ipu_nr: Iterative Proportional Updating (Newton-Raphson)
In ipfr: List Balancing for Reweighting and Population Synthesis

List balancing similar to ipu, but using the Newton-Raphson approach to optimization. Created primarily as a point of comparison for ipu.

ipu_nr(
  primary_seed,
  primary_targets,
  secondary_seed = NULL,
  secondary_targets = NULL,
  target_priority = 1e+07,
  relative_gap = 0.01,
  max_iterations = 100,
  absolute_diff = 10,
  weight_floor = 1e-05,
  verbose = FALSE,
  max_ratio = 10000,
  min_ratio = 1e-04
)

`primary_seed`	In population synthesis or household survey expansion, this would be the household seed table (each record would represent a household). It could also be a trip table, where each row represents an origin-destination pair. Must contain a `pid` ("primary ID") field that is unique for each row. Must also contain a geography field that starts with "geo_".
`primary_targets`	A `named list` of data frames. Each name in the list defines a marginal dimension and must match a column from the `primary_seed` table. The data frame associated with each named list element must contain a geography field (starts with "geo_"). Each row in the target table defines a new geography (these could be TAZs, tracts, clusters, etc.). The other column names define the marginal categories that targets are provided for. The vignette provides more detail.
`secondary_seed`	Most commonly, if the primary_seed describes households, the secondary seed table would describe a unique person with each row. Must also contain the `pid` column that links each person to their respective household in `primary_seed`. Must not contain any geography fields (starting with "geo_").
`secondary_targets`	Same format as `primary_targets`, but they constrain the `secondary_seed` table.
`target_priority`	This argument controls how quickly each set of targets is relaxed. In other words: how important it is to match the target exactly. Defaults to `10,000,000`, which means that all targets should be matched exactly. `real` This priority value will be used for each target table. `named list` Each named entry must match an entry in either `primary_targets` or `secondary_targets` and have a `real`. This priority will be applied to that target table. Any targets not in the list will default to `10,000,000`. `data.frame` Column `target` must have values that match an entry in either `primary_targets` or `secondary_targets`. Column `priority` contains the values to use for priority. Any targets not in the table will default to `10,000,000`.
`relative_gap`	After each iteration, the weights are compared to the previous weights and the the `relative_gap` threshold, then the process terminates.
`max_iterations`	maximum number of iterations to perform, even if `relative_gap` is not reached.
`absolute_diff`	Upon completion, the `ipu()` function will report the worst-performing marginal category and geography based on the percent difference from the target. `absolute_diff` is a threshold below which percent differences don't matter. For example, if if a target value was 2, and the expanded weights equaled 1, that's a 100 is only 1. Defaults to 10.
`weight_floor`	Minimum weight to allow in any cell to prevent zero weights. Set to .0001 by default. Should be arbitrarily small compared to your seed table weights.
`verbose`	Print iteration details and worst marginal stats upon completion? Default `FALSE`.
`max_ratio`	`real` number. The average weight per seed record is calculated by dividing the total of the targets by the number of records. The max_scale caps the maximum weight at a multiple of that average. Defaults to `10000` (basically turned off).
`min_ratio`	`real` number. The average weight per seed record is calculated by dividing the total of the targets by the number of records. The min_scale caps the minimum weight at a multiple of that average. Defaults to `0.0001` (basically turned off).