scenario: scenario: Construct reduced trees with a predefined nodal...
In swd-turner/scenario: Construct Reduced Trees with Predefined Nodal Structures

The buildtree function uses the neural gas method to generate a scenario tree of predefined nodal structure. The checktree function plots a scenario tree structure as defined by a nodal parition matrix.

Latorre, J.M., Cerisola, S. and Ramos, A. (2007) Clustering algorithms for scenario tree generation: Application to natural hydro flows, European Journal of Operational Research, 181, 1339-1353.

Xu, B., Zhong, P.A., Zambon, R.C., Zhao, Y., Yeh, W. (2015) Scenario tree reduction in stochastic programming with recourse for hydropower operations, Water Resources Research, 51, 6359-6380.

Dupacova, Jitka, Giorgio Consigli, and Stein W. Wallace. "Scenarios for multistage stochastic programs." Annals of operations research 100.1-4 (2000): 25-53.

# TEST BY GENERATING SCENARIOS FROM KNOWN CENTROIDS AND THEN
# COMPARING FIT BETWEEN THE GENERATED TREE AND INTIAL CENTROIDS.

# 1. Generate scenarios with known centroids:

centroids <- cbind(c(0,2,3), c(0,2,1), c(0,-2,-3),c(0,-2,-1))
matplot(centroids, type="l", lwd = 3, col = "black", lty = 3)
scenarios <- matrix(rep(centroids,5), ncol=20) + matrix(rnorm(60,0,0.25),ncol=20)
matlines(scenarios, col = "grey")


# 2. Assign and check nodal structure for tree:

treeStruct <- rbind(c(1,1,1,1),
                    c(2,2,5,5),
                    c(3,4,6,7))
checktree(treeStruct)


# 3. Build scenario tree:

tree <- buildtree(scenarios, treeStruct, jMax = 1000)


#4. Compare original centroids

matlines(centroids,lwd = 3, col = "black", lty = 3)
# Improved convergence is achieved by increasing the number of iterations, jMax.