def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def log_linear_vinterp(T,P,levs):
'''
# Author Charles Doutriaux
# Version 1.1
# Expect 2D field here so there''s no reorder which I suspect to do a memory leak
# email: [email protected]
# Converts a field from sigma levels to pressure levels
# Log linear interpolation
# Input
# T : temperature on sigma levels
# P : pressure field from TOP (level 0) to BOTTOM (last level)
# levs : pressure levels to interplate to (same units as P)
# Output
# t : temperature on pressure levels (levs)
# External: Numeric'''
import numpy.ma as MA
## from numpy.oldnumeric.ma import ones,Float,greater,less,logical_and,where,equal,log,asarray,Float16
sh=P.shape
nsigma=sh[0] # Number of sigma levels
try:
nlev=len(levs) # Number of pressure levels
except:
nlev=1 # if only one level len(levs) would breaks
t=[]
for ilv in range(nlev): # loop through pressure levels
try:
lev=levs[ilv] # get value for the level
except:
lev=levs # only 1 level passed
# print ' ......... level:',lev
Pabv=MA.ones(P[0].shape,Numeric.Float)
Tabv=-Pabv # Temperature on sigma level Above
Tbel=-Pabv # Temperature on sigma level Below
Pbel=-Pabv # Pressure on sigma level Below
Pabv=-Pabv # Pressure on sigma level Above
for isg in range(1,nsigma): # loop from second sigma level to last one
## print 'Sigma level #',isg
a = MA.greater(P[isg], lev) # Where is the pressure greater than lev
b = MA.less(P[isg-1],lev) # Where is the pressure less than lev
# Now looks if the pressure level is in between the 2 sigma levels
# If yes, sets Pabv, Pbel and Tabv, Tbel
Pabv=MA.where(MA.logical_and(a,b),P[isg],Pabv) # Pressure on sigma level Above
Tabv=MA.where(MA.logical_and(a,b),T[isg],Tabv) # Temperature on sigma level Above
Pbel=MA.where(MA.logical_and(a,b),P[isg-1],Pbel) # Pressure on sigma level Below
Tbel=MA.where(MA.logical_and(a,b),T[isg-1],Tbel) # Temperature on sigma level Below
# end of for isg in range(1,nsigma)
# val=where(equal(Pbel,-1.),Pbel.missing_value,lev) # set to missing value if no data below lev if there is
tl=MA.masked_where(MA.equal(Pbel,-1.),MA.log(lev/MA.absolute(Pbel))/MA.log(Pabv/Pbel)*(Tabv-Tbel)+Tbel) # Interpolation
t.append(tl) # add a level to the output
# end of for ilv in range(nlev)
return asMA(t).astype(Numeric.Float32) # convert t to an array
def test_testMinMax2(self):
# Test of minimum, maximum.
assert_(eq(minimum([1, 2, 3], [4, 0, 9]), [1, 0, 3]))
assert_(eq(maximum([1, 2, 3], [4, 0, 9]), [4, 2, 9]))
x = arange(5)
y = arange(5) - 2
x[3] = masked
y[0] = masked
assert_(eq(minimum(x, y), where(less(x, y), x, y)))
assert_(eq(maximum(x, y), where(greater(x, y), x, y)))
assert_(minimum.reduce(x) == 0)
assert_(maximum.reduce(x) == 4)
def test_testMinMax2(self):
# Test of minimum, maximum.
assert_(eq(minimum([1, 2, 3], [4, 0, 9]), [1, 0, 3]))
assert_(eq(maximum([1, 2, 3], [4, 0, 9]), [4, 2, 9]))
x = arange(5)
y = arange(5) - 2
x[3] = masked
y[0] = masked
assert_(eq(minimum(x, y), where(less(x, y), x, y)))
assert_(eq(maximum(x, y), where(greater(x, y), x, y)))
assert_(minimum.reduce(x) == 0)
assert_(maximum.reduce(x) == 4)
def log_linear_vinterp(T, P, levs):
'''
# Author Charles Doutriaux
# Version 1.1
# Expect 2D field here so there''s no reorder which I suspect to do a memory leak
# email: [email protected]
# Converts a field from sigma levels to pressure levels
# Log linear interpolation
# Input
# T : temperature on sigma levels
# P : pressure field from TOP (level 0) to BOTTOM (last level)
# levs : pressure levels to interplate to (same units as P)
# Output
# t : temperature on pressure levels (levs)
# External: Numeric'''
import numpy.ma as MA
## from numpy.oldnumeric.ma import ones,Float,greater,less,logical_and,where,equal,log,asarray,Float16
sh = P.shape
nsigma = sh[0] # Number of sigma levels
try:
nlev = len(levs) # Number of pressure levels
except:
nlev = 1 # if only one level len(levs) would breaks
t = []
for ilv in range(nlev): # loop through pressure levels
try:
lev = levs[ilv] # get value for the level
except:
lev = levs # only 1 level passed
# print ' ......... level:',lev
Pabv = MA.ones(P[0].shape, Numeric.Float)
Tabv = -Pabv # Temperature on sigma level Above
Tbel = -Pabv # Temperature on sigma level Below
Pbel = -Pabv # Pressure on sigma level Below
Pabv = -Pabv # Pressure on sigma level Above
for isg in range(1,
nsigma): # loop from second sigma level to last one
## print 'Sigma level #',isg
a = MA.greater(P[isg],
lev) # Where is the pressure greater than lev
b = MA.less(P[isg - 1], lev) # Where is the pressure less than lev
# Now looks if the pressure level is in between the 2 sigma levels
# If yes, sets Pabv, Pbel and Tabv, Tbel
Pabv = MA.where(MA.logical_and(a, b), P[isg],
Pabv) # Pressure on sigma level Above
Tabv = MA.where(MA.logical_and(a, b), T[isg],
Tabv) # Temperature on sigma level Above
Pbel = MA.where(MA.logical_and(a, b), P[isg - 1],
Pbel) # Pressure on sigma level Below
Tbel = MA.where(MA.logical_and(a, b), T[isg - 1],
Tbel) # Temperature on sigma level Below
# end of for isg in range(1,nsigma)
# val=where(equal(Pbel,-1.),Pbel.missing_value,lev) # set to missing value if no data below lev if there is
tl = MA.masked_where(
MA.equal(Pbel, -1.),
MA.log(lev / MA.absolute(Pbel)) / MA.log(Pabv / Pbel) *
(Tabv - Tbel) + Tbel) # Interpolation
t.append(tl) # add a level to the output
# end of for ilv in range(nlev)
return asMA(t).astype(Numeric.Float32) # convert t to an array
def test_testOddFeatures(self):
# Test of other odd features
x = arange(20)
x = x.reshape(4, 5)
x.flat[5] = 12
assert_(x[1, 0] == 12)
z = x + 10j * x
assert_(eq(z.real, x))
assert_(eq(z.imag, 10 * x))
assert_(eq((z * conjugate(z)).real, 101 * x * x))
z.imag[...] = 0.0
x = arange(10)
x[3] = masked
assert_(str(x[3]) == str(masked))
c = x >= 8
assert_(count(where(c, masked, masked)) == 0)
assert_(shape(where(c, masked, masked)) == c.shape)
z = where(c, x, masked)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is masked)
assert_(z[7] is masked)
assert_(z[8] is not masked)
assert_(z[9] is not masked)
assert_(eq(x, z))
z = where(c, masked, x)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is not masked)
assert_(z[7] is not masked)
assert_(z[8] is masked)
assert_(z[9] is masked)
z = masked_where(c, x)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is not masked)
assert_(z[7] is not masked)
assert_(z[8] is masked)
assert_(z[9] is masked)
assert_(eq(x, z))
x = array([1., 2., 3., 4., 5.])
c = array([1, 1, 1, 0, 0])
x[2] = masked
z = where(c, x, -x)
assert_(eq(z, [1., 2., 0., -4., -5]))
c[0] = masked
z = where(c, x, -x)
assert_(eq(z, [1., 2., 0., -4., -5]))
assert_(z[0] is masked)
assert_(z[1] is not masked)
assert_(z[2] is masked)
assert_(eq(masked_where(greater(x, 2), x), masked_greater(x, 2)))
assert_(eq(masked_where(greater_equal(x, 2), x),
masked_greater_equal(x, 2)))
assert_(eq(masked_where(less(x, 2), x), masked_less(x, 2)))
assert_(eq(masked_where(less_equal(x, 2), x), masked_less_equal(x, 2)))
assert_(eq(masked_where(not_equal(x, 2), x), masked_not_equal(x, 2)))
assert_(eq(masked_where(equal(x, 2), x), masked_equal(x, 2)))
assert_(eq(masked_where(not_equal(x, 2), x), masked_not_equal(x, 2)))
assert_(eq(masked_inside(list(range(5)), 1, 3), [0, 199, 199, 199, 4]))
assert_(eq(masked_outside(list(range(5)), 1, 3), [199, 1, 2, 3, 199]))
assert_(eq(masked_inside(array(list(range(5)),
mask=[1, 0, 0, 0, 0]), 1, 3).mask,
[1, 1, 1, 1, 0]))
assert_(eq(masked_outside(array(list(range(5)),
mask=[0, 1, 0, 0, 0]), 1, 3).mask,
[1, 1, 0, 0, 1]))
assert_(eq(masked_equal(array(list(range(5)),
mask=[1, 0, 0, 0, 0]), 2).mask,
[1, 0, 1, 0, 0]))
assert_(eq(masked_not_equal(array([2, 2, 1, 2, 1],
mask=[1, 0, 0, 0, 0]), 2).mask,
[1, 0, 1, 0, 1]))
assert_(eq(masked_where([1, 1, 0, 0, 0], [1, 2, 3, 4, 5]),
[99, 99, 3, 4, 5]))
atest = ones((10, 10, 10), dtype=np.float32)
btest = zeros(atest.shape, MaskType)
ctest = masked_where(btest, atest)
assert_(eq(atest, ctest))
z = choose(c, (-x, x))
assert_(eq(z, [1., 2., 0., -4., -5]))
assert_(z[0] is masked)
assert_(z[1] is not masked)
assert_(z[2] is masked)
x = arange(6)
x[5] = masked
y = arange(6) * 10
y[2] = masked
c = array([1, 1, 1, 0, 0, 0], mask=[1, 0, 0, 0, 0, 0])
cm = c.filled(1)
z = where(c, x, y)
zm = where(cm, x, y)
assert_(eq(z, zm))
assert_(getmask(zm) is nomask)
assert_(eq(zm, [0, 1, 2, 30, 40, 50]))
z = where(c, masked, 1)
assert_(eq(z, [99, 99, 99, 1, 1, 1]))
z = where(c, 1, masked)
assert_(eq(z, [99, 1, 1, 99, 99, 99]))
def test_testOddFeatures(self):
# Test of other odd features
x = arange(20)
x = x.reshape(4, 5)
x.flat[5] = 12
assert_(x[1, 0] == 12)
z = x + 10j * x
assert_(eq(z.real, x))
assert_(eq(z.imag, 10 * x))
assert_(eq((z * conjugate(z)).real, 101 * x * x))
z.imag[...] = 0.0
x = arange(10)
x[3] = masked
assert_(str(x[3]) == str(masked))
c = x >= 8
assert_(count(where(c, masked, masked)) == 0)
assert_(shape(where(c, masked, masked)) == c.shape)
z = where(c, x, masked)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is masked)
assert_(z[7] is masked)
assert_(z[8] is not masked)
assert_(z[9] is not masked)
assert_(eq(x, z))
z = where(c, masked, x)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is not masked)
assert_(z[7] is not masked)
assert_(z[8] is masked)
assert_(z[9] is masked)
z = masked_where(c, x)
assert_(z.dtype is x.dtype)
assert_(z[3] is masked)
assert_(z[4] is not masked)
assert_(z[7] is not masked)
assert_(z[8] is masked)
assert_(z[9] is masked)
assert_(eq(x, z))
x = array([1., 2., 3., 4., 5.])
c = array([1, 1, 1, 0, 0])
x[2] = masked
z = where(c, x, -x)
assert_(eq(z, [1., 2., 0., -4., -5]))
c[0] = masked
z = where(c, x, -x)
assert_(eq(z, [1., 2., 0., -4., -5]))
assert_(z[0] is masked)
assert_(z[1] is not masked)
assert_(z[2] is masked)
assert_(eq(masked_where(greater(x, 2), x), masked_greater(x, 2)))
assert_(eq(masked_where(greater_equal(x, 2), x),
masked_greater_equal(x, 2)))
assert_(eq(masked_where(less(x, 2), x), masked_less(x, 2)))
assert_(eq(masked_where(less_equal(x, 2), x), masked_less_equal(x, 2)))
assert_(eq(masked_where(not_equal(x, 2), x), masked_not_equal(x, 2)))
assert_(eq(masked_where(equal(x, 2), x), masked_equal(x, 2)))
assert_(eq(masked_where(not_equal(x, 2), x), masked_not_equal(x, 2)))
assert_(eq(masked_inside(list(range(5)), 1, 3), [0, 199, 199, 199, 4]))
assert_(eq(masked_outside(list(range(5)), 1, 3), [199, 1, 2, 3, 199]))
assert_(eq(masked_inside(array(list(range(5)),
mask=[1, 0, 0, 0, 0]), 1, 3).mask,
[1, 1, 1, 1, 0]))
assert_(eq(masked_outside(array(list(range(5)),
mask=[0, 1, 0, 0, 0]), 1, 3).mask,
[1, 1, 0, 0, 1]))
assert_(eq(masked_equal(array(list(range(5)),
mask=[1, 0, 0, 0, 0]), 2).mask,
[1, 0, 1, 0, 0]))
assert_(eq(masked_not_equal(array([2, 2, 1, 2, 1],
mask=[1, 0, 0, 0, 0]), 2).mask,
[1, 0, 1, 0, 1]))
assert_(eq(masked_where([1, 1, 0, 0, 0], [1, 2, 3, 4, 5]),
[99, 99, 3, 4, 5]))
atest = ones((10, 10, 10), dtype=np.float32)
btest = zeros(atest.shape, MaskType)
ctest = masked_where(btest, atest)
assert_(eq(atest, ctest))
z = choose(c, (-x, x))
assert_(eq(z, [1., 2., 0., -4., -5]))
assert_(z[0] is masked)
assert_(z[1] is not masked)
assert_(z[2] is masked)
x = arange(6)
x[5] = masked
y = arange(6) * 10
y[2] = masked
c = array([1, 1, 1, 0, 0, 0], mask=[1, 0, 0, 0, 0, 0])
cm = c.filled(1)
z = where(c, x, y)
zm = where(cm, x, y)
assert_(eq(z, zm))
assert_(getmask(zm) is nomask)
assert_(eq(zm, [0, 1, 2, 30, 40, 50]))
z = where(c, masked, 1)
assert_(eq(z, [99, 99, 99, 1, 1, 1]))
z = where(c, 1, masked)
assert_(eq(z, [99, 1, 1, 99, 99, 99]))
def preprocess_ncc_impl(image, ncc_size):
"""
Prepare normalized patch vectors according to normalized cross
correlation.
This is a preprocessing step for the NCC pipeline. It is expected that
'preprocess_ncc' is called on every input image to preprocess the NCC
vectors and then 'compute_ncc' is called to compute the dot product
between these vectors in two images.
NCC preprocessing has two steps.
(1) Compute and subtract the mean.
(2) Normalize the vector.
The mean is per channel. i.e. For an RGB image, over the ncc_size**2
patch, compute the R, G, and B means separately. The normalization
is over all channels. i.e. For an RGB image, after subtracting out the
RGB mean, compute the norm over the entire (ncc_size**2 * channels)
vector and divide.
If the norm of the vector is < 1e-6, then set the entire vector for that
patch to zero.
Patches that extend past the offset of the input image at all should be
considered zero. Their entire vector should be set to 0.
Patches of shape channels x height x width (e.g. 3 x ncc_size x ncc_size)
are to be flattened into vectors with the default numpy row major order.
For example, given the following 2 (channels) x 2 (height) x 2 (width)
patch, here is how the output vector should be arranged.
channel1 channel2
+------+------+ +------+------+ height
| x111 | x121 | | x112 | x122 | |
+------+------+ +------+------+ |
| x211 | x221 | | x212 | x222 | |
+------+------+ +------+------+ v
width ------->
v = [ x111, x121, x211, x221, x112, x122, x212, x222 ]
Input:
image -- height x width x channels image of type float32
ncc_size -- integer width and height of NCC patch region. ncc_size
will always be odd.
Output:
normalized -- heigth x width x (channels * ncc_size**2) array
"""
height,width,channel = image.shape
patches = np.zeros((height,width, channel, ncc_size * ncc_size),dtype='float32')
normalized = np.zeros((height,width,channel*ncc_size**2),dtype='float32')
offset = int(np.floor(ncc_size/2.0))
for h in xrange(offset,height-offset):
for w in xrange(offset, width-offset):
patches[h,w] = np.transpose(image[h-offset:h+offset+1,w-offset:w+offset+1],axes=(2,0,1)).reshape(channel,ncc_size**2)
patches = patches - np.mean(patches,axis=3)[:,:,:,np.newaxis]
norm = np.linalg.norm(patches, axis=(2,3))
mask = ma.less(norm, 1.0e-6)
norm[mask] = 1.0
patches = patches / norm[:,:,np.newaxis,np.newaxis]
patches[mask] = 0.0
normalized = patches.reshape(height,width,channel*ncc_size**2)
return normalized
