### Dyadic combining

In dyadic combining two mappings `W1`

and `W2`

are related by one of the `Matlab`

operators

+, -, .*, .^ , /, , ./, |, &, ~, xor, >, >=, <, <=, =, ~=, ~

e.g.

W = W1 + W2

The `*`

-operator (matrix multiplication) is already overloaded as a sequential mapping and falls thereby outside this group. The `~`

-operator (logical not) is a monadic operator but is implemented similarly as the other logical operators.

For every of the above operators, like `+ holds that the following should be true:`

A*W = A*(W1+W2) A*W = A*W1 + A*W2 A*W = B1 + B2

Here `A`

is a dataset or a datafile that is applied to the mappings `W`

, `W1`

or `W2`

. The two mappings to be combined should thereby be of the same type (untrained, fixed or trained) and have the same sizes. There are a few exceptions. Fixed and trained mappings of the same input and output dimensions can be combined. One of the two mappings can also be a matrix of doubles, in which case it is treated as a fixed mapping. A scalar used instead of `W1`

or `W2`

just multiplies all elements of the dataset `A`

and is thereby also treated as a fixed mapping.

In case `W1`

and `W2`

are untrained mappings, they are trained by `A`

. The results `B1`

and `B2`

are thereby trained mappings.

The resulting mapping `W`

is always given the same annotation as `W1`

, unless it is a scalar or a matrix of doubles. In that case `W`

copies the annotation of `W2`

.

### Links

operations: basic, datasets, datafiles, mappings, classifiers, stacked, parallel, sequential, dyadic

commands: datasets, representation , classifiers, evaluation, clustering and regression, examples, support