def _make_complex_eigvecs(w,vin,cmplx_tcode):
v = scipy_base.array(vin,typecode=cmplx_tcode)
ind = scipy_base.nonzero(scipy_base.not_equal(w.imag,0.0))
vnew = scipy_base.zeros((v.shape[0],len(ind)>>1),cmplx_tcode)
vnew.real = scipy_base.take(vin,ind[::2],1)
vnew.imag = scipy_base.take(vin,ind[1::2],1)
count = 0
conj = scipy_base.conjugate
for i in range(len(ind)/2):
v[:,ind[2*i]] = vnew[:,count]
v[:,ind[2*i+1]] = conj(vnew[:,count])
count += 1
return v
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 ifftshift(x,axes=None):
""" ifftshift(x,axes=None) - > y
Inverse of fftshift.
"""
tmp = asarray(x)
ndim = len(tmp.shape)
if axes is None:
axes = range(ndim)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = n-(n+1)/2
mylist = concatenate((arange(p2,n),arange(p2)))
y = take(y,mylist,k)
return y
def fftshift(x,axes=None):
""" fftshift(x, axes=None) -> y
Shift zero-frequency component to center of spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Notes:
If len(x) is even then the Nyquist component is y[0].
"""
tmp = asarray(x)
ndim = len(tmp.shape)
if axes is None:
axes = range(ndim)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = (n+1)/2
mylist = concatenate((arange(p2,n),arange(p2)))
y = take(y,mylist,k)
return y
