Mapper for log-sum-exp aggregation

Constructs a mapper that aggregates elements of exp(state), with optional non-negative weighting, and then takes the log(), so it can be used e.g. for \(v_k=\log[\sum_{i\in I_k} w_i \exp(u_i)] \) and \(v_k=\log[\sum_{i\in I_k} w_i \exp(u_i) / \sum_{i\in I_k} w_i] \) calculations. Relies on the input handling methods for bm_aggregate, but also allows the weights to be supplied on a logarithmic scale as log_weights. To avoid numerical overflow, it uses the common method of internally shifting the state blockwise; \(v_k=s_k+\log[\sum_{i\in I_k} \exp(u_i + \log(w_i)- s_k)] \), where \(s_k=\max_{i\in I_k} u_i + \log(w_i)\) is the shift for block \(k\).

Usage

bm_logsumexp(rescale = FALSE, n_block = NULL)

bru_mapper_logsumexp(...)

Arguments

rescale

logical; For bm_aggregate and bm_logsumexp, specifies if the blockwise sums should be normalised by the blockwise weight sums or not:

• FALSE: (default) Straight weighted sum, no rescaling.

• TRUE: Divide by the sum of the weight values within each block. This is useful for integration averages, when the given weights are plain integration weights. If the weights are NULL or all ones, this is the same as dividing by the number of entries in each block.

n_block

Predetermined number of output blocks. If NULL, overrides the maximum block index in the inputs. The priority order is input$n_block, the mapper definition n_block, then max(input$block).

...

Arguments passed on to bm_logsumexp()

See also

bru_mapper, bru_mapper_generics

Other mappers: bm_aggregate(), bm_collect(), bm_const(), bm_factor(), bm_fm_mesh_1d, bm_fmesher(), bm_harmonics(), bm_index(), bm_linear(), bm_marginal(), bm_matrix(), bm_mesh_B(), bm_multi(), bm_pipe(), bm_repeat(), bm_scale(), bm_shift(), bm_sum(), bm_taylor(), bru_get_mapper(), bru_mapper()

Other specific bm_logsumexp method implementations: ibm_eval(), ibm_jacobian()

Examples

m <- bm_logsumexp()
ibm_eval2(m, list(block = c(1, 2, 1, 2), weights = 1:4), 11:14)
#> $offset
#> [1] 14.14274 15.45177
#> 
#> $jacobian
#> 2 x 4 sparse Matrix of class "dgCMatrix"
#>                                               
#> [1,] 0.04316453 .          0.9568355 .        
#> [2,] .          0.06337894 .         0.9366211
#> 
ibm_eval2(m, list(block = c(1, 2, 1, 2), weights = 1:4, n_block = 3), 11:14)
#> $offset
#> [1] 14.14274 15.45177     -Inf
#> 
#> $jacobian
#> 3 x 4 sparse Matrix of class "dgCMatrix"
#>                                               
#> [1,] 0.04316453 .          0.9568355 .        
#> [2,] .          0.06337894 .         0.9366211
#> [3,] .          .          .         .        
#>