最大化插值矩阵

# takes grid indices (first three dimensions) idx and interpolates on V def interpolateV(idx, V, Grid): from scipy.interpolate import interp2d f = interp2d(Grid.mGrid, Grid.aGrid, V[idx]) return f # (somewhere else:) s2 = (Grid.nM, Grid.nA, Grid.nE) v1Max = np.empty(s2) v1ArgMaxA = np.empty(s2) v1ArgMaxM = np.empty(s2) from scipy import optimize for idx in np.ndindex(V1[..., 0,0].shape): V1i = interpolateV(idx, V1, Grid) x, f, d = optimize.fmin_l_bfgs_b(lambda x: -V1i(x[0], x[1]), np.array([1, 1]), bounds=[(Grid.aMin, Grid.aMax), (Grid.mMin, Grid.mMax)], approx_grad=True) v1Max[idx] = f v1ArgMaxA[idx], v1ArgMaxM[idx] = x # let's compare with standard grid-wise optimization (without interpolation): temp = V1.max(axis=-1) # maximize over m v1Max = temp.max(axis=-1) # now max over a, given optimal m v1ArgMaxAGrid = temp.argmax(axis=-1)

In[51]: v1ArgMaxAGrid[:,:,0] Out[51]: array([[0, 0, 0, 0, 2], [0, 0, 0, 0, 2], [0, 0, 0, 2, 2], [0, 0, 0, 2, 3], [0, 0, 0, 2, 3]], dtype=int64) In[54]: Grid.aGrid[v1ArgMaxAGrid[:,:,0]] Out[54]: array([[ 0. , 0. , 0. , 0. , 3.5 ], [ 0. , 0. , 0. , 0. , 3.5 ], [ 0. , 0. , 0. , 3.5 , 3.5 ], [ 0. , 0. , 0. , 3.5 , 5.25], [ 0. , 0. , 0. , 3.5 , 5.25]]) In[52]: v1ArgMaxA[:,:,0] Out[52]: array([[ 0. , 0.75 , 2.25 , 7. , 7. ], [ 0. , 1.5 , 4.247, 7. , 7. ], [ 0.75 , 2.25 , 7. , 7. , 7. ], [ 1.5 , 1.5 , 7. , 7. , 7. ], [ 2.25 , 4.939, 7. , 7. , 7. ]])

class Grids(object): nE = 2 nA = 5 nM = 5 M = 3 A = 7 mMin = 0 mMax = M aMin = 0 aMax = A def __init__(self): self.reset(); def reset(self): self.mGrid = np.linspace(self.mMin, self.mMax, self.nM) self.aGrid = np.linspace(self.aMin, self.aMax, self.nA) self.eGrid = np.array([0.318, 3.149]) self.transitionE = np.array([[1., 0.], [0., 1.]]) import numpy as np Grid = Grids() V1 = np.array([[[[[ 1.19 , 0.975, -0.371, -2.848, -6.456], [ -1.463, -4.313, -8.294, -13.407, -19.65 ], [ -9.888, -15.377, -21.997, -29.748, -38.63 ], [-24.574, -32.701, -41.958, -52.347, -63.866], [-45.562, -56.325, -68.218, -81.242, -95.397]], [[ 64.724, 64.672, 64.567, 64.358, 54.127], [ 64.247, 63.964, 53.759, 52.687, 50.487], [ 53.526, 52.078, 49.501, 45.799, 40.969], [ 48.389, 44.307, 39.105, 32.769, 25.314], [ 37.062, 30.347, 22.52 , 13.553, 3.47 ]]], [[[ 12.624, 12.704, 12.591, 2.602, 1.618], [ 2.237, 2.011, 0.655, -1.832, -5.45 ], [ -0.064, -2.928, -6.923, -12.049, -18.306], [ -8.624, -14.126, -20.759, -28.522, -37.416], [-23.488, -31.625, -40.894, -51.293, -62.822]], [[ 65.686, 65.695, 65.679, 65.631, 65.537], [ 65.401, 65.342, 65.23 , 65.014, 54.778], [ 65.174, 64.881, 54.667, 53.59 , 51.385], [ 54.43 , 52.973, 50.396, 46.685, 41.855], [ 49.228, 45.138, 39.936, 33.594, 26.136]]], [[[ 13.681, 13.872, 14.024, 14.117, 14.093], [ 13.671, 13.74 , 13.617, 3.617, 2.624], [ 3.636, 3.397, 2.027, -0.474, -4.106], [ 1.2 , -1.677, -5.684, -10.823, -17.092], [ -7.538, -13.051, -19.694, -27.468, -36.373]], [[ 66.553, 66.597, 66.623, 66.631, 66.614], [ 66.362, 66.364, 66.342, 66.287, 66.188], [ 66.327, 66.259, 66.138, 65.917, 55.676], [ 66.077, 65.776, 55.562, 54.476, 52.271], [ 55.269, 53.804, 51.227, 47.51 , 42.677]]], [[[ 14.6 , 14.839, 15.054, 15.242, 15.394], [ 14.728, 14.909, 15.05 , 15.133, 15.098], [ 15.07 , 15.126, 14.989, 4.975, 3.968], [ 4.9 , 4.648, 3.265, 0.752, -2.892], [ 2.286, -0.601, -4.62 , -9.769, -16.048]], [[ 67.36 , 67.427, 67.481, 67.52 , 67.543], [ 67.229, 67.266, 67.286, 67.287, 67.265], [ 67.288, 67.281, 67.25 , 67.19 , 67.085], [ 67.231, 67.154, 67.033, 66.803, 56.562], [ 66.917, 66.607, 56.393, 55.301, 53.093]]], [[[ 15.442, 15.71 , 15.96 , 16.191, 16.4 ], [ 15.647, 15.875, 16.08 , 16.257, 16.399], [ 16.128, 16.294, 16.422, 16.491, 16.443], [ 16.334, 16.377, 16.227, 6.201, 5.182], [ 5.986, 5.723, 4.33 , 1.806, -1.849]], [[ 68.123, 68.207, 68.28 , 68.342, 68.391], [ 68.036, 68.096, 68.143, 68.176, 68.194], [ 68.155, 68.183, 68.195, 68.19 , 68.163], [ 68.192, 68.176, 68.145, 68.076, 67.971], [ 68.07 , 67.984, 67.864, 67.628, 57.384]]]], [[[[ 11.877, 1.81 , 1.59 , 0.238, -2.246], [ 0.873, -0.853, -3.709, -7.696, -12.814], [ -4.928, -9.292, -14.787, -21.413, -29.17 ], [-16.988, -23.99 , -32.123, -41.386, -51.78 ], [-35.352, -44.989, -55.758, -67.657, -80.686]], [[ 65.151, 65.131, 65.075, 64.966, 64.753], [ 64.779, 64.647, 64.36 , 54.151, 53.076], [ 54.24 , 53.917, 52.465, 49.888, 46.183], [ 51.728, 48.771, 44.694, 39.483, 33.153], [ 43.026, 37.436, 30.734, 22.892, 13.934]]], [[[ 13.101, 13.245, 13.318, 13.2 , 3.204], [ 12.924, 2.847, 2.616, 1.253, -1.24 ], [ 2.272, 0.533, -2.337, -6.338, -11.47 ], [ -3.664, -8.041, -13.548, -20.187, -27.956], [-15.902, -22.915, -31.058, -40.332, -50.737]], [[ 66.066, 66.092, 66.098, 66.078, 66.025], [ 65.827, 65.8 , 65.738, 65.622, 65.403], [ 65.706, 65.564, 65.268, 55.054, 53.974], [ 55.144, 54.812, 53.36 , 50.774, 47.069], [ 52.567, 49.602, 45.525, 40.308, 33.975]]], [[[ 14.087, 14.302, 14.487, 14.632, 14.72 ], [ 14.148, 14.281, 14.344, 14.216, 4.21 ], [ 14.323, 4.232, 3.987, 2.611, 0.104], [ 3.536, 1.784, -1.099, -5.112, -10.256], [ -2.578, -6.965, -12.484, -19.133, -26.912]], [[ 66.905, 66.96 , 66.999, 67.022, 67.025], [ 66.742, 66.762, 66.76 , 66.734, 66.676], [ 66.754, 66.718, 66.646, 66.525, 66.301], [ 66.609, 66.459, 66.163, 55.94 , 54.86 ], [ 55.983, 55.643, 54.191, 51.599, 47.891]]], [[[ 14.969, 15.221, 15.454, 15.663, 15.844], [ 15.134, 15.338, 15.513, 15.648, 15.725], [ 15.548, 15.667, 15.716, 15.574, 5.554], [ 15.587, 5.483, 5.226, 3.837, 1.318], [ 4.622, 2.859, -0.034, -4.058, -9.213]], [[ 67.691, 67.766, 67.829, 67.879, 67.915], [ 67.581, 67.629, 67.662, 67.678, 67.676], [ 67.669, 67.679, 67.669, 67.637, 67.574], [ 67.658, 67.612, 67.541, 67.411, 67.187], [ 67.449, 67.29 , 66.994, 56.765, 55.682]]], [[[ 15.786, 16.063, 16.324, 16.569, 16.794], [ 16.016, 16.258, 16.48 , 16.679, 16.85 ], [ 16.533, 16.724, 16.884, 17.006, 17.07 ], [ 16.811, 16.918, 16.954, 16.8 , 6.768], [ 16.673, 6.559, 6.29 , 4.891, 2.362]], [[ 68.439, 68.529, 68.61 , 68.679, 68.737], [ 68.368, 68.436, 68.492, 68.535, 68.566], [ 68.507, 68.546, 68.571, 68.581, 68.574], [ 68.572, 68.573, 68.563, 68.523, 68.46 ], [ 68.497, 68.443, 68.372, 68.236, 68.009]]]], [[[[ 12.453, 12.498, 2.425, 2.198, 0.84 ], [ 2.083, 1.483, -0.248, -3.111, -7.104], [ -1.092, -4.331, -8.701, -14.202, -20.834], [-10.528, -16.405, -23.412, -31.551, -40.82 ], [-26.266, -34.779, -44.422, -55.196, -67.101]], [[ 65.555, 65.558, 65.534, 65.474, 65.36 ], [ 65.252, 65.179, 65.043, 64.752, 54.54 ], [ 64.974, 54.631, 54.304, 52.852, 50.272], [ 53.942, 52.11 , 49.158, 45.072, 39.867], [ 47.865, 43.4 , 37.823, 31.106, 23.273]]], [[[ 13.541, 13.722, 13.859, 13.927, 13.802], [ 13.5 , 13.534, 3.451, 3.214, 1.846], [ 3.482, 2.868, 1.123, -1.753, -5.76 ], [ 0.172, -3.08 , -7.463, -12.976, -19.62 ], [ -9.442, -15.329, -22.348, -30.497, -39.776]], [[ 66.433, 66.473, 66.495, 66.496, 66.472], [ 66.231, 66.227, 66.196, 66.13 , 66.011], [ 66.178, 66.096, 65.952, 65.655, 55.438], [ 65.877, 55.526, 55.199, 53.738, 51.158], [ 54.781, 52.941, 49.989, 45.897, 40.689]]], [[[ 14.475, 14.708, 14.917, 15.095, 15.235], [ 14.588, 14.759, 14.886, 14.943, 14.808], [ 14.899, 14.92 , 4.823, 4.572, 3.19 ], [ 4.746, 4.119, 2.362, -0.527, -4.546], [ 1.258, -2.005, -6.398, -11.922, -18.577]], [[ 67.247, 67.312, 67.362, 67.398, 67.417], [ 67.109, 67.142, 67.158, 67.152, 67.123], [ 67.158, 67.145, 67.105, 67.033, 66.909], [ 67.082, 66.991, 66.847, 66.541, 56.324], [ 66.717, 56.357, 56.03 , 54.563, 51.98 ]]], [[[ 15.325, 15.59 , 15.836, 16.062, 16.265], [ 15.522, 15.744, 15.943, 16.111, 16.24 ], [ 15.987, 16.144, 16.257, 16.301, 16.152], [ 16.163, 16.171, 6.061, 5.798, 4.404], [ 5.832, 5.195, 3.426, 0.527, -3.502]], [[ 68.016, 68.098, 68.169, 68.228, 68.274], [ 67.924, 67.981, 68.025, 68.054, 68.067], [ 68.036, 68.059, 68.066, 68.056, 68.021], [ 68.061, 68.039, 68. , 67.919, 67.794], [ 67.921, 67.822, 67.677, 67.366, 57.146]]], [[[ 16.121, 16.406, 16.678, 16.933, 17.171], [ 16.372, 16.626, 16.862, 17.078, 17.271], [ 16.921, 17.13 , 17.314, 17.469, 17.585], [ 17.251, 17.395, 17.496, 17.527, 17.366], [ 17.249, 17.246, 7.126, 6.852, 5.447]], [[ 68.749, 68.846, 68.932, 69.008, 69.074], [ 68.692, 68.768, 68.832, 68.884, 68.925], [ 68.85 , 68.898, 68.934, 68.957, 68.965], [ 68.939, 68.954, 68.961, 68.941, 68.906], [ 68.901, 68.87 , 68.831, 68.744, 68.617]]]], [[[[ 12.947, 13.074, 13.112, 3.034, 2.8 ], [ 12.693, 2.693, 2.087, 0.35 , -2.518], [ 1.618, -0.496, -3.741, -8.117, -13.624], [ -5.192, -9.944, -15.827, -22.84 , -30.984], [-18.306, -25.693, -34.212, -43.861, -54.64 ]], [[ 65.941, 65.962, 65.961, 65.932, 65.868], [ 65.688, 65.652, 65.575, 65.435, 65.141], [ 65.537, 65.364, 55.018, 54.691, 53.236], [ 55.031, 54.324, 52.497, 49.536, 45.456], [ 51.579, 48.239, 43.787, 38.195, 31.487]]], [[[ 13.954, 14.162, 14.337, 14.468, 14.529], [ 13.994, 14.11 , 14.139, 4.049, 3.806], [ 14.093, 4.079, 3.459, 1.708, -1.174], [ 2.882, 0.755, -2.502, -6.891, -12.41 ], [ -4.106, -8.869, -14.762, -21.786, -29.941]], [[ 66.789, 66.84 , 66.876, 66.893, 66.891], [ 66.617, 66.631, 66.623, 66.588, 66.519], [ 66.614, 66.569, 66.484, 66.339, 66.039], [ 66.441, 66.259, 55.913, 55.577, 54.122], [ 55.87 , 55.155, 53.328, 50.361, 46.278]]], [[[ 14.847, 15.096, 15.323, 15.525, 15.698], [ 15.001, 15.198, 15.363, 15.484, 15.535], [ 15.394, 15.496, 15.51 , 5.407, 5.15 ], [ 15.356, 5.33 , 4.697, 2.934, 0.04 ], [ 3.968, 1.831, -1.438, -5.837, -11.366]], [[ 67.582, 67.654, 67.714, 67.761, 67.792], [ 67.465, 67.509, 67.538, 67.549, 67.542], [ 67.543, 67.548, 67.532, 67.492, 67.417], [ 67.518, 67.463, 67.379, 67.224, 66.925], [ 67.28 , 67.09 , 56.744, 56.402, 54.944]]], [[[ 15.672, 15.946, 16.204, 16.444, 16.665], [ 15.894, 16.132, 16.349, 16.541, 16.703], [ 16.4 , 16.584, 16.734, 16.842, 16.879], [ 16.657, 16.746, 16.749, 6.633, 6.364], [ 16.443, 6.405, 5.762, 3.988, 1.083]], [[ 68.334, 68.423, 68.501, 68.568, 68.623], [ 68.258, 68.324, 68.377, 68.417, 68.443], [ 68.391, 68.426, 68.447, 68.453, 68.439], [ 68.447, 68.443, 68.427, 68.378, 68.302], [ 68.357, 68.294, 68.209, 68.049, 67.747]]], [[[ 16.448, 16.742, 17.021, 17.286, 17.535], [ 16.719, 16.983, 17.23 , 17.46 , 17.67 ], [ 17.294, 17.517, 17.72 , 17.899, 18.048], [ 17.664, 17.835, 17.973, 18.068, 18.093], [ 17.744, 17.822, 17.813, 7.687, 7.408]], [[ 69.055, 69.156, 69.248, 69.331, 69.403], [ 69.01 , 69.092, 69.163, 69.224, 69.273], [ 69.184, 69.241, 69.286, 69.32 , 69.341], [ 69.295, 69.321, 69.341, 69.339, 69.325], [ 69.286, 69.274, 69.257, 69.203, 69.125]]]], [[[[ 13.398, 13.568, 13.688, 13.721, 3.636], [ 13.32 , 13.303, 3.298, 2.685, 0.942], [ 3.204, 2.215, 0.095, -3.156, -7.538], [ -0.982, -4.609, -9.366, -15.255, -22.274], [-11.47 , -17.733, -25.126, -33.65 , -43.305]], [[ 66.312, 66.348, 66.364, 66.359, 66.327], [ 66.099, 66.088, 66.048, 65.967, 65.825], [ 66.025, 65.928, 65.752, 55.405, 55.075], [ 65.656, 55.413, 54.711, 52.875, 49.92 ], [ 54.168, 51.953, 48.626, 44.159, 38.576]]], [[[ 14.347, 14.575, 14.776, 14.945, 15.07 ], [ 14.445, 14.605, 14.714, 14.737, 4.642], [ 14.72 , 14.689, 4.669, 4.043, 2.286], [ 4.468, 3.466, 1.333, -1.93 , -6.324], [ 0.104, -3.533, -8.302, -14.201, -21.23 ]], [[ 67.134, 67.195, 67.243, 67.274, 67.288], [ 66.988, 67.017, 67.027, 67.015, 66.978], [ 67.025, 67.005, 66.956, 66.871, 66.722], [ 66.929, 66.822, 66.646, 56.291, 55.961], [ 66.496, 56.244, 55.542, 53.7 , 50.742]]], [[[ 15.208, 15.468, 15.71 , 15.931, 16.128], [ 15.394, 15.611, 15.802, 15.961, 16.076], [ 15.844, 15.99 , 16.086, 16.095, 5.986], [ 15.983, 15.94 , 5.908, 5.269, 3.5 ], [ 5.554, 4.541, 2.398, -0.876, -5.281]], [[ 67.909, 67.988, 68.057, 68.113, 68.155], [ 67.81 , 67.865, 67.905, 67.93 , 67.939], [ 67.915, 67.934, 67.936, 67.919, 67.875], [ 67.929, 67.9 , 67.851, 67.756, 67.608], [ 67.768, 67.653, 67.477, 57.116, 56.783]]], [[[ 16.01 , 16.293, 16.561, 16.813, 17.047], [ 16.255, 16.505, 16.736, 16.947, 17.133], [ 16.794, 16.997, 17.174, 17.319, 17.42 ], [ 17.108, 17.241, 17.324, 17.321, 7.2 ], [ 17.07 , 17.015, 6.972, 6.323, 4.544]], [[ 68.647, 68.741, 68.825, 68.899, 68.962], [ 68.585, 68.658, 68.719, 68.769, 68.806], [ 68.737, 68.782, 68.814, 68.834, 68.836], [ 68.818, 68.829, 68.83 , 68.804, 68.761], [ 68.768, 68.731, 68.682, 68.581, 68.431]]], [[[ 16.769, 17.069, 17.356, 17.63 , 17.888], [ 17.057, 17.329, 17.587, 17.829, 18.053], [ 17.654, 17.89 , 18.108, 18.305, 18.477], [ 18.057, 18.248, 18.412, 18.545, 18.634], [ 18.194, 18.316, 18.389, 18.375, 8.243]], [[ 69.355, 69.461, 69.559, 69.647, 69.725], [ 69.323, 69.41 , 69.488, 69.555, 69.613], [ 69.511, 69.575, 69.628, 69.672, 69.704], [ 69.64 , 69.677, 69.708, 69.719, 69.722], [ 69.658, 69.66 , 69.661, 69.63 , 69.584]]]]])

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