From 4ca1c0dffe78a0038185ea1122f21c58e8980638 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Mon, 5 Apr 2021 14:03:04 +0200
Subject: [PATCH 01/21] init files

---
 tests/regression/test_pearson.py              |  0
 .../functional/regression/__init__.py         |  1 +
 torchmetrics/functional/regression/pearson.py | 86 +++++++++++++++++++
 torchmetrics/regression/__init__.py           |  1 +
 torchmetrics/regression/pearson.py            | 13 +++
 5 files changed, 101 insertions(+)
 create mode 100644 tests/regression/test_pearson.py
 create mode 100644 torchmetrics/functional/regression/pearson.py
 create mode 100644 torchmetrics/regression/pearson.py

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/torchmetrics/functional/regression/__init__.py b/torchmetrics/functional/regression/__init__.py
index 63c2aabb1e2..9684b5642b4 100644
--- a/torchmetrics/functional/regression/__init__.py
+++ b/torchmetrics/functional/regression/__init__.py
@@ -15,6 +15,7 @@
 from torchmetrics.functional.regression.mean_absolute_error import mean_absolute_error  # noqa: F401
 from torchmetrics.functional.regression.mean_squared_error import mean_squared_error  # noqa: F401
 from torchmetrics.functional.regression.mean_squared_log_error import mean_squared_log_error  # noqa: F401
+from torchmetrics.functional.regression.pearson import pearson_corrcoef  # noqa: F401
 from torchmetrics.functional.regression.psnr import psnr  # noqa: F401
 from torchmetrics.functional.regression.r2score import r2score  # noqa: F401
 from torchmetrics.functional.regression.ssim import ssim  # noqa: F401
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
new file mode 100644
index 00000000000..a1829c6443c
--- /dev/null
+++ b/torchmetrics/functional/regression/pearson.py
@@ -0,0 +1,86 @@
+# Copyright The PyTorch Lightning team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+from typing import Sequence, Tuple, Union, Optional
+
+import torch
+from torch import Tensor
+
+from torchmetrics.utilities.checks import _check_same_shape
+
+
+def _update_mean(old_mean: torch.Tensor, old_nobs: torch.Tensor, data: torch.Tensor) -> torch.Tensor:
+    """ Update a mean estimate given new data
+    Args:
+        old_mean: current mean estimate
+        old_nobs: number of observation until now
+        data: data used for updating the estimate
+    Returns:
+        new_mean: updated mean estimate
+    """
+    data_size = data.shape[0]
+    return (old_mean * old_nobs + data.mean(dim=0) * data_size) / (old_nobs + data_size)
+
+
+def _update_cov(old_cov: torch.Tensor, old_mean: torch.Tensor, new_mean: torch.Tensor, data: torch.Tensor):
+    """ Update a covariance estimate given new data
+    Args:
+        old_cov: current covariance estimate
+        old_mean: current mean estimate
+        new_mean: updated mean estimate
+        data: data used for updating the estimate
+    Returns:
+        new_mean: updated covariance estimate
+    """
+    return old_cov + (data - new_mean).T @ (data - old_mean)
+
+
+def _pearson_corrcoef_update(
+        preds: Tensor, 
+        target: Tensor, 
+        old_mean: Optional[Tensor] = None, 
+        old_cov: Optional[Tensor] = None,
+        old_nobs: Optional[Tensor] = None
+) -> Tuple[Tensor, Tensor, Tensor, Tensor]:
+    # Data checking
+    _check_same_shape(preds, target)
+    preds = preds.squeeze()
+    target = target.squeeze()
+    if preds.ndim > 1 or target.ndim > 1:
+        raise ValueError('Expected both predictions and target to be 1 dimensional tensors. Please flatten.')
+    data = torch.stack([preds, target], dim=1)
+
+    if old_mean is None:
+        old_mean = 0
+    if old_cov is None:
+        old_cov = 0
+    if old_nobs is None:
+        old_nobs = 0
+    
+    new_mean = _update_mean(old_mean, old_nobs, data)
+    new_cov = _update_cov(old_cov, old_mean, new_mean, data)
+    new_size = old_nobs + preds.numel()
+    
+    return new_mean, new_cov, new_size
+    
+    
+def _pearson_corrcoef_compute(c: torch.Tensor):
+    x_var = c[0,0]
+    y_var = c[1,1]
+    cov = c[1,1]
+    return cov / (x_var * y_var)
+
+
+def pearson_corrcoef(preds: Tensor, target: Tensor) -> Tensor:
+    _, c, _ = _pearson_corrcoef_update(preds, target)
+    return _pearson_corrcoef_compute(c)
diff --git a/torchmetrics/regression/__init__.py b/torchmetrics/regression/__init__.py
index bf2da61095e..5c405e10ff3 100644
--- a/torchmetrics/regression/__init__.py
+++ b/torchmetrics/regression/__init__.py
@@ -15,6 +15,7 @@
 from torchmetrics.regression.mean_absolute_error import MeanAbsoluteError  # noqa: F401
 from torchmetrics.regression.mean_squared_error import MeanSquaredError  # noqa: F401
 from torchmetrics.regression.mean_squared_log_error import MeanSquaredLogError  # noqa: F401
+from torchmetrics.regression.pearson import PearsonCorrcoef  # noqa: F401
 from torchmetrics.regression.psnr import PSNR  # noqa: F401
 from torchmetrics.regression.r2score import R2Score  # noqa: F401
 from torchmetrics.regression.ssim import SSIM  # noqa: F401
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
new file mode 100644
index 00000000000..e708df58645
--- /dev/null
+++ b/torchmetrics/regression/pearson.py
@@ -0,0 +1,13 @@
+# Copyright The PyTorch Lightning team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
\ No newline at end of file

From d25bcf6d669ba71af459dd2b00ec7daf0a5307a0 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Mon, 5 Apr 2021 15:04:19 +0200
Subject: [PATCH 02/21] rest

---
 docs/source/references/functional.rst         |   7 +
 docs/source/references/modules.rst            |   7 +
 tests/regression/test_pearson.py              | 120 ++++++++++++++++++
 torchmetrics/__init__.py                      |   1 +
 torchmetrics/functional/__init__.py           |   1 +
 torchmetrics/functional/regression/pearson.py |  28 +++-
 torchmetrics/regression/pearson.py            |  84 +++++++++++-
 7 files changed, 241 insertions(+), 7 deletions(-)

diff --git a/docs/source/references/functional.rst b/docs/source/references/functional.rst
index 5f450eca1df..8c56cf1287c 100644
--- a/docs/source/references/functional.rst
+++ b/docs/source/references/functional.rst
@@ -196,6 +196,13 @@ mean_squared_log_error [func]
     :noindex:
 
 
+pearson_corrcoef [func]
+~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: torchmetrics.functional.pearson_corrcoef
+    :noindex:
+
+
 psnr [func]
 ~~~~~~~~~~~
 
diff --git a/docs/source/references/modules.rst b/docs/source/references/modules.rst
index f6f6d32af86..dc20c58dec0 100644
--- a/docs/source/references/modules.rst
+++ b/docs/source/references/modules.rst
@@ -250,6 +250,13 @@ MeanSquaredLogError
     :noindex:
 
 
+PearsonCorrcoef
+~~~~~~~~~~~~~~~
+
+.. autoclass:: torchmetrics.PearsonCorrcoef
+    :noindex:
+
+
 PSNR
 ~~~~
 
diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index e69de29bb2d..ce46deae1c7 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -0,0 +1,120 @@
+# Copyright The PyTorch Lightning team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import pytest
+import pickle
+from collections import namedtuple
+from functools import partial
+import torch
+from tests.helpers import seed_all
+from scipy.stats import pearsonr
+
+from torchmetrics.regression.pearson import PearsonCorrcoef
+from torchmetrics.functional.regression.pearson import  pearson_corrcoef, _update_cov, _update_mean
+from tests.helpers.testers import BATCH_SIZE, NUM_BATCHES, MetricTester
+seed_all(42)
+
+
+def test_update_functions(tmpdir):
+    """ Test that updating the estimates are equal to estimating them on all data """
+    data = torch.randn(100, 2)
+    batch1, batch2 = data.chunk(2)
+
+    def _mean_cov(data):
+        mean = data.mean(0)
+        diff = data - mean
+        cov = diff.T @ diff
+        return mean, cov
+
+    mean_update, cov_update, size_update = torch.zeros(2), torch.zeros(2,2), torch.zeros(1)
+    for batch in [batch1, batch2]:
+        new_mean = _update_mean(mean_update, size_update, batch) 
+        new_cov = _update_cov(cov_update, mean_update, new_mean, batch)
+
+        assert not torch.allclose(new_mean, mean_update), "mean estimate did not update"
+        assert not torch.allclose(new_cov, cov_update), "covariance estimate did not update"
+
+        size_update += batch.shape[0]
+        mean_update = new_mean
+        cov_update = new_cov
+
+    mean, cov = _mean_cov(data)
+
+    assert torch.allclose(mean, mean_update), "updated mean does not correspond to mean of all data"
+    assert torch.allclose(cov, cov_update), "updated covariance does not correspond to covariance of all data"
+    
+
+Input = namedtuple('Input', ["preds", "target"])
+
+_single_target_inputs1 = Input(
+    preds=torch.rand(NUM_BATCHES, BATCH_SIZE),
+    target=torch.rand(NUM_BATCHES, BATCH_SIZE),
+)
+
+_single_target_inputs2 = Input(
+    preds=torch.randn(NUM_BATCHES, BATCH_SIZE),
+    target=torch.randn(NUM_BATCHES, BATCH_SIZE),
+)
+
+
+def _sk_metric(preds, target):
+    sk_preds = preds.view(-1).numpy()
+    sk_target = target.view(-1).numpy()
+    return pearsonr(sk_target, sk_preds)[0]
+
+
+@pytest.mark.parametrize("preds, target",
+    [
+        (_single_target_inputs1.preds, _single_target_inputs1.target),
+        (_single_target_inputs2.preds, _single_target_inputs2.target),
+    ],
+)
+class TestPearsonCorrcoef(MetricTester):
+    atol=1e-4
+    @pytest.mark.parametrize("ddp", [True, False])
+    @pytest.mark.parametrize("dist_sync_on_step", [True, False])
+    def test_explained_variance(self, preds, target, ddp, dist_sync_on_step):
+        self.run_class_metric_test(
+            ddp,
+            preds,
+            target,
+            PearsonCorrcoef,
+            _sk_metric, 
+            dist_sync_on_step,
+        )
+
+    def test_pearson_corrcoef_functional(self, preds, target):
+        self.run_functional_metric_test(
+            preds,
+            target,
+            pearson_corrcoef,
+            _sk_metric
+        )
+
+    # Pearson half + cpu does not work due to missing support in torch.sqrt
+    @pytest.mark.xfail(reason="PSNR metric does not support cpu + half precision")
+    def test_pearson_corrcoef_half_cpu(self, preds, target):
+        self.run_precision_test_cpu(preds, target, PearsonCorrcoef, pearson_corrcoef)
+
+    @pytest.mark.skipif(not torch.cuda.is_available(), reason='test requires cuda')
+    def test_pearson_corrcoef_half_gpu(self, preds, target):
+        self.run_precision_test_gpu(preds, target, PearsonCorrcoef, pearson_corrcoef)
+
+
+def test_error_on_different_shape():
+    metric = PearsonCorrcoef()
+    with pytest.raises(RuntimeError, match='Predictions and targets are expected to have the same shape'):
+        metric(torch.randn(100, ), torch.randn(50, ))
+        
+    with pytest.raises(ValueError, match='Expected both predictions and target to be 1 dimensional tensors.'):
+        metric(torch.randn(100, 2), torch.randn(100, 2))
diff --git a/torchmetrics/__init__.py b/torchmetrics/__init__.py
index 7e21b7886df..8af309c46d6 100644
--- a/torchmetrics/__init__.py
+++ b/torchmetrics/__init__.py
@@ -41,6 +41,7 @@
 from torchmetrics.collections import MetricCollection  # noqa: F401 E402
 from torchmetrics.metric import Metric  # noqa: F401 E402
 from torchmetrics.regression import (  # noqa: F401 E402
+    PearsonCorrcoef,
     PSNR,
     SSIM,
     ExplainedVariance,
diff --git a/torchmetrics/functional/__init__.py b/torchmetrics/functional/__init__.py
index 18d90b6d9ce..428ddd54d97 100644
--- a/torchmetrics/functional/__init__.py
+++ b/torchmetrics/functional/__init__.py
@@ -34,6 +34,7 @@
 from torchmetrics.functional.regression.mean_relative_error import mean_relative_error  # noqa: F401
 from torchmetrics.functional.regression.mean_squared_error import mean_squared_error  # noqa: F401
 from torchmetrics.functional.regression.mean_squared_log_error import mean_squared_log_error  # noqa: F401
+from torchmetrics.functional.regression.pearson import pearson_corrcoef  # noqa: F401
 from torchmetrics.functional.regression.psnr import psnr  # noqa: F401
 from torchmetrics.functional.regression.r2score import r2score  # noqa: F401
 from torchmetrics.functional.regression.ssim import ssim  # noqa: F401
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index a1829c6443c..d6061ded778 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -57,7 +57,7 @@ def _pearson_corrcoef_update(
     preds = preds.squeeze()
     target = target.squeeze()
     if preds.ndim > 1 or target.ndim > 1:
-        raise ValueError('Expected both predictions and target to be 1 dimensional tensors. Please flatten.')
+        raise ValueError('Expected both predictions and target to be 1 dimensional tensors.')
     data = torch.stack([preds, target], dim=1)
 
     if old_mean is None:
@@ -74,13 +74,29 @@ def _pearson_corrcoef_update(
     return new_mean, new_cov, new_size
     
     
-def _pearson_corrcoef_compute(c: torch.Tensor):
+def _pearson_corrcoef_compute(c: Tensor, nobs: Tensor):
+    c /= (nobs-1)
     x_var = c[0,0]
     y_var = c[1,1]
-    cov = c[1,1]
-    return cov / (x_var * y_var)
+    cov = c[0,1]
+    corrcoef = cov / (x_var * y_var).sqrt()
+    return torch.clip(corrcoef, -1.0, 1.0)
 
 
 def pearson_corrcoef(preds: Tensor, target: Tensor) -> Tensor:
-    _, c, _ = _pearson_corrcoef_update(preds, target)
-    return _pearson_corrcoef_compute(c)
+    """
+    Computes pearson correlation coefficient.
+
+    Args:
+        preds: estimated scores
+        target: ground truth scores
+
+    Example:
+        >>> from torchmetrics.functional import pearson_corrcoef
+        >>> target = torch.tensor([3, -0.5, 2, 7])
+        >>> preds = torch.tensor([2.5, 0.0, 2, 8])
+        >>> pearson_corrcoef(preds, target)
+        tensor(0.9849)
+    """
+    _, c, nobs = _pearson_corrcoef_update(preds, target)
+    return _pearson_corrcoef_compute(c, nobs)
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index e708df58645..aed0a460502 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -10,4 +10,86 @@
 # distributed under the License is distributed on an "AS IS" BASIS,
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
-# limitations under the License.
\ No newline at end of file
+# limitations under the License.
+from typing import Any, Callable, Optional
+
+import torch
+from torch import Tensor, tensor
+
+from torchmetrics.functional.regression.pearson import (
+    _pearson_corrcoef_compute,
+    _pearson_corrcoef_update
+)
+from torchmetrics.metric import Metric
+
+
+class PearsonCorrcoef(Metric):
+    r"""
+    Computes `pearson correlation coefficient
+    <https://en.wikipedia.org/wiki/Pearson_correlation_coefficient>`_:
+
+    .. math:: \text{P_corr}(x,y) = \frac{cov(x,y)}{\sigma_x \times \sigma_y}
+
+    Where :math:`y` is a tensor of target values, and :math:`x` is a
+    tensor of predictions.
+
+    Forward accepts
+
+    - ``preds`` (float tensor): ``(N,)`` 
+    - ``target``(float tensor): ``(N,)``
+
+    Args:
+        compute_on_step:
+            Forward only calls ``update()`` and return None if this is set to False. default: True
+        dist_sync_on_step:
+            Synchronize metric state across processes at each ``forward()``
+            before returning the value at the step. default: False
+        process_group:
+            Specify the process group on which synchronization is called. default: None (which selects the entire world)
+        dist_sync_fn:
+            Callback that performs the allgather operation on the metric state. When ``None``, DDP
+            will be used to perform the allgather
+
+    Example:
+        >>> from torchmetrics import PearsonCorrcoef
+        >>> target = torch.tensor([3, -0.5, 2, 7])
+        >>> preds = torch.tensor([2.5, 0.0, 2, 8])
+        >>> pearson = PearsonCorrcoef()
+        >>> pearson(preds, target)
+        tensor(0.9849)
+
+    """
+    def __init__(
+        self,
+        compute_on_step: bool = True,
+        dist_sync_on_step: bool = False,
+        process_group: Optional[Any] = None,
+        dist_sync_fn: Callable = None,
+    ):
+        super().__init__(
+            compute_on_step=compute_on_step,
+            dist_sync_on_step=dist_sync_on_step,
+            process_group=process_group,
+            dist_sync_fn=dist_sync_fn,
+        )
+        self.add_state("cov", default=torch.zeros(2,2), dist_reduce_fx="sum")
+        self.add_state("mean", default=torch.zeros(2), dist_reduce_fx="sum")
+        self.add_state("n_obs", default=torch.zeros(1), dist_reduce_fx="sum")
+
+    def update(self, preds: Tensor, target: Tensor):
+        """
+        Update state with predictions and targets.
+
+        Args:
+            preds: Predictions from model
+            target: Ground truth values
+        """
+        self.mean, self.cov, self.n_obs = _pearson_corrcoef_update(
+            preds, target, self.mean, self.cov, self.n_obs
+        )
+
+    def compute(self):
+        """
+        Computes pearson correlation coefficient over state.
+        """
+        return _pearson_corrcoef_compute(self.cov, self.n_obs)

From ff5326e73743c3f88d61536afdcc155f92074d0c Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Mon, 5 Apr 2021 15:10:11 +0200
Subject: [PATCH 03/21] pep8

---
 tests/regression/test_pearson.py              | 35 +++++++++----------
 torchmetrics/functional/regression/pearson.py | 28 +++++++--------
 torchmetrics/regression/pearson.py            | 11 +++---
 3 files changed, 35 insertions(+), 39 deletions(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index ce46deae1c7..d59b88773d1 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -11,17 +11,17 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-import pytest
-import pickle
 from collections import namedtuple
-from functools import partial
+
+import pytest
 import torch
-from tests.helpers import seed_all
 from scipy.stats import pearsonr
 
-from torchmetrics.regression.pearson import PearsonCorrcoef
-from torchmetrics.functional.regression.pearson import  pearson_corrcoef, _update_cov, _update_mean
+from tests.helpers import seed_all
 from tests.helpers.testers import BATCH_SIZE, NUM_BATCHES, MetricTester
+from torchmetrics.functional.regression.pearson import _update_cov, _update_mean, pearson_corrcoef
+from torchmetrics.regression.pearson import PearsonCorrcoef
+
 seed_all(42)
 
 
@@ -36,9 +36,9 @@ def _mean_cov(data):
         cov = diff.T @ diff
         return mean, cov
 
-    mean_update, cov_update, size_update = torch.zeros(2), torch.zeros(2,2), torch.zeros(1)
+    mean_update, cov_update, size_update = torch.zeros(2), torch.zeros(2, 2), torch.zeros(1)
     for batch in [batch1, batch2]:
-        new_mean = _update_mean(mean_update, size_update, batch) 
+        new_mean = _update_mean(mean_update, size_update, batch)
         new_cov = _update_cov(cov_update, mean_update, new_mean, batch)
 
         assert not torch.allclose(new_mean, mean_update), "mean estimate did not update"
@@ -52,7 +52,7 @@ def _mean_cov(data):
 
     assert torch.allclose(mean, mean_update), "updated mean does not correspond to mean of all data"
     assert torch.allclose(cov, cov_update), "updated covariance does not correspond to covariance of all data"
-    
+
 
 Input = namedtuple('Input', ["preds", "target"])
 
@@ -73,14 +73,13 @@ def _sk_metric(preds, target):
     return pearsonr(sk_target, sk_preds)[0]
 
 
-@pytest.mark.parametrize("preds, target",
-    [
-        (_single_target_inputs1.preds, _single_target_inputs1.target),
-        (_single_target_inputs2.preds, _single_target_inputs2.target),
-    ],
-)
+@pytest.mark.parametrize("preds, target", [
+    (_single_target_inputs1.preds, _single_target_inputs1.target),
+    (_single_target_inputs2.preds, _single_target_inputs2.target),
+])
 class TestPearsonCorrcoef(MetricTester):
-    atol=1e-4
+    atol = 1e-4
+
     @pytest.mark.parametrize("ddp", [True, False])
     @pytest.mark.parametrize("dist_sync_on_step", [True, False])
     def test_explained_variance(self, preds, target, ddp, dist_sync_on_step):
@@ -89,7 +88,7 @@ def test_explained_variance(self, preds, target, ddp, dist_sync_on_step):
             preds,
             target,
             PearsonCorrcoef,
-            _sk_metric, 
+            _sk_metric,
             dist_sync_on_step,
         )
 
@@ -115,6 +114,6 @@ def test_error_on_different_shape():
     metric = PearsonCorrcoef()
     with pytest.raises(RuntimeError, match='Predictions and targets are expected to have the same shape'):
         metric(torch.randn(100, ), torch.randn(50, ))
-        
+
     with pytest.raises(ValueError, match='Expected both predictions and target to be 1 dimensional tensors.'):
         metric(torch.randn(100, 2), torch.randn(100, 2))
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index d6061ded778..86dd79a0987 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Sequence, Tuple, Union, Optional
+from typing import Optional, Tuple
 
 import torch
 from torch import Tensor
@@ -46,11 +46,11 @@ def _update_cov(old_cov: torch.Tensor, old_mean: torch.Tensor, new_mean: torch.T
 
 
 def _pearson_corrcoef_update(
-        preds: Tensor, 
-        target: Tensor, 
-        old_mean: Optional[Tensor] = None, 
-        old_cov: Optional[Tensor] = None,
-        old_nobs: Optional[Tensor] = None
+    preds: Tensor,
+    target: Tensor,
+    old_mean: Optional[Tensor] = None,
+    old_cov: Optional[Tensor] = None,
+    old_nobs: Optional[Tensor] = None
 ) -> Tuple[Tensor, Tensor, Tensor, Tensor]:
     # Data checking
     _check_same_shape(preds, target)
@@ -66,19 +66,19 @@ def _pearson_corrcoef_update(
         old_cov = 0
     if old_nobs is None:
         old_nobs = 0
-    
+
     new_mean = _update_mean(old_mean, old_nobs, data)
     new_cov = _update_cov(old_cov, old_mean, new_mean, data)
     new_size = old_nobs + preds.numel()
-    
+
     return new_mean, new_cov, new_size
-    
-    
+
+
 def _pearson_corrcoef_compute(c: Tensor, nobs: Tensor):
-    c /= (nobs-1)
-    x_var = c[0,0]
-    y_var = c[1,1]
-    cov = c[0,1]
+    c /= (nobs - 1)
+    x_var = c[0, 0]
+    y_var = c[1, 1]
+    cov = c[0, 1]
     corrcoef = cov / (x_var * y_var).sqrt()
     return torch.clip(corrcoef, -1.0, 1.0)
 
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index aed0a460502..8598c86117a 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -14,12 +14,9 @@
 from typing import Any, Callable, Optional
 
 import torch
-from torch import Tensor, tensor
+from torch import Tensor
 
-from torchmetrics.functional.regression.pearson import (
-    _pearson_corrcoef_compute,
-    _pearson_corrcoef_update
-)
+from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update
 from torchmetrics.metric import Metric
 
 
@@ -35,7 +32,7 @@ class PearsonCorrcoef(Metric):
 
     Forward accepts
 
-    - ``preds`` (float tensor): ``(N,)`` 
+    - ``preds`` (float tensor): ``(N,)``
     - ``target``(float tensor): ``(N,)``
 
     Args:
@@ -72,7 +69,7 @@ def __init__(
             process_group=process_group,
             dist_sync_fn=dist_sync_fn,
         )
-        self.add_state("cov", default=torch.zeros(2,2), dist_reduce_fx="sum")
+        self.add_state("cov", default=torch.zeros(2, 2), dist_reduce_fx="sum")
         self.add_state("mean", default=torch.zeros(2), dist_reduce_fx="sum")
         self.add_state("n_obs", default=torch.zeros(1), dist_reduce_fx="sum")
 

From 0ae07326d4a559b979e05e4d71f90fea458fd548 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Mon, 5 Apr 2021 15:14:20 +0200
Subject: [PATCH 04/21] changelog

---
 CHANGELOG.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1ab569b5666..9483904dced 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -47,6 +47,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added `__getitem__` as metric arithmetic operation ([#142](https://github.com/PyTorchLightning/metrics/pull/142))
 
 
+- Added `PearsonCorrcoef` metric ([#157](https://github.com/PyTorchLightning/metrics/pull/157))
+
+
 ### Changed
 
 - Changed `ExplainedVariance` from storing all preds/targets to tracking 5 statistics ([#68](https://github.com/PyTorchLightning/metrics/pull/68))

From ff36a0ea1a02fe93c21eeeb3b141ed2f20f9887b Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Mon, 5 Apr 2021 16:03:06 +0200
Subject: [PATCH 05/21] clamp

---
 torchmetrics/functional/regression/pearson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index 86dd79a0987..7ce53b3a4fe 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -80,7 +80,7 @@ def _pearson_corrcoef_compute(c: Tensor, nobs: Tensor):
     y_var = c[1, 1]
     cov = c[0, 1]
     corrcoef = cov / (x_var * y_var).sqrt()
-    return torch.clip(corrcoef, -1.0, 1.0)
+    return torch.clamp(corrcoef, -1.0, 1.0)
 
 
 def pearson_corrcoef(preds: Tensor, target: Tensor) -> Tensor:

From ca7cb99a24463c13c360665b9d2c147c944b2dbf Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 6 Apr 2021 09:54:16 +0200
Subject: [PATCH 06/21] suggestions

---
 tests/regression/test_pearson.py              | 24 +++++++++----------
 torchmetrics/functional/regression/pearson.py |  4 ++++
 torchmetrics/regression/pearson.py            |  2 +-
 3 files changed, 17 insertions(+), 13 deletions(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index d59b88773d1..0e0642355dd 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -82,26 +82,26 @@ class TestPearsonCorrcoef(MetricTester):
 
     @pytest.mark.parametrize("ddp", [True, False])
     @pytest.mark.parametrize("dist_sync_on_step", [True, False])
-    def test_explained_variance(self, preds, target, ddp, dist_sync_on_step):
+    def test_pearson_corrcoef(self, preds, target, ddp, dist_sync_on_step):
         self.run_class_metric_test(
-            ddp,
-            preds,
-            target,
-            PearsonCorrcoef,
-            _sk_metric,
-            dist_sync_on_step,
+            ddp=ddp,
+            preds=preds,
+            target=target,
+            metric_class=PearsonCorrcoef,
+            sk_metric=_sk_metric,
+            dist_sync_on_step=dist_sync_on_step,
         )
 
     def test_pearson_corrcoef_functional(self, preds, target):
         self.run_functional_metric_test(
-            preds,
-            target,
-            pearson_corrcoef,
-            _sk_metric
+            preds=preds,
+            target=target,
+            metric_functional=pearson_corrcoef,
+            sk_metric=_sk_metric
         )
 
     # Pearson half + cpu does not work due to missing support in torch.sqrt
-    @pytest.mark.xfail(reason="PSNR metric does not support cpu + half precision")
+    @pytest.mark.xfail(reason="PearsonCorrcoef metric does not support cpu + half precision")
     def test_pearson_corrcoef_half_cpu(self, preds, target):
         self.run_precision_test_cpu(preds, target, PearsonCorrcoef, pearson_corrcoef)
 
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index 7ce53b3a4fe..d87b994ceb7 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -52,6 +52,9 @@ def _pearson_corrcoef_update(
     old_cov: Optional[Tensor] = None,
     old_nobs: Optional[Tensor] = None
 ) -> Tuple[Tensor, Tensor, Tensor, Tensor]:
+    """ updates current estimates of the mean, cov and n_obs with new data for calculating
+        pearsons correlation
+    """
     # Data checking
     _check_same_shape(preds, target)
     preds = preds.squeeze()
@@ -75,6 +78,7 @@ def _pearson_corrcoef_update(
 
 
 def _pearson_corrcoef_compute(c: Tensor, nobs: Tensor):
+    """ computes the final pearson correlation based on covariance matrix and number of observatiosn """
     c /= (nobs - 1)
     x_var = c[0, 0]
     y_var = c[1, 1]
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index 8598c86117a..9275869dbc5 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -61,7 +61,7 @@ def __init__(
         compute_on_step: bool = True,
         dist_sync_on_step: bool = False,
         process_group: Optional[Any] = None,
-        dist_sync_fn: Callable = None,
+        dist_sync_fn: Optional[Callable] = None,
     ):
         super().__init__(
             compute_on_step=compute_on_step,

From 1188d0d82ac895ede50d90381730b69689468f66 Mon Sep 17 00:00:00 2001
From: Jirka Borovec <Borda@users.noreply.github.com>
Date: Tue, 6 Apr 2021 10:46:18 +0200
Subject: [PATCH 07/21] rename

---
 tests/regression/test_pearson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index 0e0642355dd..1f05d4f958e 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -67,7 +67,7 @@ def _mean_cov(data):
 )
 
 
-def _sk_metric(preds, target):
+def _sk_pearsonr(preds, target):
     sk_preds = preds.view(-1).numpy()
     sk_target = target.view(-1).numpy()
     return pearsonr(sk_target, sk_preds)[0]

From df47c7fea5833d8e39d7e750fee2daf7bfc9ae31 Mon Sep 17 00:00:00 2001
From: Jirka Borovec <jirka.borovec@seznam.cz>
Date: Tue, 6 Apr 2021 10:47:31 +0200
Subject: [PATCH 08/21] format

---
 torchmetrics/functional/classification/f_beta.py | 2 +-
 torchmetrics/functional/regression/pearson.py    | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/torchmetrics/functional/classification/f_beta.py b/torchmetrics/functional/classification/f_beta.py
index 70e0687e2da..e477cc51c4b 100644
--- a/torchmetrics/functional/classification/f_beta.py
+++ b/torchmetrics/functional/classification/f_beta.py
@@ -21,7 +21,7 @@
 from torchmetrics.utilities.enums import AverageMethod, MDMCAverageMethod
 
 
-def _safe_divide(num: torch.Tensor, denom: torch.Tensor):
+def _safe_divide(num: Tensor, denom: Tensor):
     """ prevent zero division """
     denom[denom == 0.] = 1
     return num / denom
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index d87b994ceb7..ac11514c75f 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -19,7 +19,7 @@
 from torchmetrics.utilities.checks import _check_same_shape
 
 
-def _update_mean(old_mean: torch.Tensor, old_nobs: torch.Tensor, data: torch.Tensor) -> torch.Tensor:
+def _update_mean(old_mean: Tensor, old_nobs: Tensor, data: Tensor) -> Tensor:
     """ Update a mean estimate given new data
     Args:
         old_mean: current mean estimate
@@ -32,7 +32,7 @@ def _update_mean(old_mean: torch.Tensor, old_nobs: torch.Tensor, data: torch.Ten
     return (old_mean * old_nobs + data.mean(dim=0) * data_size) / (old_nobs + data_size)
 
 
-def _update_cov(old_cov: torch.Tensor, old_mean: torch.Tensor, new_mean: torch.Tensor, data: torch.Tensor):
+def _update_cov(old_cov: Tensor, old_mean: Tensor, new_mean: Tensor, data: Tensor):
     """ Update a covariance estimate given new data
     Args:
         old_cov: current covariance estimate

From 6b0795c6780065e247946ffa4f4fd186da4819b8 Mon Sep 17 00:00:00 2001
From: Jirka Borovec <jirka.borovec@seznam.cz>
Date: Tue, 6 Apr 2021 11:04:01 +0200
Subject: [PATCH 09/21] _sk_pearsonr

---
 tests/regression/test_pearson.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index 1f05d4f958e..4152965381e 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -88,7 +88,7 @@ def test_pearson_corrcoef(self, preds, target, ddp, dist_sync_on_step):
             preds=preds,
             target=target,
             metric_class=PearsonCorrcoef,
-            sk_metric=_sk_metric,
+            sk_metric=_sk_pearsonr,
             dist_sync_on_step=dist_sync_on_step,
         )
 
@@ -97,7 +97,7 @@ def test_pearson_corrcoef_functional(self, preds, target):
             preds=preds,
             target=target,
             metric_functional=pearson_corrcoef,
-            sk_metric=_sk_metric
+            sk_metric=_sk_pearsonr
         )
 
     # Pearson half + cpu does not work due to missing support in torch.sqrt

From e939d278c2c6c85cba3368fa4e2a3e68738223c7 Mon Sep 17 00:00:00 2001
From: Jirka Borovec <Borda@users.noreply.github.com>
Date: Tue, 6 Apr 2021 11:13:17 +0200
Subject: [PATCH 10/21] inline

---
 torchmetrics/functional/regression/pearson.py | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index ac11514c75f..25636388231 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -63,12 +63,9 @@ def _pearson_corrcoef_update(
         raise ValueError('Expected both predictions and target to be 1 dimensional tensors.')
     data = torch.stack([preds, target], dim=1)
 
-    if old_mean is None:
-        old_mean = 0
-    if old_cov is None:
-        old_cov = 0
-    if old_nobs is None:
-        old_nobs = 0
+    old_mean = 0 if old_mean is None else old_mean
+    old_cov = 0 if old_cov is None else old_cov
+    old_nobs = 0 if old_nobs is None else old_nobs
 
     new_mean = _update_mean(old_mean, old_nobs, data)
     new_cov = _update_cov(old_cov, old_mean, new_mean, data)

From 24198009ab1b2f8b424717c7d378db61e0a43adf Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 6 Apr 2021 19:15:11 +0200
Subject: [PATCH 11/21] fix sync

---
 torchmetrics/regression/pearson.py | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index 9275869dbc5..264f92318ac 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -43,9 +43,6 @@ class PearsonCorrcoef(Metric):
             before returning the value at the step. default: False
         process_group:
             Specify the process group on which synchronization is called. default: None (which selects the entire world)
-        dist_sync_fn:
-            Callback that performs the allgather operation on the metric state. When ``None``, DDP
-            will be used to perform the allgather
 
     Example:
         >>> from torchmetrics import PearsonCorrcoef
@@ -61,13 +58,11 @@ def __init__(
         compute_on_step: bool = True,
         dist_sync_on_step: bool = False,
         process_group: Optional[Any] = None,
-        dist_sync_fn: Optional[Callable] = None,
     ):
         super().__init__(
             compute_on_step=compute_on_step,
             dist_sync_on_step=dist_sync_on_step,
             process_group=process_group,
-            dist_sync_fn=dist_sync_fn,
         )
         self.add_state("cov", default=torch.zeros(2, 2), dist_reduce_fx="sum")
         self.add_state("mean", default=torch.zeros(2), dist_reduce_fx="sum")

From 7fa6530c24dc04102d72aef51b3e5f94d29bda1b Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 11:31:54 +0200
Subject: [PATCH 12/21] fix tests

---
 tests/regression/test_pearson.py              | 33 +-----------
 torchmetrics/__init__.py                      |  2 +-
 torchmetrics/functional/regression/pearson.py | 54 ++++---------------
 torchmetrics/regression/pearson.py            | 24 ++++++---
 4 files changed, 29 insertions(+), 84 deletions(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index 4152965381e..ec66fd459e9 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -19,41 +19,12 @@
 
 from tests.helpers import seed_all
 from tests.helpers.testers import BATCH_SIZE, NUM_BATCHES, MetricTester
-from torchmetrics.functional.regression.pearson import _update_cov, _update_mean, pearson_corrcoef
+from torchmetrics.functional.regression.pearson import pearson_corrcoef
 from torchmetrics.regression.pearson import PearsonCorrcoef
 
 seed_all(42)
 
 
-def test_update_functions(tmpdir):
-    """ Test that updating the estimates are equal to estimating them on all data """
-    data = torch.randn(100, 2)
-    batch1, batch2 = data.chunk(2)
-
-    def _mean_cov(data):
-        mean = data.mean(0)
-        diff = data - mean
-        cov = diff.T @ diff
-        return mean, cov
-
-    mean_update, cov_update, size_update = torch.zeros(2), torch.zeros(2, 2), torch.zeros(1)
-    for batch in [batch1, batch2]:
-        new_mean = _update_mean(mean_update, size_update, batch)
-        new_cov = _update_cov(cov_update, mean_update, new_mean, batch)
-
-        assert not torch.allclose(new_mean, mean_update), "mean estimate did not update"
-        assert not torch.allclose(new_cov, cov_update), "covariance estimate did not update"
-
-        size_update += batch.shape[0]
-        mean_update = new_mean
-        cov_update = new_cov
-
-    mean, cov = _mean_cov(data)
-
-    assert torch.allclose(mean, mean_update), "updated mean does not correspond to mean of all data"
-    assert torch.allclose(cov, cov_update), "updated covariance does not correspond to covariance of all data"
-
-
 Input = namedtuple('Input', ["preds", "target"])
 
 _single_target_inputs1 = Input(
@@ -78,8 +49,6 @@ def _sk_pearsonr(preds, target):
     (_single_target_inputs2.preds, _single_target_inputs2.target),
 ])
 class TestPearsonCorrcoef(MetricTester):
-    atol = 1e-4
-
     @pytest.mark.parametrize("ddp", [True, False])
     @pytest.mark.parametrize("dist_sync_on_step", [True, False])
     def test_pearson_corrcoef(self, preds, target, ddp, dist_sync_on_step):
diff --git a/torchmetrics/__init__.py b/torchmetrics/__init__.py
index 9cab9e0cf2b..e115f00af18 100644
--- a/torchmetrics/__init__.py
+++ b/torchmetrics/__init__.py
@@ -41,13 +41,13 @@
 from torchmetrics.collections import MetricCollection  # noqa: F401 E402
 from torchmetrics.metric import Metric  # noqa: F401 E402
 from torchmetrics.regression import (  # noqa: F401 E402
-    PearsonCorrcoef,
     PSNR,
     SSIM,
     ExplainedVariance,
     MeanAbsoluteError,
     MeanSquaredError,
     MeanSquaredLogError,
+    PearsonCorrcoef,
     R2Score,
 )
 from torchmetrics.retrieval import (  # noqa: F401 E402
diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index 25636388231..d0bd78c948a 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -19,32 +19,6 @@
 from torchmetrics.utilities.checks import _check_same_shape
 
 
-def _update_mean(old_mean: Tensor, old_nobs: Tensor, data: Tensor) -> Tensor:
-    """ Update a mean estimate given new data
-    Args:
-        old_mean: current mean estimate
-        old_nobs: number of observation until now
-        data: data used for updating the estimate
-    Returns:
-        new_mean: updated mean estimate
-    """
-    data_size = data.shape[0]
-    return (old_mean * old_nobs + data.mean(dim=0) * data_size) / (old_nobs + data_size)
-
-
-def _update_cov(old_cov: Tensor, old_mean: Tensor, new_mean: Tensor, data: Tensor):
-    """ Update a covariance estimate given new data
-    Args:
-        old_cov: current covariance estimate
-        old_mean: current mean estimate
-        new_mean: updated mean estimate
-        data: data used for updating the estimate
-    Returns:
-        new_mean: updated covariance estimate
-    """
-    return old_cov + (data - new_mean).T @ (data - old_mean)
-
-
 def _pearson_corrcoef_update(
     preds: Tensor,
     target: Tensor,
@@ -61,26 +35,20 @@ def _pearson_corrcoef_update(
     target = target.squeeze()
     if preds.ndim > 1 or target.ndim > 1:
         raise ValueError('Expected both predictions and target to be 1 dimensional tensors.')
-    data = torch.stack([preds, target], dim=1)
 
-    old_mean = 0 if old_mean is None else old_mean
-    old_cov = 0 if old_cov is None else old_cov
-    old_nobs = 0 if old_nobs is None else old_nobs
+    return preds, target
 
-    new_mean = _update_mean(old_mean, old_nobs, data)
-    new_cov = _update_cov(old_cov, old_mean, new_mean, data)
-    new_size = old_nobs + preds.numel()
 
-    return new_mean, new_cov, new_size
+def _pearson_corrcoef_compute(preds: Tensor, target: Tensor) -> Tensor:
+    """ computes the final pearson correlation based on covariance matrix and number of observatiosn """
+    preds_diff = preds - preds.mean()
+    target_diff = target - target.mean()
 
+    cov = (preds_diff * target_diff).mean()
+    preds_std = torch.sqrt((preds_diff * preds_diff).mean())
+    target_std = torch.sqrt((target_diff * target_diff).mean())
 
-def _pearson_corrcoef_compute(c: Tensor, nobs: Tensor):
-    """ computes the final pearson correlation based on covariance matrix and number of observatiosn """
-    c /= (nobs - 1)
-    x_var = c[0, 0]
-    y_var = c[1, 1]
-    cov = c[0, 1]
-    corrcoef = cov / (x_var * y_var).sqrt()
+    corrcoef = cov / (preds_std * target_std)
     return torch.clamp(corrcoef, -1.0, 1.0)
 
 
@@ -99,5 +67,5 @@ def pearson_corrcoef(preds: Tensor, target: Tensor) -> Tensor:
         >>> pearson_corrcoef(preds, target)
         tensor(0.9849)
     """
-    _, c, nobs = _pearson_corrcoef_update(preds, target)
-    return _pearson_corrcoef_compute(c, nobs)
+    preds, target = _pearson_corrcoef_update(preds, target)
+    return _pearson_corrcoef_compute(preds, target)
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index 264f92318ac..6f497c6340f 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -11,13 +11,14 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Callable, Optional
+from typing import Any, Optional
 
 import torch
 from torch import Tensor
 
 from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update
 from torchmetrics.metric import Metric
+from torchmetrics.utilities import rank_zero_warn
 
 
 class PearsonCorrcoef(Metric):
@@ -64,9 +65,14 @@ def __init__(
             dist_sync_on_step=dist_sync_on_step,
             process_group=process_group,
         )
-        self.add_state("cov", default=torch.zeros(2, 2), dist_reduce_fx="sum")
-        self.add_state("mean", default=torch.zeros(2), dist_reduce_fx="sum")
-        self.add_state("n_obs", default=torch.zeros(1), dist_reduce_fx="sum")
+
+        rank_zero_warn(
+            'Metric `PearsonCorrcoef` will save all targets and predictions in buffer.'
+            ' For large datasets this may lead to large memory footprint.'
+        )
+
+        self.add_state("preds", default=[], dist_reduce_fx=None)
+        self.add_state("target", default=[], dist_reduce_fx=None)
 
     def update(self, preds: Tensor, target: Tensor):
         """
@@ -76,12 +82,14 @@ def update(self, preds: Tensor, target: Tensor):
             preds: Predictions from model
             target: Ground truth values
         """
-        self.mean, self.cov, self.n_obs = _pearson_corrcoef_update(
-            preds, target, self.mean, self.cov, self.n_obs
-        )
+        preds, target = _pearson_corrcoef_update(preds, target)
+        self.preds.append(preds)
+        self.target.append(target)
 
     def compute(self):
         """
         Computes pearson correlation coefficient over state.
         """
-        return _pearson_corrcoef_compute(self.cov, self.n_obs)
+        preds = torch.cat(self.preds, dim=0)
+        target = torch.cat(self.target, dim=0)
+        return _pearson_corrcoef_compute(preds, target)

From 61d2d900264fbd4023a85d0c4350d1ad666df132 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 12:24:10 +0200
Subject: [PATCH 13/21] fix docs

---
 torchmetrics/regression/pearson.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index 6f497c6340f..15efce09330 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -26,7 +26,8 @@ class PearsonCorrcoef(Metric):
     Computes `pearson correlation coefficient
     <https://en.wikipedia.org/wiki/Pearson_correlation_coefficient>`_:
 
-    .. math:: \text{P_corr}(x,y) = \frac{cov(x,y)}{\sigma_x \times \sigma_y}
+    .. math::
+        P_{corr}(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}
 
     Where :math:`y` is a tensor of target values, and :math:`x` is a
     tensor of predictions.

From eab5638cae77aa3ea2f8cdf6d1c2f36cc5fd6c3c Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 13:43:22 +0200
Subject: [PATCH 14/21] Apply suggestions from code review

---
 torchmetrics/functional/regression/pearson.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index d0bd78c948a..8911d27bf92 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -39,7 +39,7 @@ def _pearson_corrcoef_update(
     return preds, target
 
 
-def _pearson_corrcoef_compute(preds: Tensor, target: Tensor) -> Tensor:
+def _pearson_corrcoef_compute(preds: Tensor, target: Tensor, eps: float=1e-6) -> Tensor:
     """ computes the final pearson correlation based on covariance matrix and number of observatiosn """
     preds_diff = preds - preds.mean()
     target_diff = target - target.mean()
@@ -48,7 +48,7 @@ def _pearson_corrcoef_compute(preds: Tensor, target: Tensor) -> Tensor:
     preds_std = torch.sqrt((preds_diff * preds_diff).mean())
     target_std = torch.sqrt((target_diff * target_diff).mean())
 
-    corrcoef = cov / (preds_std * target_std)
+    corrcoef = cov / (preds_std * target_std + eps)
     return torch.clamp(corrcoef, -1.0, 1.0)
 
 

From dba602bac8b3439701496d789a1b48ca1da92823 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 13:44:02 +0200
Subject: [PATCH 15/21] Update torchmetrics/functional/regression/pearson.py

---
 torchmetrics/functional/regression/pearson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index 8911d27bf92..dabb203569e 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -39,7 +39,7 @@ def _pearson_corrcoef_update(
     return preds, target
 
 
-def _pearson_corrcoef_compute(preds: Tensor, target: Tensor, eps: float=1e-6) -> Tensor:
+def _pearson_corrcoef_compute(preds: Tensor, target: Tensor, eps: float = 1e-6) -> Tensor:
     """ computes the final pearson correlation based on covariance matrix and number of observatiosn """
     preds_diff = preds - preds.mean()
     target_diff = target - target.mean()

From d41e551616ca092c5313cae749e2483a3662fbf0 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 14:26:19 +0200
Subject: [PATCH 16/21] atol

---
 tests/regression/test_pearson.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index ec66fd459e9..b2630d62959 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -49,6 +49,8 @@ def _sk_pearsonr(preds, target):
     (_single_target_inputs2.preds, _single_target_inputs2.target),
 ])
 class TestPearsonCorrcoef(MetricTester):
+    atol = 1e-2
+    
     @pytest.mark.parametrize("ddp", [True, False])
     @pytest.mark.parametrize("dist_sync_on_step", [True, False])
     def test_pearson_corrcoef(self, preds, target, ddp, dist_sync_on_step):

From 402ac9f82b1df9802cd48698e11e98a5cf75e335 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 14:31:14 +0200
Subject: [PATCH 17/21] update

---
 torchmetrics/functional/regression/pearson.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index dabb203569e..5c22ddad198 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -47,8 +47,13 @@ def _pearson_corrcoef_compute(preds: Tensor, target: Tensor, eps: float = 1e-6)
     cov = (preds_diff * target_diff).mean()
     preds_std = torch.sqrt((preds_diff * preds_diff).mean())
     target_std = torch.sqrt((target_diff * target_diff).mean())
+    
+    denom = preds_std * target_std
+    # prevent division by zero
+    if denom == 0:
+        denom += eps
 
-    corrcoef = cov / (preds_std * target_std + eps)
+    corrcoef = cov / denom
     return torch.clamp(corrcoef, -1.0, 1.0)
 
 

From 0db3f4ce7a4e77b0400ad73a8682d3bb6aebbd4a Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 14:35:57 +0200
Subject: [PATCH 18/21] pep8

---
 tests/regression/test_pearson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index b2630d62959..d01952ee38c 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -50,7 +50,7 @@ def _sk_pearsonr(preds, target):
 ])
 class TestPearsonCorrcoef(MetricTester):
     atol = 1e-2
-    
+
     @pytest.mark.parametrize("ddp", [True, False])
     @pytest.mark.parametrize("dist_sync_on_step", [True, False])
     def test_pearson_corrcoef(self, preds, target, ddp, dist_sync_on_step):

From 40ab5fac9c8644e6207bee1c58f55e9f731590c0 Mon Sep 17 00:00:00 2001
From: Nicki Skafte <skaftenicki@gmail.com>
Date: Tue, 13 Apr 2021 14:38:42 +0200
Subject: [PATCH 19/21] pep8

---
 torchmetrics/functional/regression/pearson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/torchmetrics/functional/regression/pearson.py b/torchmetrics/functional/regression/pearson.py
index 5c22ddad198..5382c88bb55 100644
--- a/torchmetrics/functional/regression/pearson.py
+++ b/torchmetrics/functional/regression/pearson.py
@@ -47,7 +47,7 @@ def _pearson_corrcoef_compute(preds: Tensor, target: Tensor, eps: float = 1e-6)
     cov = (preds_diff * target_diff).mean()
     preds_std = torch.sqrt((preds_diff * preds_diff).mean())
     target_std = torch.sqrt((target_diff * target_diff).mean())
-    
+
     denom = preds_std * target_std
     # prevent division by zero
     if denom == 0:

From 662b22ce9ea2fefdfe6acbfad7dd704983760748 Mon Sep 17 00:00:00 2001
From: Jirka Borovec <Borda@users.noreply.github.com>
Date: Tue, 13 Apr 2021 16:06:57 +0200
Subject: [PATCH 20/21] chlog

---
 CHANGELOG.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7f924191b54..0721ac183f0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added other metrics:
     * Added `CohenKappa` ([#69](https://github.com/PyTorchLightning/metrics/pull/69))
     * Added `MatthewsCorrcoef` ([#98](https://github.com/PyTorchLightning/metrics/pull/98))
+    * Added `PearsonCorrcoef` metric ([#157](https://github.com/PyTorchLightning/metrics/pull/157))
     * Added `Hinge` ([#120](https://github.com/PyTorchLightning/metrics/pull/120))
 - Added `average='micro'` as an option in AUROC for multilabel problems ([#110](https://github.com/PyTorchLightning/metrics/pull/110))
 - Added multilabel support to `ROC` metric ([#114](https://github.com/PyTorchLightning/metrics/pull/114))
@@ -28,7 +29,6 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 )
 - Added `prefix` argument to `MetricCollection` ([#70](https://github.com/PyTorchLightning/metrics/pull/70))
 - Added `__getitem__` as metric arithmetic operation ([#142](https://github.com/PyTorchLightning/metrics/pull/142))
-- Added `PearsonCorrcoef` metric ([#157](https://github.com/PyTorchLightning/metrics/pull/157))
 
 
 ### Changed

From bead3ed8f73515818c5b3580b1a3afb559d0c7aa Mon Sep 17 00:00:00 2001
From: Jirka Borovec <Borda@users.noreply.github.com>
Date: Tue, 13 Apr 2021 16:07:15 +0200
Subject: [PATCH 21/21] .

---
 CHANGELOG.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0721ac183f0..7d73cba87cd 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,7 +20,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added other metrics:
     * Added `CohenKappa` ([#69](https://github.com/PyTorchLightning/metrics/pull/69))
     * Added `MatthewsCorrcoef` ([#98](https://github.com/PyTorchLightning/metrics/pull/98))
-    * Added `PearsonCorrcoef` metric ([#157](https://github.com/PyTorchLightning/metrics/pull/157))
+    * Added `PearsonCorrcoef` ([#157](https://github.com/PyTorchLightning/metrics/pull/157))
     * Added `Hinge` ([#120](https://github.com/PyTorchLightning/metrics/pull/120))
 - Added `average='micro'` as an option in AUROC for multilabel problems ([#110](https://github.com/PyTorchLightning/metrics/pull/110))
 - Added multilabel support to `ROC` metric ([#114](https://github.com/PyTorchLightning/metrics/pull/114))