Python numpy.reshape() Examples

def train_lr_rfeinman(densities_pos, densities_neg, uncerts_pos, uncerts_neg):
    """
    TODO
    :param densities_pos:
    :param densities_neg:
    :param uncerts_pos:
    :param uncerts_neg:
    :return:
    """
    values_neg = np.concatenate(
        (densities_neg.reshape((1, -1)),
         uncerts_neg.reshape((1, -1))),
        axis=0).transpose([1, 0])
    values_pos = np.concatenate(
        (densities_pos.reshape((1, -1)),
         uncerts_pos.reshape((1, -1))),
        axis=0).transpose([1, 0])

    values = np.concatenate((values_neg, values_pos))
    labels = np.concatenate(
        (np.zeros_like(densities_neg), np.ones_like(densities_pos)))

    lr = LogisticRegressionCV(n_jobs=-1).fit(values, labels)

    return values, labels, lr 

def wave2input_image(wave, window, pos=0, pad=0):
    wave_image = np.hstack([wave[pos+i*sride:pos+(i+pad*2)*sride+dif].reshape(height+pad*2, sride) for i in range(256//sride)])[:,:254]
    wave_image *= window
    spectrum_image = np.fft.fft(wave_image, axis=1)
    input_image = np.abs(spectrum_image[:,:128].reshape(1, height+pad*2, 128), dtype=np.float32)

    np.clip(input_image, 1000, None, out=input_image)
    np.log(input_image, out=input_image)
    input_image += bias
    input_image /= scale

    if np.max(input_image) > 0.95:
        print('input image max bigger than 0.95', np.max(input_image))
    if np.min(input_image) < 0.05:
        print('input image min smaller than 0.05', np.min(input_image))

    return input_image 

def parse_dataobj(self, dataobj, hdat={}):
        # first, see if we have a specified shape/size
        ish = next((hdat[k] for k in ('image_size', 'image_shape', 'shape') if k in hdat), None)
        if ish is Ellipsis: ish = None
        # make a numpy array of the appropriate dtype
        dtype = self.parse_type(hdat, dataobj=dataobj)
        try:    dataobj = dataobj.dataobj
        except Exception: pass
        if   dataobj is not None: arr = np.asarray(dataobj).astype(dtype)
        elif ish:                 arr = np.zeros(ish,       dtype=dtype)
        else:                     arr = np.zeros([1,1,1,0], dtype=dtype)
        # reshape to the requested shape if need-be
        if ish and ish != arr.shape: arr = np.reshape(arr, ish)
        # then reshape to a valid (4D) shape
        sh = arr.shape
        if   len(sh) == 2: arr = np.reshape(arr, (sh[0], 1, 1, sh[1]))
        elif len(sh) == 1: arr = np.reshape(arr, (sh[0], 1, 1))
        elif len(sh) == 3: arr = np.reshape(arr, sh)
        elif len(sh) != 4: raise ValueError('Cannot convert n-dimensional array to image if n > 4')
        # and return
        return arr 

def image_reslice(image, spec, method=None, fill=0, dtype=None, weights=None, image_type=None):
    '''
    image_reslice(image, spec) yields a duplicate of the given image resliced to have the voxels
      indicated by the given image spec. Note that spec may be an image itself.

    Optional arguments that can be passed to image_interpolate() (asside from affine) are allowed
    here and are passed through.
    '''
    if image_type is None and is_image(image): image_type = to_image_type(image)
    spec = to_image_spec(spec)
    image = to_image(image)
    # we make a big mesh and interpolate at these points...
    imsh = spec['image_shape']
    (args, kw) = ([np.arange(n) for n in imsh[:3]], {'indexing': 'ij'})
    ijk = np.asarray([u.flatten() for u in np.meshgrid(*args, **kw)])
    ijk = np.dot(spec['affine'], np.vstack([ijk, np.ones([1,ijk.shape[1]])]))[:3]
    # interpolate here...
    u = image_interpolate(image, ijk, method=method, fill=fill, dtype=dtype, weights=weights)
    return to_image((np.reshape(u, imsh), spec), image_type=image_type) 

def set_values(name, param, pretrained):
#{{{
    """
    Initialize a network parameter with pretrained values.
    We check that sizes are compatible.
    """
    param_value = param.get_value()
    if pretrained.size != param_value.size:
        raise Exception(
            "Size mismatch for parameter %s. Expected %i, found %i."
            % (name, param_value.size, pretrained.size)
        )
    param.set_value(np.reshape(
        pretrained, param_value.shape
    ).astype(np.float32))
#}}} 

def auto_inverse(self, whole_spectrum):
        whole_spectrum = np.copy(whole_spectrum).astype(complex)
        whole_spectrum[whole_spectrum < 1] = 1
        overwrap = self.buffer_size * 2
        height = whole_spectrum.shape[0]
        parallel_dif = (height-overwrap) // self.parallel
        if height < self.parallel*overwrap:
            raise Exception('voice length is too small to use gpu, or parallel number is too big')

        spec = [self.inverse(whole_spectrum[range(i, i+parallel_dif*self.parallel, parallel_dif), :]) for i in tqdm.tqdm(range(parallel_dif+overwrap))]
        spec = spec[overwrap:]
        spec = np.concatenate(spec, axis=1)
        spec = spec.reshape(-1, self.wave_len)

        #Below code don't consider wave_len and wave_dif, I'll fix.
        wave = np.fft.ifft(spec, axis=1).real
        pad = np.zeros((wave.shape[0], 2), dtype=float)
        wave = np.concatenate([wave, pad], axis=1)

        dst = np.zeros((wave.shape[0]+3)*self.wave_dif, dtype=float)
        for i in range(4):
            w = wave[range(i, wave.shape[0], 4),:]
            w = w.reshape(-1)
            dst[i*self.wave_dif:i*self.wave_dif+len(w)] += w
        return dst*0.5 

def cplus(*args):
    '''
    cplus(a, b...) returns the sum of all the values as a numpy array object. Like numpy's add
      function or a+b syntax, plus will thread over the latest dimension possible.

    Additionally, cplus works correctly with sparse arrays.
    '''
    n = len(args)
    if   n == 0: return np.asarray(0)
    elif n == 1: return np.asarray(args[0])
    elif n >  2: return reduce(plus, args)
    (a,b) = args
    if sps.issparse(a):
        if not sps.issparse(b):
            b = np.asarray(b)
            if len(b.shape) == 0: b = np.reshape(b, (1,1))
    elif sps.issparse(b):
        a = np.asarray(a)
        if len(a.shape) == 0: a = np.reshape(a, (1,1))
    else:
        a = np.asarray(a)
        b = np.asarray(b)
    return a + b 

def point_on_segment(ac, b, atol=1e-8):
    '''
    point_on_segment((a,b), c) yields True if point x is on segment (a,b) and False otherwise. Note
    that this differs from point_in_segment in that a point that if c is equal to a or b it is
    considered 'on' but not 'in' the segment.
    The option atol can be given and is used only to test for difference from 0; by default it is
    1e-8.
    '''
    (a,c) = ac
    abc = [np.asarray(u) for u in (a,b,c)]
    if any(len(u.shape) > 1 for u in abc): (a,b,c) = [np.reshape(u,(len(u),-1)) for u in abc]
    else:                                  (a,b,c) = abc
    vab = b - a
    vbc = c - b
    vac = c - a
    dab = np.sqrt(np.sum(vab**2, axis=0))
    dbc = np.sqrt(np.sum(vbc**2, axis=0))
    dac = np.sqrt(np.sum(vac**2, axis=0))
    return np.isclose(dab + dbc - dac, 0, atol=atol) 

def mtx_freq2visi(M, p_mic_x, p_mic_y):
    """
    build the matrix that maps the Fourier series to the visibility
    :param M: the Fourier series expansion is limited from -M to M
    :param p_mic_x: a vector that constains microphones x coordinates
    :param p_mic_y: a vector that constains microphones y coordinates
    :return:
    """
    num_mic = p_mic_x.size
    ms = np.reshape(np.arange(-M, M + 1, step=1), (1, -1), order='F')
    G = np.zeros((num_mic * (num_mic - 1), 2 * M + 1), dtype=complex, order='C')
    count_G = 0
    for q in range(num_mic):
        p_x_outer = p_mic_x[q]
        p_y_outer = p_mic_y[q]
        for qp in range(num_mic):
            if not q == qp:
                p_x_qqp = p_x_outer - p_mic_x[qp]
                p_y_qqp = p_y_outer - p_mic_y[qp]
                norm_p_qqp = np.sqrt(p_x_qqp ** 2 + p_y_qqp ** 2)
                phi_qqp = np.arctan2(p_y_qqp, p_x_qqp)
                G[count_G, :] = (-1j) ** ms * sp.special.jv(ms, norm_p_qqp) * \
                                np.exp(1j * ms * phi_qqp)
                count_G += 1
    return G 

def apply_affine(aff, coords):
    '''
    apply_affine(affine, coords) yields the result of applying the given affine transformation to
      the given coordinate or coordinates.

    This function expects coords to be a (dims X n) matrix but if the first dimension is neither 2
    nor 3, coords.T is used; i.e.:
      apply_affine(affine3x3, coords2xN) ==> newcoords2xN
      apply_affine(affine4x4, coords3xN) ==> newcoords3xN
      apply_affine(affine3x3, coordsNx2) ==> newcoordsNx2 (for N != 2)
      apply_affine(affine4x4, coordsNx3) ==> newcoordsNx3 (for N != 3)
    '''
    if aff is None: return coords
    (coords,tr) = (np.asanyarray(coords), False)
    if len(coords.shape) == 1: return np.squeeze(apply_affine(np.reshape(coords, (-1,1)), aff))
    elif len(coords.shape) > 2: raise ValueError('cannot apply affine to ND-array for N > 2')
    if   len(coords) == 2: aff = to_affine(aff, 2)
    elif len(coords) == 3: aff = to_affine(aff, 3)
    else: (coords,aff,tr) = (coords.T, to_affine(aff, coords.shape[1]), True)
    r = np.dot(aff, np.vstack([coords, np.ones([1,coords.shape[1]])]))[:-1]
    return r.T if tr else r 

def point_in_segment(ac, b, atol=1e-8):
    '''
    point_in_segment((a,b), c) yields True if point x is in segment (a,b) and False otherwise. Note
    that this differs from point_on_segment in that a point that if c is equal to a or b it is
    considered 'on' but not 'in' the segment.
    The option atol can be given and is used only to test for difference from 0; by default it is
    1e-8.
    '''
    (a,c) = ac
    abc = [np.asarray(u) for u in (a,b,c)]
    if any(len(u.shape) > 1 for u in abc): (a,b,c) = [np.reshape(u,(len(u),-1)) for u in abc]
    else:                                  (a,b,c) = abc
    vab = b - a
    vbc = c - b
    vac = c - a
    dab = np.sqrt(np.sum(vab**2, axis=0))
    dbc = np.sqrt(np.sum(vbc**2, axis=0))
    dac = np.sqrt(np.sum(vac**2, axis=0))
    return (np.isclose(dab + dbc - dac, 0, atol=atol) &
            ~np.isclose(dac - dab, 0, atol=atol) &
            ~np.isclose(dac - dbc, 0, atol=atol)) 

def jacobian(self, p, into=None):
        # transpose to be 3 x 2 x n
        p = np.transpose(np.reshape(p, (-1, 3, 2)), (1,2,0))
        # First, get the two legs...
        (dx_ab, dy_ab) = p[1] - p[0]
        (dx_ac, dy_ac) = p[2] - p[0]
        (dx_bc, dy_bc) = p[2] - p[1]
        # now, the area is half the z-value of the cross-product...
        sarea0 = 0.5 * (dx_ab*dy_ac - dx_ac*dy_ab)
        # but we want to abs it
        dsarea0 = np.sign(sarea0)
        z = np.transpose([[-dy_bc,dx_bc], [dy_ac,-dx_ac], [-dy_ab,dx_ab]], (2,0,1))
        z = times(0.5*dsarea0, z)
        m = numel(p)
        n = p.shape[2]
        ii = (np.arange(n) * np.ones([6, n])).T.flatten()
        z = sps.csr_matrix((z.flatten(), (ii, np.arange(len(ii)))), shape=(n, m))
        return safe_into(into, z) 

def mtx_updated_G(phi_recon, M, mtx_amp2visi_ri, mtx_fri2visi_ri):
    """
    Update the linear transformation matrix that links the FRI sequence to the
    visibilities by using the reconstructed Dirac locations.
    :param phi_recon: the reconstructed Dirac locations (azimuths)
    :param M: the Fourier series expansion is between -M to M
    :param p_mic_x: a vector that contains microphones' x-coordinates
    :param p_mic_y: a vector that contains microphones' y-coordinates
    :param mtx_freq2visi: the linear mapping from Fourier series to visibilities
    :return:
    """
    L = 2 * M + 1
    ms_half = np.reshape(np.arange(-M, 1, step=1), (-1, 1), order='F')
    phi_recon = np.reshape(phi_recon, (1, -1), order='F')
    mtx_amp2freq = np.exp(-1j * ms_half * phi_recon)  # size: (M + 1) x K
    mtx_amp2freq_ri = np.vstack((mtx_amp2freq.real, mtx_amp2freq.imag[:-1, :]))  # size: (2M + 1) x K
    mtx_fri2amp_ri = linalg.lstsq(mtx_amp2freq_ri, np.eye(L))[0]
    # projection mtx_freq2visi to the null space of mtx_fri2amp
    mtx_null_proj = np.eye(L) - np.dot(mtx_fri2amp_ri.T,
                                       linalg.lstsq(mtx_fri2amp_ri.T, np.eye(L))[0])
    G_updated = np.dot(mtx_amp2visi_ri, mtx_fri2amp_ri) + \
                np.dot(mtx_fri2visi_ri, mtx_null_proj)
    return G_updated 

def row_norms(ii, f=Ellipsis, squared=False):
    '''
    row_norms(ii) yields a potential function h(x) that calculates the vector norms of the rows of
      the matrix formed by [x[i] for i in ii] (ii is a matrix of parameter indices).
    row_norms(ii, f) yield a potential function h(x) equivalent to compose(row_norms(ii), f).
    '''
    try:
        (n,m) = ii
        # matrix shape given
        ii = np.reshape(np.arange(n*m), (n,m))
    except Exception: ii = np.asarray(ii)
    f = to_potential(f)
    if is_const_potential(f):
        q = flattest(f.c)
        q = np.sum([q[i]**2 for i in ii.T], axis=0)
        return PotentialConstant(q if squared else np.sqrt(q))
    F = reduce(lambda a,b: a + b, [part(Ellipsis, col)**2 for col in ii.T])
    F = compose(F, f)
    if not squared: F = sqrt(F)
    return F 

def col_norms(ii, f=Ellipsis, squared=False):
    '''
    col_norms(ii) yields a potential function h(x) that calculates the vector norms of the columns
      of the matrix formed by [x[i] for i in ii] (ii is a matrix of parameter indices).
    col_norms(ii, f) yield a potential function h(x) equivalent to compose(col_norms(ii), f).
    '''
    try:
        (n,m) = ii
        # matrix shape given
        ii = np.reshape(np.arange(n*m), (n,m))
    except Exception: ii = np.asarray(ii)
    f = to_potential(f)
    if is_const_potential(f):
        q = flattest(f.c)
        q = np.sum([q[i]**2 for i in ii], axis=0)
        return PotentialConstant(q if squared else np.sqrt(q))
    F = reduce(lambda a,b: a + b, [part(Ellipsis, col)**2 for col in ii])
    F = compose(F, f)
    if not squared: F = sqrt(F)
    return F 

def distances(a, b, shape, squared=False, axis=1):
    '''
    distances(a, b, (n,d)) yields a potential function whose output is equivalent to the row-norms
      of reshape(a(x), (n,d)) - reshape(b(x), (n,d)).
    
    The shape argument (n,m) may alternately be a matrix of parameter indices, as can be passed to
    row_norms and col_norms.

    The following optional arguments are accepted:
      * squared (default: False) specifies whether the output should be the square distance or the
        distance.
      * axis (default: 1) specifies whether the rows (axis = 1) or columns (axis = 0) are treated
        as the vectors between which the distances should be calculated.
    '''
    a = to_potential(a)
    b = to_potential(b)
    if axis == 1: return row_norms(shape, a - b, squared=squared)
    else:         return col_norms(shape, a - b, squared=squared) 

def __getitem__(self, index):
        img=self.adv_flat[self.sample_num,:]
        if(self.transp == False):
            # shuff is true for non-pgd attacks
            img = torch.from_numpy(np.reshape(img,(28,28)))
        else:
            img = torch.from_numpy(img).type(torch.FloatTensor)
        target = np.argmax(self.adv_dict["adv_labels"],axis=1)[self.sample_num]
        # doing this so that it is consistent with all other datasets
        # to return a PIL Image

        if self.transform is not None:
            img = self.transform(img)
        if self.target_transform is not None:
            target = self.target_transform(target)
        self.sample_num = self.sample_num + 1
        return img, target 

def __getitem__(self, index):

        img=self.adv_flat[self.sample_num,:]

        if(self.shuff == False):
            # shuff is true for non-pgd attacks
            img = torch.from_numpy(np.reshape(img,(3,32,32)))
        else:
            img = torch.from_numpy(img).type(torch.FloatTensor)
        target = np.argmax(self.adv_dict["adv_labels"],axis=1)[self.sample_num]
        # doing this so that it is consistent with all other datasets
        # to return a PIL Image
        if self.transform is not None:
            img = self.transform(img)

        if self.target_transform is not None:
            target = self.target_transform(target)

        self.sample_num = self.sample_num + 1
        return img, target 

def __getitem__(self, index):

        img=self.adv_flat[self.sample_num,:]

        if(self.shuff == False):
            # shuff is true for non-pgd attacks
            img = torch.from_numpy(np.reshape(img,(3,224,224)))
        else:
            img = torch.from_numpy(img).type(torch.FloatTensor)
        target = self.adv_dict["adv_labels"][self.sample_num]
        # doing this so that it is consistent with all other datasets
        # to return a PIL Image
        if self.transform is not None:
            img = self.transform(img)

        if self.target_transform is not None:
            target = self.target_transform(target)

        self.sample_num = self.sample_num + 1
        return img, target 

def __getitem__(self, index):

        img=self.adv_flat[self.sample_num,:]

        if(self.shuff == False):
            # shuff is true for non-pgd attacks
            img = torch.from_numpy(np.reshape(img,(3,32,32)))
        else:
            img = torch.from_numpy(img).type(torch.FloatTensor)
        target = np.argmax(self.adv_dict["adv_labels"],axis=1)[self.sample_num]
        # doing this so that it is consistent with all other datasets
        # to return a PIL Image
        if self.transform is not None:
            img = self.transform(img)

        if self.target_transform is not None:
            target = self.target_transform(target)

        self.sample_num = self.sample_num + 1
        return img, target 

def signed_face_areas(faces, axis=1):
    '''
    signed_face_areas(faces) yields a potential function f(x) that calculates the signed area of
      each face represented by the simplices matrix faces.

    If faces is None, then the parameters must arrive in the form of a flattened (n x 3 x 2) matrix
    where n is the number of triangles. Otherwise, the faces matrix must be either (n x 3) or (n x 3
    x s); if the former, each row must list the vertex indices for the faces where the vertex matrix
    is presumed to be shaped (V x 2). Alternately, faces may be a full (n x 3 x 2) simplex array of
    the indices into the parameters.

    The optional argument axis (default: 1) may be set to 0 if the faces argument is a matrix but
    the coordinate matrix will be (2 x V) instead of (V x 2).
    '''
    faces = np.asarray(faces)
    if len(faces.shape) == 2:
        if faces.shape[1] != 3: faces = faces.T
        n = 2 * (np.max(faces) + 1)
        if axis == 0: tmp = np.reshape(np.arange(n), (2,-1)).T
        else:         tmp = np.reshape(np.arange(n), (-1,2))
        faces = np.reshape(tmp[faces.flat], (-1,3,2))
    faces = faces.flatten()
    return compose(TriangleSignedArea2DPotential(), part(Ellipsis, faces)) 

def face_areas(faces, axis=1):
    '''
    face_areas(faces) yields a potential function f(x) that calculates the unsigned area of each
      faces represented by the simplices matrix faces.

    If faces is None, then the parameters must arrive in the form of a flattened (n x 3 x 2) matrix
    where n is the number of triangles. Otherwise, the faces matrix must be either (n x 3) or (n x 3
    x s); if the former, each row must list the vertex indices for the faces where the vertex matrix
    is presumed to be shaped (V x 2). Alternately, faces may be a full (n x 3 x 2) simplex array of
    the indices into the parameters.

    The optional argument axis (default: 1) may be set to 0 if the faces argument is a matrix but
    the coordinate matrix will be (2 x V) instead of (V x 2).
    '''
    faces = np.asarray(faces)
    if len(faces.shape) == 2:
        if faces.shape[1] != 3: faces = faces.T
        n = 2 * (np.max(faces) + 1)
        if axis == 0: tmp = np.reshape(np.arange(n), (2,-1)).T
        else:         tmp = np.reshape(np.arange(n), (-1,2))
        faces = np.reshape(tmp[faces.flat], (-1,3,2))
    faces = faces.flatten()
    return compose(TriangleArea2DPotential(), part(Ellipsis, faces)) 

def one_vs_all(X, y, num_labels, learning_rate):
    rows = X.shape[0]
    params = X.shape[1]
    
    # k X (n + 1) array for the parameters of each of the k classifiers
    all_theta = np.zeros((num_labels, params + 1))
    
    # insert a column of ones at the beginning for the intercept term
    X = np.insert(X, 0, values=np.ones(rows), axis=1)
    
    # labels are 1-indexed instead of 0-indexed
    for i in range(1, num_labels + 1):
        theta = np.zeros(params + 1)
        y_i = np.array([1 if label == i else 0 for label in y])
        y_i = np.reshape(y_i, (rows, 1))
        
        # minimize the objective function
        fmin = minimize(fun=cost, x0=theta, args=(X, y_i, learning_rate), method='TNC', jac=gradient)
        all_theta[i-1,:] = fmin.x
    
    return all_theta 

def dice(preds: torch.Tensor, trues: torch.Tensor) -> np.ndarray:
    preds_inner = preds.data.cpu().numpy().copy()
    trues_inner = trues.data.cpu().numpy().copy()

    preds_inner = np.reshape(preds_inner, (preds_inner.shape[0], preds_inner.size // preds_inner.shape[0]))
    trues_inner = np.reshape(trues_inner, (trues_inner.shape[0], trues_inner.size // trues_inner.shape[0]))

    intersection = (preds_inner * trues_inner).sum(1)
    scores = (2. * intersection + eps) / (preds_inner.sum(1) + trues_inner.sum(1) + eps)

    return scores 

def jaccard(preds: torch.Tensor, trues: torch.Tensor):
    preds_inner = preds.cpu().data.numpy().copy()
    trues_inner = trues.cpu().data.numpy().copy()

    preds_inner = np.reshape(preds_inner, (preds_inner.shape[0], preds_inner.size // preds_inner.shape[0]))
    trues_inner = np.reshape(trues_inner, (trues_inner.shape[0], trues_inner.size // trues_inner.shape[0]))
    intersection = (preds_inner * trues_inner).sum(1)
    scores = (intersection + eps) / ((preds_inner + trues_inner).sum(1) - intersection + eps)

    return scores 

def to_image(self, arr, hdat={}):
        # reshape the data object or create it empty if None was given:
        arr = self.parse_dataobj(arr, hdat)
        # get the affine
        aff = self.parse_affine(hdat, dataobj=arr)
        # get the keyword arguments
        kw = self.parse_kwargs(arr, hdat)
        # create an image of the appropriate type
        cls = self.image_type()
        img = cls(arr, aff, **kw)
        # post-process the image
        return self.postprocess_image(img, hdat) 

def load_weights(self, weights_filename):
        """
        Load weights file of trained Neural Network Potential.

        Args
            weights_filename (str): The weights file.
        """
        with open(weights_filename) as f:
            weights_lines = f.readlines()

        weight_param = pd.DataFrame([line.split() for line in weights_lines
                                     if "#" not in line])
        weight_param.columns = ['value', 'type', 'index', 'start_layer',
                                'start_neuron', 'end_layer', 'end_neuron']

        for layer_index in range(1, len(self.layer_sizes)):
            weights_group = weight_param[(weight_param['start_layer'] == str(layer_index - 1))
                                         & (weight_param['end_layer'] == str(layer_index))]

            weights = np.reshape(np.array(weights_group['value'], dtype=np.float),
                                 (self.layer_sizes[layer_index - 1],
                                  self.layer_sizes[layer_index]))
            self.weights.append(weights)

            bs_group = weight_param[(weight_param['type'] == 'b') &
                                    (weight_param['start_layer'] == str(layer_index))]
            bs = np.array(bs_group['value'], dtype=np.float)
            self.bs.append(bs)

        self.weight_param = weight_param 

def points_close(a,b, atol=1e-8):
    '''
    points_close(a,b) yields True if points a and b are close to each other and False otherwise.
    '''
    (a,b) = [np.asarray(u) for u in (a,b)]
    if len(a.shape) == 2 or len(b.shape) == 2: (a,b) = [np.reshape(u,(len(u),-1)) for u in (a,b)]
    return np.isclose(np.sqrt(np.sum((a - b)**2, axis=0)), 0, atol=atol) 

def minimize(self, x0, **kwargs):
        '''
        pf.minimize(x0) minimizes the given potential function starting at the given point x0; any
          additional options are passed along to scipy.optimize.minimize.
        '''
        x0 = np.asarray(x0)
        kwargs = pimms.merge({'jac':self.jac(), 'method':'CG'}, kwargs)
        res = spopt.minimize(self.fun(), x0.flatten(), **kwargs)
        res.x = np.reshape(res.x, x0.shape)
        return res 

def _diff_order(n):
        u0 = np.arange(n)
        d = int(np.ceil(np.sqrt(n)))
        mtx = np.reshape(np.pad(u0, [(0,d*d-n)], 'constant', constant_values=[(0,-1)]), (d,d))
        h = int((d+1)/2)
        u = np.vstack([mtx[::2], mtx[1::2]]).T.flatten()
        return u[u >= 0]