Python numpy.subtract() Examples

def calWeights(self, img, kernel, y, x):
        wmax = 0
        sweight = 0
        average = 0
        for j in range(2 * self.Ds + 1 - 2 * self.ds - 1):
            for i in range(2 * self.Ds + 1 - 2 * self.ds - 1):
                start_y = y - self.Ds + self.ds + j
                start_x = x - self.Ds + self.ds + i
                neighbour_w = img[start_y - self.ds:start_y + self.ds + 1, start_x - self.ds:start_x + self.ds + 1]
                center_w = img[y-self.ds:y+self.ds+1, x-self.ds:x+self.ds+1]
                if j != y or i != x:
                    sub = np.subtract(neighbour_w, center_w)
                    dist = np.sum(np.multiply(kernel, np.multiply(sub, sub)))
                    w = np.exp(-dist/pow(self.h, 2))    # replaced by look up table
                    if w > wmax:
                        wmax = w
                    sweight = sweight + w
                    average = average + w * img[start_y, start_x]
        return sweight, average, wmax 

def app_entropy(x, order=2, metric='chebyshev'):
    """Approximate Entropy
    Parameters
    ----------
    x : list or np.array
        One-dimensional time series of shape (n_times)
    order : int (default: 2)
        Embedding dimension.
    metric : str (default: chebyshev)
        Name of the metric function used with
        :class:`~sklearn.neighbors.KDTree`. The list of available
        metric functions is given by: ``KDTree.valid_metrics``.
    Returns
    -------
    ae : float
        Approximate Entropy.
 
    """
    phi = _app_samp_entropy(x, order=order, metric=metric, approximate=True)
    return np.subtract(phi[0], phi[1]) 

def _unsigned_subtract(a, b):
    """
    Subtract two values where a >= b, and produce an unsigned result

    This is needed when finding the difference between the upper and lower
    bound of an int16 histogram
    """
    # coerce to a single type
    signed_to_unsigned = {
        np.byte: np.ubyte,
        np.short: np.ushort,
        np.intc: np.uintc,
        np.int_: np.uint,
        np.longlong: np.ulonglong
    }
    dt = np.result_type(a, b)
    try:
        dt = signed_to_unsigned[dt.type]
    except KeyError:  # pragma: no cover
        return np.subtract(a, b, dtype=dt)
    else:
        # we know the inputs are integers, and we are deliberately casting
        # signed to unsigned
        return np.subtract(a, b, casting='unsafe', dtype=dt) 

def make_img_gt_pair(self, idx):
        """
        Make the image-ground-truth pair
        """
        img = cv2.imread(os.path.join(self.db_root_dir, self.img_list[idx]))
        if self.labels[idx] is not None:
            label = cv2.imread(os.path.join(self.db_root_dir, self.labels[idx]), 0)
        else:
            gt = np.zeros(img.shape[:-1], dtype=np.uint8)

        if self.inputRes is not None:
            img = imresize(img, self.inputRes)
            if self.labels[idx] is not None:
                label = imresize(label, self.inputRes, interp='nearest')

        img = np.array(img, dtype=np.float32)
        img = np.subtract(img, np.array(self.meanval, dtype=np.float32))

        if self.labels[idx] is not None:
                gt = np.array(label, dtype=np.float32)
                gt = gt/np.max([gt.max(), 1e-8])

        return img, gt 

def apply_val_transform_image(image,inputRes=None):
    meanval = (104.00699, 116.66877, 122.67892)

    if inputRes is not None:
        image = sm.imresize(image, inputRes)

    image = np.array(image, dtype=np.float32)
    image = np.subtract(image, np.array(meanval, dtype=np.float32))



    if image.ndim == 2:
        image = image[:, :, np.newaxis]

    # swap color axis because
    # numpy image: H x W x C
    # torch image: C X H X W

    image = image.transpose((2, 0, 1))
    image = torch.from_numpy(image)

    return image 

def VOCap(rec,prec):

    mpre = np.zeros([1,2+len(prec)])
    mpre[0,1:len(prec)+1] = prec
    mrec = np.zeros([1,2+len(rec)])
    mrec[0,1:len(rec)+1] = rec
    mrec[0,len(rec)+1] = 1.0

    for i in range(mpre.size-2,-1,-1):
        mpre[0,i] = max(mpre[0,i],mpre[0,i+1])

    i = np.argwhere( ~np.equal( mrec[0,1:], mrec[0,:mrec.shape[1]-1]) )+1
    i = i.flatten()

    # compute area under the curve
    ap = np.sum( np.multiply( np.subtract( mrec[0,i], mrec[0,i-1]), mpre[0,i] ) )

    return ap 

def triplet_loss(anchor, positive, negative, alpha):
    """Calculate the triplet loss according to the FaceNet paper
    
    Args:
      anchor: the embeddings for the anchor images.
      positive: the embeddings for the positive images.
      negative: the embeddings for the negative images.
  
    Returns:
      the triplet loss according to the FaceNet paper as a float tensor.
    """
    with tf.variable_scope('triplet_loss'):
        pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, positive)), 1)
        neg_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, negative)), 1)
        
        basic_loss = tf.add(tf.subtract(pos_dist,neg_dist), alpha)
        loss = tf.reduce_mean(tf.maximum(basic_loss, 0.0), 0)
      
    return loss 

def test_mutate_all():
    df = pd.DataFrame({
        'alpha': list('aaabbb'),
        'beta': list('babruq'),
        'theta': list('cdecde'),
        'x': [1, 2, 3, 4, 5, 6],
        'y': [6, 5, 4, 3, 2, 1],
        'z': [7, 9, 11, 8, 10, 12]
    })

    result = (df
              >> group_by('alpha')
              >> select('x', 'y', 'z')
              >> mutate_all((np.add, np.subtract), 10)
              )
    assert 'alpha' in result 

def triplet_loss(anchor, positive, negative, alpha):
    """Calculate the triplet loss according to the FaceNet paper
    
    Args:
      anchor: the embeddings for the anchor images.
      positive: the embeddings for the positive images.
      negative: the embeddings for the negative images.
  
    Returns:
      the triplet loss according to the FaceNet paper as a float tensor.
    """
    with tf.variable_scope('triplet_loss'):
        pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, positive)), 1)
        neg_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, negative)), 1)
        
        basic_loss = tf.add(tf.subtract(pos_dist,neg_dist), alpha)
        loss = tf.reduce_mean(tf.maximum(basic_loss, 0.0), 0)
      
    return loss 

def triplet_loss(anchor, positive, negative, alpha):
    """Calculate the triplet loss according to the FaceNet paper
    
    Args:
      anchor: the embeddings for the anchor images.
      positive: the embeddings for the positive images.
      negative: the embeddings for the negative images.
  
    Returns:
      the triplet loss according to the FaceNet paper as a float tensor.
    """
    with tf.variable_scope('triplet_loss'):
        pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, positive)), 1)
        neg_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, negative)), 1)
        
        basic_loss = tf.add(tf.subtract(pos_dist,neg_dist), alpha)
        loss = tf.reduce_mean(tf.maximum(basic_loss, 0.0), 0)
      
    return loss 

def test_pi_ops_array_int(self):

        idx = PeriodIndex(['2011-01', '2011-02', 'NaT', '2011-04'],
                          freq='M', name='idx')
        f = lambda x: x + np.array([1, 2, 3, 4])
        exp = PeriodIndex(['2011-02', '2011-04', 'NaT', '2011-08'],
                          freq='M', name='idx')
        self._check(idx, f, exp)

        f = lambda x: np.add(x, np.array([4, -1, 1, 2]))
        exp = PeriodIndex(['2011-05', '2011-01', 'NaT', '2011-06'],
                          freq='M', name='idx')
        self._check(idx, f, exp)

        f = lambda x: x - np.array([1, 2, 3, 4])
        exp = PeriodIndex(['2010-12', '2010-12', 'NaT', '2010-12'],
                          freq='M', name='idx')
        self._check(idx, f, exp)

        f = lambda x: np.subtract(x, np.array([3, 2, 3, -2]))
        exp = PeriodIndex(['2010-10', '2010-12', 'NaT', '2011-06'],
                          freq='M', name='idx')
        self._check(idx, f, exp) 

def test_pi_ops_nat(self):
        idx = PeriodIndex(['2011-01', '2011-02', 'NaT', '2011-04'],
                          freq='M', name='idx')
        expected = PeriodIndex(['2011-03', '2011-04', 'NaT', '2011-06'],
                               freq='M', name='idx')

        self._check(idx, lambda x: x + 2, expected)
        self._check(idx, lambda x: 2 + x, expected)
        self._check(idx, lambda x: np.add(x, 2), expected)

        self._check(idx + 2, lambda x: x - 2, idx)
        self._check(idx + 2, lambda x: np.subtract(x, 2), idx)

        # freq with mult
        idx = PeriodIndex(['2011-01', '2011-02', 'NaT', '2011-04'],
                          freq='2M', name='idx')
        expected = PeriodIndex(['2011-07', '2011-08', 'NaT', '2011-10'],
                               freq='2M', name='idx')

        self._check(idx, lambda x: x + 3, expected)
        self._check(idx, lambda x: 3 + x, expected)
        self._check(idx, lambda x: np.add(x, 3), expected)

        self._check(idx + 3, lambda x: x - 3, idx)
        self._check(idx + 3, lambda x: np.subtract(x, 3), idx) 

def load_image(img_path, net_input_shape):
    imgBGR = cv2.imread(img_path)
    img = cv2.resize(imgBGR, net_input_shape)
    # BGR -> RGB
    #img = img[:,:, (2, 1, 0)]

    ## Method 1
    # imgT = np.transpose(img, (2, 0, 1))  # c,w,h
    # imgF = np.asarray(imgT, dtype=np.float32)
    # mean = [[[88.159309]], [[97.966286]], [[103.66106]]] # Caffe image mean
    # imgS = np.subtract(imgF,mean)

    ## Method 2
    imgF = np.asarray(img, dtype=np.float32)
    mean = [88.159309, 97.966286, 103.66106] # Caffe image mean
    imgSS = np.subtract(imgF, mean)
    imgS = np.transpose(imgSS, (2, 0, 1))  # c,w,h

    # RGB_MEAN_PIXELS = np.array([88.159309, 97.966286, 103.66106]).reshape((1,1,1,3)).astype(np.float32)

    return imgBGR, np.ascontiguousarray(imgS, dtype=np.float32) # avoid error: ndarray is not contiguous 

def _unsigned_subtract(a, b):
    """
    Subtract two values where a >= b, and produce an unsigned result

    This is needed when finding the difference between the upper and lower
    bound of an int16 histogram
    """
    # coerce to a single type
    signed_to_unsigned = {
        np.byte: np.ubyte,
        np.short: np.ushort,
        np.intc: np.uintc,
        np.int_: np.uint,
        np.longlong: np.ulonglong
    }
    dt = np.result_type(a, b)
    try:
        dt = signed_to_unsigned[dt.type]
    except KeyError:
        return np.subtract(a, b, dtype=dt)
    else:
        # we know the inputs are integers, and we are deliberately casting
        # signed to unsigned
        return np.subtract(a, b, casting='unsafe', dtype=dt) 

def load_image(img_path, net_input_shape):
    img = cv2.resize(cv2.imread(img_path), net_input_shape)
    # BGR -> RGB
    #img = img[:,:, (2, 1, 0)]

    ## Method 1
    # imgT = np.transpose(img, (2, 0, 1))  # c,w,h
    # imgF = np.asarray(imgT, dtype=np.float32)
    # mean = [[[88.159309]], [[97.966286]], [[103.66106]]] # Caffe image mean
    # imgS = np.subtract(imgF,mean)

    ## Method 2
    imgF = np.asarray(img, dtype=np.float32)
    mean = [88.159309, 97.966286, 103.66106] # Caffe image mean
    imgSS = np.subtract(imgF, mean)
    imgS = np.transpose(imgSS, (2, 0, 1))  # CHW

    # RGB_MEAN_PIXELS = np.array([88.159309, 97.966286, 103.66106]).reshape((1,1,1,3)).astype(np.float32)

    return np.ascontiguousarray(imgS, dtype=np.float32)   # avoid error: ndarray is not contiguous 

def load_image(img_path, net_input_shape):
    imgBGR = cv2.imread(img_path)
    img = cv2.resize(imgBGR, net_input_shape)
    # BGR -> RGB
    #img = img[:,:, (2, 1, 0)]

    ## Method 1
    # imgT = np.transpose(img, (2, 0, 1))  # c,w,h
    # imgF = np.asarray(imgT, dtype=np.float32)
    # mean = [[[88.159309]], [[97.966286]], [[103.66106]]] # Caffe image mean
    # imgS = np.subtract(imgF,mean)

    ## Method 2
    imgF = np.asarray(img, dtype=np.float32)
    mean = [128.0, 128.0, 128.0] # Caffe image mean
    # mean = [88.159309, 97.966286, 103.66106] # Caffe image mean
    imgSS = np.subtract(imgF, mean)/128.0
    imgS = np.transpose(imgSS, (2, 0, 1))  # c,w,h

    # RGB_MEAN_PIXELS = np.array([88.159309, 97.966286, 103.66106]).reshape((1,1,1,3)).astype(np.float32)

    return imgBGR, np.ascontiguousarray(imgS, dtype=np.float32) # avoid error: ndarray is not contiguous 

def load_image(img_path, net_input_shape):
    img = cv2.resize(cv2.imread(img_path), net_input_shape)
    # BGR -> RGB
    #img = img[:,:, (2, 1, 0)]

    ## Method 1
    # imgT = np.transpose(img, (2, 0, 1))  # c,w,h
    # imgF = np.asarray(imgT, dtype=np.float32)
    # mean = [[[88.159309]], [[97.966286]], [[103.66106]]] # Caffe image mean
    # imgS = np.subtract(imgF,mean)

    ## Method 2
    imgF = np.asarray(img, dtype=np.float32)
    mean = [88.159309, 97.966286, 103.66106] # Caffe image mean
    imgSS = np.subtract(imgF, mean)
    imgS = np.transpose(imgSS, (2, 0, 1))  # CHW

    # RGB_MEAN_PIXELS = np.array([88.159309, 97.966286, 103.66106]).reshape((1,1,1,3)).astype(np.float32)

    return np.ascontiguousarray(imgS, dtype=np.float32) # avoid error: ndarray is not contiguous 

def load_image(img_path, net_input_shape):
    imgBGR = cv2.imread(img_path)
    img = cv2.resize(imgBGR, net_input_shape)
    # BGR -> RGB
    #img = img[:,:, (2, 1, 0)]

    ## Method 1
    # imgT = np.transpose(img, (2, 0, 1))  # c,w,h
    # imgF = np.asarray(imgT, dtype=np.float32)
    # mean = [[[88.159309]], [[97.966286]], [[103.66106]]] # Caffe image mean
    # imgS = np.subtract(imgF,mean)

    ## Method 2
    imgF = np.asarray(img, dtype=np.float32)
    mean = [128.0, 128.0, 128.0] # Caffe image mean
    # mean = [88.159309, 97.966286, 103.66106] # Caffe image mean
    imgSS = np.subtract(imgF, mean)/128.0
    imgS = np.transpose(imgSS, (2, 0, 1))  # c,w,h

    # RGB_MEAN_PIXELS = np.array([88.159309, 97.966286, 103.66106]).reshape((1,1,1,3)).astype(np.float32)

    return imgBGR, np.ascontiguousarray(imgS, dtype=np.float32) # avoid error: ndarray is not contiguous 

def test_testArithmetic(self):
        # Test of basic arithmetic.
        (x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
        a2d = array([[1, 2], [0, 4]])
        a2dm = masked_array(a2d, [[0, 0], [1, 0]])
        self.assertTrue(eq(a2d * a2d, a2d * a2dm))
        self.assertTrue(eq(a2d + a2d, a2d + a2dm))
        self.assertTrue(eq(a2d - a2d, a2d - a2dm))
        for s in [(12,), (4, 3), (2, 6)]:
            x = x.reshape(s)
            y = y.reshape(s)
            xm = xm.reshape(s)
            ym = ym.reshape(s)
            xf = xf.reshape(s)
            self.assertTrue(eq(-x, -xm))
            self.assertTrue(eq(x + y, xm + ym))
            self.assertTrue(eq(x - y, xm - ym))
            self.assertTrue(eq(x * y, xm * ym))
            with np.errstate(divide='ignore', invalid='ignore'):
                self.assertTrue(eq(x / y, xm / ym))
            self.assertTrue(eq(a10 + y, a10 + ym))
            self.assertTrue(eq(a10 - y, a10 - ym))
            self.assertTrue(eq(a10 * y, a10 * ym))
            with np.errstate(divide='ignore', invalid='ignore'):
                self.assertTrue(eq(a10 / y, a10 / ym))
            self.assertTrue(eq(x + a10, xm + a10))
            self.assertTrue(eq(x - a10, xm - a10))
            self.assertTrue(eq(x * a10, xm * a10))
            self.assertTrue(eq(x / a10, xm / a10))
            self.assertTrue(eq(x ** 2, xm ** 2))
            self.assertTrue(eq(abs(x) ** 2.5, abs(xm) ** 2.5))
            self.assertTrue(eq(x ** y, xm ** ym))
            self.assertTrue(eq(np.add(x, y), add(xm, ym)))
            self.assertTrue(eq(np.subtract(x, y), subtract(xm, ym)))
            self.assertTrue(eq(np.multiply(x, y), multiply(xm, ym)))
            with np.errstate(divide='ignore', invalid='ignore'):
                self.assertTrue(eq(np.divide(x, y), divide(xm, ym))) 

def _hist_bin_fd(x):
    """
    The Freedman-Diaconis histogram bin estimator.

    The Freedman-Diaconis rule uses interquartile range (IQR) to
    estimate binwidth. It is considered a variation of the Scott rule
    with more robustness as the IQR is less affected by outliers than
    the standard deviation. However, the IQR depends on fewer points
    than the standard deviation, so it is less accurate, especially for
    long tailed distributions.

    If the IQR is 0, this function returns 1 for the number of bins.
    Binwidth is inversely proportional to the cube root of data size
    (asymptotically optimal).

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    iqr = np.subtract(*np.percentile(x, [75, 25]))
    return 2.0 * iqr * x.size ** (-1.0 / 3.0) 

def test_exceptions(self):
        a = np.ones(1, dtype=np.bool_)
        assert_raises(TypeError, np.negative, a)
        assert_raises(TypeError, np.positive, a)
        assert_raises(TypeError, np.subtract, a, a) 

def test_pure_subclass_info_preservation(self):
        # Test that ufuncs and methods conserve extra information consistently;
        # see gh-7122.
        arr1 = SubMaskedArray('test', data=[1,2,3,4,5,6])
        arr2 = SubMaskedArray(data=[0,1,2,3,4,5])
        diff1 = np.subtract(arr1, arr2)
        self.assertTrue('info' in diff1._optinfo)
        self.assertTrue(diff1._optinfo['info'] == 'test')
        diff2 = arr1 - arr2
        self.assertTrue('info' in diff2._optinfo)
        self.assertTrue(diff2._optinfo['info'] == 'test')


############################################################################### 

def test_dti_isub_tdi(self, tz_naive_fixture):
        # GH#17558
        tz = tz_naive_fixture
        dti = DatetimeIndex([Timestamp('2017-01-01', tz=tz)] * 10)
        tdi = pd.timedelta_range('0 days', periods=10)
        expected = pd.date_range('2017-01-01', periods=10, tz=tz, freq='-1D')

        # isub with TimedeltaIndex
        result = DatetimeIndex([Timestamp('2017-01-01', tz=tz)] * 10)
        result -= tdi
        tm.assert_index_equal(result, expected)

        msg = 'cannot subtract .* from a TimedeltaArray'
        with pytest.raises(TypeError, match=msg):
            tdi -= dti

        # isub with timedelta64 array
        result = DatetimeIndex([Timestamp('2017-01-01', tz=tz)] * 10)
        result -= tdi.values
        tm.assert_index_equal(result, expected)

        msg = '|'.join(['cannot perform __neg__ with this index type:',
                        'ufunc subtract cannot use operands with types',
                        'cannot subtract DatetimeArray from'])
        with pytest.raises(TypeError, match=msg):
            tdi.values -= dti

    # -------------------------------------------------------------
    # Binary Operations DatetimeIndex and datetime-like
    # TODO: A couple other tests belong in this section.  Move them in
    # A PR where there isn't already a giant diff. 

def test_ufunc_coercions(self):
        idx = date_range('2011-01-01', periods=3, freq='2D', name='x')

        delta = np.timedelta64(1, 'D')
        for result in [idx + delta, np.add(idx, delta)]:
            assert isinstance(result, DatetimeIndex)
            exp = date_range('2011-01-02', periods=3, freq='2D', name='x')
            tm.assert_index_equal(result, exp)
            assert result.freq == '2D'

        for result in [idx - delta, np.subtract(idx, delta)]:
            assert isinstance(result, DatetimeIndex)
            exp = date_range('2010-12-31', periods=3, freq='2D', name='x')
            tm.assert_index_equal(result, exp)
            assert result.freq == '2D'

        delta = np.array([np.timedelta64(1, 'D'), np.timedelta64(2, 'D'),
                          np.timedelta64(3, 'D')])
        for result in [idx + delta, np.add(idx, delta)]:
            assert isinstance(result, DatetimeIndex)
            exp = DatetimeIndex(['2011-01-02', '2011-01-05', '2011-01-08'],
                                freq='3D', name='x')
            tm.assert_index_equal(result, exp)
            assert result.freq == '3D'

        for result in [idx - delta, np.subtract(idx, delta)]:
            assert isinstance(result, DatetimeIndex)
            exp = DatetimeIndex(['2010-12-31', '2011-01-01', '2011-01-02'],
                                freq='D', name='x')
            tm.assert_index_equal(result, exp)
            assert result.freq == 'D' 

def test_parr_ops_errors(self, ng, box_with_array):
        idx = PeriodIndex(['2011-01', '2011-02', '2011-03', '2011-04'],
                          freq='M', name='idx')
        obj = tm.box_expected(idx, box_with_array)

        msg = r"unsupported operand type\(s\)"
        with pytest.raises(TypeError, match=msg):
            obj + ng

        with pytest.raises(TypeError):
            # error message differs between PY2 and 3
            ng + obj

        with pytest.raises(TypeError, match=msg):
            obj - ng

        with pytest.raises(TypeError):
            np.add(obj, ng)

        with pytest.raises(TypeError):
            np.add(ng, obj)

        with pytest.raises(TypeError):
            np.subtract(obj, ng)

        with pytest.raises(TypeError):
            np.subtract(ng, obj) 

def BasicMassBalance(path, file1, file2):
    """This function checks the difference in "volume" between two rasters.

    Args:
        path (str): The path to the files
        file1 (str): The name of the first raster.
        file2 (str): The name of the second raster

    Returns:
        float: The differnece in the volume betweeen the two rasters

    Author: SMM
    """

    # make sure names are in correct format
    NewPath = LSDOst.AppendSepToDirectoryPath(path)

    raster_file1 = NewPath+file1
    raster_file2 = NewPath+file2

    PixelArea = LSDMap_IO.GetPixelArea(raster_file1)
    print("PixelArea is: " + str(PixelArea))

    print("The formatted path is: " + NewPath)
    Raster1 = LSDMap_IO.ReadRasterArrayBlocks(raster_file1,raster_band=1)
    Raster2 = LSDMap_IO.ReadRasterArrayBlocks(raster_file2,raster_band=1)

    NewRaster = np.subtract(Raster2,Raster1)

    mass_balance = np.sum(NewRaster)*PixelArea

    print("linear dif " + str(np.sum(NewRaster)))

    return mass_balance 

def r_squared(y_true, y_hat):
    ssr = 0
    sst = 0
    e = np.subtract(y_true, y_hat)
    y_mean = np.mean(y_true)
    for item in e:
        ssr += item**2
    for item in y_true:
        sst += (item - y_mean)**2
    r2 = 1 - ssr / sst
    return r2 

def r_squared(y_true, y_hat):
    ssr = 0
    sst = 0
    e = np.subtract(y_true, y_hat)
    y_mean = np.mean(y_true)
    for item in e:
        ssr += item**2
    for item in y_true:
        sst += (item - y_mean)**2
    r2 = 1 - ssr / sst
    return r2 

def log_normalize(logp):
    """Normalizes a np array of log probabilites."""
    return np.subtract(logp, logsumexp(logp)) 

def __array_wrap__(self, result, context=None):
        """
        Gets called after a ufunc. Needs additional handling as
        PeriodIndex stores internal data as int dtype

        Replace this to __numpy_ufunc__ in future version
        """
        if isinstance(context, tuple) and len(context) > 0:
            func = context[0]
            if func is np.add:
                pass
            elif func is np.subtract:
                name = self.name
                left = context[1][0]
                right = context[1][1]
                if (isinstance(left, PeriodIndex) and
                        isinstance(right, PeriodIndex)):
                    name = left.name if left.name == right.name else None
                    return Index(result, name=name)
                elif isinstance(left, Period) or isinstance(right, Period):
                    return Index(result, name=name)
            elif isinstance(func, np.ufunc):
                if 'M->M' not in func.types:
                    msg = "ufunc '{0}' not supported for the PeriodIndex"
                    # This should be TypeError, but TypeError cannot be raised
                    # from here because numpy catches.
                    raise ValueError(msg.format(func.__name__))

        if is_bool_dtype(result):
            return result
        # the result is object dtype array of Period
        # cannot pass _simple_new as it is
        return type(self)(result, freq=self.freq, name=self.name)