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demo_pspline_3d.py
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demo_pspline_3d.py
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#!/usr/bin/env python
"""
3-D spline in float64 precision
"""
import sys, time
import numpy as _np
from pypspline3.pspline_3d import pspline, griddata
eps = 1.e-6
n1, n2, n3 = 11, 21, 31
bcs1 = (0,0)
bcs2 = (0,0) # not-a-knot
bcs3 = (0,0) #
x1min, x1max = 0., 1.
x2min, x2max = 0., 1.
x3min, x3max = 0., 1. # 2*_np.pi
x1 = _np.arange(x1min, x1max+eps, (x1max-x1min)/float(n1-1))
x2 = _np.arange(x2min, x2max+eps, (x2max-x2min)/float(n2-1))
x3 = _np.arange(x3min, x3max+eps, (x3max-x3min)/float(n3-1))
tic = time.time()
xx1, xx2, xx3 = griddata(x1, x2, x3)
toc = time.time()
print("griddata : time->%10.1f secs" % (toc-tic))
tic = time.time()
####################################
f = xx1**3 + 2*xx2**3 + 3*xx2*xx3**2
####################################
toc = time.time()
print("function evaluations: time->%10.1f secs" % (toc-tic))
tic = time.time()
spl = pspline(x1, x2, x3)
# may set BCs if not-a-knot
spl.setup(f)
toc = time.time()
print("init/setup: %d original grid nodes time->%10.1f secs" %
(n1*n2*n3, toc-tic))
# save/load skipped for now
# new mesh
n1, n2, n3 = 2*n2-1, 2*n2, 2*n2+1 # 3*n2-1, 3*n2, 3*n2+1
x1 = _np.arange(x1min, x1max+eps, (x1max-x1min)/float(n1-1))
x2 = _np.arange(x2min, x2max+eps, (x2max-x2min)/float(n2-1))
x3 = _np.arange(x3min, x3max+eps, (x3max-x3min)/float(n3-1))
xx1, xx2, xx3 = griddata(x1, x2, x3)
fexact = xx1**3 + 2*xx2**3 + 3*xx2*xx3**2
# point interpolation
nint = n1*n2*n3
error = 0
tic = time.time()
for i3 in range(n3):
for i2 in range(n2):
for i1 in range(n1):
fi, ier, iwarn = spl.interp_point(x1[i1], x2[i2], x3[i3])
error += (fi - fexact[i3,i2,i1])**2
toc = time.time()
error /= nint
error = _np.sqrt(error)
print("interp_point: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# array interpolation
tic = time.time()
fi, ier, iwarn = spl.interp_array(x1, x2, x3)
toc = time.time()
error = _np.sum(_np.sum(_np.sum((fi-fexact)**2)))/nint
print("interp_array: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# cloud interpolation
n = n1*n2*n3
xc1 = _np.arange(x1min, x1max+eps, (x1max-x1min)/float(n-1))
xc2 = _np.arange(x2min, x2max+eps, (x2max-x2min)/float(n-1))
xc3 = _np.arange(x3min, x3max+eps, (x3max-x3min)/float(n-1))
fcexact = xc1**3 + 2*xc2**3 + 3*xc2*xc3**2
tic = time.time()
fi, ier, iwarn = spl.interp_cloud(xc1, xc2, xc3)
toc = time.time()
error = _np.sum((fi-fcexact)**2)/nint
print("interp_cloud: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
## df/dx
fexact = 3*xx1**2
# point df/dx
tic = time.time()
error = 0
for i3 in range(n3):
for i2 in range(n2):
for i1 in range(n1):
fi, ier, iwarn = spl.derivative_point(1, 0, 0, x1[i1], x2[i2], x3[i3])
error += (fi - fexact[i3,i2,i1])**2
toc = time.time()
error /= nint
error = _np.sqrt(error)
print("derivative_point df/dx: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# array df/dx
tic = time.time()
fi, ier, iwarn = spl.derivative_array(1, 0, 0, x1, x2, x3)
toc = time.time()
error = _np.sum(_np.sum(_np.sum((fi-fexact)**2)))/nint
print("derivative_array df/dx: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# cloud df/dx
fcexact = 3*xc1**2
tic = time.time()
fi, ier, iwarn = spl.derivative_cloud(1, 0, 0, xc1, xc2, xc3)
toc = time.time()
error = _np.sum((fi-fcexact)**2)/nint
print("derivative_cloud df/dx: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
## d^2f/dy^2
fexact = 12*xx2
# point d^2f/dy^2
error = 0
tic = time.time()
for i3 in range(n3):
for i2 in range(n2):
for i1 in range(n1):
fi, ier, iwarn = spl.derivative_point(0,2,0, x1[i1], x2[i2], x3[i3])
error += (fi - fexact[i3,i2,i1])**2
toc = time.time()
error /= nint
error = _np.sqrt(error)
print("derivative_point d^2f/dy^2: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# array d^2f/dy^2
tic = time.time()
fi, ier, iwarn = spl.derivative_array(0,2,0, x1, x2, x3)
toc = time.time()
error = _np.sum(_np.sum(_np.sum((fi-fexact)**2)))/nint
print("derivative_array d^2f/dy^2: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# cloud d^2f/dy^2
fcexact = 12*xc2
tic = time.time()
fi, ier, iwarn = spl.derivative_cloud(0,2,0, xc1, xc2, xc3)
toc = time.time()
error = _np.sum((fi-fcexact)**2)/nint
print("derivative_cloud d^2f/dy^2: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
## d^2f/dydz
fexact = 6*xx3
# point d^2f/dydz
error = 0
tic = time.time()
for i3 in range(n3):
for i2 in range(n2):
for i1 in range(n1):
fi, ier, iwarn = spl.derivative_point(0,1,1, x1[i1], x2[i2], x3[i3])
error += (fi - fexact[i3,i2,i1])**2
toc = time.time()
error /= nint
error = _np.sqrt(error)
print("derivative_point d^2f/dydz: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# array d^2f/dydz
tic = time.time()
fi, ier, iwarn = spl.derivative_array(0,1,1, x1, x2, x3)
toc = time.time()
error = _np.sum(_np.sum(_np.sum((fi-fexact)**2)))/nint
print("derivative_array d^2f/dydz: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# cloud d^2f/dydz
fcexact = 6*xc3
tic = time.time()
fi, ier, iwarn = spl.derivative_cloud(0,1,1, xc1, xc2, xc3)
toc = time.time()
error = _np.sum((fi-fcexact)**2)/nint
print("derivative_cloud d^2f/dydz: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
## gradients
f1exact = 3*xx1**2
f2exact = 6*xx2**2 + 3*xx3**2
f3exact = 6*xx2*xx3
# point
error = 0
tic = time.time()
for i3 in range(n3):
for i2 in range(n2):
for i1 in range(n1):
f1,f2,f3, ier, iwarn = spl.gradient_point(x1[i1], x2[i2], x3[i3])
error += ( \
(f1 - f1exact[i3,i2,i1])**2 +
(f2 - f2exact[i3,i2,i1])**2 + \
(f3 - f3exact[i3,i2,i1])**2
)/3
toc = time.time()
error /= nint
error = _np.sqrt(error)
print("gradient_point: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# array
tic = time.time()
f1,f2,f3, ier, iwarn = spl.gradient_array(x1, x2, x3)
toc = time.time()
error = _np.sum(_np.sum(_np.sum(((f1-f1exact)**2 + (f2-f2exact)**2 + (f3-f3exact)**2)/3)))/nint
print("gradient_array: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))
# cloud
f1cexact = 3*xc1**2
f2cexact = 6*xc2**2 + 3*xc3**2
f3cexact = 6*xc2*xc3
tic = time.time()
f1,f2,f3, ier, iwarn = spl.gradient_cloud(xc1, xc2, xc3)
toc = time.time()
error = _np.sum(((f1-f1cexact)**2 + (f2-f2cexact)**2 + (f3-f3cexact)**2)/3)/nint
print("gradient_cloud: %d evaluations (error=%g) ier=%d iwarn=%d time->%10.1f secs" %
(nint, error, ier, iwarn, toc-tic))