Comment by m101

This is really amazing, and it reminds me of an Excel modification I did 24 years ago for an animation studio. They had around 3,000 digital artists and then about 200 support staff, and around 8 different productions moving through the studio at the same time. Each production was at some different stage of completion. The studio's production management staff spent a huge amount of time negotiating what staff was assigned to what productions, and the reasonings were all hazy and non-fact based. So I wrote what people would now call a deep learning system that mined all the accounting and production tracking records the studio had, and created probability distributions and confidence intervals for every individual and every task, and every combination of people and their combined tasks, and that all composited together into a giant predictive engine of real time whatif scenarios for the entire studio in different configurations.

It was used for a series of feature films you all probably saw: the Chronicles of Narnia series, the Scooby Doo live action CG films, the Garfield films with the CG Garfield, and Life of PI.

People both loved and hated it. They loved the insights into the studio's capabilities, and they hated thinking through how the thing operated, and they hated the thought process of constructing a new whatif scenario, because they had to THINK.

Wow, this is incredibly cool. I can't believe this stuff hasn't been ported into Excel.

Off-topic: managing @Risk licenses in a fully on-prem, no-internet environment has been such a pain in the neck.

As a number of the comments have suggested there are a number of Monte Carlo methods (including this addin) but I was hoping that someone would make one which calculated based on random variables and output a resultant random variable, over brute force monte carlo. Monte Carlo is also somewhat slow, but doing the maths analytically should be fast.

The matrix product is not something specific to matrices, but it is a particular case of the contracted tensor product.

(While now almost everybody uses the names "tensor product" and "contracted tensor product", historically these names are wrong. Better names, which do not misuse the word "tensor", would have been "Zehfuss product" and "Cayley product", after the names of the mathematicians who have introduced them.)

The word "tensor" has become increasingly corrupted over the years. Originally, it had a meaning that matched its etymology, i.e. "tensor" meant "symmetric matrix", because a matrix could be decomposed through the polar decomposition into a tensor and a versor (i.e. a symmetric matrix and a rotation matrix).

Then what is now called tensor theory was created by Ricci, but without ever using the word "tensor". The meaning of the word "tensor" was changed by Einstein in his theory of the general relativity, where for unknown reasons he chose this word to refer to arrays with an arbitrary number of dimensions that satisfy a certain kind of transformation relationships when the systems of coordinates is changed.

After WWII, due to the huge popularity of Einstein, this weird usage of the word has become widespread.

Then for many decades tensors were just a subset of arrays, those that are changed in a certain specific way when the system of coordinates is changed.

Eventually, there was the second corruption of the word "tensor" which is completely unjustified, when "tensor" has become just a synonym for "array".

Vectors are 1-dimensional arrays (though originally, like tensors, vectors were only a subset of 1-dimensional arrays), matrices are 2-dimensional arrays and nowadays "tensors" means just "arrays", i.e. of an arbitrary dimension.

The tensor product and the contracted tensor product are defined for arrays of arbitrary dimensions. For 2-dimensional arrays the contracted tensor product is a.k.a. matrix product, and for 1-dimensional arrays it is a.k.a. scalar product.