def main():
gdal.AllRegister()
path = auxil.select_directory('Choose working directory')
#path = arcpy.GetParameterAsText(0)
if path:
os.chdir(path)
file1 = auxil.select_infile(title='Choose first image')
#file1 = arcpy.GetParameterAsText(1)
if file1:
inDataset1 = gdal.Open(file1, GA_ReadOnly)
cols = inDataset1.RasterXSize
rows = inDataset1.RasterYSize
bands = inDataset1.RasterCount
else:
return
pos1 = auxil.select_pos(bands)
if not pos1:
return
dims = auxil.select_dims([0, 0, cols, rows])
if dims:
x10, y10, cols1, rows1 = dims
else:
return
# second image
file2 = auxil.select_infile(title='Choose second image')
#file2 = arcpy.GetParameterAsText(2)
if file2:
inDataset2 = gdal.Open(file2, GA_ReadOnly)
cols = inDataset2.RasterXSize
rows = inDataset2.RasterYSize
bands = inDataset2.RasterCount
else:
return
pos2 = auxil.select_pos(bands)
if not pos2:
return
dims = auxil.select_dims([0, 0, cols, rows])
if dims:
x20, y20, cols, rows = dims
else:
return
# penalization
lam = auxil.select_penal(0.0)
if lam is None:
return
# outfile
outfile, fmt = auxil.select_outfilefmt()
if not outfile:
return
# match dimensions
bands = len(pos2)
if (rows1 != rows) or (cols1 != cols) or (len(pos1) != bands):
sys.stderr.write("Size mismatch")
sys.exit(1)
print('=========================')
print(' iMAD')
print('=========================')
print(time.asctime())
print('time1: ' + file1)
print('time2: ' + file2)
print('Delta [canonical correlations]')
# iteration of MAD
cpm = auxil.Cpm(2 * bands)
delta = 1.0
oldrho = np.zeros(bands)
itr = 0
tile = np.zeros((cols, 2 * bands))
sigMADs = 0
means1 = 0
means2 = 0
A = 0
B = 0
rasterBands1 = []
rasterBands2 = []
for b in pos1:
rasterBands1.append(inDataset1.GetRasterBand(b))
for b in pos2:
rasterBands2.append(inDataset2.GetRasterBand(b))
while (delta > 0.001) and (itr < 100):
# spectral tiling for statistics
for row in range(rows):
for k in range(bands):
tile[:,
k] = rasterBands1[k].ReadAsArray(x10, y10 + row, cols, 1)
tile[:, bands + k] = rasterBands2[k].ReadAsArray(
x20, y20 + row, cols, 1)
# eliminate no-data pixels (assuming all zeroes)
tst1 = np.sum(tile[:, 0:bands], axis=1)
tst2 = np.sum(tile[:, bands::], axis=1)
idx1 = set(np.where((tst1 > 0))[0])
idx2 = set(np.where((tst2 > 0))[0])
idx = list(idx1.intersection(idx2))
if itr > 0:
mads = np.asarray((tile[:, 0:bands] - means1) * A -
(tile[:, bands::] - means2) * B)
chisqr = np.sum((mads / sigMADs)**2, axis=1)
wts = 1 - stats.chi2.cdf(chisqr, [bands])
cpm.update(tile[idx, :], wts[idx])
else:
cpm.update(tile[idx, :])
# weighted covariance matrices and means
S = cpm.covariance()
means = cpm.means()
# reset prov means object
cpm.__init__(2 * bands)
s11 = S[0:bands, 0:bands]
s11 = (1 - lam) * s11 + lam * np.eye(bands)
s22 = S[bands:, bands:]
s22 = (1 - lam) * s22 + lam * np.eye(bands)
s12 = S[0:bands, bands:]
s21 = S[bands:, 0:bands]
c1 = s12 * linalg.inv(s22) * s21
b1 = s11
c2 = s21 * linalg.inv(s11) * s12
b2 = s22
# solution of generalized eigenproblems
if bands > 1:
mu2a, A = auxil.geneiv(c1, b1)
mu2b, B = auxil.geneiv(c2, b2)
# sort a
idx = np.argsort(mu2a)
A = A[:, idx]
# sort b
idx = np.argsort(mu2b)
B = B[:, idx]
mu2 = mu2b[idx]
else:
mu2 = c1 / b1
A = 1 / np.sqrt(b1)
B = 1 / np.sqrt(b2)
# canonical correlations
mu = np.sqrt(mu2)
a2 = np.diag(A.T * A)
b2 = np.diag(B.T * B)
sigma = np.sqrt((2 - lam * (a2 + b2)) / (1 - lam) - 2 * mu)
rho = mu * (1 - lam) / np.sqrt((1 - lam * a2) * (1 - lam * b2))
# stopping criterion
delta = max(abs(rho - oldrho))
print(delta, rho)
oldrho = rho
# tile the sigmas and means
sigMADs = np.tile(sigma, (cols, 1))
means1 = np.tile(means[0:bands], (cols, 1))
means2 = np.tile(means[bands::], (cols, 1))
# ensure sum of positive correlations between X and U is positive
D = np.diag(1 / np.sqrt(np.diag(s11)))
s = np.ravel(np.sum(D * s11 * A, axis=0))
A = A * np.diag(s / np.abs(s))
# ensure positive correlation between each pair of canonical variates
cov = np.diag(A.T * s12 * B)
B = B * np.diag(cov / np.abs(cov))
itr += 1
# write results to disk
driver = gdal.GetDriverByName(fmt)
outDataset = driver.Create(outfile, cols, rows, bands + 1, GDT_Float32)
projection = inDataset1.GetProjection()
geotransform = inDataset1.GetGeoTransform()
if geotransform is not None:
gt = list(geotransform)
gt[0] = gt[0] + x10 * gt[1]
gt[3] = gt[3] + y10 * gt[5]
outDataset.SetGeoTransform(tuple(gt))
if projection is not None:
outDataset.SetProjection(projection)
outBands = []
for k in range(bands + 1):
outBands.append(outDataset.GetRasterBand(k + 1))
for row in range(rows):
for k in range(bands):
tile[:, k] = rasterBands1[k].ReadAsArray(x10, y10 + row, cols, 1)
tile[:, bands + k] = rasterBands2[k].ReadAsArray(
x20, y20 + row, cols, 1)
mads = np.asarray((tile[:, 0:bands] - means1) * A -
(tile[:, bands::] - means2) * B)
chisqr = np.sum((mads / sigMADs)**2, axis=1)
for k in range(bands):
outBands[k].WriteArray(np.reshape(mads[:, k], (1, cols)), 0, row)
outBands[bands].WriteArray(np.reshape(chisqr, (1, cols)), 0, row)
for outBand in outBands:
outBand.FlushCache()
outDataset = None
inDataset1 = None
inDataset2 = None
print('result written to: ' + outfile)
print('--------done---------------------')
def main():
usage = '''
Usage:
-----------------------------------------------------
python %s [-h] [-n] [-i max iterations] [-p bandPositions]
[-d spatialDimensions] filename1 filename2
-----------------------------------------------------
bandPositions and spatialDimensions are lists,
e.g., -p [1,2,3] -d [0,0,400,400]
-n stops any graphics output
-----------------------------------------------------
The output MAD variate file is has the same format
as filename1 and is named
path/MAD(filebasename1-filebasename2).ext1
where filename1 = path/filebasename1.ext1
filename2 = path/filebasename2.ext2
For ENVI files, ext1 or ext2 is the empty string.
-----------------------------------------------------''' % sys.argv[0]
options, args = getopt.getopt(sys.argv[1:], 'hnp:i:d:')
pos = None
dims = None
niter = 50
graphics = True
for option, value in options:
if option == '-h':
print usage
return
elif option == '-n':
graphics = False
elif option == '-p':
pos = eval(value)
elif option == '-d':
dims = eval(value)
elif option == '-i':
niter = eval(value)
if len(args) != 2:
print 'Incorrect number of arguments'
print usage
return
gdal.AllRegister()
fn1 = args[0]
fn2 = args[1]
path = os.path.dirname(fn1)
basename1 = os.path.basename(fn1)
root1, ext1 = os.path.splitext(basename1)
basename2 = os.path.basename(fn2)
root2, ext2 = os.path.splitext(basename2)
outfn = path + '/' + 'MAD(%s-%s)%s' % (root1, basename2, ext1)
inDataset1 = gdal.Open(fn1, GA_ReadOnly)
inDataset2 = gdal.Open(fn2, GA_ReadOnly)
try:
cols = inDataset1.RasterXSize
rows = inDataset1.RasterYSize
bands = inDataset1.RasterCount
cols2 = inDataset2.RasterXSize
rows2 = inDataset2.RasterYSize
bands2 = inDataset2.RasterCount
except Exception as e:
print 'Error: %s --Images could not be read.' % e
sys.exit(1)
if bands != bands2:
sys.stderr.write("Size mismatch")
sys.exit(1)
if pos is None:
pos = range(1, bands + 1)
else:
bands = len(pos)
if dims is None:
x0 = 0
y0 = 0
else:
x0, y0, cols, rows = dims
# if second image is warped, assume it has same dimensions as dims
if root2.find('_warp') != -1:
x2 = 0
y2 = 0
else:
x2 = x0
y2 = y0
print '------------IRMAD -------------'
print time.asctime()
print 'time1: ' + fn1
print 'time2: ' + fn2
start = time.time()
# iteration of MAD
cpm = auxil.Cpm(2 * bands)
delta = 1.0
oldrho = np.zeros(bands)
itr = 0
tile = np.zeros((cols, 2 * bands))
sigMADs = 0
means1 = 0
means2 = 0
A = 0
B = 0
rasterBands1 = []
rasterBands2 = []
rhos = np.zeros((niter, bands))
for b in pos:
rasterBands1.append(inDataset1.GetRasterBand(b))
for b in pos:
rasterBands2.append(inDataset2.GetRasterBand(b))
while (delta > 0.001) and (itr < niter):
# spectral tiling for statistics
for row in range(rows):
for k in range(bands):
tile[:, k] = rasterBands1[k].ReadAsArray(x0, y0 + row, cols, 1)
tile[:, bands + k] = rasterBands2[k].ReadAsArray(
x2, y2 + row, cols, 1)
# eliminate no-data pixels
tile = np.nan_to_num(tile)
tst1 = np.sum(tile[:, 0:bands], axis=1)
tst2 = np.sum(tile[:, bands::], axis=1)
idx1 = set(np.where((tst1 != 0))[0])
idx2 = set(np.where((tst2 != 0))[0])
idx = list(idx1.intersection(idx2))
if itr > 0:
mads = np.asarray((tile[:, 0:bands] - means1) * A -
(tile[:, bands::] - means2) * B)
chisqr = np.sum((mads / sigMADs)**2, axis=1)
wts = 1 - stats.chi2.cdf(chisqr, [bands])
cpm.update(tile[idx, :], wts[idx])
else:
cpm.update(tile[idx, :])
# weighted covariance matrices and means
S = cpm.covariance()
means = cpm.means()
# reset prov means object
cpm.__init__(2 * bands)
s11 = S[0:bands, 0:bands]
s22 = S[bands:, bands:]
s12 = S[0:bands, bands:]
s21 = S[bands:, 0:bands]
c1 = s12 * linalg.inv(s22) * s21
b1 = s11
c2 = s21 * linalg.inv(s11) * s12
b2 = s22
# solution of generalized eigenproblems
if bands > 1:
mu2a, A = auxil.geneiv(c1, b1)
mu2b, B = auxil.geneiv(c2, b2)
# sort a
idx = np.argsort(mu2a)
A = A[:, idx]
# sort b
idx = np.argsort(mu2b)
B = B[:, idx]
mu2 = mu2b[idx]
else:
mu2 = c1 / b1
A = 1 / np.sqrt(b1)
B = 1 / np.sqrt(b2)
# canonical correlations
rho = np.sqrt(mu2)
b2 = np.diag(B.T * B)
sigma = np.sqrt(2 * (1 - rho))
# stopping criterion
delta = max(abs(rho - oldrho))
rhos[itr, :] = rho
oldrho = rho
# tile the sigmas and means
sigMADs = np.tile(sigma, (cols, 1))
means1 = np.tile(means[0:bands], (cols, 1))
means2 = np.tile(means[bands::], (cols, 1))
# ensure sum of positive correlations between X and U is positive
D = np.diag(1 / np.sqrt(np.diag(s11)))
s = np.ravel(np.sum(D * s11 * A, axis=0))
A = A * np.diag(s / np.abs(s))
# ensure positive correlation between each pair of canonical variates
cov = np.diag(A.T * s12 * B)
B = B * np.diag(cov / np.abs(cov))
itr += 1
print 'rho: %s' % str(rho)
# write results to disk
driver = inDataset1.GetDriver()
outDataset = driver.Create(outfn, cols, rows, bands + 1, GDT_Float32)
projection = inDataset1.GetProjection()
geotransform = inDataset1.GetGeoTransform()
if geotransform is not None:
gt = list(geotransform)
gt[0] = gt[0] + x0 * gt[1]
gt[3] = gt[3] + y0 * gt[5]
outDataset.SetGeoTransform(tuple(gt))
if projection is not None:
outDataset.SetProjection(projection)
outBands = []
for k in range(bands + 1):
outBands.append(outDataset.GetRasterBand(k + 1))
for row in range(rows):
for k in range(bands):
tile[:, k] = rasterBands1[k].ReadAsArray(x0, y0 + row, cols, 1)
tile[:, bands + k] = rasterBands2[k].ReadAsArray(
x2, y2 + row, cols, 1)
mads = np.asarray((tile[:, 0:bands] - means1) * A -
(tile[:, bands::] - means2) * B)
chisqr = np.sum((mads / sigMADs)**2, axis=1)
for k in range(bands):
outBands[k].WriteArray(np.reshape(mads[:, k], (1, cols)), 0, row)
outBands[bands].WriteArray(np.reshape(chisqr, (1, cols)), 0, row)
for outBand in outBands:
outBand.FlushCache()
outDataset = None
inDataset1 = None
inDataset2 = None
print 'result written to: ' + outfn
print 'elapsed time: %s' % str(time.time() - start)
x = np.array(range(itr - 1))
if graphics:
plt.plot(x, rhos[0:itr - 1, :])
plt.title('Canonical correlations')
plt.show()
def main():
gdal.AllRegister()
path = auxil.select_directory('Choose working directory')
if path:
os.chdir(path)
# first image
file1 = auxil.select_infile(title='Choose first image')
if file1:
inDataset1 = gdal.Open(file1,GA_ReadOnly)
cols = inDataset1.RasterXSize
rows = inDataset1.RasterYSize
bands = inDataset1.RasterCount
else:
return
pos1 = auxil.select_pos(bands)
if not pos1:
return
dims = auxil.select_dims([0,0,cols,rows])
if dims:
x10,y10,cols1,rows1 = dims
else:
return
# second image
file2 = auxil.select_infile(title='Choose second image')
if file2:
inDataset2 = gdal.Open(file2,GA_ReadOnly)
cols = inDataset2.RasterXSize
rows = inDataset2.RasterYSize
bands = inDataset2.RasterCount
else:
return
pos2 = auxil.select_pos(bands)
if not pos2:
return
dims=auxil.select_dims([0,0,cols,rows])
if dims:
x20,y20,cols,rows = dims
else:
return
# penalization
lam = auxil.select_penal(0.0)
if lam is None:
return
# outfile
outfile, fmt = auxil.select_outfilefmt()
if not outfile:
return
# match dimensions
bands = len(pos2)
if (rows1 != rows) or (cols1 != cols) or (len(pos1) != bands):
sys.stderr.write("Size mismatch")
sys.exit(1)
print '========================='
print ' iMAD'
print '========================='
print time.asctime()
print 'time1: '+file1
print 'time2: '+file2
print 'Delta [canonical correlations]'
# iteration of MAD
cpm = auxil.Cpm(2*bands)
delta = 1.0
oldrho = np.zeros(bands)
itr = 0
tile = np.zeros((cols,2*bands))
sigMADs = 0
means1 = 0
means2 = 0
A = 0
B = 0
rasterBands1 = []
rasterBands2 = []
for b in pos1:
rasterBands1.append(inDataset1.GetRasterBand(b))
for b in pos2:
rasterBands2.append(inDataset2.GetRasterBand(b))
while (delta > 0.001) and (itr < 100):
# spectral tiling for statistics
for row in range(rows):
for k in range(bands):
tile[:,k] = rasterBands1[k].ReadAsArray(x10,y10+row,cols,1)
tile[:,bands+k] = rasterBands2[k].ReadAsArray(x20,y20+row,cols,1)
# eliminate no-data pixels (assuming all zeroes)
tst1 = np.sum(tile[:,0:bands],axis=1)
tst2 = np.sum(tile[:,bands::],axis=1)
idx1 = set(np.where( (tst1>0) )[0])
idx2 = set(np.where( (tst2>0) )[0])
idx = list(idx1.intersection(idx2))
if itr>0:
mads = np.asarray((tile[:,0:bands]-means1)*A - (tile[:,bands::]-means2)*B)
chisqr = np.sum((mads/sigMADs)**2,axis=1)
wts = 1-stats.chi2.cdf(chisqr,[bands])
cpm.update(tile[idx,:],wts[idx])
else:
cpm.update(tile[idx,:])
# weighted covariance matrices and means
S = cpm.covariance()
means = cpm.means()
# reset prov means object
cpm.__init__(2*bands)
s11 = S[0:bands,0:bands]
s11 = (1-lam)*s11 + lam*np.eye(bands)
s22 = S[bands:,bands:]
s22 = (1-lam)*s22 + lam*np.eye(bands)
s12 = S[0:bands,bands:]
s21 = S[bands:,0:bands]
c1 = s12*linalg.inv(s22)*s21
b1 = s11
c2 = s21*linalg.inv(s11)*s12
b2 = s22
# solution of generalized eigenproblems
if bands>1:
mu2a,A = auxil.geneiv(c1,b1)
mu2b,B = auxil.geneiv(c2,b2)
# sort a
idx = np.argsort(mu2a)
A = A[:,idx]
# sort b
idx = np.argsort(mu2b)
B = B[:,idx]
mu2 = mu2b[idx]
else:
mu2 = c1/b1
A = 1/np.sqrt(b1)
B = 1/np.sqrt(b2)
# canonical correlations
mu = np.sqrt(mu2)
a2 = np.diag(A.T*A)
b2 = np.diag(B.T*B)
sigma = np.sqrt( (2-lam*(a2+b2))/(1-lam)-2*mu )
rho=mu*(1-lam)/np.sqrt( (1-lam*a2)*(1-lam*b2) )
# stopping criterion
delta = max(abs(rho-oldrho))
print delta,rho
oldrho = rho
# tile the sigmas and means
sigMADs = np.tile(sigma,(cols,1))
means1 = np.tile(means[0:bands],(cols,1))
means2 = np.tile(means[bands::],(cols,1))
# ensure sum of positive correlations between X and U is positive
D = np.diag(1/np.sqrt(np.diag(s11)))
s = np.ravel(np.sum(D*s11*A,axis=0))
A = A*np.diag(s/np.abs(s))
# ensure positive correlation between each pair of canonical variates
cov = np.diag(A.T*s12*B)
B = B*np.diag(cov/np.abs(cov))
itr += 1
# write results to disk
driver = gdal.GetDriverByName(fmt)
outDataset = driver.Create(outfile,cols,rows,bands+1,GDT_Float32)
projection = inDataset1.GetProjection()
geotransform = inDataset1.GetGeoTransform()
if geotransform is not None:
gt = list(geotransform)
gt[0] = gt[0] + x10*gt[1]
gt[3] = gt[3] + y10*gt[5]
outDataset.SetGeoTransform(tuple(gt))
if projection is not None:
outDataset.SetProjection(projection)
outBands = []
for k in range(bands+1):
outBands.append(outDataset.GetRasterBand(k+1))
for row in range(rows):
for k in range(bands):
tile[:,k] = rasterBands1[k].ReadAsArray(x10,y10+row,cols,1)
tile[:,bands+k] = rasterBands2[k].ReadAsArray(x20,y20+row,cols,1)
mads = np.asarray((tile[:,0:bands]-means1)*A - (tile[:,bands::]-means2)*B)
chisqr = np.sum((mads/sigMADs)**2,axis=1)
for k in range(bands):
outBands[k].WriteArray(np.reshape(mads[:,k],(1,cols)),0,row)
outBands[bands].WriteArray(np.reshape(chisqr,(1,cols)),0,row)
for outBand in outBands:
outBand.FlushCache()
outDataset = None
inDataset1 = None
inDataset2 = None
print 'result written to: '+outfile
print '--------done---------------------'
def imad(current, prev):
import numpy as np
from numpy import linalg
import auxil.auxil as auxil
image1 = ee.Image(ee.Dictionary(current).get('image1'))
image2 = ee.Image(ee.Dictionary(current).get('image2'))
weights = ee.Image(ee.Dictionary(prev).get('weights'))
region = image1.geometry()
bNames1 = image1.bandNames()
bNames2 = image2.bandNames()
nBands = len(bNames1.getInfo())
centeredImage1 = centerw(image1, weights)
centeredImage2 = centerw(image2, weights)
centeredImage = ee.Image.cat(centeredImage1, centeredImage2)
covarArray = covw(centeredImage, weights)
# -------- cannot be iterated!!! --------
S = np.mat(covarArray.getInfo())
# ---------------------------------------
s11 = S[0:nBands, 0:nBands]
s22 = S[nBands:, nBands:]
s12 = S[0:nBands, nBands:]
s21 = S[nBands:, 0:nBands]
c1 = s12 * linalg.inv(s22) * s21
b1 = s11
c2 = s21 * linalg.inv(s11) * s12
b2 = s22
# solution of generalized eigenproblems
mu2a, A = auxil.geneiv(c1, b1)
mu2b, B = auxil.geneiv(c2, b2)
# sort a
idx = np.argsort(mu2a)
A = A[:, idx]
# sort b
idx = np.argsort(mu2b)
B = B[:, idx]
mu2 = mu2b[idx]
# canonical correlations and MAD variances
rho = np.sqrt(mu2)
print rho
s2 = (2 * (1 - rho)).tolist()
variance = ee.Image.constant(s2)
# ensure sum of positive correlations between X and U is positive
tmp = np.diag(1 / np.sqrt(np.diag(s11)))
s = np.ravel(np.sum(tmp * s11 * A, axis=0))
A = A * np.diag(s / np.abs(s))
# ensure positive correlation
tmp = np.diag(A.T * s12 * B)
B = B * np.diag(tmp / abs(tmp))
# canonical and MAD variates
Arr = ee.Array(A.tolist())
Brr = ee.Array(B.tolist())
centeredImage1Array = centeredImage1.toArray().toArray(1)
centeredImage2Array = centeredImage2.toArray().toArray(1)
U = ee.Image(Arr).matrixMultiply(centeredImage1Array) \
.arrayProject([0]) \
.arrayFlatten([bNames1])
V = ee.Image(Brr).matrixMultiply(centeredImage2Array) \
.arrayProject([0]) \
.arrayFlatten([bNames2])
MAD = U.subtract(V)
# chi square image
chi2 = (MAD.pow(2)) \
.divide(variance) \
.reduce(ee.Reducer.sum()) \
.clip(region)
# no-change probability
weights = ee.Image.constant(1.0).subtract(chi2cdf(chi2, 6.0))
return ee.Dictionary({'weights': weights, 'MAD': MAD})
def main():
usage = '''
Usage:
-----------------------------------------------------
python %s [-h] [-n] [-i max iterations] [-p bandPositions]
[-d spatialDimensions] filename1 filename2
-----------------------------------------------------
bandPositions and spatialDimensions are lists,
e.g., -p [1,2,3] -d [0,0,400,400]
-n stops any graphics output
-----------------------------------------------------
The output MAD variate file is has the same format
as filename1 and is named
path/MAD(filebasename1-filebasename2).ext1
where filename1 = path/filebasename1.ext1
filename2 = path/filebasename2.ext2
For ENVI files, ext1 or ext2 is the empty string.
-----------------------------------------------------''' %sys.argv[0]
options, args = getopt.getopt(sys.argv[1:],'hnp:i:d:')
pos = None
dims = None
niter = 50
graphics = True
for option, value in options:
if option == '-h':
print usage
return
elif option == '-n':
graphics = False
elif option == '-p':
pos = eval(value)
elif option == '-d':
dims = eval(value)
elif option == '-i':
niter = eval(value)
if len(args) != 2:
print 'Incorrect number of arguments'
print usage
return
gdal.AllRegister()
fn1 = args[0]
fn2 = args[1]
path = os.path.dirname(fn1)
basename1 = os.path.basename(fn1)
root1, ext1 = os.path.splitext(basename1)
basename2 = os.path.basename(fn2)
root2, ext2 = os.path.splitext(basename2)
outfn = path + '/' + 'MAD(%s-%s)%s'%(root1,basename2,ext1)
inDataset1 = gdal.Open(fn1,GA_ReadOnly)
inDataset2 = gdal.Open(fn2,GA_ReadOnly)
try:
cols = inDataset1.RasterXSize
rows = inDataset1.RasterYSize
bands = inDataset1.RasterCount
cols2 = inDataset2.RasterXSize
rows2 = inDataset2.RasterYSize
bands2 = inDataset2.RasterCount
except Exception as e:
print 'Error: %s --Images could not be read.'%e
sys.exit(1)
if bands != bands2:
sys.stderr.write("Size mismatch")
sys.exit(1)
if pos is None:
pos = range(1,bands+1)
else:
bands = len(pos)
if dims is None:
x0 = 0
y0 = 0
else:
x0,y0,cols,rows = dims
# if second image is warped, assume it has same dimensions as dims
if root2.find('_warp') != -1:
x2 = 0
y2 = 0
else:
x2 = x0
y2 = y0
print '------------IRMAD -------------'
print time.asctime()
print 'time1: '+fn1
print 'time2: '+fn2
start = time.time()
# iteration of MAD
cpm = auxil.Cpm(2*bands)
delta = 1.0
oldrho = np.zeros(bands)
itr = 0
tile = np.zeros((cols,2*bands))
sigMADs = 0
means1 = 0
means2 = 0
A = 0
B = 0
rasterBands1 = []
rasterBands2 = []
rhos = np.zeros((niter,bands))
for b in pos:
rasterBands1.append(inDataset1.GetRasterBand(b))
for b in pos:
rasterBands2.append(inDataset2.GetRasterBand(b))
while (delta > 0.001) and (itr < niter):
# spectral tiling for statistics
for row in range(rows):
for k in range(bands):
tile[:,k] = rasterBands1[k].ReadAsArray(x0,y0+row,cols,1)
tile[:,bands+k] = rasterBands2[k].ReadAsArray(x2,y2+row,cols,1)
# eliminate no-data pixels
tile = np.nan_to_num(tile)
tst1 = np.sum(tile[:,0:bands],axis=1)
tst2 = np.sum(tile[:,bands::],axis=1)
idx1 = set(np.where( (tst1>0) )[0])
idx2 = set(np.where( (tst2>0) )[0])
idx = list(idx1.intersection(idx2))
if itr>0:
mads = np.asarray((tile[:,0:bands]-means1)*A - (tile[:,bands::]-means2)*B)
chisqr = np.sum((mads/sigMADs)**2,axis=1)
wts = 1-stats.chi2.cdf(chisqr,[bands])
cpm.update(tile[idx,:],wts[idx])
else:
cpm.update(tile[idx,:])
# weighted covariance matrices and means
S = cpm.covariance()
means = cpm.means()
# reset prov means object
cpm.__init__(2*bands)
s11 = S[0:bands,0:bands]
s22 = S[bands:,bands:]
s12 = S[0:bands,bands:]
s21 = S[bands:,0:bands]
c1 = s12*linalg.inv(s22)*s21
b1 = s11
c2 = s21*linalg.inv(s11)*s12
b2 = s22
# solution of generalized eigenproblems
if bands>1:
mu2a,A = auxil.geneiv(c1,b1)
mu2b,B = auxil.geneiv(c2,b2)
# sort a
idx = np.argsort(mu2a)
A = A[:,idx]
# sort b
idx = np.argsort(mu2b)
B = B[:,idx]
mu2 = mu2b[idx]
else:
mu2 = c1/b1
A = 1/np.sqrt(b1)
B = 1/np.sqrt(b2)
# canonical correlations
rho = np.sqrt(mu2)
b2 = np.diag(B.T*B)
sigma = np.sqrt( 2*(1-rho ) )
# stopping criterion
delta = max(abs(rho-oldrho))
rhos[itr,:] = rho
oldrho = rho
# tile the sigmas and means
sigMADs = np.tile(sigma,(cols,1))
means1 = np.tile(means[0:bands],(cols,1))
means2 = np.tile(means[bands::],(cols,1))
# ensure sum of positive correlations between X and U is positive
D = np.diag(1/np.sqrt(np.diag(s11)))
s = np.ravel(np.sum(D*s11*A,axis=0))
A = A*np.diag(s/np.abs(s))
# ensure positive correlation between each pair of canonical variates
cov = np.diag(A.T*s12*B)
B = B*np.diag(cov/np.abs(cov))
itr += 1
print 'rho: %s'%str(rho)
# write results to disk
driver = inDataset1.GetDriver()
outDataset = driver.Create(outfn,cols,rows,bands+1,GDT_Float32)
projection = inDataset1.GetProjection()
geotransform = inDataset1.GetGeoTransform()
if geotransform is not None:
gt = list(geotransform)
gt[0] = gt[0] + x0*gt[1]
gt[3] = gt[3] + y0*gt[5]
outDataset.SetGeoTransform(tuple(gt))
if projection is not None:
outDataset.SetProjection(projection)
outBands = []
for k in range(bands+1):
outBands.append(outDataset.GetRasterBand(k+1))
for row in range(rows):
for k in range(bands):
tile[:,k] = rasterBands1[k].ReadAsArray(x0,y0+row,cols,1)
tile[:,bands+k] = rasterBands2[k].ReadAsArray(x2,y2+row,cols,1)
mads = np.asarray((tile[:,0:bands]-means1)*A - (tile[:,bands::]-means2)*B)
chisqr = np.sum((mads/sigMADs)**2,axis=1)
for k in range(bands):
outBands[k].WriteArray(np.reshape(mads[:,k],(1,cols)),0,row)
outBands[bands].WriteArray(np.reshape(chisqr,(1,cols)),0,row)
for outBand in outBands:
outBand.FlushCache()
outDataset = None
inDataset1 = None
inDataset2 = None
print 'result written to: '+outfn
print 'elapsed time: %s'%str(time.time()-start)
x = np.array(range(itr-1))
if graphics:
plt.plot(x,rhos[0:itr-1,:])
plt.title('Canonical correlations')
plt.show()