From 1b261ab25b58dc9a012288d7b9a79ead27957021 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 16:14:45 -0600 Subject: [PATCH 01/22] Add blogpost on flox heuristics --- src/posts/flox-smart/index.md | 159 ++++++++++++++++++++++++++++++++++ 1 file changed, 159 insertions(+) create mode 100644 src/posts/flox-smart/index.md diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md new file mode 100644 index 00000000..aecc35e3 --- /dev/null +++ b/src/posts/flox-smart/index.md @@ -0,0 +1,159 @@ +--- +title: flox: GroupBy, now with smarts!' +date: '2024-05-31' +authors: + - name: Deepak Cherian + github: dcherian + +summary: 'flox adds heuristics for automatically choosing an appropriate strategy with dask arrays!' +--- + +## What is flox? + +[`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like cubed and dask using a tree reduction approach. +Tree reduction ([example](https://people.csail.mit.edu/xchen/gpu-programming/Lecture11-reduction.pdf)) are a parallel-friendly way of computing common reduction operations like `sum`, `mean` etc. +Without flox, Xarray shuffles or sorts the data to extract all values in a single group, and then runs the reduction group-by-group. +Depending on data layout ("chunking"), this shuffle can be quite expensive. +With flox installed, Xarray instead uses the parallel-friendly tree reduction approach for the same calculation. +In many cases, this is a massive improvement. +See our [previous blog post](https://xarray.dev/blog/flox) for more. + +Two key realizations influenced the development of flox: + +1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. +2. An important difference between arrays and dataframes is that chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. + +These two properties are particularly relevant for climatology calculations --- a common Xarray workload. + +## Tree reductions can be catastrophically bad + +For a catastrophic example, consider `ds.groupby("time.year").mean()`, or the equivalent `ds.resample(time="Y").mean()` for a 100 year long dataset of monthly averages with chunk size of **1** (or **4**) along the time dimension. +This is a fairly common format for climate model output. +The small chunk size along time is offset by much larger chunk sizes along the other dimensions --- commonly horizontal space (`x, y` or `latitude, longitude`). + +A naive tree reduction would accumulate all averaged values into a single output chunk of size 100. +Depending on the chunking of the input dataset, this may overload the worker memory and fail catastrophically. +More importantly, there is a lot of wasteful communication --- computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the two values need to reside in the same output chunk. + +## Avoiding catastrophe + +Thus `flox` quickly grew two new modes of computing the groupby reduction: +First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. +This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. +With an appropriate (and usually quite cheap) rechunking, the problem is embarassingly parallel. + +Second, `method="cohorts"` which is a bit more subtle. +Consider `groupby("time.month")` for the monthly mean dataset i.e. grouping by an exactly periodic array. +When the chunk size along the core dimension "time" is a divisor of the period; so either 1, 2, 3, 4, or 6 in this case; groups tend to occur in cohorts ("groups of groups"). +For example, with a chunk size of 4, monthly mean input data for Jan, Feb, Mar, and April ("one cohort") are _always_ in the same chunk, and totally separate from any of the other months. +This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. +Doing so can significantly reduce compute times and in particular memory required for the computation. + +Importantly if there isn't much separation of groups into cohorts; example, the groups are randomly distributed, then we'd like the standard `method="map-reduce"` for low overhead. + +## Choosing a strategy is hard, and hard to teach. + +These strategies are great, but the downside is some sophistication is required to apply them. +Worse, they are hard to explain conceptually! I've tried! ([example 1](https://discourse.pangeo.io/t/optimizing-climatology-calculation-with-xarray-and-dask/2453/20?u=dcherian), [example 2](https://discourse.pangeo.io/t/understanding-optimal-zarr-chunking-scheme-for-a-climatology/2335)). + +What we need is to choose the appropriate strategy automatically. +And guess what, `flox>=0.9` will now choose an appropriate method automatically! + +## Problem statement + +Fundamentally, we know: + +1. the data layout or chunking. +2. the array we are grouping by, and can detect possible patterns in that array. + +We want to find all sets of groups that occupy similar sets of chunks. +For groups `A,B,C,D` that occupy the following chunks (chunk 0 is the first chunk along the core-dimension or the axis of reduction) + +``` +A: [0, 1, 2] +B: [1, 2, 3] +D: [5, 6, 7, 8] +E: [8] +X: [0, 3] +``` + +We want to detect the cohorts `{A,B,X}` and `{C, D}` with the following chunks. + +``` +[A, B, X]: [0, 1, 2, 3] +[C, D]: [5, 6, 7, 8] +``` + +Importantly, we do _not_ want to be dependent on detecting exact patterns, and prefer approximate solutions and heuristics. + +## The solution + +After a fun exploration involving such fun ideas as [locality-sensitive hashing](http://ekzhu.com/datasketch/lshensemble.html), and [all-pair set similarity search](https://www.cse.unsw.edu.au/~lxue/WWW08.pdf), I settled on the following algorithm. + +I use set _containment_, or a "normalized intersection", to determine the similarity the sets of chunks occupied by two different groups (`Q` and `X`). + +``` +C = |Q ∩ X| / |Q| ≤ 1 +``` + +Unlike Jaccard similarity, _containment_ [isn't skewed](http://ekzhu.com/datasketch/lshensemble.html) when one of the sets is much larger than the other. + +The steps are as follows: + +1. First determine which labels are present in each chunk. The distribution of labels across chunks + is represented internally as a 2D boolean sparse array `S[chunks, labels]`. `S[i, j] = 1` when + label `j` is present in chunk `i`. + +1. Now we can quickly determine a number of special cases: + + 1. Use `"blockwise"` when every group is contained to one block each. + 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks + 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) + Here is an example: + ![bitmask-patterns](/../diagrams/bitmask-patterns-perfect.png) + + - On the left, is a monthly grouping for a monthly time series with chunk size 4. There are 3 non-overlapping cohorts so + `method="cohorts"` is perfect. + - On the right, is a resampling problem of a daily time series with chunk size 10 to 5-daily frequency. Two 5-day periods + are exactly contained in one chunk, so `method="blockwise"` is perfect. + +1. At this point, we want to merge groups in to cohorts when they occupy _approximately_ the same chunks. For each group `i` we can quickly compute containment against + all other groups `j` as `C = S.T @ S / number_chunks_per_group`. Here is `C` for a range of chunk sizes from 1 to 12, for computing + the monthly mean of a monthly time series problem, \[the title on each image is `(chunk size, sparsity)`\]. + + ```python + chunks = np.arange(1, 13) + labels = np.tile(np.arange(1, 13), 30) + ``` + + ![cohorts-schematic](/../diagrams/containment.png) + +1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with + each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. + We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. + +Cool, isn't it?! + +## What's next? + +flox' ability to do cool inferences entirely relies on the input chunking, which is a major user-tunable knob. +Perfect optimization still requires some user-tuned chunking. +Recent Xarray feature makes that a lot easier for time grouping: + +``` +from xarray.groupers import TimeResampler + +rechunked = ds.chunk(time=TimeResampler("YE")) +``` + +will rechunk so that a year of data is in a single chunk. + +Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application. +A key limitation is that we have lost context. +The string `"time.month"` tells me that I am grouping a perfectly periodic array with period 12; similarly +the _string_ `"time.dayofyear"` tells me that I am grouping by a (quasi-)\_periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). +This context is hard to infer from integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. + +One way to preserve context may be to use Xarray's new Grouper objects, and let them report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. +This would allow a downstream system like `flox` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. +That is an experiment for another day. From e04df4787e7cfb8bce7576814ad35b6962244441 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 16:19:51 -0600 Subject: [PATCH 02/22] Comment out images for now --- src/posts/flox-smart/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index aecc35e3..fd56d5f8 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -110,7 +110,7 @@ The steps are as follows: 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) Here is an example: - ![bitmask-patterns](/../diagrams/bitmask-patterns-perfect.png) + - On the left, is a monthly grouping for a monthly time series with chunk size 4. There are 3 non-overlapping cohorts so `method="cohorts"` is perfect. @@ -126,7 +126,7 @@ The steps are as follows: labels = np.tile(np.arange(1, 13), 30) ``` - ![cohorts-schematic](/../diagrams/containment.png) + 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. From 503a36bcb34e0262e83c2406a8eb423ab73eec70 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 16:35:01 -0600 Subject: [PATCH 03/22] Update src/posts/flox-smart/index.md Co-authored-by: Anderson Banihirwe <13301940+andersy005@users.noreply.github.com> --- src/posts/flox-smart/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index fd56d5f8..3b9910ff 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -1,5 +1,5 @@ --- -title: flox: GroupBy, now with smarts!' +title: 'flox: GroupBy, now with smarts!' date: '2024-05-31' authors: - name: Deepak Cherian From 093a75ee64ee84b3b8bfb76ec832c2f8f75e9146 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 16:29:01 -0600 Subject: [PATCH 04/22] edits --- src/posts/flox-smart/index.md | 48 +++++++++++++++++------------------ 1 file changed, 23 insertions(+), 25 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 3b9910ff..2d6a40f6 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -21,23 +21,24 @@ See our [previous blog post](https://xarray.dev/blog/flox) for more. Two key realizations influenced the development of flox: 1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. -2. An important difference between arrays and dataframes is that chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. +2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. This is an important difference between arrays and dataframes! -These two properties are particularly relevant for climatology calculations --- a common Xarray workload. +These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload. ## Tree reductions can be catastrophically bad For a catastrophic example, consider `ds.groupby("time.year").mean()`, or the equivalent `ds.resample(time="Y").mean()` for a 100 year long dataset of monthly averages with chunk size of **1** (or **4**) along the time dimension. This is a fairly common format for climate model output. -The small chunk size along time is offset by much larger chunk sizes along the other dimensions --- commonly horizontal space (`x, y` or `latitude, longitude`). +The small chunk size along time is offset by much larger chunk sizes along the other dimensions — commonly horizontal space (`x, y` or `latitude, longitude`). A naive tree reduction would accumulate all averaged values into a single output chunk of size 100. Depending on the chunking of the input dataset, this may overload the worker memory and fail catastrophically. -More importantly, there is a lot of wasteful communication --- computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the two values need to reside in the same output chunk. +More importantly, there is a lot of wasteful communication — computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the two values need to reside in the same output chunk. ## Avoiding catastrophe -Thus `flox` quickly grew two new modes of computing the groupby reduction: +Thus `flox` quickly grew two new modes of computing the groupby reduction. + First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. With an appropriate (and usually quite cheap) rechunking, the problem is embarassingly parallel. @@ -93,7 +94,7 @@ After a fun exploration involving such fun ideas as [locality-sensitive hashing] I use set _containment_, or a "normalized intersection", to determine the similarity the sets of chunks occupied by two different groups (`Q` and `X`). ``` -C = |Q ∩ X| / |Q| ≤ 1 +C = |Q ∩ X| / |Q| ≤ 1; (∩ is set intersection) ``` Unlike Jaccard similarity, _containment_ [isn't skewed](http://ekzhu.com/datasketch/lshensemble.html) when one of the sets is much larger than the other. @@ -109,29 +110,25 @@ The steps are as follows: 1. Use `"blockwise"` when every group is contained to one block each. 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) - Here is an example: - - - - On the left, is a monthly grouping for a monthly time series with chunk size 4. There are 3 non-overlapping cohorts so - `method="cohorts"` is perfect. - - On the right, is a resampling problem of a daily time series with chunk size 10 to 5-daily frequency. Two 5-day periods - are exactly contained in one chunk, so `method="blockwise"` is perfect. 1. At this point, we want to merge groups in to cohorts when they occupy _approximately_ the same chunks. For each group `i` we can quickly compute containment against - all other groups `j` as `C = S.T @ S / number_chunks_per_group`. Here is `C` for a range of chunk sizes from 1 to 12, for computing - the monthly mean of a monthly time series problem, \[the title on each image is `(chunk size, sparsity)`\]. - - ```python - chunks = np.arange(1, 13) - labels = np.tile(np.arange(1, 13), 30) - ``` - - + all other groups `j` as `C = S.T @ S / number_chunks_per_group`. 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. +For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementation.html#heuristics). + +Here is C for a range of chunk sizes from 1 to 12, for computing `groupby("time.month")` of a monthly mean dataset, [the title on each image is (chunk size, sparsity)]. +![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) + +flox will choose: + +1. `"blockwise"` for chunk size 1, +2. `"cohorts"` for (2, 3, 4, 6, 12), +3. and `"map-reduce"` for the rest. + Cool, isn't it?! ## What's next? @@ -140,7 +137,7 @@ flox' ability to do cool inferences entirely relies on the input chunking, which Perfect optimization still requires some user-tuned chunking. Recent Xarray feature makes that a lot easier for time grouping: -``` +```python from xarray.groupers import TimeResampler rechunked = ds.chunk(time=TimeResampler("YE")) @@ -149,10 +146,11 @@ rechunked = ds.chunk(time=TimeResampler("YE")) will rechunk so that a year of data is in a single chunk. Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application. -A key limitation is that we have lost context. +A key limitation is that we have lost _context_. The string `"time.month"` tells me that I am grouping a perfectly periodic array with period 12; similarly -the _string_ `"time.dayofyear"` tells me that I am grouping by a (quasi-)\_periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). +the _string_ `"time.dayofyear"` tells me that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). This context is hard to infer from integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. +/[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference!\*. One way to preserve context may be to use Xarray's new Grouper objects, and let them report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. This would allow a downstream system like `flox` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. From 44a8f02279d303bbeb1d5e73a5b062cd678ff534 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 16:43:41 -0600 Subject: [PATCH 05/22] more edits --- src/posts/flox-smart/index.md | 17 +++++++++++------ 1 file changed, 11 insertions(+), 6 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 2d6a40f6..aca68859 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -8,6 +8,10 @@ authors: summary: 'flox adds heuristics for automatically choosing an appropriate strategy with dask arrays!' --- +## TL;DR + +`flox>=0.9` adds heuristics for automatically choosing an appropriate strategy with dask arrays! Here I describe how. + ## What is flox? [`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like cubed and dask using a tree reduction approach. @@ -42,17 +46,19 @@ Thus `flox` quickly grew two new modes of computing the groupby reduction. First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. With an appropriate (and usually quite cheap) rechunking, the problem is embarassingly parallel. +![blockwise](https://flox.readthedocs.io/en/latest/_images/new-blockwise-annotated.svg) Second, `method="cohorts"` which is a bit more subtle. Consider `groupby("time.month")` for the monthly mean dataset i.e. grouping by an exactly periodic array. When the chunk size along the core dimension "time" is a divisor of the period; so either 1, 2, 3, 4, or 6 in this case; groups tend to occur in cohorts ("groups of groups"). For example, with a chunk size of 4, monthly mean input data for Jan, Feb, Mar, and April ("one cohort") are _always_ in the same chunk, and totally separate from any of the other months. +![monthly cohorts](https://flox.readthedocs.io/en/latest/_images/cohorts-month-chunk4.png) This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. Doing so can significantly reduce compute times and in particular memory required for the computation. Importantly if there isn't much separation of groups into cohorts; example, the groups are randomly distributed, then we'd like the standard `method="map-reduce"` for low overhead. -## Choosing a strategy is hard, and hard to teach. +## Choosing a strategy is hard, and harder to teach. These strategies are great, but the downside is some sophistication is required to apply them. Worse, they are hard to explain conceptually! I've tried! ([example 1](https://discourse.pangeo.io/t/optimizing-climatology-calculation-with-xarray-and-dask/2453/20?u=dcherian), [example 2](https://discourse.pangeo.io/t/understanding-optimal-zarr-chunking-scheme-for-a-climatology/2335)). @@ -104,16 +110,12 @@ The steps are as follows: 1. First determine which labels are present in each chunk. The distribution of labels across chunks is represented internally as a 2D boolean sparse array `S[chunks, labels]`. `S[i, j] = 1` when label `j` is present in chunk `i`. - 1. Now we can quickly determine a number of special cases: - 1. Use `"blockwise"` when every group is contained to one block each. 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) - 1. At this point, we want to merge groups in to cohorts when they occupy _approximately_ the same chunks. For each group `i` we can quickly compute containment against all other groups `j` as `C = S.T @ S / number_chunks_per_group`. - 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. @@ -131,6 +133,9 @@ flox will choose: Cool, isn't it?! +Importantly this inference is fast — 400ms for the [US county GroupBy problem in our previous post](https://xarray.dev/blog/flox)! +But we have not tried with bigger problems (example: GroupBy(100,000 watersheds) in the US). + ## What's next? flox' ability to do cool inferences entirely relies on the input chunking, which is a major user-tunable knob. @@ -150,7 +155,7 @@ A key limitation is that we have lost _context_. The string `"time.month"` tells me that I am grouping a perfectly periodic array with period 12; similarly the _string_ `"time.dayofyear"` tells me that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). This context is hard to infer from integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. -/[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference!\*. +_[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference!_. One way to preserve context may be to use Xarray's new Grouper objects, and let them report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. This would allow a downstream system like `flox` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. From 105c22d8a7ed473114674189cda2ab366947f65f Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Mon, 29 Jul 2024 20:30:23 -0600 Subject: [PATCH 06/22] more edits --- src/posts/flox-smart/index.md | 74 +++++++++++++++++++---------------- 1 file changed, 41 insertions(+), 33 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index aca68859..3b49dde3 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -14,12 +14,15 @@ summary: 'flox adds heuristics for automatically choosing an appropriate strateg ## What is flox? -[`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like cubed and dask using a tree reduction approach. -Tree reduction ([example](https://people.csail.mit.edu/xchen/gpu-programming/Lecture11-reduction.pdf)) are a parallel-friendly way of computing common reduction operations like `sum`, `mean` etc. -Without flox, Xarray shuffles or sorts the data to extract all values in a single group, and then runs the reduction group-by-group. -Depending on data layout ("chunking"), this shuffle can be quite expensive. -With flox installed, Xarray instead uses the parallel-friendly tree reduction approach for the same calculation. +[`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like [cubed](https://cubed-dev.github.io/cubed/) and [dask](https://docs.dask.org/en/stable/array.html) using tree reductions. +Tree reductions ([example](https://people.csail.mit.edu/xchen/gpu-programming/Lecture11-reduction.pdf)) are a parallel-friendly way of computing common reduction operations like `sum`, `mean` etc. +Without flox, Xarray effectively shuffles — sorts the data to extract all values in a single group — and then runs the reduction group-by-group. +Depending on data layout or "chunking" this shuffle can be quite expensive. +![shuffle](https://flox.readthedocs.io/en/latest/_images/new-split-apply-combine-annotated.svg) +With flox installed, Xarray instead uses its parallel-friendly tree reduction. In many cases, this is a massive improvement. +Notice how much cleaner the graph is in this image: +![map-reduce](https://flox.readthedocs.io/en/latest/_images/new-map-reduce-reindex-True-annotated.svg) See our [previous blog post](https://xarray.dev/blog/flox) for more. Two key realizations influenced the development of flox: @@ -27,17 +30,18 @@ Two key realizations influenced the development of flox: 1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. 2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. This is an important difference between arrays and dataframes! -These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload. +These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. ## Tree reductions can be catastrophically bad -For a catastrophic example, consider `ds.groupby("time.year").mean()`, or the equivalent `ds.resample(time="Y").mean()` for a 100 year long dataset of monthly averages with chunk size of **1** (or **4**) along the time dimension. +Consider `ds.groupby("time.year").mean()`, or the equivalent `ds.resample(time="Y").mean()` for a 100 year long dataset of monthly averages with chunk size of **1** (or **4**) along the time dimension. This is a fairly common format for climate model output. The small chunk size along time is offset by much larger chunk sizes along the other dimensions — commonly horizontal space (`x, y` or `latitude, longitude`). -A naive tree reduction would accumulate all averaged values into a single output chunk of size 100. -Depending on the chunking of the input dataset, this may overload the worker memory and fail catastrophically. -More importantly, there is a lot of wasteful communication — computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the two values need to reside in the same output chunk. +A naive tree reduction would accumulate all averaged values into a single output chunk of size 100 — one value per year for 100 years. +Depending on the chunking of the input dataset, this may overload the final worker's memory and fail catastrophically. +More importantly, there is a lot of wasteful communication — computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the results for the two years need to reside in the same output chunk. +This issue does not arise for regular reductions where the final result depends on the values in all chunks, and all data along the reduced axes are reduced down to one final value. ## Avoiding catastrophe @@ -45,26 +49,26 @@ Thus `flox` quickly grew two new modes of computing the groupby reduction. First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. -With an appropriate (and usually quite cheap) rechunking, the problem is embarassingly parallel. +With an appropriate (and usually quite cheap) rechunking, the problem is embarrassingly parallel. ![blockwise](https://flox.readthedocs.io/en/latest/_images/new-blockwise-annotated.svg) Second, `method="cohorts"` which is a bit more subtle. Consider `groupby("time.month")` for the monthly mean dataset i.e. grouping by an exactly periodic array. When the chunk size along the core dimension "time" is a divisor of the period; so either 1, 2, 3, 4, or 6 in this case; groups tend to occur in cohorts ("groups of groups"). -For example, with a chunk size of 4, monthly mean input data for Jan, Feb, Mar, and April ("one cohort") are _always_ in the same chunk, and totally separate from any of the other months. +For example, with a chunk size of 4, monthly mean input data for the "cohort" Jan/Feb/Mar/Apr are _always_ in the same chunk, and totally separate from any of the other months. +Here is a schematic illustration where each month is represented by a different shade of red: ![monthly cohorts](https://flox.readthedocs.io/en/latest/_images/cohorts-month-chunk4.png) This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. Doing so can significantly reduce compute times and in particular memory required for the computation. -Importantly if there isn't much separation of groups into cohorts; example, the groups are randomly distributed, then we'd like the standard `method="map-reduce"` for low overhead. +Importantly if there isn't much separation of groups into cohorts; example, the groups are randomly distributed, then it's hard to do better than the standard `method="map-reduce"`. ## Choosing a strategy is hard, and harder to teach. -These strategies are great, but the downside is some sophistication is required to apply them. +These strategies are great, but the downside is that some sophistication is required to apply them. Worse, they are hard to explain conceptually! I've tried! ([example 1](https://discourse.pangeo.io/t/optimizing-climatology-calculation-with-xarray-and-dask/2453/20?u=dcherian), [example 2](https://discourse.pangeo.io/t/understanding-optimal-zarr-chunking-scheme-for-a-climatology/2335)). What we need is to choose the appropriate strategy automatically. -And guess what, `flox>=0.9` will now choose an appropriate method automatically! ## Problem statement @@ -103,7 +107,7 @@ I use set _containment_, or a "normalized intersection", to determine the simila C = |Q ∩ X| / |Q| ≤ 1; (∩ is set intersection) ``` -Unlike Jaccard similarity, _containment_ [isn't skewed](http://ekzhu.com/datasketch/lshensemble.html) when one of the sets is much larger than the other. +Unlike [Jaccard similarity](https://en.wikipedia.org/wiki/Jaccard_index), _containment_ [isn't skewed](http://ekzhu.com/datasketch/lshensemble.html) when one of the sets is much larger than the other. The steps are as follows: @@ -114,18 +118,22 @@ The steps are as follows: 1. Use `"blockwise"` when every group is contained to one block each. 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) -1. At this point, we want to merge groups in to cohorts when they occupy _approximately_ the same chunks. For each group `i` we can quickly compute containment against - all other groups `j` as `C = S.T @ S / number_chunks_per_group`. +1. Now invert `S` to compute an initial set of cohorts whose groups are in the same exact chunks (this is another groupby!). + Later we will want to merge together the detected cohorts when they occupy _approximately_ the same chunks, using the containment metric. +1. For that we first quickly compute containment for all groups `i` against all other groups `j` as `C = S.T @ S / number_chunks_per_group`. 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. +1. If the sparsity is high enough, we merge together similar cohorts using a for-loop. +1. Finally we execute one tree-reduction per cohort and concatenate the results. -For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementation.html#heuristics). +For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementation.html#heuristics) or [the code](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L336). +Suggestions and improvements are very welcome! -Here is C for a range of chunk sizes from 1 to 12, for computing `groupby("time.month")` of a monthly mean dataset, [the title on each image is (chunk size, sparsity)]. +Here is `C` for a range of chunk sizes from 1 to 12, for computing `groupby("time.month")` of a monthly mean dataset, [the title on each image is (chunk size, sparsity)]. ![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) -flox will choose: +Given the above `C`, flox will choose: 1. `"blockwise"` for chunk size 1, 2. `"cohorts"` for (2, 3, 4, 6, 12), @@ -133,14 +141,13 @@ flox will choose: Cool, isn't it?! -Importantly this inference is fast — 400ms for the [US county GroupBy problem in our previous post](https://xarray.dev/blog/flox)! +Importantly this inference is fast — [400ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox)! But we have not tried with bigger problems (example: GroupBy(100,000 watersheds) in the US). ## What's next? -flox' ability to do cool inferences entirely relies on the input chunking, which is a major user-tunable knob. -Perfect optimization still requires some user-tuned chunking. -Recent Xarray feature makes that a lot easier for time grouping: +flox' ability to do such inferences relies entirely on the input chunking, a big knob. +A recent Xarray feature makes such rechunking a lot easier for time grouping: ```python from xarray.groupers import TimeResampler @@ -150,13 +157,14 @@ rechunked = ds.chunk(time=TimeResampler("YE")) will rechunk so that a year of data is in a single chunk. -Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application. -A key limitation is that we have lost _context_. -The string `"time.month"` tells me that I am grouping a perfectly periodic array with period 12; similarly -the _string_ `"time.dayofyear"` tells me that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). -This context is hard to infer from integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. -_[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference!_. +Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application when that's cheap. +A challenge here is that we have lost _context_ when moving from Xarray to flox. +The string `"time.month"` tells Xarray that I am grouping a perfectly periodic array with period 12; similarly +the _string_ `"time.dayofyear"` tells Xarray that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). +But Xarray passes flox an array of integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. +It's hard to infer the context from that! +_[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference._ -One way to preserve context may be to use Xarray's new Grouper objects, and let them report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. -This would allow a downstream system like `flox` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. +One way to preserve context may be be to have Xarray's new Grouper objects report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. +This would allow a downstream system like `flox` or `cubed` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. That is an experiment for another day. From 010f01d69ed7a416ac2201930d631126857bd107 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 16:50:23 -0600 Subject: [PATCH 07/22] more edits --- src/posts/flox-smart/index.md | 61 ++++++++++++++++++++++------------- 1 file changed, 38 insertions(+), 23 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 3b49dde3..42a5cbde 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -10,12 +10,14 @@ summary: 'flox adds heuristics for automatically choosing an appropriate strateg ## TL;DR -`flox>=0.9` adds heuristics for automatically choosing an appropriate strategy with dask arrays! Here I describe how. +`flox>=0.9` now automatically optimizes GroupBy reductions with dask arrays to reduce memory usage and increase parallelism! Here I describe how. ## What is flox? [`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like [cubed](https://cubed-dev.github.io/cubed/) and [dask](https://docs.dask.org/en/stable/array.html) using tree reductions. Tree reductions ([example](https://people.csail.mit.edu/xchen/gpu-programming/Lecture11-reduction.pdf)) are a parallel-friendly way of computing common reduction operations like `sum`, `mean` etc. +Briefly, one computes the reduction for a subset of the array $N$ chunks at a time in parallel, then combines those results together again $N$ chunks at a time, until we have the final result. + Without flox, Xarray effectively shuffles — sorts the data to extract all values in a single group — and then runs the reduction group-by-group. Depending on data layout or "chunking" this shuffle can be quite expensive. ![shuffle](https://flox.readthedocs.io/en/latest/_images/new-split-apply-combine-annotated.svg) @@ -25,13 +27,6 @@ Notice how much cleaner the graph is in this image: ![map-reduce](https://flox.readthedocs.io/en/latest/_images/new-map-reduce-reindex-True-annotated.svg) See our [previous blog post](https://xarray.dev/blog/flox) for more. -Two key realizations influenced the development of flox: - -1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. -2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. This is an important difference between arrays and dataframes! - -These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. - ## Tree reductions can be catastrophically bad Consider `ds.groupby("time.year").mean()`, or the equivalent `ds.resample(time="Y").mean()` for a 100 year long dataset of monthly averages with chunk size of **1** (or **4**) along the time dimension. @@ -41,11 +36,17 @@ The small chunk size along time is offset by much larger chunk sizes along the o A naive tree reduction would accumulate all averaged values into a single output chunk of size 100 — one value per year for 100 years. Depending on the chunking of the input dataset, this may overload the final worker's memory and fail catastrophically. More importantly, there is a lot of wasteful communication — computing on the last year of data is completely independent of computing on the first year of the data, and there is no reason the results for the two years need to reside in the same output chunk. -This issue does not arise for regular reductions where the final result depends on the values in all chunks, and all data along the reduced axes are reduced down to one final value. +This issue does _not_ arise for regular reductions where the final result depends on the values in all chunks, and all data along the reduced axes are reduced down to one final value. ## Avoiding catastrophe Thus `flox` quickly grew two new modes of computing the groupby reduction. +Two key realizations influenced that development: + +1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. +2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. This is an important difference between arrays and dataframes! + +These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. @@ -61,7 +62,7 @@ Here is a schematic illustration where each month is represented by a different This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. Doing so can significantly reduce compute times and in particular memory required for the computation. -Importantly if there isn't much separation of groups into cohorts; example, the groups are randomly distributed, then it's hard to do better than the standard `method="map-reduce"`. +If there isn't much separation of groups into cohorts, like when groups are randomly distributed across chunks, then it's hard to do better than the standard `method="map-reduce"`. ## Choosing a strategy is hard, and harder to teach. @@ -101,7 +102,7 @@ Importantly, we do _not_ want to be dependent on detecting exact patterns, and p After a fun exploration involving such fun ideas as [locality-sensitive hashing](http://ekzhu.com/datasketch/lshensemble.html), and [all-pair set similarity search](https://www.cse.unsw.edu.au/~lxue/WWW08.pdf), I settled on the following algorithm. -I use set _containment_, or a "normalized intersection", to determine the similarity the sets of chunks occupied by two different groups (`Q` and `X`). +I use set _containment_, or a "normalized intersection", to determine the similarity between the sets of chunks occupied by two different groups (`Q` and `X`). ``` C = |Q ∩ X| / |Q| ≤ 1; (∩ is set intersection) @@ -114,23 +115,34 @@ The steps are as follows: 1. First determine which labels are present in each chunk. The distribution of labels across chunks is represented internally as a 2D boolean sparse array `S[chunks, labels]`. `S[i, j] = 1` when label `j` is present in chunk `i`. -1. Now we can quickly determine a number of special cases: - 1. Use `"blockwise"` when every group is contained to one block each. - 1. Use `"cohorts"` when every chunk only has a single group, but that group might extend across multiple chunks - 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) 1. Now invert `S` to compute an initial set of cohorts whose groups are in the same exact chunks (this is another groupby!). Later we will want to merge together the detected cohorts when they occupy _approximately_ the same chunks, using the containment metric. +1. Now we can quickly determine a number of special cases and exit early: + 1. Use `"blockwise"` when every group is contained to one block each. + 1. Use `"cohorts"` when + 1. every chunk only has a single group, but that group might extend across multiple chunks; and + 1. existing cohorts don't overlap at all. +1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) + +If we reach here, then we want to merge together any detected cohorts that substantially overlap with each other. + 1. For that we first quickly compute containment for all groups `i` against all other groups `j` as `C = S.T @ S / number_chunks_per_group`. 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with - each other. We can use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. - We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. -1. If the sparsity is high enough, we merge together similar cohorts using a for-loop. -1. Finally we execute one tree-reduction per cohort and concatenate the results. + each other. We use _sparsity_ --- the number of non-zero elements in `C` divided by the number of elements in `C`, `C.nnz/C.size`. + When sparsity is relatively high, we use `"map-reduce"`, otherwise we use `"cohorts"`. +1. If the sparsity is low enough, we merge together similar cohorts using a for-loop. For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementation.html#heuristics) or [the code](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L336). Suggestions and improvements are very welcome! -Here is `C` for a range of chunk sizes from 1 to 12, for computing `groupby("time.month")` of a monthly mean dataset, [the title on each image is (chunk size, sparsity)]. +Here is containment `C[i, j]` for a range of chunk sizes from 1 to 12, for an input array with 12 monthly mean time steps, +for computing `groupby("time.month")` of a monthly mean dataset. +These are colored so that light yellow is $C=0$, and dark purple is $C=1$. +The title on each image is (chunk size, sparsity). +`C[i,j] = 1` when the chunks occupied by group `i` perfectly overlaps with those occupied by group `j` (so the diagonal elements +are always 1). +When the chunksize _is_ a divisor of the period 12, $C$ is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. +When the chunksize _is not_ a divisor of the period 12, $C$ is much less sparse in comparison. ![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) Given the above `C`, flox will choose: @@ -146,8 +158,10 @@ But we have not tried with bigger problems (example: GroupBy(100,000 watersheds) ## What's next? -flox' ability to do such inferences relies entirely on the input chunking, a big knob. -A recent Xarray feature makes such rechunking a lot easier for time grouping: +flox' ability to do cleanly infer an optimal strategy relies entirely on the input chunking making such optimization possible. +This is a big knob. +A brand new [Xarray feature](https://docs.xarray.dev/en/stable/user-guide/groupby.html#grouper-objects) does make such rechunking +a lot easier for time grouping in particular: ```python from xarray.groupers import TimeResampler @@ -156,13 +170,14 @@ rechunked = ds.chunk(time=TimeResampler("YE")) ``` will rechunk so that a year of data is in a single chunk. - Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application when that's cheap. + A challenge here is that we have lost _context_ when moving from Xarray to flox. The string `"time.month"` tells Xarray that I am grouping a perfectly periodic array with period 12; similarly the _string_ `"time.dayofyear"` tells Xarray that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). But Xarray passes flox an array of integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. It's hard to infer the context from that! +Though one approach might frame the problem as: what rechunking would transform `C` to a block diagonal matrix. _[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference._ One way to preserve context may be be to have Xarray's new Grouper objects report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. From 1136f29e10a0956d6b57ed9534cc6084008cd921 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 20:55:09 -0600 Subject: [PATCH 08/22] more edits --- src/posts/flox-smart/index.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 42a5cbde..7c027ec9 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -16,7 +16,7 @@ summary: 'flox adds heuristics for automatically choosing an appropriate strateg [`flox` implements](https://flox.readthedocs.io/) grouped reductions for chunked array types like [cubed](https://cubed-dev.github.io/cubed/) and [dask](https://docs.dask.org/en/stable/array.html) using tree reductions. Tree reductions ([example](https://people.csail.mit.edu/xchen/gpu-programming/Lecture11-reduction.pdf)) are a parallel-friendly way of computing common reduction operations like `sum`, `mean` etc. -Briefly, one computes the reduction for a subset of the array $N$ chunks at a time in parallel, then combines those results together again $N$ chunks at a time, until we have the final result. +Briefly, one computes the reduction for a subset of the array N chunks at a time in parallel, then combines those results together again N chunks at a time, until we have the final result. Without flox, Xarray effectively shuffles — sorts the data to extract all values in a single group — and then runs the reduction group-by-group. Depending on data layout or "chunking" this shuffle can be quite expensive. @@ -57,12 +57,12 @@ Second, `method="cohorts"` which is a bit more subtle. Consider `groupby("time.month")` for the monthly mean dataset i.e. grouping by an exactly periodic array. When the chunk size along the core dimension "time" is a divisor of the period; so either 1, 2, 3, 4, or 6 in this case; groups tend to occur in cohorts ("groups of groups"). For example, with a chunk size of 4, monthly mean input data for the "cohort" Jan/Feb/Mar/Apr are _always_ in the same chunk, and totally separate from any of the other months. -Here is a schematic illustration where each month is represented by a different shade of red: +Here is a schematic illustration where each month is represented by a different shade of red and a single chunk contains 4 months: ![monthly cohorts](https://flox.readthedocs.io/en/latest/_images/cohorts-month-chunk4.png) This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. Doing so can significantly reduce compute times and in particular memory required for the computation. -If there isn't much separation of groups into cohorts, like when groups are randomly distributed across chunks, then it's hard to do better than the standard `method="map-reduce"`. +Finally, if there isn't much separation of groups into cohorts, like when groups are randomly distributed across chunks, then it's hard to do better than the standard `method="map-reduce"`. ## Choosing a strategy is hard, and harder to teach. From 1383ad8a1a2689a5b019ecc397f8f70ff79c9d05 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 22:01:33 -0600 Subject: [PATCH 09/22] more edits --- src/posts/flox-smart/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 7c027ec9..03d530fa 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -20,6 +20,7 @@ Briefly, one computes the reduction for a subset of the array N chunks at a time Without flox, Xarray effectively shuffles — sorts the data to extract all values in a single group — and then runs the reduction group-by-group. Depending on data layout or "chunking" this shuffle can be quite expensive. +Here's a schematic of an array with 5 chunks arranged vertically, and each chunk has 10 elements each of which are colored by group. ![shuffle](https://flox.readthedocs.io/en/latest/_images/new-split-apply-combine-annotated.svg) With flox installed, Xarray instead uses its parallel-friendly tree reduction. In many cases, this is a massive improvement. From 5a2bb655fc0af625c012485e6ca05ebba5785bd7 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 22:02:58 -0600 Subject: [PATCH 10/22] edit --- src/posts/flox-smart/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 03d530fa..f9694f3b 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -10,7 +10,7 @@ summary: 'flox adds heuristics for automatically choosing an appropriate strateg ## TL;DR -`flox>=0.9` now automatically optimizes GroupBy reductions with dask arrays to reduce memory usage and increase parallelism! Here I describe how. +`flox>=0.9` now automatically optimizes GroupBy reductions with dask arrays to reduce memory usage and increase parallelism! Here I describe how. To opt in, simply set `method=None` if you were setting it explicitly previously. ## What is flox? From 1cc7eb5b9a30381e11e3504f51edbb83aa147c41 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 22:06:14 -0600 Subject: [PATCH 11/22] edits --- src/posts/flox-smart/index.md | 40 ++++++++++++++++------------------- 1 file changed, 18 insertions(+), 22 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index f9694f3b..a5bb9434 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -26,7 +26,7 @@ With flox installed, Xarray instead uses its parallel-friendly tree reduction. In many cases, this is a massive improvement. Notice how much cleaner the graph is in this image: ![map-reduce](https://flox.readthedocs.io/en/latest/_images/new-map-reduce-reindex-True-annotated.svg) -See our [previous blog post](https://xarray.dev/blog/flox) for more. +See our [previous blog post](https://xarray.dev/blog/flox) or the [docs](https://flox.readthedocs.io/en/latest/implementation.html#method-map-reduce) for more. ## Tree reductions can be catastrophically bad @@ -45,7 +45,7 @@ Thus `flox` quickly grew two new modes of computing the groupby reduction. Two key realizations influenced that development: 1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. -2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. This is an important difference between arrays and dataframes! +2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. So a grouped reduction applied blockwise need not reduce the data by much (or any!) at all. This is an important difference between arrays and dataframes! These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. @@ -84,16 +84,16 @@ For groups `A,B,C,D` that occupy the following chunks (chunk 0 is the first chun ``` A: [0, 1, 2] -B: [1, 2, 3] -D: [5, 6, 7, 8] -E: [8] -X: [0, 3] +B: [1, 2, 3, 4] +C: [5, 6, 7, 8] +D: [8] +X: [0, 4] ``` We want to detect the cohorts `{A,B,X}` and `{C, D}` with the following chunks. ``` -[A, B, X]: [0, 1, 2, 3] +[A, B, X]: [0, 1, 2, 3, 4] [C, D]: [5, 6, 7, 8] ``` @@ -101,7 +101,7 @@ Importantly, we do _not_ want to be dependent on detecting exact patterns, and p ## The solution -After a fun exploration involving such fun ideas as [locality-sensitive hashing](http://ekzhu.com/datasketch/lshensemble.html), and [all-pair set similarity search](https://www.cse.unsw.edu.au/~lxue/WWW08.pdf), I settled on the following algorithm. +After a fun exploration involving such fun ideas as [locality-sensitive hashing](http://ekzhu.com/datasketch/lshensemble.html), and [all-pairs set similarity search](https://www.cse.unsw.edu.au/~lxue/WWW08.pdf), I settled on the following algorithm. I use set _containment_, or a "normalized intersection", to determine the similarity between the sets of chunks occupied by two different groups (`Q` and `X`). @@ -121,11 +121,11 @@ The steps are as follows: 1. Now we can quickly determine a number of special cases and exit early: 1. Use `"blockwise"` when every group is contained to one block each. 1. Use `"cohorts"` when - 1. every chunk only has a single group, but that group might extend across multiple chunks; and - 1. existing cohorts don't overlap at all. -1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) + 1. every chunk only has a single group, but that group might extend across multiple chunks; and + 1. existing cohorts don't overlap at all. + 1. [and more](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L408-L426) -If we reach here, then we want to merge together any detected cohorts that substantially overlap with each other. +If we haven't exited yet, then we want to merge together any detected cohorts that substantially overlap with each other using the containment metric. 1. For that we first quickly compute containment for all groups `i` against all other groups `j` as `C = S.T @ S / number_chunks_per_group`. 1. To choose between `"map-reduce"` and `"cohorts"`, we need a summary measure of the degree to which the labels overlap with @@ -136,25 +136,21 @@ If we reach here, then we want to merge together any detected cohorts that subst For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementation.html#heuristics) or [the code](https://github.com/xarray-contrib/flox/blob/e6159a657c55fa4aeb31bcbcecb341a4849da9fe/flox/core.py#L336). Suggestions and improvements are very welcome! -Here is containment `C[i, j]` for a range of chunk sizes from 1 to 12, for an input array with 12 monthly mean time steps, -for computing `groupby("time.month")` of a monthly mean dataset. -These are colored so that light yellow is $C=0$, and dark purple is $C=1$. -The title on each image is (chunk size, sparsity). +Here is containment `C[i, j]` for a range of chunk sizes from 1 to 12 for computing `groupby("time.month")` of a monthly mean dataset. +The images only show 12 time steps. +These are colored so that light yellow is C=0, and dark purple is C=1. `C[i,j] = 1` when the chunks occupied by group `i` perfectly overlaps with those occupied by group `j` (so the diagonal elements are always 1). +The title on each image is `(chunk size, sparsity)`. When the chunksize _is_ a divisor of the period 12, $C$ is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. When the chunksize _is not_ a divisor of the period 12, $C$ is much less sparse in comparison. ![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) -Given the above `C`, flox will choose: - -1. `"blockwise"` for chunk size 1, -2. `"cohorts"` for (2, 3, 4, 6, 12), -3. and `"map-reduce"` for the rest. +Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6, 12), and `"map-reduce"` for the rest. Cool, isn't it?! -Importantly this inference is fast — [400ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox)! +Importantly this inference is fast — [400ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox) where the group labels are a 2GB 2D array! But we have not tried with bigger problems (example: GroupBy(100,000 watersheds) in the US). ## What's next? From 53e1c3ae408b577e7fda4d6e69ab12bdf4e608af Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 22:15:37 -0600 Subject: [PATCH 12/22] more edits --- src/posts/flox-smart/index.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index a5bb9434..fa886baa 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -137,16 +137,16 @@ For more detail [see the docs](https://flox.readthedocs.io/en/latest/implementat Suggestions and improvements are very welcome! Here is containment `C[i, j]` for a range of chunk sizes from 1 to 12 for computing `groupby("time.month")` of a monthly mean dataset. -The images only show 12 time steps. -These are colored so that light yellow is C=0, and dark purple is C=1. +These panels are colored so that light yellow is `C=0`, and dark purple is `C=1`. `C[i,j] = 1` when the chunks occupied by group `i` perfectly overlaps with those occupied by group `j` (so the diagonal elements are always 1). +Since there are 12 groups, `C` is a 12x12 matrix. The title on each image is `(chunk size, sparsity)`. -When the chunksize _is_ a divisor of the period 12, $C$ is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. -When the chunksize _is not_ a divisor of the period 12, $C$ is much less sparse in comparison. +When the chunksize _is_ a divisor of the period 12, `C` is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. +When the chunksize _is not_ a divisor of the period 12, `C` is much less sparse in comparison. ![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) -Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6, 12), and `"map-reduce"` for the rest. +Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6), and `"map-reduce"` for the rest. Cool, isn't it?! From ff8ccff80f3ca801ad3e635fe295a27f5883e0d5 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 30 Jul 2024 22:21:13 -0600 Subject: [PATCH 13/22] tweak --- src/posts/flox-smart/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index fa886baa..c339deba 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -142,10 +142,10 @@ These panels are colored so that light yellow is `C=0`, and dark purple is `C=1` are always 1). Since there are 12 groups, `C` is a 12x12 matrix. The title on each image is `(chunk size, sparsity)`. -When the chunksize _is_ a divisor of the period 12, `C` is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. -When the chunksize _is not_ a divisor of the period 12, `C` is much less sparse in comparison. ![flox sparsity image](https://flox.readthedocs.io/en/latest/_images/containment.png) +When the chunksize _is_ a divisor of the period 12, `C` is a [block diagonal](https://en.wikipedia.org/wiki/Block_matrix) matrix. +When the chunksize _is not_ a divisor of the period 12, `C` is much less sparse in comparison. Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6), and `"map-reduce"` for the rest. Cool, isn't it?! From 1c19f7fd486b67ffe120f73e799bcb07a4e068a4 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Thu, 1 Aug 2024 09:57:02 -0600 Subject: [PATCH 14/22] Update --- src/posts/flox-smart/index.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index c339deba..379772d3 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -150,8 +150,7 @@ Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6 Cool, isn't it?! -Importantly this inference is fast — [400ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox) where the group labels are a 2GB 2D array! -But we have not tried with bigger problems (example: GroupBy(100,000 watersheds) in the US). +Importantly this inference is fast — [~250ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox) where approximately 3000 groups are distributed over 2500 chunks; and ~1.25s for grouping by US watersheds ~87000 groups across 640 chunks. ## What's next? From 5da929515255d1bcad5e909cde88a251c1f4205f Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Fri, 2 Aug 2024 21:21:19 -0600 Subject: [PATCH 15/22] Add demo. --- src/posts/flox-smart/index.md | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 379772d3..421edd9a 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -61,7 +61,7 @@ For example, with a chunk size of 4, monthly mean input data for the "cohort" Ja Here is a schematic illustration where each month is represented by a different shade of red and a single chunk contains 4 months: ![monthly cohorts](https://flox.readthedocs.io/en/latest/_images/cohorts-month-chunk4.png) This means that we can run the tree reduction for each cohort (three cohorts in total: `JFMA | MJJA | SOND`) independently and expose more parallelism. -Doing so can significantly reduce compute times and in particular memory required for the computation. +Doing so can significantly reduce memory required for the computation. Finally, if there isn't much separation of groups into cohorts, like when groups are randomly distributed across chunks, then it's hard to do better than the standard `method="map-reduce"`. @@ -72,6 +72,18 @@ Worse, they are hard to explain conceptually! I've tried! ([example 1](https://d What we need is to choose the appropriate strategy automatically. +## Demo + +Here's a quick demo of computing monthly mean climatologies with the National Water Model. + +For this input dataset, chunked so that approximately a month of data is in a single chunk, + + +we run ``` mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") mean_cohorts += ds.groupby("time.month").mean() # this is auto-detected! ``` Using the algorithm +described below, flox will **automatically** set `method="cohorts"` for this dataset +unless specified, yielding a 5X decrease in memory need, and 2X longer in time ![](/posts/flox-smart/mem.png) + ## Problem statement Fundamentally, we know: From ad8caea930eec317b3a5bd39f7ab825bf0b09825 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Sat, 3 Aug 2024 03:21:54 +0000 Subject: [PATCH 16/22] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- src/posts/flox-smart/index.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 421edd9a..9c1bc16f 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -79,10 +79,11 @@ Here's a quick demo of computing monthly mean climatologies with the National Wa For this input dataset, chunked so that approximately a month of data is in a single chunk, -we run ``` mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") mean_cohorts -= ds.groupby("time.month").mean() # this is auto-detected! ``` Using the algorithm -described below, flox will **automatically** set `method="cohorts"` for this dataset -unless specified, yielding a 5X decrease in memory need, and 2X longer in time ![](/posts/flox-smart/mem.png) +we run ``` mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") +mean_cohorts = ds.groupby("time.month").mean() # this is auto-detected! ``` +Using the algorithm described below, flox will **automatically** set +`method="cohorts"` for this dataset unless specified, yielding a 5X decrease in +memory need, and 2X longer in time ![](/posts/flox-smart/mem.png) ## Problem statement From 2203a345b1d27694018365327461e4931d587f7c Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Fri, 2 Aug 2024 21:27:47 -0600 Subject: [PATCH 17/22] Fix --- src/posts/flox-smart/index.md | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 9c1bc16f..7074dcae 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -79,11 +79,19 @@ Here's a quick demo of computing monthly mean climatologies with the National Wa For this input dataset, chunked so that approximately a month of data is in a single chunk, -we run ``` mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") -mean_cohorts = ds.groupby("time.month").mean() # this is auto-detected! ``` + +we run + +```python +mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") +mean_cohorts = ds.groupby("time.month").mean() # this is auto-detected! +``` + Using the algorithm described below, flox will **automatically** set `method="cohorts"` for this dataset unless specified, yielding a 5X decrease in -memory need, and 2X longer in time ![](/posts/flox-smart/mem.png) +memory need, and 2X longer in time + +Memory usage ## Problem statement From ebbd00797b2691307e298e65dd5eba9a3a3ce160 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Fri, 2 Aug 2024 21:30:20 -0600 Subject: [PATCH 18/22] Add assets --- public/posts/flox-smart/dataset-repr.html | 1 + public/posts/flox-smart/mem.png | Bin 0 -> 124001 bytes 2 files changed, 1 insertion(+) create mode 100644 public/posts/flox-smart/dataset-repr.html create mode 100644 public/posts/flox-smart/mem.png diff --git a/public/posts/flox-smart/dataset-repr.html b/public/posts/flox-smart/dataset-repr.html new file mode 100644 index 00000000..26984fa4 --- /dev/null +++ b/public/posts/flox-smart/dataset-repr.html @@ -0,0 +1 @@ +
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    PROJCS["Lambert_Conformal_Conic",GEOGCS["GCS_Sphere",DATUM["D_Sphere",SPHEROID["Sphere",6370000.0,0.0]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Lambert_Conformal_Conic_2SP"],PARAMETER["false_easting",0.0],PARAMETER["false_northing",0.0],PARAMETER["central_meridian",-97.0],PARAMETER["standard_parallel_1",30.0],PARAMETER["standard_parallel_2",60.0],PARAMETER["latitude_of_origin",40.0],UNIT["Meter",1.0]];-35691800 -29075200 10000;-100000 10000;-100000 10000;0.001;0.001;0.001;IsHighPrecision
    grid_mapping :
    crs
    long_name :
    depth to saturation, rounded to highest saturated layer
    units :
    m
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xarray.DataArray
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From ab715b9d0dd2d7b564b398fb25033f3152687bd5 Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Fri, 2 Aug 2024 21:35:10 -0600 Subject: [PATCH 20/22] edit --- src/posts/flox-smart/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 7074dcae..e56e30a6 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -5,7 +5,7 @@ authors: - name: Deepak Cherian github: dcherian -summary: 'flox adds heuristics for automatically choosing an appropriate strategy with dask arrays!' +summary: 'flox adds heuristics for automatically choosing an appropriate reduction strategy with dask arrays!' --- ## TL;DR @@ -89,7 +89,7 @@ mean_cohorts = ds.groupby("time.month").mean() # this is auto-detected! Using the algorithm described below, flox will **automatically** set `method="cohorts"` for this dataset unless specified, yielding a 5X decrease in -memory need, and 2X longer in time +memory used and a 2X increase in runtime. Read on to figure out how! 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Using the algorithm described below, flox will **automatically** set `method="cohorts"` for this dataset unless specified, yielding a 5X decrease in memory used and a 2X increase in runtime. Read on to figure out how! +Read on to figure out how! + +_Note that the improvements here are strongly dependent on the details +of the grouping variable, the chunksize, and even dask's scheduler. In fact, writing this post +prompted the discovery of a bug in dask's scheduler that should substantially improve the "map-reduce" +case._ Memory usage @@ -200,3 +206,10 @@ _[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas One way to preserve context may be be to have Xarray's new Grouper objects report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. This would allow a downstream system like `flox` or `cubed` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. That is an experiment for another day. + +The improvements described here are strongly dependent on the details +of the grouping variable, the chunksize, and even dask's scheduler. +In fact, writing this post prompted the discovery of a bug in dask's scheduler +that should substantially improve the "map-reduce" case. In parallel, there's been work around +improving shuffling along dask arrays. +Clearly the last word on the GroupBy problem has not been said! From 8b39d32978230174391a5571508a5a1308499a3b Mon Sep 17 00:00:00 2001 From: Deepak Cherian Date: Tue, 12 Nov 2024 14:41:26 -0700 Subject: [PATCH 22/22] edits --- src/posts/flox-smart/index.md | 80 ++++++++++++++++------------------- 1 file changed, 37 insertions(+), 43 deletions(-) diff --git a/src/posts/flox-smart/index.md b/src/posts/flox-smart/index.md index 2d6075de..5159ffd3 100644 --- a/src/posts/flox-smart/index.md +++ b/src/posts/flox-smart/index.md @@ -41,13 +41,12 @@ This issue does _not_ arise for regular reductions where the final result depend ## Avoiding catastrophe -Thus `flox` quickly grew two new modes of computing the groupby reduction. -Two key realizations influenced that development: +Two key realizations: 1. Array workloads frequently group by a relatively small in-memory array. Quite frequently those arrays have patterns to their values e.g. `"time.month"` is exactly periodic, `"time.dayofyear"` is approximately periodic (depending on calendar), `"time.year"` is commonly a monotonic increasing array. 2. Chunk sizes (or "partition sizes") for arrays can be quite small along the core-dimension of an operation. So a grouped reduction applied blockwise need not reduce the data by much (or any!) at all. This is an important difference between arrays and dataframes! -These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. +These two properties are particularly relevant for "climatology" calculations (e.g. `groupby("time.month").mean()`) — a common Xarray workload in the Earth Sciences. Thus `flox` quickly grew two new modes of computing the groupby reduction. First, `method="blockwise"` which applies the grouped-reduction in a blockwise fashion. This is great for `resample(time="Y").mean()` where we group by `"time.year"`, which is a monotonic increasing array. @@ -83,13 +82,13 @@ For this input dataset, chunked so that approximately a month of data is in a si we run ```python -mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") -mean_cohorts = ds.groupby("time.month").mean() # this is auto-detected! +mean_mapreduce = ds.groupby("time.month").mean(method="map-reduce") # mapreduce is a suboptimal manual choice here +mean_cohorts = ds.groupby("time.month").mean() # cohorts is a better choice - auto-detected! ``` Using the algorithm described below, flox will **automatically** set `method="cohorts"` for this dataset unless specified, yielding a 5X decrease in -memory used and a 2X increase in runtime. Read on to figure out how! +memory used and a 2X increase in runtime. Read on to figure out how! _Note that the improvements here are strongly dependent on the details @@ -99,7 +98,37 @@ case._ Memory usage -## Problem statement +## What's next? + +flox' ability to do cleanly infer an optimal strategy relies entirely on the input chunking making such optimization possible. +This is a big knob. +A brand new [Xarray feature](https://docs.xarray.dev/en/stable/user-guide/groupby.html#grouper-objects) does make such rechunking +a lot easier for time grouping in particular: + +```python +from xarray.groupers import TimeResampler + +rechunked = ds.chunk(time=TimeResampler("YE")) +``` + +will rechunk so that a year of data is in a single chunk. +Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application when that's cheap. + +A challenge here is that we have lost _context_ when moving from Xarray to flox. +The string `"time.month"` tells Xarray that I am grouping a perfectly periodic array with period 12; similarly +the _string_ `"time.dayofyear"` tells Xarray that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). +But Xarray passes flox an array of integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. +It's hard to infer the context from that! +Though one approach might frame the problem as: what rechunking would transform `C` to a block diagonal matrix. +_[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference._ + +One way to preserve context may be be to have Xarray's new Grouper objects report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. +This would allow a downstream system like `flox` or `cubed` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. +That is an experiment for another day. + +## Appendix: automatically detecting group patterns + +### Problem statement Fundamentally, we know: @@ -126,7 +155,7 @@ We want to detect the cohorts `{A,B,X}` and `{C, D}` with the following chunks. Importantly, we do _not_ want to be dependent on detecting exact patterns, and prefer approximate solutions and heuristics. -## The solution +### The solution After a fun exploration involving such fun ideas as [locality-sensitive hashing](http://ekzhu.com/datasketch/lshensemble.html), and [all-pairs set similarity search](https://www.cse.unsw.edu.au/~lxue/WWW08.pdf), I settled on the following algorithm. @@ -178,38 +207,3 @@ Given the above `C`, flox will choose `"cohorts"` for chunk sizes (1, 2, 3, 4, 6 Cool, isn't it?! Importantly this inference is fast — [~250ms for the US county](https://flox.readthedocs.io/en/latest/implementation.html#example-spatial-grouping) GroupBy problem in our [previous post](https://xarray.dev/blog/flox) where approximately 3000 groups are distributed over 2500 chunks; and ~1.25s for grouping by US watersheds ~87000 groups across 640 chunks. - -## What's next? - -flox' ability to do cleanly infer an optimal strategy relies entirely on the input chunking making such optimization possible. -This is a big knob. -A brand new [Xarray feature](https://docs.xarray.dev/en/stable/user-guide/groupby.html#grouper-objects) does make such rechunking -a lot easier for time grouping in particular: - -```python -from xarray.groupers import TimeResampler - -rechunked = ds.chunk(time=TimeResampler("YE")) -``` - -will rechunk so that a year of data is in a single chunk. -Even so, it would be nice to automatically rechunk to minimize number of cohorts detected, or to a perfectly blockwise application when that's cheap. - -A challenge here is that we have lost _context_ when moving from Xarray to flox. -The string `"time.month"` tells Xarray that I am grouping a perfectly periodic array with period 12; similarly -the _string_ `"time.dayofyear"` tells Xarray that I am grouping by a (quasi-)periodic array with period 365, and that group `366` may occur occasionally (depending on calendar). -But Xarray passes flox an array of integer group labels `[1, 2, 3, 4, 5, ..., 1, 2, 3, 4, 5]`. -It's hard to infer the context from that! -Though one approach might frame the problem as: what rechunking would transform `C` to a block diagonal matrix. -_[Get in touch](https://github.com/xarray-contrib/flox/issues) if you have ideas for how to do this inference._ - -One way to preserve context may be be to have Xarray's new Grouper objects report ["preferred chunks"](https://github.com/pydata/xarray/blob/main/design_notes/grouper_objects.md#the-preferred_chunks-method-) for a particular grouping. -This would allow a downstream system like `flox` or `cubed` or `dask-expr` to take this in to account later (or even earlier!) in the pipeline. -That is an experiment for another day. - -The improvements described here are strongly dependent on the details -of the grouping variable, the chunksize, and even dask's scheduler. -In fact, writing this post prompted the discovery of a bug in dask's scheduler -that should substantially improve the "map-reduce" case. In parallel, there's been work around -improving shuffling along dask arrays. -Clearly the last word on the GroupBy problem has not been said!