVector(jgs.getDimension())
err = DataVector(n)
for i in range(n):
samples.getRow(i, p)
y = nodalValues1[i] * nodalValues2[i]
if abs(jnodalValues[i]) > 1e100:
err[i] = 0.0
else:
err[i] = abs(y - jnodalValues[i])
# get error statistics
# l2
l2norm = err.l2Norm()
# maxdrift
err.abs()
maxdrift = err.max()
return maxdrift, l2norm
def computeErrors(jgrid, jalpha,
grid1, alpha1,
grid2, alpha2,
n=200):
"""
Compute some errors to estimate the quality of the
interpolation.
@param jgrid: Grid, new discretization
@param jalpha: DataVector, new surpluses
@param grid1: Grid, old discretization
@param alpha1: DataVector, old surpluses
@param grid2: Grid, old discretization
@param alpha2: DataVector, old surpluses
@return: tuple(<float>, <float>), maxdrift, l2norm
"""
jgs = jgrid.getStorage()
# create control samples
samples = DataMatrix(np.random.rand(n, jgs.dim()))
# evaluate the sparse grid functions
jnodalValues = evalSGFunctionMulti(jgrid, jalpha, samples)
# eval grids
nodalValues1 = evalSGFunctionMulti(grid1, alpha1, samples)
nodalValues2 = evalSGFunctionMulti(grid2, alpha2, samples)
# compute errors
p = DataVector(jgs.dim())
err = DataVector(n)
for i in xrange(n):
samples.getRow(i, p)
y = nodalValues1[i] * nodalValues2[i]
if abs(jnodalValues[i]) > 1e100:
err[i] = 0.0
else:
err[i] = abs(y - jnodalValues[i])
# get error statistics
# l2
l2norm = err.l2Norm()
# maxdrift
err.abs()
maxdrift = err.max()
return maxdrift, l2norm
def computeErrors(jgrid, jalpha, grid, alpha, f, n=200):
"""
Compute some errors to estimate the quality of the
interpolation.
@param jgrid: Grid, new discretization
@param jalpha: DataVector, new surpluses
@param grid: Grid, old discretization
@param alpha: DataVector, old surpluses
@param f: function, to be interpolated
@param n: int, number of Monte Carlo estimates for error estimation
@return: tuple(<float>, <float>), maxdrift, l2norm
"""
jgs = jgrid.getStorage()
# create control samples
samples = DataMatrix(np.random.rand(n, jgs.dim()))
# evaluate the sparse grid functions
jnodalValues = evalSGFunctionMulti(jgrid, jalpha, samples)
nodalValues = evalSGFunctionMulti(grid, alpha, samples)
# compute errors
p = DataVector(jgs.dim())
err = DataVector(n)
for i in xrange(n):
samples.getRow(i, p)
y = f(p.array(), nodalValues[i])
err[i] = abs(y - jnodalValues[i])
# get error statistics
# l2
l2norm = err.l2Norm()
# maxdrift
err.abs()
maxdrift = err.max()
return maxdrift, l2norm
def computeErrors(jgrid, jalpha, grid, alpha, f, n=200):
"""
Compute some errors to estimate the quality of the
interpolation.
@param jgrid: Grid, new discretization
@param jalpha: DataVector, new surpluses
@param grid: Grid, old discretization
@param alpha: DataVector, old surpluses
@param f: function, to be interpolated
@param n: int, number of Monte Carlo estimates for error estimation
@return: tuple(<float>, <float>), maxdrift, l2norm
"""
jgs = jgrid.getStorage()
# create control samples
samples = DataMatrix(np.random.rand(n, jgs.dim()))
# evaluate the sparse grid functions
jnodalValues = evalSGFunctionMulti(jgrid, jalpha, samples)
nodalValues = evalSGFunctionMulti(grid, alpha, samples)
# compute errors
p = DataVector(jgs.dim())
err = DataVector(n)
for i in xrange(n):
samples.getRow(i, p)
y = f(p.array(), nodalValues[i])
err[i] = abs(y - jnodalValues[i])
# get error statistics
# l2
l2norm = err.l2Norm()
# maxdrift
err.abs()
maxdrift = err.max()
return maxdrift, l2norm
