def hankel(c,r=None):
""" Construct a hankel matrix (i.e. matrix with constant anti-diagonals).
Description:
hankel(c,r) is a Hankel matrix whose first column is c and whose
last row is r.
hankel(c) is a square Hankel matrix whose first column is C.
Elements below the first anti-diagonal are zero.
See also: toeplitz
"""
isscalar = scipy_base.isscalar
if isscalar(c) or isscalar(r):
return c
if r is None:
r = zeros(len(c))
elif r[0] != c[-1]:
print "Warning: column and row values don't agree; column value used."
r,c = map(asarray_chkfinite,(r,c))
r,c = map(ravel,(r,c))
rN,cN = map(len,(r,c))
vals = r_[c, r[1:rN]]
cols = mgrid[1:cN+1]
rows = mgrid[0:rN]
indx = cols[:,NewAxis]*ones((1,rN)) + \
rows[NewAxis,:]*ones((cN,1)) - 1
return take(vals, indx)
def toeplitz(c,r=None):
""" Construct a toeplitz matrix (i.e. a matrix with constant diagonals).
Description:
toeplitz(c,r) is a non-symmetric Toeplitz matrix with c as its first
column and r as its first row.
toeplitz(c) is a symmetric (Hermitian) Toeplitz matrix (r=c).
See also: hankel
"""
isscalar = scipy_base.isscalar
if isscalar(c) or isscalar(r):
return c
if r is None:
r = c
r[0] = conjugate(r[0])
c = conjugate(c)
r,c = map(asarray_chkfinite,(r,c))
r,c = map(ravel,(r,c))
rN,cN = map(len,(r,c))
if r[0] != c[0]:
print "Warning: column and row values don't agree; column value used."
vals = r_[r[rN-1:0:-1], c]
cols = mgrid[0:cN]
rows = mgrid[rN:0:-1]
indx = cols[:,NewAxis]*ones((1,rN)) + \
rows[NewAxis,:]*ones((cN,1)) - 1
return take(vals, indx)
def hessenberg(a,calc_q=0,overwrite_a=0):
""" Compute Hessenberg form of a matrix.
Inputs:
a -- the matrix
calc_q -- if non-zero then calculate unitary similarity
transformation matrix q.
overwrite_a=0 -- if non-zero then discard the contents of a,
i.e. a is used as a work array if possible.
Outputs:
h -- Hessenberg form of a [calc_q=0]
h, q -- matrices such that a = q * h * q^T [calc_q=1]
"""
a1 = asarray(a)
if len(a1.shape) != 2 or (a1.shape[0] != a1.shape[1]):
raise ValueError, 'expected square matrix'
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a,'__array__'))
gehrd,gebal = get_lapack_funcs(('gehrd','gebal'),(a1,))
ba,lo,hi,pivscale,info = gebal(a,permute=1,overwrite_a = overwrite_a)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal gebal (hessenberg)'%(-info)
n = len(a1)
lwork = calc_lwork.gehrd(gehrd.prefix,n,lo,hi)
hq,tau,info = gehrd(ba,lo=lo,hi=hi,lwork=lwork,overwrite_a=1)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal gehrd (hessenberg)'%(-info)
if not calc_q:
for i in range(lo,hi):
hq[i+2:hi+1,i] = 0.0
return hq
# XXX: Use ORGHR routines to compute q.
ger,gemm = get_blas_funcs(('ger','gemm'),(hq,))
typecode = hq.typecode()
q = None
for i in range(lo,hi):
if tau[i]==0.0:
continue
v = zeros(n,typecode=typecode)
v[i+1] = 1.0
v[i+2:hi+1] = hq[i+2:hi+1,i]
hq[i+2:hi+1,i] = 0.0
h = ger(-tau[i],v,v,a=diag(ones(n,typecode=typecode)),overwrite_a=1)
if q is None:
q = h
else:
q = gemm(1.0,q,h)
if q is None:
q = diag(ones(n,typecode=typecode))
return hq,q
def toimage(arr,high=255,low=0,cmin=None,cmax=None,pal=None,
mode=None,channel_axis=None):
"""Takes a Numeric array and returns a PIL image. The mode of the
PIL image depends on the array shape, the pal keyword, and the mode
keyword.
For 2-D arrays, if pal is a valid (N,3) byte-array giving the RGB values
(from 0 to 255) then mode='P', otherwise mode='L', unless mode is given
as 'F' or 'I' in which case a float and/or integer array is made
For 3-D arrays, the channel_axis argument tells which dimension of the
array holds the channel data.
For 3-D arrays if one of the dimensions is 3, the mode is 'RGB'
by default or 'YCbCr' if selected.
if the
The Numeric array must be either 2 dimensional or 3 dimensional.
"""
data = asarray(arr)
if iscomplexobj(data):
raise ValueError, "Cannot convert a complex-valued array."
shape = list(data.shape)
valid = len(shape)==2 or ((len(shape)==3) and \
((3 in shape) or (4 in shape)))
assert valid, "Not a suitable array shape for any mode."
if len(shape) == 2:
shape = (shape[1],shape[0]) # columns show up first
if mode == 'F':
image = Image.fromstring(mode,shape,data.astype('f').tostring())
return image
if mode in [None, 'L', 'P']:
bytedata = bytescale(data,high=high,low=low,cmin=cmin,cmax=cmax)
image = Image.fromstring('L',shape,bytedata.tostring())
if pal is not None:
image.putpalette(asarray(pal,typecode=_UInt8).tostring())
# Becomes a mode='P' automagically.
elif mode == 'P': # default gray-scale
pal = arange(0,256,1,typecode='b')[:,NewAxis] * \
ones((3,),typecode='b')[NewAxis,:]
image.putpalette(asarray(pal,typecode=_UInt8).tostring())
return image
if mode == '1': # high input gives threshold for 1
bytedata = ((data > high)*255).astype('b')
image = Image.fromstring('L',shape,bytedata.tostring())
image = image.convert(mode='1')
return image
if cmin is None:
cmin = amin(ravel(data))
if cmax is None:
cmax = amax(ravel(data))
data = (data*1.0 - cmin)*(high-low)/(cmax-cmin) + low
if mode == 'I':
image = Image.fromstring(mode,shape,data.astype('i').tostring())
else:
raise ValueError, _errstr
return image
# if here then 3-d array with a 3 or a 4 in the shape length.
# Check for 3 in datacube shape --- 'RGB' or 'YCbCr'
if channel_axis is None:
if (3 in shape):
ca = Numeric.nonzero(asarray(shape) == 3)[0]
else:
ca = Numeric.nonzero(asarray(shape) == 4)
if len(ca):
ca = ca[0]
else:
raise ValueError, "Could not find channel dimension."
else:
ca = channel_axis
numch = shape[ca]
if numch not in [3,4]:
raise ValueError, "Channel axis dimension is not valid."
bytedata = bytescale(data,high=high,low=low,cmin=cmin,cmax=cmax)
if ca == 2:
strdata = bytedata.tostring()
shape = (shape[1],shape[0])
elif ca == 1:
strdata = transpose(bytedata,(0,2,1)).tostring()
shape = (shape[2],shape[0])
elif ca == 0:
strdata = transpose(bytedata,(1,2,0)).tostring()
shape = (shape[2],shape[1])
if mode is None:
if numch == 3: mode = 'RGB'
else: mode = 'RGBA'
if mode not in ['RGB','RGBA','YCbCr','CMYK']:
raise ValueError, _errstr
if mode in ['RGB', 'YCbCr']:
assert numch == 3, "Invalid array shape for mode."
if mode in ['RGBA', 'CMYK']:
assert numch == 4, "Invalid array shape for mode."
# Here we know data and mode is coorect
image = Image.fromstring(mode, shape, strdata)
return image