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new 60f1150 [SYSTEMDS-2968] Cumulative sum with decay multiplier (#1260)
60f1150 is described below
commit 60f11504af19af33cf4104e3fae00417e3c6f0a8
Author: j143 <[email protected]>
AuthorDate: Thu May 6 01:37:04 2021 +0530
[SYSTEMDS-2968] Cumulative sum with decay multiplier (#1260)
Generally used for efficient calculation with the help of
momentum as discussed at https://cs.stackexchange.com/a/73760
--
For people familiar with python
```py
import numpy as np
data = np.array([2, 3, 0, 0, 4, 3], dtype=float)
result = []
last_value = 0
for d in data:
last_value = (last_value + d)*.95 # apply decay=0.95
result.append(last_value)
```
Related discussion as to how to cumsum with decay with:
NumPy - https://stackoverflow.com/q/28915088
Tensorflow 2.0 - https://stackoverflow.com/a/60635516
R - https://stackoverflow.com/q/14814752
---
docs/site/dml-vs-r-guide.md | 32 ++++++++++++++++++++++++++++++++
1 file changed, 32 insertions(+)
diff --git a/docs/site/dml-vs-r-guide.md b/docs/site/dml-vs-r-guide.md
index dbf62e6..7780704 100644
--- a/docs/site/dml-vs-r-guide.md
+++ b/docs/site/dml-vs-r-guide.md
@@ -295,3 +295,35 @@ L = (A %*% t(A)) * Mask
X = invert_lower_triangular (L);
```
+#### Cumulative summation with Decay multiplier
+
+Given matrix X, compute:
+
+Y[i] = X[i]
+ + X[i-1] * C[i]
+ + X[i-2] * C[i] * C[i-1]
+ + X[i-3] * C[i] * C[i-1] * C[i-2]
+ + ...
+
+```dml
+cumsum_prod = function (Matrix[double] X, Matrix[double] C, double start)
+ return (Matrix[double] Y)
+{
+ Y = X; P = C; m = nrow(X); k = 1;
+ Y[1,] = Y[1,] + C[1,] * start
+ while (k < m) {
+ Y[k + 1:m,] = Y[k + 1:m,] +
+ Y[1:m - k,] * P[k + 1:m,]
+ P[k + 1:m,] = P[1:m - k,] * P[k + 1:m,]
+ k = 2 * k
+ }
+}
+
+X = matrix ("1 2 3 4 5 6 7 8 9", rows = 9, cols = 1)
+
+# Zeros in C cause "breaks" that restart the cumulative summation from 0
+C = matrix ("0 1 1 0 1 1 1 0 1", rows = 9, cols = 1)
+
+Y = cumsum_prod(X, C, 0)
+```
+
