#include "obj.h" /********************************************************************* Mixed Grass Stage Return Function for ASDP Clint Moore, USGS August 2011, April 2012 Revised 4/9/12 as part of EVPI analysis. Under a model-averaged run, the Aug 2011 version computed the objective for a model-averaged transition. This version computes the objective under each model prior to the averaging, which is the appropriate way. Provides stage return for mixed grass units. Partial controllability is accounted for as a submodel. Can be run with full or partial controllability; as single-model, averaged, or adaptive; and with or without management choice constraints, with these selections controlled in the scenario file. Although this program has been used by the U.S. Geological Survey (USGS), no warranty, expressed or implied, is made by the USGS or the U.S. Government as to the accuracy and functioning of the program and related program material nor shall the fact of distribution constitute any such warranty, and no responsibility is assumed by the USGS in connection therewith. *********************************************************************/ { INT d, cs, ns, idxcs, idxns, h, i, j, k, l, pc_index, s_dx, c, nt, modsel, act, /** Use for 16x16 **/ map[16] = {0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3}, /** Mapping of defoliation states (7) into model-specific defoliation level indices **/ /** Row 1: Last defoliation 5+ years ago -- applies only to model 1 **/ /** Rows 2-4: Last defoliation 2-4 years ago **/ /** Rows 5-7: Last defoliation 1 year ago **/ defmap[7][4] = { { 0, 0, 0, 0 }, { 1, 0, 0, 0 }, { 1, 0, 1, 1 }, { 1, 0, 2, 2 }, { 1, 0, 0, 0 }, { 1, 0, 1, 1 }, { 1, 0, 2, 2 } }, /** Mapping of defoliation states (7) into preceding-year defoliation states (no, yes) **/ pcmap[7] = { 0, 0, 0, 0, 1, 1, 1 }, /** Mapping of management constraints (3) into treatment options **/ /** Row 1: No constraint -- all 4 treatments available **/ /** Row 2: Rest and Graze are only treatments available (columns 1-2) **/ /** Row 3: Rest and Burn are only treatments available (columns 1-2) **/ mcmap[3][4] = { { 0, 1, 2, 3 }, { 0, 1, -1, -1 }, { 0, 2, -1, -1 } } ; DECIMAL /** Model weights for weighted-average single model run **/ w[4] = { 0.25, 0.25, 0.25, 0.25 }, /** Decision selection cumulative probabilities for mixed grass units **/ /** 1st level: 3 cases of management constraint: None, No Burn, No Graze /** 2nd level: 2 cases of preceding-year defoliation (No, Yes) /** 3rd & 4th levels: 4x4 treatments [Rest, Graze, Burn, B/G Combo] /***** Prior-year defoliation reduces BURN and B/G by 75% **/ a[3][2][4][4] = { { { { 0.918059195, 0.979336423, 0.993916246, 1.01 }, { 0.0970144 , 0.907664751, 0.964599455, 1.01 }, { 0.153148213, 0.330225834, 0.942021038, 1.01 }, { 0.121850799, 0.375355357, 0.510146064, 1.01 } }, { { 0.924611654, 0.994834106, 0.998479062, 1.01 }, { 0.125436777, 0.976916188, 0.991149864, 1.01 }, { 0.380062734, 0.832556458, 0.985505259, 1.01 }, { 0.287999692, 0.843838839, 0.877536516, 1.01 } } }, { { { 0.937429848, 1.01 , 1.01 , 1.01 }, { 0.106883516, 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } }, { { 0.937429848, 1.01 , 1.01 , 1.01 }, { 0.106883516, 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } } }, { { { 0.984367131, 1.01 , 1.01 , 1.01 }, { 0.200208551, 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } }, { { 0.996091783, 1.01 , 1.01 , 1.01 }, { 0.800052138, 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } } } }, /** 2-D utility associated with each treatment. **/ /** 4 treatments [rest, graze, burn, combo] x 4 NP input states x 4 NP output states **/ dv[4][4][4] = { { { 0.9225, 0.610360523, 0.348765191, 0.17875 }, { 0.948903051, 0.750625, 0.50716179, 0.294896762 }, { 0.959182697, 0.792052498, 0.5925, 0.371436749 }, { 0.96625, 0.822708801, 0.639173028, 0.44125 } }, { { 0.871611111, 0.551729101, 0.293726952, 0.13175 }, { 0.897669091, 0.687236111, 0.426099931, 0.213156359 }, { 0.911690075, 0.721132719, 0.517611111, 0.28135534 }, { 0.923138889, 0.750525943, 0.555225187, 0.355361111 } }, { { 0.833444444, 0.504102013, 0.248946974, 0.0965 }, { 0.859692009, 0.639694444, 0.366652069, 0.15721424 }, { 0.876003009, 0.671817343, 0.461444444, 0.216356658 }, { 0.890805556, 0.702723313, 0.497338718, 0.290944444 } }, { { 0.808, 0.469415734, 0.216368196, 0.073 }, { 0.834286263, 0.608, 0.32617098, 0.121309127 }, { 0.851972121, 0.639397817, 0.424, 0.173516017 }, { 0.86925, 0.671933258, 0.459542713, 0.248 } } }, /** Model transition *cumulative* probabilities for mixed grass /** (4 models x 4 treatments x 3 defoliation states x 16 input states x 16 outcome states) **/ p[4][4][3][16][16] = { { { { { 0.752, 0.843, 0.888, 0.933, 0.987, 0.993, 0.997, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.233, 0.467, 0.700, 0.933, 0.950, 0.967, 0.983, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.045, 0.136, 0.888, 0.933, 0.936, 0.943, 0.997, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.045, 0.136, 0.181, 0.933, 0.937, 0.943, 0.946, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.064, 0.072, 0.076, 0.080, 0.649, 0.718, 0.752, 0.787, 0.958, 0.979, 0.989, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.020, 0.039, 0.059, 0.079, 0.256, 0.433, 0.611, 0.788, 0.841, 0.894, 0.947, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.004, 0.012, 0.075, 0.079, 0.113, 0.182, 0.752, 0.786, 0.796, 0.817, 0.989, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.004, 0.012, 0.015, 0.079, 0.114, 0.183, 0.217, 0.789, 0.799, 0.820, 0.830, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.050, 0.056, 0.059, 0.062, 0.652, 0.723, 0.758, 0.794, 0.960, 0.980, 0.990, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.015, 0.031, 0.046, 0.061, 0.244, 0.427, 0.610, 0.792, 0.844, 0.896, 0.948, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.003, 0.009, 0.060, 0.063, 0.098, 0.170, 0.759, 0.794, 0.804, 0.824, 0.990, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.003, 0.009, 0.012, 0.061, 0.096, 0.168, 0.203, 0.793, 0.803, 0.823, 0.834, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.027, 0.030, 0.032, 0.033, 0.812, 0.906, 0.953, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.008, 0.016, 0.025, 0.033, 0.275, 0.517, 0.758, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.002, 0.005, 0.032, 0.033, 0.080, 0.174, 0.953, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.002, 0.005, 0.006, 0.033, 0.080, 0.174, 0.221, 1.100 } }, { { 0.579, 0.768, 0.862, 0.956, 0.983, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.190, 0.574, 0.764, 0.955, 0.964, 0.982, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.863, 0.957, 0.961, 0.970, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.378, 0.956, 0.961, 0.969, 0.974, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.077, 0.103, 0.115, 0.128, 0.569, 0.713, 0.785, 0.857, 0.943, 0.972, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.025, 0.076, 0.102, 0.127, 0.272, 0.566, 0.712, 0.857, 0.886, 0.943, 0.972, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.116, 0.128, 0.200, 0.344, 0.783, 0.855, 0.869, 0.898, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.051, 0.128, 0.200, 0.345, 0.417, 0.858, 0.872, 0.900, 0.914, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.064, 0.084, 0.095, 0.105, 0.563, 0.713, 0.787, 0.862, 0.945, 0.973, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.021, 0.063, 0.084, 0.105, 0.256, 0.560, 0.711, 0.862, 0.890, 0.945, 0.973, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.031, 0.094, 0.104, 0.179, 0.330, 0.790, 0.865, 0.878, 0.905, 0.987, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.031, 0.041, 0.105, 0.180, 0.330, 0.405, 0.864, 0.877, 0.904, 0.918, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.033, 0.044, 0.050, 0.055, 0.627, 0.814, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.011, 0.034, 0.045, 0.057, 0.244, 0.624, 0.812, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.051, 0.056, 0.149, 0.336, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.016, 0.022, 0.056, 0.149, 0.336, 0.429, 1.100 } }, { { 0.579, 0.768, 0.862, 0.956, 0.983, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.190, 0.574, 0.764, 0.955, 0.964, 0.982, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.863, 0.957, 0.961, 0.970, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.378, 0.956, 0.961, 0.969, 0.974, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.077, 0.103, 0.115, 0.128, 0.569, 0.713, 0.785, 0.857, 0.943, 0.972, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.025, 0.076, 0.102, 0.127, 0.272, 0.566, 0.712, 0.857, 0.886, 0.943, 0.972, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.116, 0.128, 0.200, 0.344, 0.783, 0.855, 0.869, 0.898, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.051, 0.128, 0.200, 0.345, 0.417, 0.858, 0.872, 0.900, 0.914, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.064, 0.084, 0.095, 0.105, 0.563, 0.713, 0.787, 0.862, 0.945, 0.973, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.021, 0.063, 0.084, 0.105, 0.256, 0.560, 0.711, 0.862, 0.890, 0.945, 0.973, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.031, 0.094, 0.104, 0.179, 0.330, 0.790, 0.865, 0.878, 0.905, 0.987, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.031, 0.041, 0.105, 0.180, 0.330, 0.405, 0.864, 0.877, 0.904, 0.918, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.033, 0.044, 0.050, 0.055, 0.627, 0.814, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.011, 0.034, 0.045, 0.057, 0.244, 0.624, 0.812, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.051, 0.056, 0.149, 0.336, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.016, 0.022, 0.056, 0.149, 0.336, 0.429, 1.100 } } }, { { { 0.394, 0.888, 0.936, 0.985, 0.991, 0.998, 0.999, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.146, 0.692, 0.839, 0.985, 0.987, 0.995, 0.998, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.048, 0.543, 0.937, 0.986, 0.986, 0.994, 0.999, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.049, 0.543, 0.591, 0.986, 0.986, 0.994, 0.994, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.107, 0.242, 0.255, 0.268, 0.538, 0.877, 0.910, 0.944, 0.966, 0.994, 0.997, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.040, 0.188, 0.227, 0.267, 0.367, 0.743, 0.843, 0.944, 0.952, 0.983, 0.992, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.147, 0.254, 0.267, 0.300, 0.640, 0.910, 0.944, 0.947, 0.975, 0.997, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.148, 0.161, 0.269, 0.302, 0.641, 0.674, 0.944, 0.946, 0.975, 0.977, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.001, 0.001, 0.001, 0.090, 0.201, 0.212, 0.223, 0.511, 0.871, 0.907, 0.942, 0.965, 0.994, 0.997, 1.100 }, { 0.000, 0.000, 0.000, 0.001, 0.033, 0.157, 0.190, 0.223, 0.329, 0.728, 0.835, 0.942, 0.951, 0.983, 0.991, 1.100 }, { 0.000, 0.000, 0.001, 0.001, 0.012, 0.123, 0.212, 0.223, 0.258, 0.619, 0.907, 0.943, 0.946, 0.974, 0.997, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.122, 0.133, 0.221, 0.257, 0.618, 0.654, 0.942, 0.945, 0.974, 0.977, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.045, 0.100, 0.106, 0.111, 0.467, 0.913, 0.956, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.017, 0.078, 0.095, 0.111, 0.243, 0.736, 0.868, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.061, 0.105, 0.111, 0.155, 0.601, 0.956, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.061, 0.067, 0.111, 0.155, 0.601, 0.645, 1.100 } }, { { 0.579, 0.768, 0.862, 0.956, 0.983, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.191, 0.575, 0.766, 0.956, 0.965, 0.983, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.283, 0.861, 0.956, 0.960, 0.969, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.378, 0.956, 0.961, 0.969, 0.974, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.079, 0.105, 0.118, 0.131, 0.572, 0.716, 0.788, 0.859, 0.945, 0.972, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.026, 0.078, 0.104, 0.129, 0.275, 0.567, 0.712, 0.857, 0.885, 0.943, 0.971, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.117, 0.130, 0.201, 0.346, 0.786, 0.857, 0.871, 0.900, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.038, 0.051, 0.129, 0.201, 0.345, 0.417, 0.858, 0.872, 0.900, 0.914, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.064, 0.084, 0.095, 0.105, 0.564, 0.714, 0.789, 0.864, 0.946, 0.973, 0.987, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.021, 0.063, 0.084, 0.105, 0.256, 0.562, 0.713, 0.864, 0.891, 0.946, 0.973, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.032, 0.096, 0.106, 0.181, 0.331, 0.790, 0.865, 0.878, 0.905, 0.987, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.031, 0.041, 0.104, 0.179, 0.329, 0.403, 0.863, 0.876, 0.903, 0.917, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 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{ 0.000, 0.000, 0.000, 0.000, 0.000, 0.103, 0.132, 0.143, 0.143, 0.663, 0.808, 0.864, 0.864, 0.962, 0.990, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.014, 0.097, 0.105, 0.139, 0.213, 0.646, 0.685, 0.861, 0.876, 0.959, 0.966, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.017, 0.046, 0.046, 0.049, 0.385, 0.953, 0.953, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.042, 0.044, 0.048, 0.143, 0.883, 0.932, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.036, 0.046, 0.049, 0.049, 0.735, 0.927, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.033, 0.036, 0.048, 0.146, 0.717, 0.767, 1.100 } } } } }, z1, z_np, q[4][7][16][16], res[4]; /** Management constraint type (0, 1, 2) -- indexes row of mcmap matrix **/ c = (int)outcome[4]; /** Number of treatments available **/ nt = 4*(c==0) + 2*(c>0); /** Decision values -- actual treatment types are inferred from d according values of mcmap matrix **/ /** (first row of mcmap: 0 = Rest, 1 = Graze, 2 = Burn, 3 = B/G) **/ d = (int)dec[0]; /** Read current and next NP states **/ cs = (int)cur_state[1]; ns = (int)nxt_state[1]; /** Read current defoliation state **/ s_dx = (int)cur_state[0]; /** Determine from DX state whether defoliated in prior year **/ pc_index = pcmap[s_dx]; /** Determine whether to use partial/full control from scenario file **/ z1 = outcome[2]; if (z1<0) act = d; /** Full control **/ /** Otherwise, take stochastic action, given decision **/ else { act = 0; while (z1 > a[c][pc_index][d][act]) act++; } /** Map states into native prairie reduced states **/ idxcs = map[cs]; idxns = map[ns]; /** Draw utility value based on utility function, stochastic decision, and reduced states **/ result = dv[mcmap[c][act]][idxcs][idxns]; /** If model-averaged run, compute transition probability for each model, /** then determine return for each transition. Average these by model /** weights to compute decision value **/ modsel = (int)outcome[3]; if (modsel>10) { /** Stochastic NP transition outcome **/ z_np = outcome[1]; for (h=0; h<4; h++) { for (i=0; i q[act][s_dx][cs][i]) i++; idxns = map[i]; res[h] = dv[mcmap[c][act]][idxcs][idxns]; } result = w[0]*res[0] + w[1]*res[1] + w[2]*res[2] + w[3]*res[3]; } return (result); }