def centerOfMass(img, yx, window=5):
"""
find peak by center of mass in a 2D image
img: a 2D image array
yx: (y,x) in the image
window: a window where CM calculation is performed on
return yx
"""
# prepare small image
s = N.array([window, window])
c = s / 2.
yx = N.round_(yx)
yx -= c
yi, xi = N.indices(s)
yi += yx[0]
xi += yx[1]
cc = img[yi, xi]
# calculate center of mass
yxi = N.indices(s)
yxi *= cc
yxi = yxi.T
vv = N.sum(yxi, axis=0)
vv = N.sum(vv, axis=0)
yxs = vv / float(N.sum(cc))
yxs += yx
return yxs
def centerOfMass(img, yx, window=5):
"""
find peak by center of mass in a 2D image
img: a 2D image array
yx: (y,x) in the image
window: a window where CM calculation is performed on
return yx
"""
# prepare small image
s = N.array([window,window])
c = s/2.
yx = N.round_(yx)
yx -= c
yi, xi = N.indices(s)
yi += yx[0]
xi += yx[1]
cc = img[yi,xi]
# calculate center of mass
yxi = N.indices(s)
yxi *= cc
yxi = yxi.T
vv = N.sum(yxi, axis=0)
vv = N.sum(vv, axis=0)
yxs = vv / float(N.sum(cc))
yxs += yx
return yxs
def rotateIndices2DNew(shape, rot, orig=None, dtype=N.float64):
"""
shape: 2D
rot: anti-clockwise
orig: (y, x)
return: yi, xi
"""
# FIX ME Rot is something wrong!! 081027
shape = N.asarray(shape, N.int)
if orig is None:
y, x = shape / 2.
else:
y, x = orig
print(y, x)
if not rot:
yi, xi = N.indices(shape, dtype=N.float64)
yi -= y - 0.5 # remove pix center
xi -= x - 0.5
return yi, xi
# twice as large window
# mo = N.abs(N.mod(shape, 2) + [-1,-1])
s2 = shape * 2 #+ mo # always odd for even shape, even for odd shape
yi, xi = N.indices(s2, dtype=N.float32)
mm = N.ceil(shape / 2.) #(s2 -1 - shape)//2 # offset always int
yi -= mm[0]
xi -= mm[1]
pxc = imgGeo.RotateXY((0.5, 0.5), rot) # remove pix center
yi += pxc[0]
xi += pxc[1]
y0, x0 = shape / 2. #N.ceil(shape / 2) # img center
yc = y0 - y # delta rotation center
xc = x0 - x
yi = U.trans2d(yi, None, (xc, yc, rot, 1, 0, 1))
xi = U.trans2d(xi, None, (xc, yc, rot, 1, 0, 1))
yi = U.trans2d(yi, None, (-xc, -yc, 0, 1, 0, 1))
xi = U.trans2d(xi, None, (-xc, -yc, 0, 1, 0, 1))
yi = yi.astype(dtype)
xi = xi.astype(dtype)
yi -= y
xi -= x
yi = imgFilters.cutOutCenter(yi, shape)
xi = imgFilters.cutOutCenter(xi, shape)
return yi, xi
def rotateIndices2DNew(shape, rot, orig=None, dtype=N.float64):
"""
shape: 2D
rot: anti-clockwise
orig: (y, x)
return: yi, xi
"""
# FIX ME Rot is something wrong!! 081027
shape = N.asarray(shape, N.int)
if orig is None:
y, x = shape / 2.
else:
y, x = orig
print(y,x)
if not rot:
yi,xi = N.indices(shape, dtype=N.float64)
yi -= y - 0.5 # remove pix center
xi -= x - 0.5
return yi,xi
# twice as large window
# mo = N.abs(N.mod(shape, 2) + [-1,-1])
s2 = shape * 2 #+ mo # always odd for even shape, even for odd shape
yi, xi = N.indices(s2, dtype=N.float32)
mm = N.ceil(shape / 2.)#(s2 -1 - shape)//2 # offset always int
yi -= mm[0]
xi -= mm[1]
pxc = imgGeo.RotateXY((0.5,0.5), rot) # remove pix center
yi += pxc[0]
xi += pxc[1]
y0, x0 = shape / 2. #N.ceil(shape / 2) # img center
yc = y0 - y # delta rotation center
xc = x0 - x
yi = U.trans2d(yi, None, (xc,yc,rot,1,0,1))
xi = U.trans2d(xi, None, (xc,yc,rot,1,0,1))
yi = U.trans2d(yi, None, (-xc,-yc,0,1,0,1))
xi = U.trans2d(xi, None, (-xc,-yc,0,1,0,1))
yi = yi.astype(dtype)
xi = xi.astype(dtype)
yi -= y
xi -= x
yi = imgFilters.cutOutCenter(yi, shape)
xi = imgFilters.cutOutCenter(xi, shape)
return yi, xi
def _indLD(win, y, x):
"""
return yi, xi, LD
"""
try:
len(win)
yi, xi = N.indices(int(win))
except TypeError:
yi, xi = N.indices((int(win), int(win)))
yx = N.asarray((y, x))
LD = yx - win / 2. + 0.5 # use pixel center
yi += LD[0]
xi += LD[1]
return yi, xi, LD
def _indLD(win, y, x):
"""
return yi, xi, LD
"""
try:
len(win)
yi, xi = N.indices(int(win))
except TypeError:
yi, xi = N.indices((int(win), int(win)))
yx = N.asarray((y, x))
LD = yx - win/2. + 0.5 # use pixel center
yi += LD[0]
xi += LD[1]
return yi, xi, LD
def indicesFromSlice(slicelist, dtype=N.float64):
"""
return inds, LD
"""
shape = []
LD = []
for sl in slicelist:
if isinstance(sl, slice):
shape.append(sl.stop - sl.start)
LD.append(sl.start)
inds = N.indices(shape, dtype)
for i, ld in enumerate(LD):
inds[i] += ld
return inds, LD
def indicesFromSlice(slicelist, dtype=N.float64):
"""
return inds, LD
"""
shape = []
LD = []
for sl in slicelist:
if isinstance(sl, slice):
shape.append(sl.stop - sl.start)
LD.append(sl.start)
inds = N.indices(shape, dtype)
for i, ld in enumerate(LD):
inds[i] += ld
return inds, LD
def gaussianArr2D(shape=(256,256), sigma=[2.,2.], peakVal=None, orig=None, rot=0):
"""
>1.5x faster implemetation than gaussianArrND
shape: (y,x)
sigma: scaler or [sigmay, sigmax]
orig: (y,x)
rot: scaler anti-clockwise
return N.float32
"""
shape = N.asarray(shape, N.uint)
try:
if len(sigma) == len(shape):
sy = 2*(sigma[0]*sigma[0])
sx = 2*(sigma[1]*sigma[1])
elif len(sigma) == 1:
sx = sy = 2*(sigma[0]*sigma[0])
else:
raise ValueError('sigma must be scaler or [sigmay, sigmax]')
except TypeError: # sigma scaler
sx = sy = 2*(sigma*sigma)
# print y, x
if rot:
yyi, xxi = imgFit.rotateIndices2D(shape, rot, orig, N.float32)
else:
if orig is None:
y, x = shape / 2. - 0.5 # pixel center remove
else:
y, x = N.subtract(orig, 0.5) # pixel center remove
yi, xi = N.indices(shape, dtype=N.float32)
yyi = y-yi
xxi = x-xi
k1 = -(yyi)*(yyi)/(sy) - (xxi)*(xxi)/(sx)
if peakVal:
k0 = peakVal
else:
k0 = 1. / ((sx+sy)/2. * ((2*N.pi)**0.5))
return k0 * N.exp(k1)
def gaussianArr2D(
shape=(256, 256), sigma=[2., 2.], peakVal=None, orig=None, rot=0):
"""
>1.5x faster implemetation than gaussianArrND
shape: (y,x)
sigma: scaler or [sigmay, sigmax]
orig: (y,x)
rot: scaler anti-clockwise
return N.float32
"""
shape = N.asarray(shape, N.uint)
try:
if len(sigma) == len(shape):
sy = 2 * (sigma[0] * sigma[0])
sx = 2 * (sigma[1] * sigma[1])
elif len(sigma) == 1:
sx = sy = 2 * (sigma[0] * sigma[0])
else:
raise ValueError('sigma must be scaler or [sigmay, sigmax]')
except TypeError: # sigma scaler
sx = sy = 2 * (sigma * sigma)
# print y, x
if rot:
yyi, xxi = imgFit.rotateIndices2D(shape, rot, orig, N.float32)
else:
if orig is None:
y, x = shape / 2. - 0.5 # pixel center remove
else:
y, x = N.subtract(orig, 0.5) # pixel center remove
yi, xi = N.indices(shape, dtype=N.float32)
yyi = y - yi
xxi = x - xi
k1 = -(yyi) * (yyi) / (sy) - (xxi) * (xxi) / (sx)
if peakVal:
k0 = peakVal
else:
k0 = 1. / ((sx + sy) / 2. * ((2 * N.pi)**0.5))
return k0 * N.exp(k1)
def radialaverage(data, center=None, useMaxShape=False):
"""
data: ND array
center: coordinate of center of radii
useMinShape: the output uses the maximum shape available
return 1D array
"""
if center is None:
center = N.array(data.shape) // 2
if len(center) != data.ndim:
raise ValueError(
'dimension of center (%i) does not match the dimension of data (%i)'
% (len(center), data.ndim))
zyx = N.indices((data.shape))
r = N.zeros(data.shape, N.float32)
for i, t in enumerate(zyx):
r += (t - center[i])**2
r = N.sqrt(r)
#y, x = N.indices((data.shape))
#r = N.sqrt((x - center[0])**2 + (y - center[1])**2) # distance from the center
r = r.astype(N.int)
if data.dtype.type in (N.complex64, N.complex128):
rbin = N.bincount(r.ravel(), data.real.ravel())
ibin = N.bincount(r.ravel(), data.imag.ravel())
tbin = N.empty(rbin.shape, data.dtype.type)
tbin.real = rbin
tbin.imag = ibin
else:
tbin = N.bincount(r.ravel(), data.ravel())
nr = N.bincount(r.ravel())
radialprofile = tbin / nr.astype(N.float32)
if not useMaxShape:
minShape = min(list(N.array(data.shape) - center) + list(center))
radialprofile = radialprofile[:minShape]
return radialprofile
def radialaverage(data, center=None, useMaxShape=False):
"""
data: ND array
center: coordinate of center of radii
useMinShape: the output uses the maximum shape available
return 1D array
"""
if center is None:
center = N.array(data.shape) // 2
if len(center) != data.ndim:
raise ValueError('dimension of center (%i) does not match the dimension of data (%i)' % (len(center), data.ndim))
zyx = N.indices((data.shape))
r = N.zeros(data.shape, N.float32)
for i, t in enumerate(zyx):
r += (t - center[i])**2
r = N.sqrt(r)
#y, x = N.indices((data.shape))
#r = N.sqrt((x - center[0])**2 + (y - center[1])**2) # distance from the center
r = r.astype(N.int)
if data.dtype.type in (N.complex64, N.complex128):
rbin = N.bincount(r.ravel(), data.real.ravel())
ibin = N.bincount(r.ravel(), data.imag.ravel())
tbin = N.empty(rbin.shape, data.dtype.type)
tbin.real = rbin
tbin.imag = ibin
else:
tbin = N.bincount(r.ravel(), data.ravel())
nr = N.bincount(r.ravel())
radialprofile = tbin / nr.astype(N.float32)
if not useMaxShape:
minShape = min(list(N.array(data.shape) - center) + list(center))
radialprofile = radialprofile[:minShape]
return radialprofile
def rotateIndicesND(slicelist, dtype=N.float64, rot=0, mode=2):
"""
slicelist: even shape works much better than odd shape
rot: counter-clockwise, xy-plane
mode: testing different ways of doing, (1 or 2 and the same result)
return inds, LD
"""
global INDS_DIC
shape = []
LD = []
for sl in slicelist:
if isinstance(sl, slice):
shape.append(sl.stop - sl.start)
LD.append(sl.start)
shapeTuple = tuple(shape + [rot])
if shapeTuple in INDS_DIC:
inds = INDS_DIC[shapeTuple]
else:
shape = N.array(shape)
ndim = len(shape)
odd_even = shape % 2
s2 = N.ceil(shape * (2**0.5))
if mode == 1: # everything is even
s2 = N.where(s2 % 2, s2 + 1, s2)
elif mode == 2: # even & even or odd & odd
for d, s in enumerate(shape):
if (s % 2 and not s2[d] % 2) or (not s % 2 and s2[d] % 2):
s2[d] += 1
cent = s2 / 2.
dif = (s2 - shape) / 2.
dm = dif % 1
# print s2, cent, dif, dm
slc = [Ellipsis] + [
slice(int(d),
int(d) + shape[i]) for i, d in enumerate(dif)
]
# This slice is float which shift array when cutting out!!
s2 = tuple([int(ss)
for ss in s2]) # numpy array cannot use used for slice
inds = N.indices(s2, N.float32)
ind_shape = inds.shape
nz = N.product(ind_shape[:-2])
nsec = nz / float(ndim)
if ndim > 2:
inds = N.reshape(inds, (nz, ) + ind_shape[-2:])
irs = N.empty_like(inds)
for d, ind in enumerate(inds):
idx = int(d // nsec)
c = cent[idx]
if rot and inds.ndim > 2:
U.trans2d(ind - c, irs[d], (0, 0, rot, 1, 0, 1))
irs[d] += c - dif[idx]
else:
irs[d] = ind - dif[idx]
if len(ind_shape) > 2:
irs = N.reshape(irs, ind_shape)
irs = irs[slc]
if mode == 1 and N.sometrue(dm):
inds = N.empty_like(irs)
# print 'translate', dm
for d, ind in enumerate(irs):
U.trans2d(ind, inds[d], (-dm[1], -dm[0], 0, 1, 0, 1))
else:
inds = irs
INDS_DIC[shapeTuple] = inds
r_inds = N.empty_like(inds)
for d, ld in enumerate(LD):
r_inds[d] = inds[d] + ld
return r_inds, LD
def Xcorr(a, b, highpassSigma=2.5, wiener=0.2, cutoffFreq=3,
forceSecondPeak=None, acceptOrigin=True, maskSigmaFact=1., removeY=None, removeX=None, ret=None, normalize=True, gFit=True, lap=None, win=11):
"""
returns (y,x), image
if ret is True, returns [v, yx, image]
to get yx cordinate of the image,
yx += N.divide(picture.shape, 2)
a, b: 2D array
highpassSigma: sigma value used for highpass pre-filter
wiener: wiener value used for highpass pre-filter
cutoffFreq: kill lowest frequency component from 0 to this level
forceSecondPeak: If input is n>0 (True is 1), pick up n-th peak
acceptOrigin: If None, result at origin is rejected, look for the next peak
maskSigmaFact: Modifier to remove previous peak to look for another peak
removeYX: Rremove given number of pixel high intensity lines of the Xcorr
Y: Vertical, X: Horizontal
normalize: intensity normalized
gFit: peak is fitted to 2D gaussian array, if None use center of mass
win: window for gFit
if b is a + (y,x) then, answer is (-y,-x)
"""
shapeA = N.asarray(a.shape)
shapeB = N.asarray(b.shape)
shapeM = N.max([shapeA, shapeB], axis=0)
shapeM = N.where(shapeM % 2, shapeM+1, shapeM)
center = shapeM / 2.
arrs = [a,b]
arrsS = ['a','b']
arrsF = []
for i, arr in enumerate(arrs):
if arr.dtype not in [N.float32, N.float64]:
arr = N.asarray(arr, N.float32)
# this convolution has to be done beforehand to remove 2 pixels at the edge
if lap == 'nothing':
pass
elif lap:
arr = arr_Laplace(arr, mask=2)
else:
arr = arr_sorbel(arr, mask=1)
if N.sometrue(shapeA < shapeM):
arr = paddingMed(arr, shapeM)
if normalize:
mi, ma, me, sd = U.mmms(arr)
arr = (arr - me) / sd
if i ==1:
arr = F.shift(arr)
af = F.rfft(arr)
af = highPassF(af, highpassSigma, wiener, cutoffFreq)
arrsF.append(af)
# start cross correlation
af, bf = arrsF
bf = bf.conjugate()
cf = af * bf
# go back to space domain
c = F.irfft(cf)
# c = _changeOrigin(cr)
# removing lines
if removeX:
yi, xi = N.indices((removeX, shapeM[-1]))#sx))
yi += center[-2] - removeX/2.#sy/2 - removeX/2
c[yi, xi] = 0
if removeY:
yi, xi = N.indices((shapeM[-2], removeY))#sy, removeY))
xi += center[-1] - removeY/2.#sx/2 - removeY/2
c[yi, xi] = 0
# find the first peak
if gFit:
v, yx, s = findMaxWithGFit(c, win=win)#, window=win, gFit=gFit)
if v == 0:
v, yx, s = findMaxWithGFit(c, win=win+2)#, window=win+2, gFit=gFit)
if v == 0:
v = U.findMax(c)[0]
yx = N.add(yx, 0.5)
#yx += 0.5
else:
vzyx = U.findMax(c)
v = vzyx[0]
yx = vzyx[-2:]
s = 2.5
yx -= center
if N.alltrue(N.abs(yx) < 1.0) and not acceptOrigin:
forceSecondPeak = True
# forceSecondPeak:
if not forceSecondPeak:
forceSecondPeak = 0
for i in range(int(forceSecondPeak)):
print('%i peak was removed' % (i+1)) #, sigma: %.2f' % (i+1, s)
yx += center
g = gaussianArr2D(c.shape, sigma=s/maskSigmaFact, peakVal=v, orig=yx)
c = c - g
#c = mask_gaussian(c, yx[0], yx[1], v, s)
if gFit:
v, yx, s = findMaxWithGFit(c, win=win)#, window=win, gFit=gFit)
if v == 0:
v, yx, s = findMaxWithGFit(c, win=win+2)#, window=win+2, gFit=gFit)
if v == 0:
v = U.findMax(c)[0]
yx -= (center - 0.5)
else:
vzyx = U.findMax(c)
v = vzyx[0]
if not gFit:
yx = centerOfMass(c, vzyx[-2:]) - center
if lap is not 'nothing':
c = paddingValue(c, shapeM+2)
if ret == 2:
return yx, af, bf.conjugate()
elif ret:
return v, yx, c
else:
return yx, c
def Xcorr(a,
b,
highpassSigma=2.5,
wiener=0.2,
cutoffFreq=3,
forceSecondPeak=None,
acceptOrigin=True,
maskSigmaFact=1.,
removeY=None,
removeX=None,
ret=None,
normalize=True,
gFit=True,
lap=None,
win=11):
"""
returns (y,x), image
if ret is True, returns [v, yx, image]
to get yx cordinate of the image,
yx += N.divide(picture.shape, 2)
a, b: 2D array
highpassSigma: sigma value used for highpass pre-filter
wiener: wiener value used for highpass pre-filter
cutoffFreq: kill lowest frequency component from 0 to this level
forceSecondPeak: If input is n>0 (True is 1), pick up n-th peak
acceptOrigin: If None, result at origin is rejected, look for the next peak
maskSigmaFact: Modifier to remove previous peak to look for another peak
removeYX: Rremove given number of pixel high intensity lines of the Xcorr
Y: Vertical, X: Horizontal
normalize: intensity normalized
gFit: peak is fitted to 2D gaussian array, if None use center of mass
win: window for gFit
if b is a + (y,x) then, answer is (-y,-x)
"""
shapeA = N.asarray(a.shape)
shapeB = N.asarray(b.shape)
shapeM = N.max([shapeA, shapeB], axis=0)
shapeM = N.where(shapeM % 2, shapeM + 1, shapeM)
center = shapeM / 2.
arrs = [a, b]
arrsS = ['a', 'b']
arrsF = []
for i, arr in enumerate(arrs):
if arr.dtype not in [N.float32, N.float64]:
arr = N.asarray(arr, N.float32)
# this convolution has to be done beforehand to remove 2 pixels at the edge
if lap == 'nothing':
pass
elif lap:
arr = arr_Laplace(arr, mask=2)
else:
arr = arr_sorbel(arr, mask=1)
if N.sometrue(shapeA < shapeM):
arr = paddingMed(arr, shapeM)
if normalize:
mi, ma, me, sd = U.mmms(arr)
arr = (arr - me) / sd
if i == 1:
arr = F.shift(arr)
af = F.rfft(arr)
af = highPassF(af, highpassSigma, wiener, cutoffFreq)
arrsF.append(af)
# start cross correlation
af, bf = arrsF
bf = bf.conjugate()
cf = af * bf
# go back to space domain
c = F.irfft(cf)
# c = _changeOrigin(cr)
# removing lines
if removeX:
yi, xi = N.indices((removeX, shapeM[-1])) #sx))
yi += center[-2] - removeX / 2. #sy/2 - removeX/2
c[yi, xi] = 0
if removeY:
yi, xi = N.indices((shapeM[-2], removeY)) #sy, removeY))
xi += center[-1] - removeY / 2. #sx/2 - removeY/2
c[yi, xi] = 0
# find the first peak
if gFit:
v, yx, s = findMaxWithGFit(c, win=win) #, window=win, gFit=gFit)
if v == 0:
v, yx, s = findMaxWithGFit(c, win=win +
2) #, window=win+2, gFit=gFit)
if v == 0:
v = U.findMax(c)[0]
yx = N.add(yx, 0.5)
#yx += 0.5
else:
vzyx = U.findMax(c)
v = vzyx[0]
yx = vzyx[-2:]
s = 2.5
yx -= center
if N.alltrue(N.abs(yx) < 1.0) and not acceptOrigin:
forceSecondPeak = True
# forceSecondPeak:
if not forceSecondPeak:
forceSecondPeak = 0
for i in range(int(forceSecondPeak)):
print('%i peak was removed' % (i + 1)) #, sigma: %.2f' % (i+1, s)
yx += center
g = gaussianArr2D(c.shape, sigma=s / maskSigmaFact, peakVal=v, orig=yx)
c = c - g
#c = mask_gaussian(c, yx[0], yx[1], v, s)
if gFit:
v, yx, s = findMaxWithGFit(c, win=win) #, window=win, gFit=gFit)
if v == 0:
v, yx, s = findMaxWithGFit(c, win=win +
2) #, window=win+2, gFit=gFit)
if v == 0:
v = U.findMax(c)[0]
yx -= (center - 0.5)
else:
vzyx = U.findMax(c)
v = vzyx[0]
if not gFit:
yx = centerOfMass(c, vzyx[-2:]) - center
if lap is not 'nothing':
c = paddingValue(c, shapeM + 2)
if ret == 2:
return yx, af, bf.conjugate()
elif ret:
return v, yx, c
else:
return yx, c
def rotateIndicesND(slicelist, dtype=N.float64, rot=0, mode=2):
"""
slicelist: even shape works much better than odd shape
rot: counter-clockwise, xy-plane
mode: testing different ways of doing, (1 or 2 and the same result)
return inds, LD
"""
global INDS_DIC
shape = []
LD = []
for sl in slicelist:
if isinstance(sl, slice):
shape.append(sl.stop - sl.start)
LD.append(sl.start)
shapeTuple = tuple(shape+[rot])
if shapeTuple in INDS_DIC:
inds = INDS_DIC[shapeTuple]
else:
shape = N.array(shape)
ndim = len(shape)
odd_even = shape % 2
s2 = N.ceil(shape * (2**0.5))
if mode == 1: # everything is even
s2 = N.where(s2 % 2, s2 + 1, s2)
elif mode == 2: # even & even or odd & odd
for d, s in enumerate(shape):
if (s % 2 and not s2[d] % 2) or (not s % 2 and s2[d] % 2):
s2[d] += 1
cent = s2 / 2.
dif = (s2 - shape) / 2.
dm = dif % 1
# print s2, cent, dif, dm
slc = [Ellipsis] + [slice(int(d), int(d)+shape[i]) for i, d in enumerate(dif)]
# This slice is float which shift array when cutting out!!
s2 = tuple([int(ss) for ss in s2]) # numpy array cannot use used for slice
inds = N.indices(s2, N.float32)
ind_shape = inds.shape
nz = N.product(ind_shape[:-2])
nsec = nz / float(ndim)
if ndim > 2:
inds = N.reshape(inds, (nz,)+ind_shape[-2:])
irs = N.empty_like(inds)
for d, ind in enumerate(inds):
idx = int(d//nsec)
c = cent[idx]
if rot and inds.ndim > 2:
U.trans2d(ind - c, irs[d], (0,0,rot,1,0,1))
irs[d] += c - dif[idx]
else:
irs[d] = ind - dif[idx]
if len(ind_shape) > 2:
irs = N.reshape(irs, ind_shape)
irs = irs[slc]
if mode == 1 and N.sometrue(dm):
inds = N.empty_like(irs)
# print 'translate', dm
for d, ind in enumerate(irs):
U.trans2d(ind, inds[d], (-dm[1], -dm[0], 0, 1, 0, 1))
else:
inds = irs
INDS_DIC[shapeTuple] = inds
r_inds = N.empty_like(inds)
for d, ld in enumerate(LD):
r_inds[d] = inds[d] + ld
return r_inds, LD
