Beispiel #1
0
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)
Beispiel #2
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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)
Beispiel #3
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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
Beispiel #4
0
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