3816: 矩阵变换

本文通过一个简单的C++程序示例介绍了如何使用标准输入输出流,并展示了如何编写一个基本的main函数。虽然代码简单,但它是理解更复杂C++程序的基础。

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题目链接

题目大意:

题解:题目无数据……

我的收获:……………………

#include <iostream>
using namespace std;
int main()
{
    return 0;
}
import numpy as np import pandas as pd from scipy import interpolate from scipy.spatial import ConvexHull from scipy.optimize import minimize from scipy.integrate import simpson import matplotlib.pyplot as plt import re # ====================== # 1. 数据准备与预处理 # ====================== # 读取SPD数据(修复版) def read_spd_data(file_path): """读取SPD数据并进行预处理""" # 读取Excel文件 df = pd.read_excel(file_path, header=None, skiprows=1) # 处理波长列:提取数值部分 wavelength_strs = df.iloc[:, 0].astype(str) # 使用正则表达式提取数字部分 wavelengths = wavelength_strs.str.extract(r'(\d+)', expand=False).astype(float) spectral_power = df.iloc[:, 1].values.astype(float) # 转换单位:mW/m²/nm -> W/m²/nm spectral_power /= 1000.0 # 检查波长和功率数组长度 if len(wavelengths) != len(spectral_power): raise ValueError(f"波长和光谱功率数组长度不一致: {len(wavelengths)} vs {len(spectral_power)}") return wavelengths.values, spectral_power # 加载CIE标准观察者函数(完整版) def load_cie_observer(): """CIE 1931标准观察者函数 (2度视场)""" # 完整CIE 1931数据 (360-830nm, 1nm间隔) cie_data = np.array([ [360, 0.0001299, 0.000003917, 0.0006061], [361, 0.000145847, 0.000004393, 0.000680879], [362, 0.000163802, 0.00000493, 0.000765146], [363, 0.000184004, 0.000005532, 0.000860012], [364, 0.00020669, 0.000006208, 0.000966593], [365, 0.0002321, 0.000006965, 0.001086], [366, 0.000260728, 0.000007813, 0.001220586], [367, 0.000293075, 0.000008767, 0.001372729], [368, 0.000329388, 0.000009839, 0.001543579], [369, 0.000369914, 0.000011043, 0.001734286], [370, 0.0004149, 0.00001239, 0.001946], [371, 0.000464159, 0.000013889, 0.002177777], [372, 0.000518986, 0.000015591, 0.002435809], [373, 0.000581854, 0.00001754, 0.002731953], [374, 0.000655235, 0.00001975, 0.003078064], [375, 0.0007416, 0.0000222, 0.003486], [376, 0.00084503, 0.0000249, 0.003975227], [377, 0.000964526, 0.0000279, 0.00454088], [378, 1.094949, 0.0000312, 0.00515832], [379, 1.231154, 0.0000349, 0.005802907], [380, 1.368, 0.000039, 0.006450001], [381, 1.50205, 0.0000437, 0.007083216], [382, 1.642328, 0.000049, 0.007745488], [383, 1.802382, 0.000055, 0.008501152], [384, 1.995757, 0.0000618, 0.009414544], [385, 2.236, 0.000069, 0.01054999], [386, 2.535385, 0.0000777, 0.0119658], [387, 2.892603, 0.000087, 0.01365587], [388, 3.300829, 0.000097, 0.01558805], [389, 3.753446, 0.000108, 0.01773015], [390, 4.243, 0.00012, 0.02005001], [391, 4.762389, 0.000133, 0.02251136], [392, 5.330048, 0.000147, 0.02520288], [393, 5.978712, 0.000163, 0.02827972], [394, 6.741117, 0.00018, 0.03189704], [395, 7.65, 0.0002, 0.03621], [396, 8.751373, 0.000222, 0.04143771], [397, 10.00886, 0.000247, 0.04750372], [398, 11.327, 0.000274, 0.05411988], [399, 12.614, 0.000304, 0.06099803], [400, 13.8, 0.000336, 0.06785001], [401, 14.86, 0.000372, 0.07448632], [402, 15.805, 0.000411, 0.08136156], [403, 16.7, 0.000454, 0.08947764], [404, 17.635, 0.000502, 0.0997224], [405, 18.7, 0.000555, 0.1122], [406, 19.99, 0.000616, 0.1269], [407, 21.6, 0.000686, 0.14385], [408, 23.6, 0.000766, 0.163], [409, 26.0, 0.000857, 0.1832], [410, 28.7, 0.00096, 0.2054], [411, 31.6, 0.001075, 0.2296], [412, 34.7, 0.001206, 0.2558], [413, 38.0, 0.001354, 0.284], [414, 41.5, 0.001522, 0.3142], [415, 45.1, 0.001714, 0.3464], [416, 48.8, 0.001932, 0.3806], [417, 52.6, 0.002178, 0.4168], [418, 56.5, 0.002454, 0.455], [419, 60.4, 0.002764, 0.4952], [420, 64.3, 0.003112, 0.5374], [421, 68.2, 0.0035, 0.5816], [422, 72.1, 0.003932, 0.6278], [423, 76.0, 0.004411, 0.676], [424, 79.9, 0.004941, 0.7262], [425, 83.8, 0.005528, 0.7784], [426, 87.7, 0.006176, 0.8326], [427, 91.6, 0.00689, 0.8888], [428, 95.5, 0.007674, 0.947], [429, 99.4, 0.008535, 1.0072], [430, 103.3, 0.009479, 1.0694], [431, 107.2, 0.01051, 1.1336], [432, 111.1, 0.01163, 1.1998], [433, 115.0, 0.01285, 1.268], [434, 118.9, 0.01417, 1.3382], [435, 122.8, 0.01559, 1.4104], [436, 126.7, 0.01712, 1.4846], [437, 130.6, 0.01876, 1.5608], [438, 134.5, 0.02052, 1.639], [439, 138.4, 0.02241, 1.7192], [440, 142.3, 0.02443, 1.8014], [441, 146.2, 0.02658, 1.8856], [442, 150.1, 0.02886, 1.9718], [443, 154.0, 0.03128, 2.06], [444, 157.9, 0.03384, 2.1502], [445, 161.8, 0.03655, 2.2424], [446, 165.7, 0.03941, 2.3366], [447, 169.6, 0.04243, 2.4328], [448, 173.5, 0.04561, 2.531], [449, 177.4, 0.04896, 2.6312], [450, 181.3, 0.05248, 2.7334], [451, 185.2, 0.05618, 2.8376], [452, 189.1, 0.06008, 2.9438], [453, 193.0, 0.06418, 3.052], [454, 196.9, 0.06849, 3.1622], [455, 200.8, 0.07302, 3.2744], [456, 204.7, 0.07778, 3.3886], [457, 208.6, 0.08278, 3.5048], [458, 212.5, 0.08803, 3.623], [459, 216.4, 0.09353, 3.7432], [460, 220.3, 0.09929, 3.8654], [461, 224.2, 0.1053, 3.9896], [462, 228.1, 0.1116, 4.1158], [463, 232.0, 0.1182, 4.244], [464, 235.9, 0.1251, 4.3742], [465, 239.8, 0.1323, 4.5064], [466, 243.7, 0.1398, 4.6406], [467, 247.6, 0.1476, 4.7768], [468, 251.5, 0.1558, 4.915], [469, 255.4, 0.1643, 5.0552], [470, 259.3, 0.1732, 5.1974], [471, 263.2, 0.1824, 5.3416], [472, 267.1, 0.192, 5.4878], [473, 271.0, 0.2019, 5.636], [474, 274.9, 0.2122, 5.7862], [475, 278.8, 0.2229, 5.9384], [476, 282.7, 0.234, 6.0926], [477, 286.6, 0.2455, 6.2488], [478, 290.5, 0.2574, 6.407], [479, 294.4, 0.2698, 6.5672], [480, 298.3, 0.2826, 6.7294], [481, 302.2, 0.2958, 6.8936], [482, 306.1, 0.3096, 7.0598], [483, 310.0, 0.3239, 7.228], [484, 313.9, 0.3387, 7.3982], [485, 317.8, 0.354, 7.5704], [486, 321.7, 0.3698, 7.7446], [487, 325.6, 0.3861, 7.9208], [488, 329.5, 0.403, 8.099], [489, 333.4, 0.4204, 8.2792], [490, 337.3, 0.4384, 8.4614], [491, 341.2, 0.4569, 8.6456], [492, 345.1, 0.476, 8.8318], [493, 349.0, 0.4957, 9.02], [494, 352.9, 0.516, 9.2102], [495, 356.8, 0.5369, 9.4024], [496, 360.7, 0.5584, 9.5966], [497, 364.6, 0.5806, 9.7928], [498, 368.5, 0.6034, 9.991], [499, 372.4, 0.6269, 10.1912], [500, 376.3, 0.651, 10.3934], [501, 380.2, 0.6758, 10.5976], [502, 384.1, 0.7013, 10.8038], [503, 388.0, 0.7275, 11.012], [504, 391.9, 0.7544, 11.2222], [505, 395.8, 0.782, 11.4344], [506, 399.7, 0.8103, 11.6486], [507, 403.6, 0.8393, 11.8648], [508, 407.5, 0.869, 12.083], [509, 411.4, 0.8995, 12.3032], [510, 415.3, 0.9308, 12.5254], [511, 419.2, 0.9628, 12.7496], [512, 423.1, 0.9956, 12.9758], [513, 427.0, 1.029, 13.204], [514, 430.9, 1.063, 13.4342], [515, 434.8, 1.098, 13.6664], [516, 438.7, 1.134, 13.9006], [517, 442.6, 1.17, 14.1368], [518, 446.5, 1.207, 14.375], [519, 450.4, 1.245, 14.6152], [520, 454.3, 1.283, 14.8574], [521, 458.2, 1.322, 15.1016], [522, 462.1, 1.361, 15.3478], [523, 466.0, 1.4, 15.596], [524, 469.9, 1.44, 15.8462], [525, 473.8, 1.48, 16.0984], [526, 477.7, 1.521, 16.3526], [527, 481.6, 1.562, 16.6088], [528, 485.5, 1.604, 16.867], [529, 489.4, 1.647, 17.1272], [530, 493.3, 1.69, 17.3894], [531, 497.2, 1.734, 17.6536], [532, 501.1, 1.778, 17.9198], [533, 505.0, 1.823, 18.188], [534, 508.9, 1.868, 18.4582], [535, 512.8, 1.914, 18.7304], [536, 516.7, 1.96, 19.0046], [537, 520.6, 2.007, 19.2808], [538, 524.5, 2.055, 19.559], [539, 528.4, 2.103, 19.8392], [540, 532.3, 2.152, 20.1214], [541, 536.2, 2.201, 20.4056], [542, 540.1, 2.251, 20.6918], [543, 544.0, 2.301, 20.98], [544, 547.9, 2.352, 21.2702], [545, 551.8, 2.404, 21.5624], [546, 555.7, 2.456, 21.8566], [547, 559.6, 2.509, 22.1528], [548, 563.5, 2.562, 22.451], [549, 567.4, 2.616, 22.7512], [550, 571.3, 2.67, 23.0534], [551, 575.2, 2.725, 23.3576], [552, 579.1, 2.78, 23.6638], [553, 583.0, 2.836, 23.972], [554, 586.9, 2.892, 24.2822], [555, 590.8, 2.949, 24.5944], [556, 594.7, 3.006, 24.9086], [557, 598.6, 3.064, 25.2248], [558, 602.5, 3.122, 25.543], [559, 606.4, 3.181, 25.8632], [560, 610.3, 3.24, 26.1854], [561, 614.2, 3.3, 26.5096], [562, 618.1, 3.36, 26.8358], [563, 622.0, 3.421, 27.164], [564, 625.9, 3.482, 27.4942], [565, 629.8, 3.544, 27.8264], [566, 633.7, 3.606, 28.1606], [567, 637.6, 3.669, 28.4968], [568, 641.5, 3.732, 28.835], [569, 645.4, 3.796, 29.1752], [570, 649.3, 3.86, 29.5174], [571, 653.2, 3.925, 29.8616], [572, 657.1, 3.99, 30.2078], [573, 661.0, 4.056, 30.556], [574, 664.9, 4.122, 30.9062], [575, 668.8, 4.189, 31.2584], [576, 672.7, 4.256, 31.6126], [577, 676.6, 4.324, 31.9688], [578, 680.5, 4.392, 32.327], [579, 684.4, 4.461, 32.6872], [580, 688.3, 4.53, 33.0494], [581, 692.2, 4.6, 33.4136], [582, 696.1, 4.67, 33.7798], [583, 700.0, 4.741, 34.148], [584, 703.9, 4.812, 34.5182], [585, 707.8, 4.884, 34.8904], [586, 711.7, 4.956, 35.2646], [587, 715.6, 5.029, 35.6408], [588, 719.5, 5.102, 36.019], [589, 723.4, 5.176, 36.3992], [590, 727.3, 5.25, 36.7814], [591, 731.2, 5.325, 37.1656], [592, 735.1, 5.4, 37.5518], [593, 739.0, 5.476, 37.94], [594, 742.9, 5.552, 38.3302], [595, 746.8, 5.629, 38.7224], [596, 750.7, 5.706, 39.1166], [597, 754.6, 5.784, 39.5128], [598, 758.5, 5.862, 39.911], [599, 762.4, 5.941, 40.3112], [600, 766.3, 6.02, 40.7134], [601, 770.2, 6.1, 41.1176], [602, 774.1, 6.18, 41.5238], [603, 778.0, 6.261, 41.932], [604, 781.9, 6.342, 42.3422], [605, 785.8, 6.424, 42.7544], [606, 789.7, 6.506, 43.1686], [607, 793.6, 6.589, 43.5848], [608, 797.5, 6.672, 44.003], [609, 801.4, 6.756, 44.4232], [610, 805.3, 6.84, 44.8454], [611, 809.2, 6.925, 45.2696], [612, 813.1, 7.01, 45.6958], [613, 817.0, 7.096, 46.124], [614, 820.9, 7.182, 46.5542], [615, 824.8, 7.269, 46.9864], [616, 828.7, 7.356, 47.4206], [617, 832.6, 7.444, 47.8568], [618, 836.5, 7.532, 48.295], [619, 840.4, 7.621, 48.7352], [620, 844.3, 7.71, 49.1774], [621, 848.2, 7.8, 49.6216], [622, 852.1, 7.89, 50.0678], [623, 856.0, 7.981, 50.516], [624, 859.9, 8.072, 50.9662], [625, 863.8, 8.164, 51.4184], [626, 867.7, 8.256, 51.8726], [627, 871.6, 8.349, 52.3288], [628, 875.5, 8.442, 52.787], [629, 879.4, 8.536, 53.2472], [630, 883.3, 8.63, 53.7094], [631, 887.2, 8.725, 54.1736], [632, 891.1, 8.82, 54.6398], [633, 895.0, 8.916, 55.108], [634, 898.9, 9.012, 55.5782], [635, 902.8, 9.109, 56.0504], [636, 906.7, 9.206, 56.5246], [637, 910.6, 9.304, 57.0008], [638, 914.5, 9.402, 57.479], [639, 918.4, 9.501, 57.9592], [640, 922.3, 9.6, 58.4414], [641, 926.2, 9.7, 58.9256], [642, 930.1, 9.8, 59.4118], [643, 934.0, 9.901, 59.9], [644, 937.9, 10.002, 60.3902], [645, 941.8, 10.104, 60.8824], [646, 945.7, 10.206, 61.3766], [647, 949.6, 10.309, 61.8728], [648, 953.5, 10.412, 62.371], [649, 957.4, 10.516, 62.8712], [650, 961.3, 10.62, 63.3734], [651, 965.2, 10.725, 63.8776], [652, 969.1, 10.83, 64.3838], [653, 973.0, 10.936, 64.892], [654, 976.9, 11.042, 65.4022], [655, 980.8, 11.149, 65.9144], [656, 984.7, 11.256, 66.4286], [657, 988.6, 11.364, 66.9448], [658, 992.5, 11.472, 67.463], [659, 996.4, 11.581, 67.9832], [660, 1000.3, 11.69, 68.5054], [661, 1004.2, 11.8, 69.0296], [662, 1008.1, 11.91, 69.5558], [663, 1012.0, 12.021, 70.084], [664, 1015.9, 12.132, 70.6142], [665, 1019.8, 12.244, 71.1464], [666, 1023.7, 12.356, 71.6806], [667, 1027.6, 12.469, 72.2168], [668, 1031.5, 12.582, 72.755], [669, 1035.4, 12.696, 73.2952], [670, 1039.3, 12.81, 73.8374], [671, 1043.2, 12.925, 74.3816], [672, 1047.1, 13.04, 74.9278], [673, 1051.0, 13.156, 75.476], [674, 1054.9, 13.272, 76.0262], [675, 1058.8, 13.389, 76.5784], [676, 1062.7, 13.506, 77.1326], [677, 1066.6, 13.624, 77.6888], [678, 1070.5, 13.742, 78.247], [679, 1074.4, 13.861, 78.8072], [680, 1078.3, 13.98, 79.3694], [681, 1082.2, 14.1, 79.9336], [682, 1086.1, 14.22, 80.4998], [683, 1090.0, 14.341, 81.068], [684, 1093.9, 14.462, 81.6382], [685, 1097.8, 14.584, 82.2104], [686, 1101.7, 14.706, 82.7846], [687, 1105.6, 14.829, 83.3608], [688, 1109.5, 14.952, 83.939], [689, 1113.4, 15.076, 84.5192], [690, 1117.3, 15.2, 85.1014], [691, 1121.2, 15.325, 85.6856], [692, 1125.1, 15.45, 86.2718], [693, 1129.0, 15.576, 86.86], [694, 1132.9, 15.702, 87.4502], [695, 1136.8, 15.829, 88.0424], [696, 1140.7, 15.956, 88.6366], [697, 1144.6, 16.084, 89.2328], [698, 1148.5, 16.212, 89.831], [699, 1152.4, 16.341, 90.4312], [700, 1156.3, 16.47, 91.0334], [701, 1160.2, 16.6, 91.6376], [702, 1164.1, 16.73, 92.2438], [703, 1168.0, 16.861, 92.852], [704, 1171.9, 16.992, 93.4622], [705, 1175.8, 17.124, 94.0744], [706, 1179.7, 17.256, 94.6886], [707, 1183.6, 17.389, 95.3048], [708, 1187.5, 17.522, 95.923], [709, 1191.4, 17.656, 96.5432], [710, 1195.3, 17.79, 97.1654], [711, 1199.2, 17.925, 97.7896], [712, 1203.1, 18.06, 98.4158], [713, 1207.0, 18.196, 99.044], [714, 1210.9, 18.332, 99.6742], [715, 1214.8, 18.469, 100.3064], [716, 1218.7, 18.606, 100.9406], [717, 1222.6, 18.744, 101.5768], [718, 1226.5, 18.882, 102.215], [719, 1230.4, 19.021, 102.8552], [720, 1234.3, 19.16, 103.4974], [721, 1238.2, 19.3, 104.1416], [722, 1242.1, 19.44, 104.7878], [723, 1246.0, 19.581, 105.436], [724, 1249.9, 19.722, 106.0862], [725, 1253.8, 19.864, 106.7384], [726, 1257.7, 20.006, 107.3926], [727, 1261.6, 20.149, 108.0488], [728, 1265.5, 20.292, 108.707], [729, 1269.4, 20.436, 109.3672], [730, 1273.3, 20.58, 110.0294], [731, 1277.2, 20.725, 110.6936], [732, 1281.1, 20.87, 111.3598], [733, 1285.0, 21.016, 112.028], [734, 1288.9, 21.162, 112.6982], [735, 1292.8, 21.309, 113.3704], [736, 1296.7, 21.456, 114.0446], [737, 1300.6, 21.604, 114.7208], [738, 1304.5, 21.752, 115.399], [739, 1308.4, 21.901, 116.0792], [740, 1312.3, 22.05, 116.7614], [741, 1316.2, 22.2, 117.4456], [742, 1320.1, 22.35, 118.1318], [743, 1324.0, 22.501, 118.82], [744, 1327.9, 22.652, 119.5102], [745, 1331.8, 22.804, 120.2024], [746, 1335.7, 22.956, 120.8966], [747, 1339.6, 23.109, 121.5928], [748, 1343.5, 23.262, 122.291], [749, 1347.4, 23.416, 122.9912], [750, 1351.3, 23.57, 123.6934], [751, 1355.2, 23.725, 124.3976], [752, 1359.1, 23.88, 125.1038], [753, 1363.0, 24.036, 125.812], [754, 1366.9, 24.192, 126.5222], [755, 1370.8, 24.349, 127.2344], [756, 1374.7, 24.506, 127.9486], [757, 1378.6, 24.664, 128.6648], [758, 1382.5, 24.822, 129.383], [759, 1386.4, 24.981, 130.1032], [760, 1390.3, 25.14, 130.8254], [761, 1394.2, 25.3, 131.5496], [762, 1398.1, 25.46, 132.2758], [763, 1402.0, 25.621, 133.004], [764, 1405.9, 25.782, 133.7342], [765, 1409.8, 25.944, 134.4664], [766, 1413.7, 26.106, 135.2006], [767, 1417.6, 26.269, 135.9368], [768, 1421.5, 26.432, 136.675], [769, 1425.4, 26.596, 137.4152], [770, 1429.3, 26.76, 138.1574], [771, 1433.2, 26.925, 138.9016], [772, 1437.1, 27.09, 139.6478], [773, 1441.0, 27.256, 140.396], [774, 1444.9, 27.422, 141.1462], [775, 1448.8, 27.589, 141.8984], [776, 1452.7, 27.756, 142.6526], [777, 1456.6, 27.924, 143.4088], [778, 1460.5, 28.092, 144.167], [779, 1464.4, 28.261, 144.9272], [780, 1468.3, 28.43, 145.6894], [781, 1472.2, 28.6, 146.4536], [782, 1476.1, 28.77, 147.2198], [783, 1480.0, 28.941, 147.988], [784, 1483.9, 29.112, 148.7582], [785, 1487.8, 29.284, 149.5304], [786, 1491.7, 29.456, 150.3046], [787, 1495.6, 29.629, 151.0808], [788, 1499.5, 29.802, 151.859], [789, 1503.4, 29.976, 152.6392], [790, 1507.3, 30.15, 153.4214], [791, 1511.2, 30.325, 154.2056], [792, 1515.1, 30.5, 154.9918], [793, 1519.0, 30.676, 155.78], [794, 1522.9, 30.852, 156.5702], [795, 1526.8, 31.029, 157.3624], [796, 1530.7, 31.206, 158.1566], [797, 1534.6, 31.384, 158.9528], [798, 1538.5, 31.562, 159.751], [799, 1542.4, 31.741, 160.5512], [800, 1546.3, 31.92, 161.3534], [801, 1550.2, 32.1, 162.1576], [802, 1554.1, 32.28, 162.9638], [803, 1558.0, 32.461, 163.772], [804, 1561.9, 32.642, 164.5822], [805, 1565.8, 32.824, 165.3944], [806, 1569.7, 33.006, 166.2086], [807, 1573.6, 33.189, 167.0248], [808, 1577.5, 33.372, 167.843], [809, 1581.4, 33.556, 168.6632], [810, 1585.3, 33.74, 169.4854], [811, 1589.2, 33.925, 170.3096], [812, 1593.1, 34.11, 171.1358], [813, 1597.0, 34.296, 171.964], [814, 1600.9, 34.482, 172.7942], [815, 1604.8, 34.669, 173.6264], [816, 1608.7, 34.856, 174.4606], [817, 1612.6, 35.044, 175.2968], [818, 1616.5, 35.232, 176.135], [819, 1620.4, 35.421, 176.9752], [820, 1624.3, 35.61, 177.8174], [821, 1628.2, 35.8, 178.6616], [822, 1632.1, 35.99, 179.5078], [823, 1636.0, 36.181, 180.356], [824, 1639.9, 36.372, 181.2062], [825, 1643.8, 36.564, 182.0584], [826, 1647.7, 36.756, 182.9126], [827, 1651.6, 36.949, 183.7688], [828, 1655.5, 37.142, 184.627], [829, 1659.4, 37.336, 185.4872], [830, 1663.3, 37.53, 186.3494] ]) wavelengths = cie_data[:, 0] x_bar = cie_data[:, 1] y_bar = cie_data[:, 2] z_bar = cie_data[:, 3] return wavelengths, x_bar, y_bar, z_bar # 加载TM-30测试色样反射率(简化版) def load_tm30_reflectance(): """加载ANSI/IES TM-30标准99色样反射率""" # 实际应用中应从文件读取完整数据 # 这里创建示例数据结构 wavelengths = np.arange(380, 781, 5) # 5nm间隔 # 生成随机反射率数据 (0-1之间) reflectance = np.random.rand(99, len(wavelengths)) # 确保反射率在0-1范围内 reflectance = np.clip(reflectance, 0.0, 1.0) return wavelengths, reflectance # 加载褪黑素响应函数(CIE S 026标准) def load_melanopic_response(): """CIE S 026褪黑素响应函数""" # 实际数据应来自标准 wavelengths = np.arange(380, 781, 1) # 使用高斯函数近似褪黑素响应曲线 response = np.exp(-0.5 * ((wavelengths - 480) / 30) ** 2) # 归一化 response /= np.max(response) return wavelengths, response # ====================== # 2. CIE XYZ计算 # ====================== def calculate_xyz(wavelengths, spd, cie_w, x_bar, y_bar, z_bar): """计算CIE XYZ三刺激值""" # 插值到相同波长范围 min_w = max(wavelengths.min(), cie_w.min()) max_w = min(wavelengths.max(), cie_w.max()) interp_w = np.arange(min_w, max_w + 1, 1) # 插值SPD f_spd = interpolate.interp1d(wavelengths, spd, kind='linear', bounds_error=False, fill_value=0) spd_interp = f_spd(interp_w) # 插值观察者函数 f_x = interpolate.interp1d(cie_w, x_bar, kind='linear', bounds_error=False, fill_value=0) f_y = interpolate.interp1d(cie_w, y_bar, kind='linear', bounds_error=False, fill_value=0) f_z = interpolate.interp1d(cie_w, z_bar, kind='linear', bounds_error=False, fill_value=0) x_interp = f_x(interp_w) y_interp = f_y(interp_w) z_interp = f_z(interp_w) # 计算XYZ (使用Simpson积分) X = simpson(spd_interp * x_interp, interp_w) Y = simpson(spd_interp * y_interp, interp_w) Z = simpson(spd_interp * z_interp, interp_w) # 归一化常数 k = 100 / simpson(spd_interp * y_interp, interp_w) return k * X, k * Y, k * Z # ====================== # 3. CCT和Duv计算 # ====================== def uv_from_xyz(X, Y, Z): """计算CIE 1960 UCS坐标""" denom = X + 15 * Y + 3 * Z u = 4 * X / denom if denom != 0 else 0 v = 6 * Y / denom if denom != 0 else 0 return u, v def planckian_locus(T): """计算普朗克轨迹上的uv坐标""" # 使用更精确的公式 if T < 1667 or T > 25000: raise ValueError("色温超出有效范围 (1667K - 25000K)") # 计算色温倒数 T_inv = 1e6 / T # 计算u坐标 u = 0.860117757 + 1.54118254e-4 * T_inv + 1.28641212e-7 * T_inv ** 2 # 计算v坐标 v = 0.317398726 + 4.22806245e-5 * T_inv + 4.20481691e-8 * T_inv ** 2 return u, v def calculate_cct_duv(u, v): """使用Ohno方法计算CCT和Duv""" # 1. 定义目标函数:计算测试点与普朗克轨迹的距离 def distance_to_locus(T): try: u_t, v_t = planckian_locus(T) return np.sqrt((u - u_t) ** 2 + (v - v_t) ** 2) except ValueError: return np.inf # 超出范围返回无穷大 # 2. 在合理温度范围内搜索最小值 result = minimize(distance_to_locus, 6500, bounds=[(1667, 25000)], method='L-BFGS-B') if result.success: cct = result.x[0] u_t, v_t = planckian_locus(cct) duv = np.sign(v - v_t) * result.fun return cct, duv else: # 使用备选方法:McCamy近似公式 # 仅当优化失败时使用 n = (u - 0.3320) / (v - 0.1858) cct = -449 * n ** 3 + 3525 * n ** 2 - 6823.3 * n + 5520.33 return cct, 0.0 # McCamy公式不提供Duv # ====================== # 4. Rf和Rg计算 # ====================== def calculate_cam02ucs(X, Y, Z): """计算CAM02-UCS颜色空间坐标 (简化版本)""" # 实际实现应使用完整的CAM02转换 # 这里使用简化转换作为示例 # 转换为XYZ到RGB (D65白点) R = 3.2406 * X - 1.5372 * Y - 0.4986 * Z G = -0.9689 * X + 1.8758 * Y + 0.0415 * Z B = 0.0557 * X - 0.2040 * Y + 1.0570 * Z # 非线性变换 R = np.where(R > 0.0031308, 1.055 * (R ** (1 / 2.4)) - 0.055, 12.92 * R) G = np.where(G > 0.0031308, 1.055 * (G ** (1 / 2.4)) - 0.055, 12.92 * G) B = np.where(B > 0.0031308, 1.055 * (B ** (1 / 2.4)) - 0.055, 12.92 * B) # 转换为L*a*b* L = 116 * np.cbrt(Y) - 16 a = 500 * (np.cbrt(X) - np.cbrt(Y)) b = 200 * (np.cbrt(Y) - np.cbrt(Z)) return L, a, b def calculate_rf_rg(wavelengths, spd, cct, cie_w, x_bar, y_bar, z_bar): """计算颜色保真度指数Rf和色域指数Rg""" # 1. 加载99色样反射率数据 ref_w, reflectance = load_tm30_reflectance() # 2. 创建参考光源 (根据CCT选择) if cct <= 5000: ref_spd = blackbody_spectrum(ref_w, cct) else: ref_spd = daylight_spectrum(ref_w, cct) # 3. 插值SPD到反射率波长 f_spd = interpolate.interp1d(wavelengths, spd, kind='linear', bounds_error=False, fill_value=0) spd_interp = f_spd(ref_w) # 4. 将CIE观察者函数插值到99色样的波长上 f_x = interpolate.interp1d(cie_w, x_bar, kind='linear', bounds_error=False, fill_value=0) f_y = interpolate.interp1d(cie_w, y_bar, kind='linear', bounds_error=False, fill_value=0) f_z = interpolate.interp1d(cie_w, z_bar, kind='linear', bounds_error=False, fill_value=0) x_bar_ref = f_x(ref_w) y_bar_ref = f_y(ref_w) z_bar_ref = f_z(ref_w) # 5. 计算每个色样在测试光源和参考光源下的颜色 test_colors = [] ref_colors = [] for i in range(99): # 计算测试光源下的XYZ X_test = simpson(spd_interp * reflectance[i] * x_bar_ref, ref_w) Y_test = simpson(spd_interp * reflectance[i] * y_bar_ref, ref_w) Z_test = simpson(spd_interp * reflectance[i] * z_bar_ref, ref_w) # 计算参考光源下的XYZ X_ref = simpson(ref_spd * reflectance[i] * x_bar_ref, ref_w) Y_ref = simpson(ref_spd * reflectance[i] * y_bar_ref, ref_w) Z_ref = simpson(ref_spd * reflectance[i] * z_bar_ref, ref_w) # 转换为CAM02-UCS L_test, a_test, b_test = calculate_cam02ucs(X_test, Y_test, Z_test) L_ref, a_ref, b_ref = calculate_cam02ucs(X_ref, Y_ref, Z_ref) test_colors.append([a_test, b_test]) ref_colors.append([a_ref, b_ref]) # 6. 计算色差ΔE delta_e = [] for i in range(99): de = np.sqrt((test_colors[i][0] - ref_colors[i][0]) ** 2 + (test_colors[i][1] - ref_colors[i][1]) ** 2) delta_e.append(de) # 7. 计算Rf avg_delta_e = np.mean(delta_e) Rf = 100 - 4.6 * avg_delta_e # 8. 计算色域面积 test_hull = ConvexHull(test_colors) ref_hull = ConvexHull(ref_colors) Rg = (test_hull.volume / ref_hull.volume) * 100 return Rf, Rg def blackbody_spectrum(wavelengths, T): """生成黑体辐射光谱""" c1 = 3.741771e-16 # W·m² c2 = 1.438776e-2 # m·K wavelengths_m = wavelengths * 1e-9 spd = c1 / (wavelengths_m ** 5 * (np.exp(c2 / (wavelengths_m * T)) - 1)) return spd / np.max(spd) # 归一化 def daylight_spectrum(wavelengths, T): """生成日光光谱 (CIE D系列)""" # 简化实现,实际应使用CIE D系列公式 return blackbody_spectrum(wavelengths, T) # ====================== # 5. 褪黑素DER计算 # ====================== def calculate_mel_der(wavelengths, spd): """计算褪黑素日光照度比 (mel-DER)""" # 1. 加载褪黑素响应函数 mel_w, mel_response = load_melanopic_response() # 2. 插值到相同波长范围 min_w = max(wavelengths.min(), mel_w.min()) max_w = min(wavelengths.max(), mel_w.max()) interp_w = np.arange(min_w, max_w + 1, 1) f_spd = interpolate.interp1d(wavelengths, spd, kind='linear', bounds_error=False, fill_value=0) spd_interp = f_spd(interp_w) f_mel = interpolate.interp1d(mel_w, mel_response, kind='linear', bounds_error=False, fill_value=0) mel_interp = f_mel(interp_w) # 3. 计算待测光源的褪黑素刺激值 mel_edi = simpson(spd_interp * mel_interp, interp_w) # 4. 计算参考光源 (D65) 的褪黑素刺激值 d65_spd = daylight_spectrum(interp_w, 6500) mel_edi_ref = simpson(d65_spd * mel_interp, interp_w) # 5. 计算mel-DER mel_der = (mel_edi / mel_edi_ref) * 100 return mel_der # ====================== # 主程序 # ====================== def main(): # 文件路径 file_path = r"D:\BaiduNetdiskDownload\MATLAB R2024a\bin\project\附录.xlsx" try: print("开始处理光源参数计算...") # 1. 读取并预处理SPD数据 print("读取SPD数据...") wavelengths, spd = read_spd_data(file_path) print(f"读取成功: {len(wavelengths)}个数据点") # 2. 加载CIE标准观察者函数 print("加载CIE标准观察者函数...") cie_w, x_bar, y_bar, z_bar = load_cie_observer() # 3. 计算CIE XYZ print("计算CIE XYZ值...") X, Y, Z = calculate_xyz(wavelengths, spd, cie_w, x_bar, y_bar, z_bar) print(f"CIE XYZ值: X={X:.2f}, Y={Y:.2f}, Z={Z:.2f}") # 4. 计算CCT和Duv print("计算相关色温(CCT)和Duv...") u, v = uv_from_xyz(X, Y, Z) cct, duv = calculate_cct_duv(u, v) print(f"相关色温CCT: {cct:.1f}K, Duv: {duv:.4f}") # 5. 计算Rf和Rg print("计算颜色保真度指数(Rf)和色域指数(Rg)...") Rf, Rg = calculate_rf_rg(wavelengths, spd, cct, cie_w, x_bar, y_bar, z_bar) print(f"保真度指数Rf: {Rf:.1f}, 色域指数Rg: {Rg:.1f}") # 6. 计算mel-DER print("计算褪黑素日光照度比(mel-DER)...") mel_der = calculate_mel_der(wavelengths, spd) print(f"褪黑素日光照度比: {mel_der:.1f}%") # 7. 可视化结果 print("生成SPD可视化图表...") plt.figure(figsize=(12, 8)) plt.plot(wavelengths, spd, 'b-', label='光源SPD') plt.title('光源光谱功率分布', fontsize=14) plt.xlabel('波长 (nm)', fontsize=12) plt.ylabel('光谱功率 (W/m²/nm)', fontsize=12) plt.grid(True, linestyle='--', alpha=0.7) plt.legend() plt.tight_layout() plt.savefig('spd_plot.png', dpi=300) plt.show() print("\n所有参数计算完成!") print("=" * 50) print(f"相关色温(CCT): {cct:.1f} K") print(f"距离普朗克轨迹的距离(Duv): {duv:.4f}") print(f"保真度指数(Rf): {Rf:.1f}") print(f"色域指数(Rg): {Rg:.1f}") print(f"褪黑素日光照度比(mel-DER): {mel_der:.1f}%") print("=" * 50) except Exception as e: import traceback print(f"计算过程中发生错误: {str(e)}") print("详细错误信息:") print(traceback.format_exc()) if __name__ == "__main__": main() 请把代码中简化的部分都改成精确计算,其他部分的代码不要动,最后输出完整版代码
最新发布
08-09
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