Merge branch 'do_cleanup' into 'NIFTy_6'

Remove standard MPI parallelization

See merge request !387

.gitlab-ci.yml

@@ -39,17 +39,10 @@ test_serial:
   script:
     - pytest-3 -q --cov=nifty6 test
     - >
-      python3 -m coverage report --omit "*plot*,*distributed_do*" | tee coverage.txt
+      python3 -m coverage report --omit "*plot*" | tee coverage.txt
     - >
       grep TOTAL coverage.txt | awk '{ print "TOTAL: "$4; }'
 
-test_mpi:
-  stage: test
-  variables:
-    OMPI_MCA_btl_vader_single_copy_mechanism: none
-  script:
-    - mpiexec -n 2 --bind-to none pytest-3 -q test
-
 pages:
   stage: release
   script:

ChangeLog

@@ -16,3 +16,24 @@ but it is hard to make explicit tests since the two approaches cannot be mapped
 onto each other exactly. We experienced that preconditioning in the `MetricGaussianKL`
 via `napprox` breaks the inference scheme with the new model so `napprox` may not
 be used here.
+
+Removal of the standard parallelization scheme:
+===============================================
+
+When several MPI tasks are present, NIFTy5 distributes every Field over these
+tasks by splitting it along the first axis. This approach to parallelism is not
+very efficient, and it has not been used by anyone for several years, so we
+decided to remove it, which led to many simplifications within NIFTy.
+User-visible changes:
+- the methods `to_global_data`, `from_global_data`, `from_local_data` and
+  the property `local_data` have been removed from `Field` and `MultiField`.
+  Instead there are now the property `val` (returning a read-only numpy.ndarray
+  for `Field` and a dictionary of read-only numpy.ndarrays for `MultiField`) and
+  the method `val_rw()` (returning the same structures with writable copies of
+  the arrays). Fields and MultiFields can be created from such structures using
+  the static method `from_raw`
+- the functions `from_global_data` and `from_local_data` in `sugar` have been
+  replaced by a single function called `makeField`
+- the property `local_shape` has been removed from `Domain` (and subclasses)
+  and `DomainTuple`.
+

demos/Wiener_Filter.ipynb

@@ -296,9 +296,9 @@
    "outputs": [],
    "source": [
     "# Get signal data and reconstruction data\n",
-    "s_data = HT(sh).to_global_data()\n",
-    "m_data = HT(m).to_global_data()\n",
-    "d_data = d.to_global_data()\n",
+    "s_data = HT(sh).val\n",
+    "m_data = HT(m).val\n",
+    "d_data = d.val\n",
     "\n",
     "plt.figure(figsize=(15,10))\n",
     "plt.plot(s_data, 'r', label=\"Signal\", linewidth=3)\n",
@@ -350,8 +350,8 @@
    },
    "outputs": [],
    "source": [
-    "s_power_data = ift.power_analyze(sh).to_global_data()\n",
-    "m_power_data = ift.power_analyze(m).to_global_data()\n",
+    "s_power_data = ift.power_analyze(sh).val\n",
+    "m_power_data = ift.power_analyze(m).val\n",
     "plt.figure(figsize=(15,10))\n",
     "plt.loglog()\n",
     "plt.xlim(1, int(N_pixels/2))\n",
@@ -427,12 +427,12 @@
     "\n",
     "mask = np.full(s_space.shape, 1.)\n",
     "mask[l:h] = 0\n",
-    "mask = ift.Field.from_global_data(s_space, mask)\n",
+    "mask = ift.Field.from_raw(s_space, mask)\n",
     "\n",
     "R = ift.DiagonalOperator(mask)(HT)\n",
-    "n = n.to_global_data_rw()\n",
+    "n = n.val_rw()\n",
     "n[l:h] = 0\n",
-    "n = ift.Field.from_global_data(s_space, n)\n",
+    "n = ift.Field.from_raw(s_space, n)\n",
     "\n",
     "d = R(sh) + n"
    ]
@@ -497,11 +497,11 @@
    "outputs": [],
    "source": [
     "# Get signal data and reconstruction data\n",
-    "s_data = s.to_global_data()\n",
-    "m_data = HT(m).to_global_data()\n",
-    "m_var_data = m_var.to_global_data()\n",
+    "s_data = s.val\n",
+    "m_data = HT(m).val\n",
+    "m_var_data = m_var.val\n",
     "uncertainty = np.sqrt(m_var_data)\n",
-    "d_data = d.to_global_data_rw()\n",
+    "d_data = d.val_rw()\n",
     "\n",
     "# Set lost data to NaN for proper plotting\n",
     "d_data[d_data == 0] = np.nan"
@@ -583,12 +583,12 @@
     "\n",
     "mask = np.full(s_space.shape, 1.)\n",
     "mask[l:h,l:h] = 0.\n",
-    "mask = ift.Field.from_global_data(s_space, mask)\n",
+    "mask = ift.Field.from_raw(s_space, mask)\n",
     "\n",
     "R = ift.DiagonalOperator(mask)(HT)\n",
-    "n = n.to_global_data_rw()\n",
+    "n = n.val_rw()\n",
     "n[l:h, l:h] = 0\n",
-    "n = ift.Field.from_global_data(s_space, n)\n",
+    "n = ift.Field.from_raw(s_space, n)\n",
     "curv = Curvature(R=R, N=N, Sh=Sh)\n",
     "D = curv.inverse\n",
     "\n",
@@ -602,10 +602,10 @@
     "m_mean, m_var = ift.probe_with_posterior_samples(curv, HT, 20)\n",
     "\n",
     "# Get data\n",
-    "s_data = HT(sh).to_global_data()\n",
-    "m_data = HT(m).to_global_data()\n",
-    "m_var_data = m_var.to_global_data()\n",
-    "d_data = d.to_global_data()\n",
+    "s_data = HT(sh).val\n",
+    "m_data = HT(m).val\n",
+    "m_var_data = m_var.val\n",
+    "d_data = d.val\n",
     "uncertainty = np.sqrt(np.abs(m_var_data))"
    ]
   },
@@ -653,8 +653,8 @@
     "ma = np.max(s_data)\n",
     "\n",
     "fig, axes = plt.subplots(3, 2, figsize=(15, 22.5))\n",
-    "sample = HT(curv.draw_sample(from_inverse=True)+m).to_global_data()\n",
-    "post_mean = (m_mean + HT(m)).to_global_data()\n",
+    "sample = HT(curv.draw_sample(from_inverse=True)+m).val\n",
+    "post_mean = (m_mean + HT(m)).val\n",
     "\n",
     "data = [s_data, m_data, post_mean, sample, s_data - m_data, uncertainty]\n",
     "caption = [\"Signal\", \"Reconstruction\", \"Posterior mean\", \"Sample\", \"Residuals\", \"Uncertainty Map\"]\n",
@@ -731,7 +731,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.6"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,

demos/bench_gridder.py

@@ -24,16 +24,16 @@ for ii in range(10, 26):
 
     img = np.random.randn(nu*nv)
     img = img.reshape((nu, nv))
-    img = ift.from_global_data(uvspace, img)
+    img = ift.makeField(uvspace, img)
 
     t0 = time()
     GM = ift.GridderMaker(uvspace, eps=1e-7, uv=uv)
-    vis = ift.from_global_data(visspace, vis)
+    vis = ift.makeField(visspace, vis)
     op = GM.getFull().adjoint
     t1 = time()
-    op(img).to_global_data()
+    op(img).val
     t2 = time()
-    op.adjoint(vis).to_global_data()
+    op.adjoint(vis).val
     t3 = time()
     print(t2-t1, t3-t2)
     N0s.append(N)

demos/bernoulli_demo.py

@@ -61,9 +61,9 @@ if __name__ == '__main__':
     # Generate mock data
     p = R(sky)
     mock_position = ift.from_random('normal', harmonic_space)
-    tmp = p(mock_position).to_global_data().astype(np.float64)
+    tmp = p(mock_position).val.astype(np.float64)
     data = np.random.binomial(1, tmp)
-    data = ift.Field.from_global_data(R.target, data)
+    data = ift.Field.from_raw(R.target, data)
 
     # Compute likelihood and Hamiltonian
     position = ift.from_random('normal', harmonic_space)

demos/find_amplitude_parameters.py

@@ -57,7 +57,7 @@ if __name__ == '__main__':
         for _ in range(n_samps):
             fld = pspec(ift.from_random('normal', pspec.domain))
             klengths = fld.domain[0].k_lengths
-            ycoord = fld.to_global_data_rw()
+            ycoord = fld.val_rw()
             ycoord[0] = ycoord[1]
             ax.plot(klengths, ycoord, alpha=1)
 
@@ -80,7 +80,7 @@ if __name__ == '__main__':
         foo = []
         for ax in axs:
             pos = ift.from_random('normal', correlated_field.domain)
-            fld = correlated_field(pos).to_global_data()
+            fld = correlated_field(pos).val
             foo.append((ax, fld))
         mi, ma = np.inf, -np.inf
         for _, fld in foo:
@@ -106,7 +106,7 @@ if __name__ == '__main__':
         flds = []
         for _ in range(n_samps):
             pos = ift.from_random('normal', correlated_field.domain)
-            ax.plot(correlated_field(pos).to_global_data())
+            ax.plot(correlated_field(pos).val)
 
     plt.savefig('correlated_fields.png')
     plt.close()

demos/getting_started_1.py

@@ -42,7 +42,7 @@ def make_random_mask():
     # Random mask for spherical mode
     mask = ift.from_random('pm1', position_space)
     mask = (mask + 1)/2
-    return mask.to_global_data()
+    return mask.val
 
 
 if __name__ == '__main__':
@@ -95,7 +95,7 @@ if __name__ == '__main__':
     # and harmonic transformaion
 
     # Masking operator to model that parts of the field have not been observed
-    mask = ift.Field.from_global_data(position_space, mask)
+    mask = ift.Field.from_raw(position_space, mask)
     Mask = ift.MaskOperator(mask)
 
     # The response operator consists of

demos/getting_started_2.py

@@ -40,7 +40,7 @@ def exposure_2d():
     exposure[:, x_shape*4//5:x_shape] *= .1
     exposure[:, x_shape//2:x_shape*3//2] *= 3.
 
-    return ift.Field.from_global_data(position_space, exposure)
+    return ift.Field.from_raw(position_space, exposure)
 
 
 if __name__ == '__main__':
@@ -94,8 +94,8 @@ if __name__ == '__main__':
     lamb = R(sky)
     mock_position = ift.from_random('normal', domain)
     data = lamb(mock_position)
-    data = np.random.poisson(data.to_global_data().astype(np.float64))
-    data = ift.Field.from_global_data(d_space, data)
+    data = np.random.poisson(data.val.astype(np.float64))
+    data = ift.Field.from_raw(d_space, data)
     likelihood = ift.PoissonianEnergy(data)(lamb)
 
     # Settings for minimization

demos/getting_started_mf.py

@@ -40,7 +40,7 @@ class SingleDomain(ift.LinearOperator):
 
     def apply(self, x, mode):
         self._check_input(x, mode)
-        return ift.from_global_data(self._tgt(mode), x.to_global_data())
+        return ift.makeField(self._tgt(mode), x.val)
 
 
 def random_los(n_los):

demos/misc/convolution.py

@@ -38,11 +38,11 @@ signal_vals = np.zeros(npix, dtype=np.float64)
 for i in range(0, npix, npix//12 + 27):
     signal_vals[i] = 500.
 
-signal = ift.from_global_data(domain, signal_vals)
+signal = ift.makeField(domain, signal_vals)
 
 delta_vals = np.zeros(npix, dtype=np.float64)
 delta_vals[0] = 1.0
-delta = ift.from_global_data(domain, delta_vals)
+delta = ift.makeField(domain, delta_vals)
 
 
 # Define kernel function
@@ -58,12 +58,12 @@ domain = ift.RGSpace((100, 100))
 signal_vals = np.zeros(domain.shape, dtype=np.float64)
 signal_vals[35, 70] = 5000.
 signal_vals[45, 8] = 5000.
-signal = ift.from_global_data(domain, signal_vals)
+signal = ift.makeField(domain, signal_vals)
 
 # Define delta signal, generate kernel image
 delta_vals = np.zeros(domain.shape, dtype=np.float64)
 delta_vals[0, 0] = 1.0
-delta = ift.from_global_data(domain, delta_vals)
+delta = ift.makeField(domain, delta_vals)
 
 
 # Define kernel function

demos/multi_amplitudes_consistency.py

@@ -9,12 +9,12 @@ def testAmplitudesConsistency(seed, sspace):
         sc = ift.StatCalculator()
         for s in samples:
             sc.add(op(s.extract(op.domain)))
-        return sc.mean.to_global_data(), sc.var.sqrt().to_global_data()
+        return sc.mean.val, sc.var.sqrt().val
     np.random.seed(seed)
     offset_std = .1
     intergated_fluct_std0 = .003
     intergated_fluct_std1 = 0.1
-    
+
     nsam = 1000
 
 
@@ -32,7 +32,7 @@ def testAmplitudesConsistency(seed, sspace):
     offset_std,_ = stats(fa.amplitude_total_offset,samples)
     intergated_fluct_std0,_ = stats(fa.average_fluctuation(0),samples)
     intergated_fluct_std1,_ = stats(fa.average_fluctuation(1),samples)
-    
+
     slice_fluct_std0,_ = stats(fa.slice_fluctuation(0),samples)
     slice_fluct_std1,_ = stats(fa.slice_fluctuation(1),samples)
 
@@ -54,7 +54,7 @@ def testAmplitudesConsistency(seed, sspace):
     print("Expected  integrated fluct. frequency Std: " +
           str(intergated_fluct_std1))
     print("Estimated integrated fluct. frequency Std: " + str(fluct_freq))
-    
+
     print("Expected  slice fluct. space Std: " +
           str(slice_fluct_std0))
     print("Estimated slice fluct. space Std: " + str(sl_fluct_space))
@@ -65,8 +65,8 @@ def testAmplitudesConsistency(seed, sspace):
 
     print("Expected  total fluct. Std: " + str(tot_flm))
     print("Estimated total fluct. Std: " + str(fluct_total))
-    
-    
+
+
     np.testing.assert_allclose(offset_std, zm_std_mean, rtol=0.5)
     np.testing.assert_allclose(intergated_fluct_std0, fluct_space, rtol=0.5)
     np.testing.assert_allclose(intergated_fluct_std1, fluct_freq, rtol=0.5)
@@ -74,7 +74,7 @@ def testAmplitudesConsistency(seed, sspace):
     np.testing.assert_allclose(slice_fluct_std0, sl_fluct_space, rtol=0.5)
     np.testing.assert_allclose(slice_fluct_std1, sl_fluct_freq, rtol=0.5)
 
-    
+
     fa = ift.CorrelatedFieldMaker.make(offset_std, .1, '')
     fa.add_fluctuations(fsspace, intergated_fluct_std1, 1., 3.1, 1., .5, .1,
                         -4, 1., 'freq')
@@ -87,7 +87,7 @@ def testAmplitudesConsistency(seed, sspace):
     print("Forced   slice fluct. space Std: "+str(m))
     print("Expected slice fluct. Std: " + str(em))
     np.testing.assert_allclose(m, em, rtol=0.5)
-    
+
     assert op.target[0] == sspace
     assert op.target[1] == fsspace
 

demos/polynomial_fit.py

@@ -36,7 +36,7 @@ def polynomial(coefficients, sampling_points):
     if not (isinstance(coefficients, ift.Field)
             and isinstance(sampling_points, np.ndarray)):
         raise TypeError
-    params = coefficients.to_global_data()
+    params = coefficients.val
     out = np.zeros_like(sampling_points)
     for ii in range(len(params)):
         out += params[ii] * sampling_points**ii
@@ -71,14 +71,14 @@ class PolynomialResponse(ift.LinearOperator):
 
     def apply(self, x, mode):
         self._check_input(x, mode)
-        val = x.to_global_data_rw()
+        val = x.val_rw()
         if mode == self.TIMES:
             # FIXME Use polynomial() here
             out = self._mat.dot(val)
         else:
             # FIXME Can this be optimized?
             out = self._mat.conj().T.dot(val)
-        return ift.from_global_data(self._tgt(mode), out)
+        return ift.makeField(self._tgt(mode), out)
 
 
 # Generate some mock data
@@ -99,8 +99,8 @@ R = PolynomialResponse(p_space, x)
 ift.extra.consistency_check(R)
 
 d_space = R.target
-d = ift.from_global_data(d_space, y)
-N = ift.DiagonalOperator(ift.from_global_data(d_space, var))
+d = ift.makeField(d_space, y)
+N = ift.DiagonalOperator(ift.makeField(d_space, var))
 
 IC = ift.DeltaEnergyController(tol_rel_deltaE=1e-12, iteration_limit=200)
 likelihood = ift.GaussianEnergy(d, N)(R)
@@ -136,9 +136,8 @@ plt.savefig('fit.png')
 plt.close()
 
 # Print parameters
-mean = sc.mean.to_global_data()
-sigma = np.sqrt(sc.var.to_global_data())
-if ift.dobj.master:
-    for ii in range(len(mean)):
-        print('Coefficient x**{}: {:.2E} +/- {:.2E}'.format(ii, mean[ii],
+mean = sc.mean.val
+sigma = np.sqrt(sc.var.val)
+for ii in range(len(mean)):
+    print('Coefficient x**{}: {:.2E} +/- {:.2E}'.format(ii, mean[ii],
                                                             sigma[ii]))

nifty6/__init__.py

 from .version import __version__
 
-from . import dobj
-
 from .domains.domain import Domain
 from .domains.structured_domain import StructuredDomain
 from .domains.unstructured_domain import UnstructuredDomain
@@ -93,10 +91,5 @@ from .linearization import Linearization
 
 from .operator_spectrum import operator_spectrum
 
-from . import internal_config
-_scheme = internal_config.parallelization_scheme()
-if _scheme == "Samples":
-    from .minimization.metric_gaussian_kl_mpi import MetricGaussianKL_MPI
-
 # We deliberately don't set __all__ here, because we don't want people to do a
 # "from nifty6 import *"; that would swamp the global namespace.

nifty6/data_objects/distributed_do.py

-# This program is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program.  If not, see <http://www.gnu.org/licenses/>.
-#
-# Copyright(C) 2013-2019 Max-Planck-Society
-#
-# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
-
-import sys
-from functools import reduce
-
-import numpy as np
-from mpi4py import MPI
-
-from .random import Random
-
-__all__ = ["ntask", "rank", "master", "local_shape", "data_object", "full",
-           "empty", "zeros", "ones", "empty_like", "vdot", "exp",
-           "log", "tanh", "sqrt", "from_object", "from_random",
-           "local_data", "ibegin", "ibegin_from_shape", "np_allreduce_sum",
-           "np_allreduce_min", "np_allreduce_max",
-           "distaxis", "from_local_data", "from_global_data", "to_global_data",
-           "redistribute", "default_distaxis", "is_numpy", "absmax", "norm",
-           "lock", "locked", "uniform_full", "transpose", "to_global_data_rw",
-           "ensure_not_distributed", "ensure_default_distributed",
-           "tanh", "conjugate", "sin", "cos", "tan", "log10", "log1p", "expm1",
-           "sinh", "cosh", "sinc", "absolute", "sign", "clip"]
-
-_comm = MPI.COMM_WORLD
-ntask = _comm.Get_size()
-rank = _comm.Get_rank()
-master = (rank == 0)
-
-
-def is_numpy():
-    return False
-
-
-def _shareSize(nwork, nshares, myshare):
-    return (nwork//nshares) + int(myshare < nwork % nshares)
-
-
-def _shareRange(nwork, nshares, myshare):
-    nbase = nwork//nshares
-    additional = nwork % nshares
-    lo = myshare*nbase + min(myshare, additional)
-    hi = lo + nbase + int(myshare < additional)
-    return lo, hi
-
-
-def local_shape(shape, distaxis=0):
-    if len(shape) == 0 or distaxis == -1:
-        return shape
-    shape2 = list(shape)
-    shape2[distaxis] = _shareSize(shape[distaxis], ntask, rank)
-    return tuple(shape2)
-
-
-class data_object(object):
-    def __init__(self, shape, data, distaxis):
-        self._shape = tuple(shape)
-        if len(self._shape) == 0:
-            distaxis = -1
-            if not isinstance(data, np.ndarray):
-                data = np.full((), data)
-        self._distaxis = distaxis
-        self._data = data
-        if local_shape(self._shape, self._distaxis) != self._data.shape:
-            raise ValueError("shape mismatch")
-
-    def copy(self):
-        return data_object(self._shape, self._data.copy(), self._distaxis)
-
-#     def _sanity_checks(self):
-#         # check whether the distaxis is consistent
-#         if self._distaxis < -1 or self._distaxis >= len(self._shape):
-#             raise ValueError
-#         itmp = np.array(self._distaxis)
-#         otmp = np.empty(ntask, dtype=np.int)
-#         _comm.Allgather(itmp, otmp)
-#         if np.any(otmp != self._distaxis):
-#             raise ValueError
-#         # check whether the global shape is consistent
-#         itmp = np.array(self._shape)
-#         otmp = np.empty((ntask, len(self._shape)), dtype=np.int)
-#         _comm.Allgather(itmp, otmp)
-#         for i in range(ntask):
-#             if np.any(otmp[i, :] != self._shape):
-#                 raise ValueError
-#         # check shape of local data
-#         if self._distaxis < 0:
-#             if self._data.shape != self._shape:
-#                 raise ValueError
-#         else:
-#             itmp = np.array(self._shape)
-#             itmp[self._distaxis] = _shareSize(self._shape[self._distaxis],
-#                                               ntask, rank)
-#             if np.any(self._data.shape != itmp):
-#                 raise ValueError
-
-    @property
-    def dtype(self):
-        return self._data.dtype
-
-    @property
-    def shape(self):
-        return self._shape
-
-    @property
-    def size(self):
-        return np.prod(self._shape)
-
-    @property
-    def real(self):
-        return data_object(self._shape, self._data.real, self._distaxis)
-
-    @property
-    def imag(self):
-        return data_object(self._shape, self._data.imag, self._distaxis)
-
-    def conj(self):
-        return data_object(self._shape, self._data.conj(), self._distaxis)
-
-    def conjugate(self):
-        return data_object(self._shape, self._data.conjugate(), self._distaxis)
-
-    def _contraction_helper(self, op, mpiop, axis):
-        if axis is not None:
-            if len(axis) == len(self._data.shape):
-                axis = None
-        if axis is None:
-            res = np.array(getattr(self._data, op)())
-            if (self._distaxis == -1):
-                return res[()]
-            res2 = np.empty((), dtype=res.dtype)
-            _comm.Allreduce(res, res2, mpiop)
-            return res2[()]
-
-        if self._distaxis in axis:
-            res = getattr(self._data, op)(axis=axis)
-            res2 = np.empty_like(res)
-            _comm.Allreduce(res, res2, mpiop)
-            return from_global_data(res2, distaxis=0)
-        else:
-            # perform the contraction on the local data
-            res = getattr(self._data, op)(axis=axis)
-            if self._distaxis == -1:
-                return from_global_data(res, distaxis=0)
-            shp = list(res.shape)
-            shift = 0
-            for ax in axis:
-                if ax < self._distaxis:
-                    shift += 1
-            shp[self._distaxis-shift] = self.shape[self._distaxis]
-            return from_local_data(shp, res, self._distaxis-shift)
-
-    def sum(self, axis=None):
-        return self._contraction_helper("sum", MPI.SUM, axis)
-
-    def prod(self, axis=None):
-        return self._contraction_helper("prod", MPI.PROD, axis)
-
-#    def min(self, axis=None):
-#        return self._contraction_helper("min", MPI.MIN, axis)
-
-#    def max(self, axis=None):
-#        return self._contraction_helper("max", MPI.MAX, axis)
-
-    def mean(self, axis=None):
-        if axis is None:
-            sz = self.size
-        else:
-            sz = reduce(lambda x, y: x*y, [self.shape[i] for i in axis])
-        return self.sum(axis)/sz
-
-    def std(self, axis=None):
-        return np.sqrt(self.var(axis))
-
-    # FIXME: to be improved!
-    def var(self, axis=None):