def LUdecomp(a, tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n), type=Float64)
for i in range(n):
s[i] = max(abs(a[i, :]))
for k in range(0, n - 1):
# Row interchange, if needed
p = int(argmax(abs(a[k:n, k]) / s[k:n])) + k
if abs(a[p, k]) < tol:
error.err("Matrix is singular")
if p != k:
swap.swapRows(s, k, p)
swap.swapRows(a, k, p)
swap.swapRows(seq, k, p)
# Elimination
for i in range(k + 1, n):
if a[i, k] != 0.0:
lam = a[i, k] / a[k, k]
a[i, k + 1 : n] = a[i, k + 1 : n] - lam * a[k, k + 1 : n]
a[i, k] = lam
return a, seq
def gaussJordanPivot(a, tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n), type=Float64)
for i in range(n):
s[i] = max(abs(a[i, :]))
for i in range(n):
# Row interchange, if needed
p = int(argmax(abs(a[i:n, i]) / s[i:n])) + i
if abs(a[p, i]) < tol: error.err('Matrix is singular')
if p != i:
swap.swapRows(s, i, p)
swap.swapRows(a, i, p)
swap.swapRows(seq, i, p)
# Elimination phase
temp = a[i, i]
a[i, i] = 1.0
a[i, 0:n] = a[i, 0:n] / temp
for k in range(n):
if k != i:
temp = a[k, i]
a[k, i] = 0.0
a[k, 0:n] = a[k, 0:n] - a[i, 0:n] * temp
# Rearrange columns in the right sequence
for i in range(n):
swap.swapCols(a, i, seq[i])
swap.swapRows(seq, i, seq[i])
return a
def numarray_max(inputarray): ''' faster than numarray.nd_image.max ''' f = numarray.ravel(inputarray) i = numarray.argmax(f) return float(f[i])
def powell(F, x, h=0.1, tol=1.0e-6):
def f(s):
return F(x + s * v) # F in direction of v
n = len(x) # Number of design variables
df = zeros((n), type=Float64) # Decreases of F stored here
u = identity(n) * 1.0 # Vectors v stored here by rows
for j in range(30): # Allow for 30 cycles:
xOld = x.copy() # Save starting point
fOld = F(xOld)
# First n line searches record decreases of F
for i in range(n):
v = u[i]
a, b = bracket(f, 0.0, h)
s, fMin = search(f, a, b)
df[i] = fOld - fMin
fOld = fMin
x = x + s * v
# Last line search in the cycle
v = x - xOld
a, b = bracket(f, 0.0, h)
s, fLast = search(f, a, b)
x = x + s * v
# Check for convergence
if sqrt(dot(x - xOld, x - xOld) / n) < tol: return x, j + 1
# Identify biggest decrease & update search directions
iMax = int(argmax(df))
for i in range(iMax, n - 1):
u[i] = u[i + 1]
u[n - 1] = v
print "Powell did not converge"
def invwedge(q, n):
ind = argmax(abs(q), 0)[0]
q = q / q[ind]
i, j = indtoij(ind)
v1 = zeros((n, 1), Float)
v2 = zeros((n, 1), Float)
v1[i, 0] = 0
v2[j, 0] = 0
v1[j, 0] = 1
v2[i, 0] = 1
for k in range(0, i):
if k != j:
v1[k, 0] = q[ijtoind(i, k), 0]
for k in range(i + 1, n):
v1[k, 0] = -1 * q[ijtoind(k, i), 0]
for k in range(0, j):
v2[k, 0] = -1 * q[ijtoind(j, k), 0]
for k in range(j + 1, n):
if k != i:
v2[k, 0] = q[ijtoind(k, j), 0]
return v1, v2
def gaussJordanPivot(a,tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n),type=Float64)
for i in range(n):
s[i] = max(abs(a[i,:]))
for i in range(n):
# Row interchange, if needed
p = int(argmax(abs(a[i:n,i])/s[i:n])) + i
if abs(a[p,i]) < tol: error.err('Matrix is singular')
if p != i:
swap.swapRows(s,i,p)
swap.swapRows(a,i,p)
swap.swapRows(seq,i,p)
# Elimination phase
temp = a[i,i]
a[i,i] = 1.0
a[i,0:n] = a[i,0:n]/temp
for k in range(n):
if k != i:
temp = a[k,i]
a[k,i] = 0.0
a[k,0:n] = a[k,0:n] - a[i,0:n]*temp
# Rearrange columns in the right sequence
for i in range(n):
swap.swapCols(a,i,seq[i])
swap.swapRows(seq,i,seq[i])
return a
def LUdecomp(a,tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n),type=Float64)
for i in range(n):
s[i] = max(abs(a[i,:]))
for k in range(0,n-1):
# Row interchange, if needed
p = int(argmax(abs(a[k:n,k])/s[k:n])) + k
if abs(a[p,k]) < tol: error.err('Matrix is singular')
if p != k:
swap.swapRows(s,k,p)
swap.swapRows(a,k,p)
swap.swapRows(seq,k,p)
# Elimination
for i in range(k+1,n):
if a[i,k] != 0.0:
lam = a[i,k]/a[k,k]
a[i,k+1:n] = a[i,k+1:n] - lam*a[k,k+1:n]
a[i,k] = lam
return a,seq
def powell(F,x,h=0.1,tol=1.0e-6):
def f(s): return F(x + s*v) # F in direction of v
n = len(x) # Number of design variables
df = zeros((n),type=Float64) # Decreases of F stored here
u = identity(n)*1.0 # Vectors v stored here by rows
for j in range(30): # Allow for 30 cycles:
xOld = x.copy() # Save starting point
fOld = F(xOld)
# First n line searches record decreases of F
for i in range(n):
v = u[i]
a,b = bracket(f,0.0,h)
s,fMin = search(f,a,b)
df[i] = fOld - fMin
fOld = fMin
x = x + s*v
# Last line search in the cycle
v = x - xOld
a,b = bracket(f,0.0,h)
s,fLast = search(f,a,b)
x = x + s*v
# Check for convergence
if sqrt(dot(x-xOld,x-xOld)/n) < tol: return x,j+1
# Identify biggest decrease & update search directions
iMax = int(argmax(df))
for i in range(iMax,n-1):
u[i] = u[i+1]
u[n-1] = v
print "Powell did not converge"
def numarray_max(inputarray): ''' faster than numarray.nd_image.max ''' f = numarray.ravel(inputarray) i = numarray.argmax(f) return float(f[i])
def invwedge(q, n): ind = argmax(abs(q),0)[0] q = q/q[ind] i, j = indtoij(ind) v1 = zeros((n,1), Float) v2 = zeros((n,1), Float) v1[i,0] = 0 v2[j,0] = 0 v1[j,0] = 1 v2[i,0] = 1 for k in range(0,i): if k != j: v1[k,0] = q[ijtoind(i, k),0] for k in range(i+1,n): v1[k,0] = -1*q[ijtoind(k, i),0] for k in range(0,j): v2[k,0] = -1*q[ijtoind(j, k),0] for k in range(j+1,n): if k != i: v2[k,0] = q[ijtoind(k, j),0] return v1, v2
def decode_mixture(P, entropy_cutoff):
""" Given P, a (|sequences| x |models|)-matrix where P_{ij} =
P[model j| sequence i] return a list of size (|sequences|)
which contains j, the model which maximizes P[model j| sequence i]
for a sequence, if the entropy of the discrete distribution
{ P[ . | sequence i] } is less than the entropy_cutoff and None else.
"""
nr_seqs = numarray.shape(P)[0]
result = [None] * nr_seqs
for i in xrange(nr_seqs):
e = Entropy(P[i])
#print e, P[i]
if e < entropy_cutoff:
result[i] = int(numarray.argmax(P[i]))
return result
def decode_mixture(P, entropy_cutoff):
""" Given P, a (|sequences| x |models|)-matrix where P_{ij} =
P[model j| sequence i] return a list of size (|sequences|)
which contains j, the model which maximizes P[model j| sequence i]
for a sequence, if the entropy of the discrete distribution
{ P[ . | sequence i] } is less than the entropy_cutoff and None else.
"""
nr_seqs = numarray.shape(P)[0]
result = [None] * nr_seqs
for i in xrange(nr_seqs):
e = Entropy(P[i])
#print e, P[i]
if e < entropy_cutoff:
result[i] = int(numarray.argmax(P[i]))
return result
def matchum(file1,
file2,
tol=10,
perr=4,
aerr=1.0,
nmax=40,
im_masks1=[],
im_masks2=[],
debug=0,
domags=0,
xrange=None,
yrange=None,
sigma=4,
aoffset=0):
'''Take the output of two sextractor runs and match up the objects with
each other (find out which objects in the first file match up with
objects in the second file. The routine considers a 'match' to be any
two objects that are closer than tol pixels (after applying the shift).
Returns a 6-tuple: (x1,y1,x2,y2,o1,o2). o1 and o2 are the ojbects
numbers such that o1[i] in file 1 corresponds to o2[i] in file 2.'''
NA = num.NewAxis
sexdata1 = readsex(file1)
sexdata2 = readsex(file2)
# Use the readsex data to get arrays of the (x,y) positions
x1 = num.asarray(sexdata1[0]['X_IMAGE'])
y1 = num.asarray(sexdata1[0]['Y_IMAGE'])
x2 = num.asarray(sexdata2[0]['X_IMAGE'])
y2 = num.asarray(sexdata2[0]['Y_IMAGE'])
m1 = num.asarray(sexdata1[0]['MAG_BEST'])
m2 = num.asarray(sexdata2[0]['MAG_BEST'])
o1 = num.asarray(sexdata1[0]['NUMBER'])
o2 = num.asarray(sexdata2[0]['NUMBER'])
f1 = num.asarray(sexdata1[0]['FLAGS'])
f2 = num.asarray(sexdata2[0]['FLAGS'])
# First, make a cut on the flags:
gids = num.where(f1 < 4)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
gids = num.where(f2 < 4)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
# next, if there is a range to use:
if xrange is not None and yrange is not None:
cond = num.greater(x1, xrange[0])*num.less(x1,xrange[1])*\
num.greater(y1, yrange[0])*num.less(y1,yrange[1])
gids = num.where(cond)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
cond = num.greater(x2, xrange[0])*num.less(x2,xrange[1])*\
num.greater(y2, yrange[0])*num.less(y2,yrange[1])
gids = num.where(cond)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
# Use the user masks
for m in im_masks1:
print "applying mask (%d,%d,%d,%d)" % tuple(m)
condx = num.less(x1, m[0]) + num.greater(x1, m[1])
condy = num.less(y1, m[2]) + num.greater(y1, m[3])
gids = num.where(condx + condy)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
for m in im_masks2:
print "applying mask (%d,%d,%d,%d)" % tuple(m)
condx = num.less(x2, m[0]) + num.greater(x2, m[1])
condy = num.less(y2, m[2]) + num.greater(y2, m[3])
gids = num.where(condx + condy)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
if nmax:
if len(x1) > nmax:
ids = num.argsort(m1)[0:nmax]
x1 = x1[ids]
y1 = y1[ids]
m1 = m1[ids]
o1 = o1[ids]
if len(x2) > nmax:
ids = num.argsort(m2)[0:nmax]
x2 = x2[ids]
y2 = y2[ids]
m2 = m2[ids]
o2 = o2[ids]
if debug:
print "objects in frame 1:"
print o1
print "objects in frame 2:"
print o2
mp = pygplot.MPlot(2, 1, device='/XWIN')
p = pygplot.Plot()
p.point(x1, y1)
[p.label(x1[i], y1[i], "%d" % o1[i]) for i in range(len(x1))]
mp.add(p)
p = pygplot.Plot()
p.point(x2, y2)
[p.label(x2[i], y2[i], "%d" % o2[i]) for i in range(len(x2))]
mp.add(p)
mp.plot()
mp.close()
# Now, we make 2-D arrays of all the differences in x and y between each pair
# of objects. e.g., dx1[n,m] is the delta-x between object n and m in file 1 and
# dy2[n,m] is the y-distance between object n and m in file 2.
dx1 = x1[NA, :] - x1[:, NA]
dx2 = x2[NA, :] - x2[:, NA]
dy1 = y1[NA, :] - y1[:, NA]
dy2 = y2[NA, :] - y2[:, NA]
# Same, but with angles
da1 = num.arctan2(dy1, dx1) * 180 / num.pi
da2 = num.arctan2(dy2, dx2) * 180 / num.pi
# Same, but with absolute distances
ds1 = num.sqrt(num.power(dx1, 2) + num.power(dy1, 2))
ds2 = num.sqrt(num.power(dx2, 2) + num.power(dy2, 2))
# Here's the real magic: this is a matrix of matrices (4-D). Consider 4 objects:
# objects i and j in file 1 and objects m and n in file 2. dx[i,j,m,n] is the
# difference between delta-xs for objects i,j in file 1 and m,n in file 2. If object
# i corresponds to object m and object j corresponds to object n, this should be a small
# number, irregardless of an overall shift in coordinate systems between file 1 and 2.
dx = dx1[::, ::, NA, NA] - dx2[NA, NA, ::, ::]
dy = dy1[::, ::, NA, NA] - dy2[NA, NA, ::, ::]
da = da1[::, ::, NA, NA] - da2[NA, NA, ::, ::] + aoffset
ds = ds1[::, ::, NA, NA] - ds2[NA, NA, ::, ::]
# pick out close pairs.
#use = num.less(dy,perr)*num.less(dx,perr)*num.less(num.abs(da),aerr)
use = num.less(ds, perr) * num.less(num.abs(da), aerr)
use = use.astype(num.Int32)
#use = num.less(num.abs(da),perr)
suse = num.add.reduce(num.add.reduce(use, 3), 1)
print suse[0]
guse = num.greater(suse, suse.flat.max() / 2)
i = [j for j in range(x1.shape[0]) if num.sum(guse[j])]
m = [num.argmax(guse[j]) for j in range(x1.shape[0]) if num.sum(guse[j])]
xx0, yy0, oo0, mm0 = num.take([x1, y1, o1, m1], i, 1)
xx1, yy1, oo1, mm1 = num.take([x2, y2, o2, m2], m, 1)
if debug:
mp = pygplot.MPlot(2, 1, device='/XWIN')
p = pygplot.Plot()
p.point(xx0, yy0)
[p.label(xx0[i], yy0[i], "%d" % oo0[i]) for i in range(len(xx0))]
mp.add(p)
p = pygplot.Plot()
p.point(xx1, yy1)
[p.label(xx1[i], yy1[i], "%d" % oo1[i]) for i in range(len(xx1))]
mp.add(p)
mp.plot()
mp.close()
xshift, xscat = stats.bwt(xx0 - xx1)
xscat = max([1.0, xscat])
yshift, yscat = stats.bwt(yy0 - yy1)
yscat = max([1.0, yscat])
mshift, mscat = stats.bwt(mm0 - mm1)
print "xscat = ", xscat
print "yscat = ", yscat
print "xshift = ", xshift
print "yshift = ", yshift
print "mshift = ", mshift
print "mscat = ", mscat
keep = num.less(num.abs(xx0-xx1-xshift),sigma*xscat)*\
num.less(num.abs(yy0-yy1-yshift),sigma*yscat)
# This is a list of x,y,object# in each file.
xx0, yy0, oo0, xx1, yy1, oo1 = num.compress(keep,
[xx0, yy0, oo0, xx1, yy1, oo1],
1)
if debug:
print file1, oo0
print file2, oo1
mp = pygplot.MPlot(2, 1, device='temp.ps/CPS')
p1 = pygplot.Plot()
p1.point(xx0, yy0, symbol=25, color='red')
for i in range(len(xx0)):
p1.label(xx0[i], yy0[i], " %d" % oo0[i], color='red')
mp.add(p1)
p2 = pygplot.Plot()
p2.point(xx1, yy1, symbol=25, color='green')
for i in range(len(xx1)):
p2.label(xx1[i], yy1[i], " %d" % oo1[i], color='green')
mp.add(p2)
mp.plot()
mp.close()
if domags:
return (xx0, yy0, mm0, xx1, yy1, mm1, mshift, mscat, oo0, oo1)
else:
return (xx0, yy0, xx1, yy1, oo0, oo1)
def createA(n): #function to create matrix A
A = np.empty((n,n), order='F') #declare an empty array of nxn dimension
for i in range(n):
for j in range(n):
A[i,j]= -1+2*argmax([i,j])
return A