y = x.copy()
dx = dy = 2.0 / (N - 1)
xx, yy = np.meshgrid(x, y)
data = xx + yy + xx * yy + 0.5 * np.random.randn(xx.shape[0], xx.shape[1])
C = least_square_sequence(dx, dy, data)
for coeffs in C:
print "f(x,y) = %3.3f + %3.3f x + %3.3f y + %3.3f xy" % tuple(coeffs[0])
xxx = np.linspace(-1, 1, 101)
yyy = xxx.copy()
z = np.zeros((101, 101))
for j in xrange(101):
for i in xrange(101):
z[j, i] = bilinear_eval(C[0], xxx[i], yyy[j])
from pylab import *
pcolormesh(x, y, data)
colorbar()
grid(True)
cs = contour(xxx, yyy, z, 21, colors="black", linewidths=2)
clabel(cs)
axes().set_aspect("equal")
show()
x = np.linspace(-1,1,N)
y = x.copy()
xx, yy = np.meshgrid(x,y)
data = xx + yy + xx*yy + 0.5 * np.random.randn(xx.shape[0], xx.shape[1])
coeffs = least_square_fit(2.0/(N-1), 2.0/(N-1), data)
print "f(x,y) = %3.3f + %3.3f x + %3.3f y + %3.3f xy" % tuple(coeffs[0])
xxx = np.linspace(-1,1,101)
yyy = xxx.copy()
z = np.zeros((101,101))
for j in xrange(101):
for i in xrange(101):
z[j,i] = bilinear_eval(coeffs, xxx[i], yyy[j])
from pylab import *
pcolormesh(x,y,data)
colorbar()
grid(True)
cs = contour(xxx,yyy,z,21,colors='black', linewidths=2)
clabel(cs)
axes().set_aspect('equal')
show()
