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lininterp2.py
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/
lininterp2.py
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//
// Copyright (c) 2011 Ronaldo Carpio
//
// Permission to use, copy, modify, distribute and sell this software
// and its documentation for any purpose is hereby granted without fee,
// provided that the above copyright notice appear in all copies and
// that both that copyright notice and this permission notice appear
// in supporting documentation. The authors make no representations
// about the suitability of this software for any purpose.
// It is provided "as is" without express or implied warranty.
//
# classes for linear interpolation
# requires a regular grid
import scipy, types
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import pyublas, _myfuncs
import itertools
import time
class LinInterp1D_2:
def __init__(self, grid1, fArray):
assert(len(grid1) == fArray.shape[0])
(self.m_grid1, self.m_FArray) = (grid1, fArray)
def __call__(self, z):
# this is a hack, should find a better way.
arg = z
if (not isinstance(z, types.FloatType)):
arg = z[0]
return _myfuncs.interp1d(self.m_grid1, self.m_FArray, arg)
class LinInterp1D(_myfuncs.Interp1D):
def __init__(self, grid1, fArray):
super(LinInterp1D,self).__init__(grid1, fArray)
(self.m_grid1, self.m_FArray) = (grid1, fArray)
class LinInterp2D_grid:
def __init__(self, grid1, grid2, fArray):
assert(len(grid1) == fArray.shape[0] and len(grid2) == fArray.shape[1])
(self.m_grid1, self.m_grid2, self.m_FArray) = (grid1, grid2, fArray)
# def __call__(self, x1, x2):
# return _myfuncs.interp2d(self.m_grid1, self.m_grid2, self.m_FArray, x1, x2)
def __call__(self, x):
return _myfuncs.interp2d(self.m_grid1, self.m_grid2, self.m_FArray, x[0], x[1])
class LinInterp2D_obj(_myfuncs.Interp2D):
def __init__(self, grid1, grid2, fArray):
super(LinInterp2D,self).__init__(grid1, grid2, fArray)
(self.m_grid1, self.m_grid2, self.m_FArray) = (grid1, grid2, fArray)
LinInterp2D = LinInterp2D_obj
class LinInterp3D:
def __init__(self, grid1, grid2, grid3, fArray):
assert(len(grid1) == fArray.shape[0] and len(grid2) == fArray.shape[1] and len(grid3) == fArray.shape[2])
(self.m_grid1, self.m_grid2, self.m_grid3, self.m_FArray) = (grid1, grid2, grid3, fArray)
def __call__(self, x1, x2, x3):
return _myfuncs.interp3d(self.m_grid1, self.m_grid2, self.m_grid3, self.m_FArray, x1, x2, x3)
def __call__(self, x):
return _myfuncs.interp3d(self.m_grid1, self.m_grid2, self.m_grid3, self.m_FArray, x[0], x[1], x[2])
# automatically figure out the right object based on the number of dimensions. only works for 1 to 3
def GetLinterpFnObj(stateGridList, fArray):
assert(len(stateGridList) == fArray.ndim); # check the shapes match
for i in range(len(stateGridList)):
assert(len(stateGridList[i]) == fArray.shape[i])
if (fArray.ndim == 1):
return LinInterp1D(stateGridList[0], fArray)
elif (fArray.ndim == 2):
return LinInterp2D(stateGridList[0], stateGridList[1], fArray)
elif (fArray.ndim == 3):
return LinInterp3D(stateGridList[0], stateGridList[1], stateGridList[2], fArray)
else:
assert(false)
def test_1D():
innerGrid = scipy.linspace(-5, 5, 20)
fArray = scipy.sin(innerGrid)
outerGrid = scipy.linspace(-10, 10, 66)
interp1 = LinInterp1D_2(innerGrid, fArray)
interp2 = LinInterp1D(innerGrid, fArray)
fig = plt.figure()
plt.plot(outerGrid, map(interp1, outerGrid))
fig = plt.figure()
plt.plot(outerGrid, map(interp2, outerGrid))
fig = plt.figure()
plt.plot(outerGrid, interp2(outerGrid))
def test_2D():
def f(x):
return scipy.sin(x[0] + 2*x[1])
coarseGrid1 = scipy.linspace(-5, 5, 80)
coarseGrid2 = scipy.linspace(-5, 5, 100)
fineGrid1 = scipy.linspace(-6, 6, 200)
fineGrid2 = scipy.linspace(-6, 6, 220)
[c_x1list, c_x2list] = zip(*itertools.product(coarseGrid1, coarseGrid2))
[f_x1list, f_x2list] = zip(*itertools.product(fineGrid1, fineGrid2))
fList = map(f, zip(c_x1list, c_x2list))
fArray = scipy.array(fList).reshape((len(coarseGrid1), len(coarseGrid2)))
# original
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(c_x1list, c_x2list, fList)
# interp1
fig = plt.figure()
ax = Axes3D(fig)
t1 = time.time()
interp1 = LinInterp2D_grid(coarseGrid1, coarseGrid2, fArray)
t2 = time.time()
for i in range(100):
interp_fList1 = map(interp1, zip(f_x1list, f_x2list))
t3 = time.time()
print("interp grid: setup %f sec, interp %f sec" % (t2-t1, t3-t2))
ax.scatter(f_x1list, f_x2list, interp_fList1)
# interp2
fig = plt.figure()
ax = Axes3D(fig)
t1 = time.time()
interp2 = LinInterp2D_obj(coarseGrid1, coarseGrid2, fArray)
t2 = time.time()
for i in range(100):
interp_fList2 = map(interp2, zip(f_x1list, f_x2list))
t3 = time.time()
print("interp obj: setup %f sec, interp %f sec" % (t2-t1, t3-t2))
ax.scatter(f_x1list, f_x2list, interp_fList2)
diff = scipy.array(interp_fList1) - scipy.array(interp_fList2)
return scipy.sum(diff*diff)
class LinInterp1D_irreg:
def __init__(self, grid, fArray):
(self.grid, self.fArray) = grid, fArray
self.slopes = (fArray[1:] - fArray[:-1]) / (grid[1:] - grid[:-1])
def interp(self, xi):
if (xi < self.grid[0]):
return self.fArray[0]
if (xi > self.grid[-1]):
return self.fArray[-1]
cell = binarySearchForCell(self.grid, xi)
result = self.fArray[cell] + (xi - self.grid[cell]) * self.slopes[cell]
return result
def binarySearchForCell(grid, x):
assert(len(grid) > 1)
left = 0
right = len(grid)-1
while (left+1 < right):
mid = int( (left+right)/2 )
if (x < grid[mid]):
right = mid
else:
left = mid
return left
# given an n-dim array f on grids, return an interpolated array on grids of a different size.
# f must have same dimensions as grids.
def interpolateArray(gridList1, gridList2, f):
assert(len(gridList1) == len(gridList2))
assert([len(g) for g in gridList1] == list(f.shape))
interpObj = GetLinterpFnObj(gridList1, f)
# iterate through each grid point, cycle through grid 0 on the innermost loop
#interpList = [interpObj(x) for x in itertools.product(*list(reversed(gridList2)))]
interpList = []
for x in itertools.product(*gridList2):
x2 = list(x)
z = interpObj(x2)
interpList.append(z)
#print((x, z))
result = scipy.array(interpList).reshape(tuple( [len(g) for g in gridList2] ))
return result
# return an array of fn applied to each grid point in gridList. last elt of gridList will be the innermost loop
def applyGrid(gridList, fn):
z_list = list(itertools.product(*gridList))
x_list = zip(*z_list)
f = scipy.array([fn(z) for z in z_list])
f = f.reshape(tuple( [len(g) for g in gridList] ))
return (x_list, f)
def test_interpolateArray():
grid_x = scipy.linspace(1, 5, 20)
grid_y = scipy.linspace(-1, 1, 10)
def fn(x):
return scipy.sin(x[0] + x[1])
((xlist, ylist), f) = applyGrid([grid_x, grid_y], fn)
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(xlist, ylist, f.ravel())
grid2_x = scipy.linspace(1, 5, 40)
grid2_y = scipy.linspace(-1, 1, 20)
f2 = interpolateArray([grid_x, grid_y], [grid2_x, grid2_y], f)
xy_list = itertools.product(grid2_x, grid2_y)
(xlist2, ylist2) = zip(*xy_list)
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(xlist2, ylist2, f2.ravel())
grid3_x = grid_x
grid3_y = grid_y
f3 = interpolateArray([grid2_x, grid2_y], [grid3_x, grid3_y], f2)
xy_list = itertools.product(grid3_x, grid3_y)
(xlist3, ylist3) = zip(*xy_list)
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(xlist3, ylist3, f3.ravel())