‣ MultiplicationForMorphisms( alpha, beta ) | ( operation ) |
Returns: a morphism
Compute the pointwise multiplication of two morphisms with the same source and target. For morphisms f, g: A \to B, returns a morphism whose output at each component is the product of the outputs of f and g.
‣ ReverseDifferentialWithGivenObjects( source, alpha, range ) | ( operation ) |
Returns: a morphism
Compute the reverse differential of a morphism alpha with given source and target objects. For a morphism f: \mathbb{R}^m \to \mathbb{R}^n, the reverse differential is a morphism Df: \mathbb{R}^m \times \mathbb{R}^n \to \mathbb{R}^m that computes y \cdot J_f(x) where J_f is the Jacobian matrix of f.
‣ ReverseDifferential( alpha ) | ( attribute ) |
Returns: a morphism
Compute the reverse differential of a morphism alpha. This is equivalent to ReverseDifferentialWithGivenObjects with automatically computed source and target.
‣ AddMultiplicationForMorphisms( C, F ) | ( operation ) |
‣ AddMultiplicationForMorphisms( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation MultiplicationForMorphisms. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha, beta ) \mapsto \mathtt{MultiplicationForMorphisms}(alpha, beta).
‣ AddReverseDifferential( C, F ) | ( operation ) |
‣ AddReverseDifferential( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation ReverseDifferential. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha ) \mapsto \mathtt{ReverseDifferential}(alpha).
‣ AddReverseDifferentialWithGivenObjects( C, F ) | ( operation ) |
‣ AddReverseDifferentialWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation ReverseDifferentialWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( source, alpha, range ) \mapsto \mathtt{ReverseDifferentialWithGivenObjects}(source, alpha, range).
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