def fromfile(k):
'''
See if the two-scale coeffs have already been computed and stored on disk.
Return the data are successfully read from disk, otherwise None.
'''
fname = '/tmp/two-scale-coeffs.' + str(k)
try:
f = open(fname, 'rb')
data = array('d', [])
data.fromfile(f, 4 * k * k)
h0 = mathutil.zeromatrix(k, k)
h1 = mathutil.zeromatrix(k, k)
g0 = mathutil.zeromatrix(k, k)
g1 = mathutil.zeromatrix(k, k)
pt = 0
for i in range(k):
for j in range(k):
h0[i][j] = data[pt]
h1[i][j] = data[pt + 1]
g0[i][j] = data[pt + 2]
g1[i][j] = data[pt + 3]
pt = pt + 4
#print ' Read two-scale coefficients from file',fname
return (h0, h1, g0, g1)
except IOError, EOFError:
return None
def fromfile(k):
'''
See if the two-scale coeffs have already been computed and stored on disk.
Return the data are successfully read from disk, otherwise None.
'''
fname = '/tmp/two-scale-coeffs.' + str(k)
try:
f = open(fname,'rb')
data = array('d',[])
data.fromfile(f,4*k*k)
h0 = mathutil.zeromatrix(k,k)
h1 = mathutil.zeromatrix(k,k)
g0 = mathutil.zeromatrix(k,k)
g1 = mathutil.zeromatrix(k,k)
pt = 0
for i in range(k):
for j in range(k):
h0[i][j] = data[pt]
h1[i][j] = data[pt+1]
g0[i][j] = data[pt+2]
g1[i][j] = data[pt+3]
pt = pt + 4
#print ' Read two-scale coefficients from file',fname
return (h0,h1,g0,g1)
except IOError, EOFError:
return None
def twoscalecoeffs(k, usecached=1):
'''
Return the two-scale coefficients for Alperts basis of given order
coarser <= finer
phi_i(x) = sqrt(2)*sum(j) h0_ij*phi_j(2x) + h1_ij*phi_j(2x-1)
ditto for psi_i(x) with g instead of h
s_n,i,l = sum(j) h0_ij*s_n+1,j,2l + h1_ij*s_n+1,j,2l+1
ditto for d with g instead of h
finer <= coarser
phi_i(2x) = (1/sqrt(2))*sum(j) h0_ji*phi_j(x) + g0_ji*psi(x)
phi_i(2x-1) = (1/sqrt(2))*sum(j) h1_ji*phi_j(x) + g1_ji*psi(x)
s_n+1,i,2l = sum(j) h0_ji*sn,j,l + g0_ji*d_n,j,l
s_n+1,i,2l+1 = sum(j) h1_ji*sn,j,l + g1_ji*d_n,j,l
'''
global phi_norms_long
if usecached:
cached = fromfile(k)
if cached:
return cached
nbitssave = longfloat.nbits
if k < 11:
longfloat.nbits = 156
elif k < 19:
longfloat.nbits = 208
elif k < 24:
longfloat.nbits = 260
elif k < 29:
longfloat.nbits = 320
elif k < 33:
longfloat.nbits = 360
elif k < 37:
longfloat.nbits = 400
elif k < 42:
longfloat.nbits = 440
elif k < 46:
longfloat.nbits = 480
elif k < 49:
longfloat.nbits = 520
else:
longfloat.nbits = 800
longfloat.nbits = 800
print ' Generating two-scale coeffcients for k=%d using %d-bit floating point numbers' \
% (k, longfloat.nbits)
# Force recomputation of the cached sqrt(2*j+1) values
phi_norms_long = []
# Compute the coeffcicients to high precision using longfloats
(h0l, h1l) = h0h1(k)
(g0l, g1l) = g0g1(k)
# Copy them into arrays of floats
h0 = mathutil.zeromatrix(k, k)
g0 = mathutil.zeromatrix(k, k)
h1 = mathutil.zeromatrix(k, k)
g1 = mathutil.zeromatrix(k, k)
gerr = 0.0
herr = 0.0
for i in range(k):
for j in range(k):
hphase = (-1)**(i + j)
gphase = (-1)**(i + j + k)
h0[i][j] = float(h0l[i][j])
h1[i][j] = h0[i][j] * hphase
g0[i][j] = float(g0l[i][j])
g1[i][j] = g0[i][j] * gphase
if abs(h0[i][j]) < 4e-16: h0[i][j] = 0.0
if abs(h1[i][j]) < 4e-16: h1[i][j] = 0.0
if abs(g0[i][j]) < 4e-16: g0[i][j] = 0.0
if abs(g1[i][j]) < 4e-16: g1[i][j] = 0.0
testerr = float(abs(g0l[i][j] - gphase * g1l[i][j]))
if g0[i][j] != 0.0: testerr = testerr / abs(g0[i][j])
gerr = max(gerr, testerr)
testerr = float(abs(h0l[i][j] - hphase * h1l[i][j]))
if h0[i][j] != 0.0: testerr = testerr / abs(h0[i][j])
herr = max(herr, testerr)
print ' maximum symmetry error in h ', float(herr)
print ' maximum symmetry error in g ', float(gerr)
longfloat.nbits = nbitssave
if max(float(herr), float(gerr)) > 4e-16:
raise "twoscalecoeffs have inadequate precision"
tofile(h0, h1, g0, g1)
return (h0, h1, g0, g1)
def twoscalecoeffs(k,usecached=1):
'''
Return the two-scale coefficients for Alperts basis of given order
coarser <= finer
phi_i(x) = sqrt(2)*sum(j) h0_ij*phi_j(2x) + h1_ij*phi_j(2x-1)
ditto for psi_i(x) with g instead of h
s_n,i,l = sum(j) h0_ij*s_n+1,j,2l + h1_ij*s_n+1,j,2l+1
ditto for d with g instead of h
finer <= coarser
phi_i(2x) = (1/sqrt(2))*sum(j) h0_ji*phi_j(x) + g0_ji*psi(x)
phi_i(2x-1) = (1/sqrt(2))*sum(j) h1_ji*phi_j(x) + g1_ji*psi(x)
s_n+1,i,2l = sum(j) h0_ji*sn,j,l + g0_ji*d_n,j,l
s_n+1,i,2l+1 = sum(j) h1_ji*sn,j,l + g1_ji*d_n,j,l
'''
global phi_norms_long
if usecached:
cached = fromfile(k)
if cached:
return cached
nbitssave = longfloat.nbits
if k < 11:
longfloat.nbits = 156
elif k < 19:
longfloat.nbits = 208
elif k < 24:
longfloat.nbits = 260
elif k < 29:
longfloat.nbits = 320
elif k < 33:
longfloat.nbits = 360
elif k < 37:
longfloat.nbits = 400
elif k < 42:
longfloat.nbits = 440
elif k < 46:
longfloat.nbits = 480
elif k < 49:
longfloat.nbits = 520
else:
longfloat.nbits = 800
longfloat.nbits = 800
print ' Generating two-scale coeffcients for k=%d using %d-bit floating point numbers' \
% (k, longfloat.nbits)
# Force recomputation of the cached sqrt(2*j+1) values
phi_norms_long = []
# Compute the coeffcicients to high precision using longfloats
(h0l,h1l) = h0h1(k)
(g0l,g1l) = g0g1(k)
# Copy them into arrays of floats
h0 = mathutil.zeromatrix(k,k)
g0 = mathutil.zeromatrix(k,k)
h1 = mathutil.zeromatrix(k,k)
g1 = mathutil.zeromatrix(k,k)
gerr = 0.0
herr = 0.0
for i in range(k):
for j in range(k):
hphase = (-1)**(i+j)
gphase = (-1)**(i+j+k)
h0[i][j] = float(h0l[i][j])
h1[i][j] = h0[i][j]*hphase
g0[i][j] = float(g0l[i][j])
g1[i][j] = g0[i][j]*gphase
if abs(h0[i][j]) < 4e-16: h0[i][j] = 0.0
if abs(h1[i][j]) < 4e-16: h1[i][j] = 0.0
if abs(g0[i][j]) < 4e-16: g0[i][j] = 0.0
if abs(g1[i][j]) < 4e-16: g1[i][j] = 0.0
testerr = float(abs(g0l[i][j]-gphase*g1l[i][j]))
if g0[i][j] != 0.0: testerr = testerr/abs(g0[i][j])
gerr = max(gerr,testerr)
testerr = float(abs(h0l[i][j]-hphase*h1l[i][j]))
if h0[i][j] != 0.0: testerr = testerr/abs(h0[i][j])
herr = max(herr,testerr)
print ' maximum symmetry error in h ', float(herr)
print ' maximum symmetry error in g ', float(gerr)
longfloat.nbits = nbitssave
if max(float(herr),float(gerr)) > 4e-16:
raise "twoscalecoeffs have inadequate precision"
tofile(h0,h1,g0,g1)
return (h0,h1,g0,g1)
