Sum of weighted Soft-Max reduction.

Usage

sumsoftmaxweight(x, index, weight)

sumsoftmaxweight_reduction(x, index, weight)

Arguments

x: a LazyTensor or a ComplexLazyTensor.
index: a character corresponding to the reduction dimension that should be either "i" or "j" to specify whether if the reduction is indexed by "i" or "j".
weight: an optional object (LazyTensor or ComplexLazyTensor) that specifies scalar or vector-valued weights.

Value

a matrix corresponding to the Sum of weighted Soft-Max reduction.

Details

If x is a LazyTensor or a ComplexLazyTensor, sumsoftmaxweight(x, index, weight) will:

if index = "i", return the Sum of weighted Soft-Max reduction of x over the i indexes;
if index = "j", return the Sum of weighted Soft-Max reduction of x over the j indexes.

Note: Run browseVignettes("rkeops") to access the vignettes and find details about this function in the "RKeOps LazyTensor" vignette, at section "Reductions".

Author

Chloe Serre-Combe, Amelie Vernay

Examples

if (FALSE) {
x <- matrix(runif(150 * 3), 150, 3) 
x_i <- LazyTensor(x, index = 'i') 
y <- matrix(runif(100 * 3), 100, 3)
y_j <- LazyTensor(y, index = 'j')

V_ij <- x_i - y_j   # weight matrix
S_ij = sum(V_ij^2)     

ssmaxweight <- sumsoftmaxweight(S_ij, 'i', V_ij) # sumsoftmaxweight reduction
                                                 # over the 'i' indices
}
if (FALSE) {
x <- matrix(runif(150 * 3), 150, 3) 
x_i <- LazyTensor(x, index = 'i') 
y <- matrix(runif(100 * 3), 100, 3)
y_j <- LazyTensor(y, index = 'j')

V_ij <- x_i - y_j   # weight matrix
S_ij = sum(V-ij^2)     

# sumsoftmaxweight reduction over the 'i' indices
ssmaxw_red <- sumsoftmaxweight_reduction(S_ij, 'i', V_ij) 

}