def unittest_interpolation(fill='simplex', quadrature=QuadraturePatterson()):
"""Verify interpolation implementation against some function f().
Plot key - black surface: original, red: reconstruction."""
dim, level = 2, 5
sp = SparseGrid(dim, quadrature, level=level, fill=fill)
def f(x):
return np.cos(2 * np.pi * x[0]) * np.cos(2 * np.pi * x[1] + 2)
fval = sp.sample_fn(f)
sx = np.array(sp.get_nodes().values())
# Plotting interpolation
M = 41
x1 = np.linspace(0, 1, M)
xy = mylib.meshgrid_flatten(x1, x1)
X, Y = xy[:, 0].reshape(M, M), xy[:, 1].reshape(M, M)
# 2d sampling
F, Fa = np.zeros(xy.shape[0]), np.zeros(xy.shape[0])
for i, x in enumerate(xy):
F[i] = f(x)
Fa[i] = sp.interpolate(x, fval)
# Plotting
if plt_loaded:
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, F.reshape(M, M), colors='k')
ax.plot_wireframe(X, Y, Fa.reshape(M, M), colors='r')
ax.scatter(sx[:, 0], sx[:, 1], 0, c='k')
fig.savefig('unittest_interpolation.pdf')
def unittest_interpolation(fill='simplex', quadrature=QuadraturePatterson()):
"""Verify interpolation implementation against some function f().
Plot key - black surface: original, red: reconstruction."""
dim, level = 2, 5
sp = SparseGrid(dim, quadrature, level=level, fill=fill)
def f(x): return np.cos(2*np.pi*x[0])*np.cos(2*np.pi*x[1]+2)
fval = sp.sample_fn(f)
sx = np.array(sp.get_nodes().values())
# Plotting interpolation
M = 41
x1 = np.linspace(0,1,M)
xy = mylib.meshgrid_flatten(x1, x1)
X, Y = xy[:,0].reshape(M,M), xy[:,1].reshape(M,M)
# 2d sampling
F, Fa = np.zeros(xy.shape[0]), np.zeros(xy.shape[0])
for i,x in enumerate(xy):
F[i] = f(x)
Fa[i] = sp.interpolate(x, fval)
# Plotting
if plt_loaded:
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, F.reshape(M,M), colors='k')
ax.plot_wireframe(X, Y, Fa.reshape(M,M), colors='r')
ax.scatter(sx[:,0], sx[:,1], 0, c='k')
fig.savefig('unittest_interpolation.pdf')
def init_full_factor(self, level):
"""
Initialize with the full tensor-product (non-sparse) of level level>0.
This is just for reference purposes.
"""
self.I = set([])
for mi in mylib.meshgrid_flatten(*(range(1, level + 1), ) * self.dim):
self.I |= set([tuple(mi)])
def __init__(self, quad, levelidx, delta=False):
i_1d = [quad.idx[l-1] for l in levelidx]
w = quad.dw if delta else quad.w
w_1d = [w[l-1] for l in levelidx]
self.delta = delta # Original rule or difference rule
self.levelidx = levelidx
self.dim = len(self.levelidx)
self.quad = quad # 1d quadrature rule
self.nnodes = np.array([quad.nnode(l-1) for l in self.levelidx])
self.i = mylib.meshgrid_flatten(*i_1d)
self.w = mylib.meshprod_flatten(*w_1d)
def __init__(self, quad, levelidx, delta=False):
i_1d = [quad.idx[l - 1] for l in levelidx]
w = quad.dw if delta else quad.w
w_1d = [w[l - 1] for l in levelidx]
self.delta = delta # Original rule or difference rule
self.levelidx = levelidx
self.dim = len(self.levelidx)
self.quad = quad # 1d quadrature rule
self.nnodes = np.array([quad.nnode(l - 1) for l in self.levelidx])
self.i = mylib.meshgrid_flatten(*i_1d)
self.w = mylib.meshprod_flatten(*w_1d)
def init_full_factor(self, l):
"""
Initialize with the full tensor-product (non-sparse) of level l>0. This
is just for reference purposes, this call will be way too expensive in
high-dimensions, and the implementation of this rule via sparse-grids is
ridiculously convoluted.
"""
self.active_to_old(0)
Itmp = mylib.meshgrid_flatten( *(range(1,l+1),)*self.dim )
for k in Itmp[1:]: # 1st entry is already there
i = self.add(k)
if max(k) < l: self.active_to_old(i)
def init_full_factor(self, l):
"""
Initialize with the full tensor-product (non-sparse) of level l>0. This
is just for reference purposes, this call will be way too expensive in
high-dimensions, and the implementation of this rule via sparse-grids is
ridiculously convoluted.
"""
self.active_to_old(0)
Itmp = mylib.meshgrid_flatten(*(range(1, l + 1), ) * self.dim)
for k in Itmp[1:]: # 1st entry is already there
i = self.add(k)
if max(k) < l: self.active_to_old(i)
def plot_testfn():
"""Make contour plots of all 6 test functions in 2d."""
assert plt_loaded, 'Matplotlib not installed'
dim = 2
global c, w
c = np.array([0.5] * dim); c = c / sum(c) * 9.
w = np.array([0.5] * dim)
xi = np.linspace(0., 1., 100)
xx = mylib.meshgrid_flatten(xi, xi)
fig = plt.figure(figsize=(12, 8))
for i in range(1, 7):
fn = get_fn(i)
ax = fig.add_subplot(2, 3, i)
F = np.zeros(xx.shape[0])
for i, x in enumerate(xx):
F[i] = fn(np.array(x))
F.reshape(xi.size, xi.size)
ax.contour(xi, xi, F.reshape(xi.size, xi.size).T)
fig.savefig('test_genz.contours.pdf')
def plot_testfn():
"""Make contour plots of all 6 test functions in 2d."""
assert plt_loaded, 'Matplotlib not installed'
dim = 2
global c, w
c = np.array([0.5] * dim)
c = c / sum(c) * 9.
w = np.array([0.5] * dim)
xi = np.linspace(0., 1., 100)
xx = mylib.meshgrid_flatten(xi, xi)
fig = plt.figure(figsize=(12, 8))
for i in range(1, 7):
fn = get_fn(i)
ax = fig.add_subplot(2, 3, i)
F = np.zeros(xx.shape[0])
for i, x in enumerate(xx):
F[i] = fn(np.array(x))
F.reshape(xi.size, xi.size)
ax.contour(xi, xi, F.reshape(xi.size, xi.size).T)
fig.savefig('test_genz.contours.pdf')