In [1]:
import numpy as np
import matplotlib.pyplot as plt
In [2]:
x = np.arange(0., 10., 0.2)
m = len(x)
target_data = 2 * x + 5 + np.random.randn(m) #从标准正态分布中返回一个或多个样本值
loop_max = 200 # 循环的次数
epsilon = 1e-3 # 正则化参数？
theta = np.random.randn(2)
alpha = 0.001
count = 0
finish = 0
costs = []
In [6]:
x0 = np.full(m, 1.0) #创建一个由常数填充的数组,第一个参数是数组的形状，第二个参数是数组中填充的常数
input_data = np.vstack([x0, x]).T
In [7]:
for count in range(loop_max):
cost = 0
err = 0
gtheta0 = 0
gtheta1 = 0
for i in range(m):
err = target_data[i] - np.dot(theta,input_data[i])
cost += err**2
gtheta0 += -(err) * input_data[i,0]
gtheta1 += -(err) * input_data[i,1]
theta[0] += alpha * (-gtheta0)
theta[1] += alpha * (-gtheta1)
print('loop count = ',count,'\t theta:',theta,'\t cost:',cost/2)
costs.append(cost)
# if np.linalg.norm(theta - error) < epsilon:
# break
# else:
# error = theta
loop count = 0 theta: [0.54909476 4.39950514] cost: 5461.633645802776 loop count = 1 theta: [0.19683033 1.68378975] cost: 2433.4900476167077 loop count = 2 theta: [0.52752938 3.44569093] cost: 1134.5477286620378 loop count = 3 theta: [0.41002769 2.27757663] cost: 576.1987377794693 loop count = 4 theta: [0.5845891 3.02709107] cost: 335.064801577717 loop count = 5 theta: [0.56679139 2.52187312] cost: 229.8304853613327 loop count = 6 theta: [0.67366197 2.83795303] cost: 182.84516619584218 loop count = 7 theta: [0.69774944 2.61674843] cost: 160.85329452323265 loop count = 8 theta: [0.77482766 2.74733024] cost: 149.6117927816864 loop count = 9 theta: [0.81605943 2.6478771 ] cost: 143.0198120739934 loop count = 10 theta: [0.87959563 2.6991379 ] cost: 138.46348824630107 loop count = 11 theta: [0.92739612 2.65194362] cost: 134.82230662438297 loop count = 12 theta: [0.98436919 2.66935137] cost: 131.6153157252562 loop count = 13 theta: [1.0342287 2.64465239] cost: 128.6354877553649 loop count = 14 theta: [1.08764649 2.64767608] cost: 125.79313074763888 loop count = 15 theta: [1.13765259 2.6327231 ] cost: 123.04882826191887 loop count = 16 theta: [1.18882186 2.62969759] cost: 120.38471978716235 loop count = 17 theta: [1.23817391 2.61902786] cost: 117.79220078212056 loop count = 18 theta: [1.28767245 2.61351983] cost: 115.26665453477054 loop count = 19 theta: [1.33604553 2.60479114] cost: 112.80519545323651 loop count = 20 theta: [1.38413848 2.59832534] cost: 110.4057020342342 loop count = 21 theta: [1.43141091 2.59053197] cost: 108.06640215779674 loop count = 22 theta: [1.47822909 2.58375873] cost: 105.78569493307546 loop count = 23 theta: [1.52436581 2.57646736] cost: 103.56207386234328 loop count = 24 theta: [1.56998207 2.56966264] cost: 101.39409340861208 loop count = 25 theta: [1.61498468 2.56268517] cost: 99.28035416427493 loop count = 26 theta: [1.65944664 2.55596463] cost: 97.21949599859484 loop count = 27 theta: [1.70333203 2.54921803] cost: 95.2101946347101 loop count = 28 theta: [1.74667607 2.54262876] cost: 93.25115970756812 loop count = 29 theta: [1.78946728 2.53607505] cost: 91.34113346798425 loop count = 30 theta: [1.83172459 2.52963484] cost: 89.47888977502456 loop count = 31 theta: [1.87344688 2.52325541] cost: 87.66323322318506 loop count = 32 theta: [1.91464602 2.51696956] cost: 85.89299833833955 loop count = 33 theta: [1.95532524 2.51075414] cost: 84.16704881390233 loop count = 34 theta: [1.99549327 2.50462264] cost: 82.48427677470555 loop count = 35 theta: [2.03515512 2.49856461] cost: 80.84360206297974 loop count = 36 theta: [2.0743181 2.49258526] cost: 79.2439715437749 loop count = 37 theta: [2.11298786 2.48667959] cost: 77.68435842843287 loop count = 38 theta: [2.15117103 2.4808493 ] cost: 76.163761615275 loop count = 39 theta: [2.18887346 2.47509171] cost: 74.68120504690688 loop count = 40 theta: [2.22610138 2.46940705] cost: 73.23573708365392 loop count = 41 theta: [2.26286064 2.46379365] cost: 71.82642989269542 loop count = 42 theta: [2.29915723 2.45825109] cost: 70.4523788524888 loop count = 43 theta: [2.33499691 2.45277819] cost: 69.11270197209824 loop count = 44 theta: [2.37038546 2.44737425] cost: 67.80653932505128 loop count = 45 theta: [2.40532856 2.44203828] cost: 66.53305249735902 loop count = 46 theta: [2.43983181 2.43676951] cost: 65.29142404934575 loop count = 47 theta: [2.47390075 2.43156705] cost: 64.08085699094161 loop count = 48 theta: [2.50754085 2.42643008] cost: 62.900574270101686 loop count = 49 theta: [2.54075749 2.42135776] cost: 61.74981827402346 loop count = 50 theta: [2.57355603 2.4163493 ] cost: 60.62785034284207 loop count = 51 theta: [2.60594171 2.41140388] cost: 59.533950295490975 loop count = 52 theta: [2.63791973 2.40652072] cost: 58.46741596742451 loop count = 53 theta: [2.66949523 2.40169902] cost: 57.4275627599046 loop count = 54 theta: [2.70067327 2.39693801] cost: 56.41372320056316 loop count = 55 theta: [2.73145885 2.39223693] cost: 55.42524651495754 loop count = 56 theta: [2.76185692 2.38759503] cost: 54.4614982088443 loop count = 57 theta: [2.79187235 2.38301155] cost: 53.52185966090321 loop count = 58 theta: [2.82150996 2.37848578] cost: 52.6057277256496 loop count = 59 theta: [2.85077451 2.37401697] cost: 51.71251434628105 loop count = 60 theta: [2.87967069 2.36960441] cost: 50.84164617720862 loop count = 61 theta: [2.90820313 2.36524739] cost: 49.992564216031965 loop count = 62 theta: [2.93637642 2.36094522] cost: 49.164723444720316 loop count = 63 theta: [2.96419508 2.35669721] cost: 48.35759247977076 loop count = 64 theta: [2.99166357 2.35250266] cost: 47.57065323111755 loop count = 65 theta: [3.0187863 2.34836091] cost: 46.80340056957517 loop count = 66 theta: [3.04556762 2.3442713 ] cost: 46.05534200260018 loop count = 67 theta: [3.07201183 2.34023317] cost: 45.32599735816488 loop count = 68 theta: [3.09812317 2.33624587] cost: 44.61489847653913 loop count = 69 theta: [3.12390584 2.33230875] cost: 43.92158890978296 loop count = 70 theta: [3.14936396 2.3284212 ] cost: 43.24562362875669 loop count = 71 theta: [3.17450163 2.32458258] cost: 42.586568737460695 loop count = 72 theta: [3.19932287 2.32079228] cost: 41.944001194521654 loop count = 73 theta: [3.22383168 2.31704969] cost: 41.31750854164597 loop count = 74 theta: [3.24803198 2.31335421] cost: 40.70668863886658 loop count = 75 theta: [3.27192766 2.30970525] cost: 40.11114940641296 loop count = 76 theta: [3.29552255 2.30610222] cost: 39.53050857303863 loop count = 77 theta: [3.31882044 2.30254454] cost: 38.964393430644755 loop count = 78 theta: [3.34182507 2.29903164] cost: 38.412440595042035 loop count = 79 theta: [3.36454012 2.29556297] cost: 37.874295772698005 loop count = 80 theta: [3.38696925 2.29213795] cost: 37.34961353331883 loop count = 81 theta: [3.40911605 2.28875605] cost: 36.838057088121 loop count = 82 theta: [3.43098407 2.28541672] cost: 36.33929807364947 loop count = 83 theta: [3.45257683 2.28211942] cost: 35.85301634100436 loop count = 84 theta: [3.47389779 2.27886363] cost: 35.37889975034 loop count = 85 theta: [3.49495037 2.27564882] cost: 34.9166439705054 loop count = 86 theta: [3.51573796 2.27247447] cost: 34.46595228369673 loop count = 87 theta: [3.53626387 2.26934008] cost: 34.02653539499688 loop count = 88 theta: [3.55653142 2.26624515] cost: 33.59811124667968 loop count = 89 theta: [3.57654384 2.26318918] cost: 33.1804048371595 loop count = 90 theta: [3.59630436 2.26017167] cost: 32.77314804447044 loop count = 91 theta: [3.61581615 2.25719214] cost: 32.376079454160944 loop count = 92 theta: [3.63508232 2.25425012] cost: 31.98894419149457 loop count = 93 theta: [3.65410599 2.25134514] cost: 31.611493757847967 loop count = 94 theta: [3.67289019 2.24847672] cost: 31.243485871201898 loop count = 95 theta: [3.69143794 2.2456444 ] cost: 30.884684310622717 loop count = 96 theta: [3.70975223 2.24284774] cost: 30.534858764634127 loop count = 97 theta: [3.72783598 2.24008628] cost: 30.193784683382457 loop count = 98 theta: [3.7456921 2.23735958] cost: 29.861243134500093 loop count = 99 theta: [3.76332346 2.2346672 ] cost: 29.537020662574715 loop count = 100 theta: [3.78073288 2.23200872] cost: 29.220909152134325 loop count = 101 theta: [3.79792316 2.2293837 ] cost: 28.91270569405966 loop count = 102 theta: [3.81489706 2.22679172] cost: 28.612212455338796 loop count = 103 theta: [3.83165729 2.22423236] cost: 28.319236552079886 loop count = 104 theta: [3.84820656 2.22170523] cost: 28.033589925700646 loop count = 105 theta: [3.86454751 2.2192099 ] cost: 27.755089222215396 loop count = 106 theta: [3.88068277 2.21674598] cost: 27.483555674541673 loop count = 107 theta: [3.89661492 2.21431308] cost: 27.218814987751347 loop count = 108 theta: [3.91234653 2.2119108 ] cost: 26.96069722719223 loop count = 109 theta: [3.92788012 2.20953876] cost: 26.709036709408558 loop count = 110 theta: [3.94321817 2.20719658] cost: 26.46367189579035 loop count = 111 theta: [3.95836316 2.20488389] cost: 26.22444528888309 loop count = 112 theta: [3.97331751 2.2026003 ] cost: 25.99120333129176 loop count = 113 theta: [3.98808362 2.20034546] cost: 25.76379630711347 loop count = 114 theta: [4.00266386 2.198119 ] cost: 25.5420782458364 loop count = 115 theta: [4.01706058 2.19592056] cost: 25.325906828642506 loop count = 116 theta: [4.03127607 2.1937498 ] cost: 25.115143297054455 loop count = 117 theta: [4.04531262 2.19160637] cost: 24.909652363867707 loop count = 118 theta: [4.05917249 2.18948991] cost: 24.70930212631102 loop count = 119 theta: [4.0728579 2.1874001] cost: 24.513963981379092 loop count = 120 theta: [4.08637104 2.18533659] cost: 24.32351254328362 loop count = 121 theta: [4.09971408 2.18329905] cost: 24.137825562969198 loop count = 122 theta: [4.11288917 2.18128717] cost: 23.95678384964273 loop count = 123 theta: [4.12589842 2.1793006 ] cost: 23.780271194266 loop count = 124 theta: [4.13874391 2.17733905] cost: 23.60817429496217 loop count = 125 theta: [4.15142771 2.17540218] cost: 23.440382684288238 loop count = 126 theta: [4.16395185 2.1734897 ] cost: 23.276788658327025 loop count = 127 theta: [4.17631834 2.17160129] cost: 23.117287207553037 loop count = 128 theta: [4.18852917 2.16973665] cost: 22.961775949427786 loop count = 129 theta: [4.20058629 2.16789548] cost: 22.810155062681286 loop count = 130 theta: [4.21249164 2.16607748] cost: 22.662327223237842 loop count = 131 theta: [4.22424714 2.16428237] cost: 22.518197541744406 loop count = 132 theta: [4.23585466 2.16250986] cost: 22.37767350266216 loop count = 133 theta: [4.24731607 2.16075966] cost: 22.240664904881502 loop count = 134 theta: [4.25863321 2.15903149] cost: 22.107083803822814 loop count = 135 theta: [4.26980789 2.15732507] cost: 21.97684445498556 loop count = 136 theta: [4.28084192 2.15564013] cost: 21.84986325890985 loop count = 137 theta: [4.29173705 2.1539764 ] cost: 21.726058707514465 loop count = 138 theta: [4.30249504 2.15233361] cost: 21.605351331777698 loop count = 139 theta: [4.31311761 2.15071151] cost: 21.48766365072694 loop count = 140 theta: [4.32360647 2.14910982] cost: 21.372920121704258 loop count = 141 theta: [4.3339633 2.14752829] cost: 21.261047091876183 loop count = 142 theta: [4.34418977 2.14596667] cost: 21.151972750956904 loop count = 143 theta: [4.3542875 2.1444247] cost: 21.04562708511351 loop count = 144 theta: [4.36425814 2.14290215] cost: 20.94194183202506 loop count = 145 theta: [4.37410326 2.14139876] cost: 20.840850437065463 loop count = 146 theta: [4.38382446 2.1399143 ] cost: 20.74228801058268 loop count = 147 theta: [4.3934233 2.13844852] cost: 20.64619128624674 loop count = 148 theta: [4.4029013 2.13700119] cost: 20.552498580439426 loop count = 149 theta: [4.41226001 2.13557208] cost: 20.461149752660425 loop count = 150 theta: [4.42150091 2.13416096] cost: 20.372086166923474 loop count = 151 theta: [4.43062549 2.1327676 ] cost: 20.28525065411842 loop count = 152 theta: [4.43963521 2.13139178] cost: 20.20058747531514 loop count = 153 theta: [4.44853152 2.13003328] cost: 20.11804228598489 loop count = 154 theta: [4.45731585 2.12869188] cost: 20.037562101117338 loop count = 155 theta: [4.46598961 2.12736736] cost: 19.95909526120979 loop count = 156 theta: [4.47455419 2.12605952] cost: 19.882591399107415 loop count = 157 theta: [4.48301096 2.12476813] cost: 19.808001407673157 loop count = 158 theta: [4.49136128 2.12349301] cost: 19.735277408266228 loop count = 159 theta: [4.49960648 2.12223393] cost: 19.66437272000918 loop count = 160 theta: [4.50774791 2.12099071] cost: 19.59524182982401 loop count = 161 theta: [4.51578685 2.11976313] cost: 19.527840363217642 loop count = 162 theta: [4.5237246 2.118551 ] cost: 19.46212505579825 loop count = 163 theta: [4.53156243 2.11735414] cost: 19.398053725504464 loop count = 164 theta: [4.53930161 2.11617233] cost: 19.335585245528925 loop count = 165 theta: [4.54694336 2.11500541] cost: 19.274679517919342 loop count = 166 theta: [4.55448893 2.11385317] cost: 19.215297447840108 loop count = 167 theta: [4.56193952 2.11271544] cost: 19.157400918477578 loop count = 168 theta: [4.56929632 2.11159202] cost: 19.100952766573233 loop count = 169 theta: [4.57656052 2.11048275] cost: 19.04591675856893 loop count = 170 theta: [4.58373328 2.10938745] cost: 18.992257567348993 loop count = 171 theta: [4.59081575 2.10830592] cost: 18.939940749563927 loop count = 172 theta: [4.59780907 2.10723802] cost: 18.888932723521588 loop count = 173 theta: [4.60471436 2.10618355] cost: 18.839200747631498 loop count = 174 theta: [4.61153273 2.10514236] cost: 18.790712899388136 loop count = 175 theta: [4.61826528 2.10411428] cost: 18.74343805488032 loop count = 176 theta: [4.62491307 2.10309913] cost: 18.697345868812963 loop count = 177 theta: [4.63147719 2.10209676] cost: 18.652406755028743 loop count = 178 theta: [4.63795869 2.10110702] cost: 18.608591867517028 loop count = 179 theta: [4.64435859 2.10012972] cost: 18.565873081897827 loop count = 180 theta: [4.65067794 2.09916474] cost: 18.52422297736908 loop count = 181 theta: [4.65691774 2.09821189] cost: 18.483614819105398 loop count = 182 theta: [4.663079 2.09727105] cost: 18.444022541097333 loop count = 183 theta: [4.6691627 2.09634204] cost: 18.405420729419728 loop count = 184 theta: [4.67516983 2.09542473] cost: 18.36778460591889 loop count = 185 theta: [4.68110134 2.09451897] cost: 18.331090012307495 loop count = 186 theta: [4.68695818 2.0936246 ] cost: 18.295313394657857 loop count = 187 theta: [4.69274131 2.0927415 ] cost: 18.26043178828273 loop count = 188 theta: [4.69845163 2.09186951] cost: 18.22642280299446 loop count = 189 theta: [4.70409008 2.09100849] cost: 18.193264608733056 loop count = 190 theta: [4.70965756 2.09015832] cost: 18.16093592155353 loop count = 191 theta: [4.71515495 2.08931885] cost: 18.12941598996398 loop count = 192 theta: [4.72058315 2.08848994] cost: 18.09868458160547 loop count = 193 theta: [4.72594301 2.08767147] cost: 18.06872197026494 loop count = 194 theta: [4.73123541 2.0868633 ] cost: 18.039508923213155 loop count = 195 theta: [4.73646119 2.0860653 ] cost: 18.01102668885949 loop count = 196 theta: [4.74162119 2.08527735] cost: 17.983256984715336 loop count = 197 theta: [4.74671624 2.08449931] cost: 17.95618198565879 loop count = 198 theta: [4.75174716 2.08373107] cost: 17.929784312492842 loop count = 199 theta: [4.75671475 2.0829725 ] cost: 17.90404702078989
In [8]:
plt.plot(x,target_data,'g*')
plt.plot(x,theta[1] * x + theta[0],'r')
plt.show()
In [9]:
plt.scatter(range(len(costs)), costs) #画散点图
plt.show()
