Spidr.Optimize

(source)

Function optimizers.

Definitions

0 Optimizer : (0 _ : Type) -> Type

  An `Optimizer` finds the value, in a `Tensor`-valued feature space, which (typically
  approximately) optimizes a scalar-valued function over that space.
  
  @domain The type of the domain over which to find the optimal value.

Totality: total
Visibility: public export

meshGrid : (density : List Nat) -> HasLength d density => All (\{arg:0} => GT {arg:0} 1) density => Tensor [d] F64 -> Tensor [d] F64 -> Tag (Vect d (Tensor density F64))

  For each of `d` axes, return a grid of values that scales linearly between `bound` and `bound'`.
  Bounds need not be ordered. In the n-th grid, values vary along the n-th axis, and are constant
  across other axes. The number of values along the axis is the n-th `density`.
  
  For example, for
  ```
  lo, hi : Tensor [2] F64
  lo = tensor [0.0, -0.5]
  hi = tensor [1.5, 1.0]
  ```
  `meshGrid [3, 4] lo hi` yields `[x, y]` where
  ```
  x, y : Tensor [3, 4] F64
  x = tensor [
      [0.0 , 0.0 , 0.0 , 0.0 ]
    , [0.75, 0.75, 0.75, 0.75]
    , [1.5 , 1.5 , 1.5 , 1.5 ]
    ]
  y = tensor [
      [-0.5, 0.0, 0.5, 1.0]
    , [-0.5, 0.0, 0.5, 1.0]
    , [-0.5, 0.0, 0.5, 1.0]
    ]
  ```
  
  @density The number of values for each axis.
  @bound One bound of the values for each axis.
  @bound' The other bounds.

Totality: total
Visibility: export

gridSearch : (density : List Nat) -> HasLength d density => All (\{arg:0} => GT {arg:0} 1) density => Tensor [d] F64 -> Tensor [d] F64 -> Optimizer (Tensor [d] F64)

  Grid search of a scalar-valued function. Grid search approximates the optimum by evaluating the
  objective over a bounded, evenly-spaced grid. Bounds need not be ordered.
  
  @density The density of the grid.
  @bound One bound of the grid.
  @bound' The other bound of the grid.

Totality: total
Visibility: export

lbfgs : Tensor [n] F64 -> Optimizer (Tensor [n] F64)

  The limited-memory BFGS (L-BFGS) optimization tactic, see
  
  Nocedal, Jorge, Updating quasi-Newton matrices with limited storage.
  Math. Comp. 35 (1980), no. 151, 773–782.
  
  available at
  
  https://www.ams.org/journals/mcom/1980-35-151/S0025-5718-1980-0572855-7/
  
  **NOTE** This function is not yet implemented.
  
  @initialPoints The points from which to start optimization.