Method generalInverse
val generalInverse: Tensor<'T> -> Tensor<'T> * Tensor<'T> * Tensor<'T>
Computes the generalized inverse I, solvability constraints S
and null-space N of the specified matrix L.
L can be of any shape and rank.
The return values is a tuple (I, S, N).
The following properties are fulfilled.
Inverse: M .* I .* M = M.
Solvability: S .* M = 0.
Null-space: M .* N = 0.
This has the following consequences for a linear equation system of the
form y = M .* x:
If y comes from the solvable space (i.e. S .* y = 0),
then the value x = I .* y gives one solution of y = M .* x.
Adding any linear combination of the columns of N to this x yields
another solution, i.e. y = M .* x = M .* (x + N .* z) for any z.
If x contains no component from the null-space (i.e. N^T .* x = 0),
then we can recover x from y = M .* x by x = I .* y.
(TODO: check last sentence, because it was violated in test1)
Declaration
val generalInverse: L:Tensor<'T> -> Tensor<'T> * Tensor<'T> * Tensor<'T>
Parameters
| Type |
Name |
Description |
| Tensor<'T> |
L |
|
Returns
Type Parameters