add support jt.var / Var.var to compute variance.

Acknowledgement:
    Thanks fangtiancheng https://discuss.jittor.org/t/topic/193/3 for a demo implementation.

python/jittor/__init__.py

@@ -394,6 +394,58 @@ def zeros_like(x):
 
 flags = core.Flags()
 
+def var(x, dim=None, dims=None, unbiased=False, keepdims=False):
+    """ return the sample variance. If unbiased is True, Bessel's correction will be used.
+
+    :param x: the input jittor Var.
+    :type x: jt.Var.
+    :param dim: the dimension to compute the variance. If both dim and dims are None, the variance of the whole tensor will be computed.
+    :type dim: int.
+    :param dims: the dimensions to compute the variance. If both dim and dims are None, the variance of the whole tensor will be computed.
+    :type dims: tuple of int.
+    :param unbiased: if True, Bessel's correction will be used.
+    :type unbiased: bool.
+    :param keepdim: if True, the output shape is same as input shape except for the dimension in dim.
+    :type keepdim: bool.
+
+    Example:
+
+        >>> a = jt.rand(3)
+        >>> a
+        jt.Var([0.79613626 0.29322362 0.19785859], dtype=float32)
+        >>> a.var()
+        jt.Var([0.06888353], dtype=float32)
+        >>> a.var(unbiased=True)
+        jt.Var([0.10332529], dtype=float32)
+    """
+    shape = x.shape
+    new_shape = list(x.shape)
+
+    assert dim is None or dims is None, "dim and dims can not be both set"
+    if dim is None and dims is None:
+        dims = list(range(len(shape)))
+    elif dim is not None:
+        dims = [dim]
+
+    mean = jt.mean(x, dims, keepdims=True)
+    mean = jt.broadcast(mean, shape)
+
+    n = 1
+    for d in dims:
+        n *= shape[d]
+        new_shape[d] = 1
+
+    sqr = (x - mean) ** 2
+    sqr = jt.sum(sqr, dims=dims, keepdims=False)
+    if unbiased:
+        n -= 1
+    sqr /= n
+
+    if keepdims:
+        sqr = sqr.view(new_shape)
+    return sqr
+Var.var = var
+
 def std(x):
     matsize=1
     for i in x.shape:

python/jittor/test/test_std.py

@@ -1,43 +0,0 @@
-# ***************************************************************
-# Copyright (c) 2021 Jittor. All Rights Reserved. 
-# Maintainers: 
-#     Dun Liang <randonlang@gmail.com>. 
-# 
-# This file is subject to the terms and conditions defined in
-# file 'LICENSE.txt', which is part of this source code package.
-# ***************************************************************
-import unittest
-import jittor as jt
-import os
-import numpy as np
-import jittor.nn as jnn
-
-from jittor.test.test_log import find_log_with_re
-skip_this_test = False
-
-try:
-    jt.dirty_fix_pytorch_runtime_error()
-    import torch
-    import torch.nn as tnn
-except:
-    skip_this_test = True
-
-@unittest.skipIf(skip_this_test, "No Torch found")
-class TestStd(unittest.TestCase):
-    def test_std(self):
-        x=np.random.randn(100,1000).astype(np.float32)
-        jt_x=jt.array(x)
-        tc_x=torch.from_numpy(x)
-        assert np.allclose(jt_x.std().numpy(), tc_x.std().numpy(), 1e-4) ,(x, jt_x.std().numpy(), tc_x.std().numpy())
-
-    def test_norm(self):
-        x=np.random.randn(100,1000).astype(np.float32)
-        jt_x=jt.array(x)
-        tc_x=torch.from_numpy(x)
-        assert np.allclose(jt_x.norm(1,1).numpy(), tc_x.norm(1,1).numpy())
-        assert np.allclose(jt_x.norm(1,0).numpy(), tc_x.norm(1,0).numpy())
-        assert np.allclose(jt_x.norm(2,1).numpy(), tc_x.norm(2,1).numpy())
-        assert np.allclose(jt_x.norm(2,0).numpy(), tc_x.norm(2,0).numpy())
-        
-if __name__ == "__main__":
-    unittest.main()

python/jittor/test/test_var.py

@@ -0,0 +1,51 @@
+# ***************************************************************
+# Copyright (c) 2021 Jittor. All Rights Reserved. 
+# Maintainers: 
+#     Dun Liang <randonlang@gmail.com>. 
+#     Zheng-Ning Liu <lzhengning@gmail.com>
+# This file is subject to the terms and conditions defined in
+# file 'LICENSE.txt', which is part of this source code package.
+# ***************************************************************
+import unittest
+import jittor as jt
+import numpy as np
+import jittor.nn as jnn
+
+skip_this_test = False
+
+try:
+    jt.dirty_fix_pytorch_runtime_error()
+    import torch
+    import torch.nn as tnn
+except:
+    skip_this_test = True
+
+@unittest.skipIf(skip_this_test, "No Torch found")
+class TestVarFunctions(unittest.TestCase):
+    def test_var(self):
+        x = np.random.randn(100, 1000).astype(np.float32)
+
+        jt_x = jt.array(x)
+        tc_x = torch.from_numpy(x)
+        np.testing.assert_allclose(jt_x.var().numpy(), tc_x.var().numpy(), rtol=1e-3, atol=1e-4)
+        np.testing.assert_allclose(jt_x.var(dim=1).numpy(), tc_x.var(dim=1).numpy(), rtol=1e-3, atol=1e-4)
+        np.testing.assert_allclose(jt_x.var(dim=0, unbiased=True).numpy(), tc_x.var(dim=0, unbiased=True).numpy(), rtol=1e-3, atol=1e-4)
+        
+    def test_std(self):
+        x=np.random.randn(100, 1000).astype(np.float32)
+        jt_x = jt.array(x)
+        tc_x = torch.from_numpy(x)
+        np.testing.assert_allclose(jt_x.std().numpy(), tc_x.std().numpy(), 1e-4)
+
+    def test_norm(self):
+        x = np.random.randn(100, 1000).astype(np.float32)
+        jt_x = jt.array(x)
+        tc_x = torch.from_numpy(x)
+        np.testing.assert_allclose(jt_x.norm(1,1).numpy(), tc_x.norm(1,1).numpy(), atol=1e-6)
+        np.testing.assert_allclose(jt_x.norm(1,0).numpy(), tc_x.norm(1,0).numpy(), atol=1e-6)
+        np.testing.assert_allclose(jt_x.norm(2,1).numpy(), tc_x.norm(2,1).numpy(), atol=1e-6)
+        np.testing.assert_allclose(jt_x.norm(2,0).numpy(), tc_x.norm(2,0).numpy(), atol=1e-6)
+
+
+if __name__ == "__main__":
+    unittest.main()