PearsonCorrcoef Causing OOM

[Divide-By-0]

🐛 Bug

When using torchmetrics.PearsonCorrcoef as a validation metric, I get
UserWarning: Metric PearsonCorrcoef will save all targets and predictions in buffer. For large datasets this may lead to large memory footprint.

To Reproduce

Steps to reproduce the behavior:

1. Use torchmetrics.PearsonCorrcoef as a validation_metric in any existing model.

Code sample

1. Use torchmetrics.PearsonCorrcoef as a validation_metric in any existing model.

Expected behavior

An iterative batch-by-batch algorithm is implemented for Pearson R calculation so memory is not maintained long-term.

For example, stack overflow suggests this (unverified algorithm) https://stackoverflow.com/a/65132700 and one would expect that Keras/other Pytorch alternatives possibly have an internal accumulative algorithm.

Environment

• PyTorch Version (e.g., 1.0): 1.9
• OS (e.g., Linux): Linux
• How you installed PyTorch (conda, pip, source): conda
• Build command you used (if compiling from source):
• Python version: 3.8
• CUDA/cuDNN version: 11.1
• GPU models and configuration: 2080Ti (7GB RAM)
• Any other relevant information:

Additional context

[github-actions]

Hi! thanks for your contribution!, great first issue!