吴恩达471机器学习入门课程1第1周

文章目录

  • 1加载数据集
  • 2计算COST(均值平方差,1/2m(y_pre - y)²)
  • 3计算梯度
  • 4画出成本曲线
  • 5梯度下降

import math, copy
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('./deeplearning.mplstyle')
from lab_utils_uni import plt_house_x, plt_contour_wgrad, plt_divergence, plt_gradients

1加载数据集

# train data
x = np.array([1.0,2.0])
y = np.array([300.0,500.0])

2计算COST(均值平方差,1/2m(y_pre - y)²)

#通过w*x+b得到y_pre,
def costFun(x,y,w,b):
    m = x.shape[0] #数据长度,一维数组的长度
    cost = 0 #初始化
    for i in range(m):
        f_wb = w*x[i]+b
        cost += (f_wb-y[i])**2
    return 1/(2*m)*cost

3计算梯度

∂ J ( w , b ) ∂ w = 1 m ∑ i = 0 m − 1 ( f w , b ( x ( i ) ) − y ( i ) ) x ( i ) ∂ J ( w , b ) ∂ b = 1 m ∑ i = 0 m − 1 ( f w , b ( x ( i ) ) − y ( i ) ) \begin{align} \frac{\partial J(w,b)}{\partial w} &= \frac{1}{m} \sum\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})x^{(i)} \tag{4}\\ \frac{\partial J(w,b)}{\partial b} &= \frac{1}{m} \sum\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)}) \tag{5}\\ \end{align} wJ(w,b)bJ(w,b)=m1i=0m1(fw,b(x(i))y(i))x(i)=m1i=0m1(fw,b(x(i))y(i))(4)(5)

def gradientFun(x,y,w,b):
    m = x.shape[0]
    dj_dw = 0
    dj_db = 0
    
    for i in range(m):
        f_wb = w*x[i]+b
#         dj_dw += (f_wb - y[i])*x[i]
#         dj_db += f_wb - y[i]
#     dj_dw /= m
#     dj_dw /= m
        dj_dw_i = (f_wb - y[i]) * x[i] 
        dj_db_i = f_wb - y[i] 
        dj_db += dj_db_i
        dj_dw += dj_dw_i 
    dj_dw = dj_dw / m 
    dj_db = dj_db / m 
    return dj_dw,dj_db

4画出成本曲线

plt_gradients(x,y,costFun,gradientFun)
plt.show()

吴恩达471机器学习入门课程1第1周_第1张图片

5梯度下降

def gradient_descent(x,y,w_in,b_in,a,num_item,costFun,gradientFun):
    w = copy.deepcopy(w_in) #避免改变原来的w
    # 用数组存储用于在每次迭代时存储成本 J 和 w,主要用于以后绘制图形
    J_history = []
    p_history = []
    b = b_in
    w = w_in
    
    for i in range(num_item):
        #计算梯度
        dj_dw,dj_db = gradientFun(x,y,w,b)
        # 更新w,b
        b = b - a * dj_db                            
        w = w - a * dj_dw 
        # 保存每一次成本J
        if i < 100000:#避免资源浪费
            J_history.append(costFun(x,y,w,b))
            p_history.append([w,b])
        #输出10次结果,打印出来  
        #math.ceil(a),取a的最小整数 4.2取5
        if i % math.ceil(num_item/10) == 0:
            '''
            Iteration {i:4}::表示当前循环迭代次数,用 4 位数字的方式呈现,比如第一次迭代就是 "Iteration 1:"。
            Cost {J_history[-1]:0.2e}:表示模型当前的代价函数值,用科学计数法表示,保留两位小数。
            dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e}:表示代价函数对权值和偏置的梯度值,用科学计数法表示,保留三位小数。
            w: {w: 0.3e}, b:{b: 0.5e}:表示当前的权值 w 和偏置 b 的值,用科学计数法表示,分别保留三位和五位小数。
            '''
            print(f"Iteration {i:4}: Cost {J_history[-1]:0.2e} ",
                  f"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e}  ",
                  f"w: {w: 0.3e}, b:{b: 0.5e}")
    return w,b,J_history,p_history
# 初始化
w_init = 0
b_init = 0
iterations = 10000
tmp_alpha = 1.0e-2
# 
w_final, b_final, J_hist, p_hist = gradient_descent(x ,y, w_init, b_init, tmp_alpha, iterations, costFun, gradientFun)
print(f"(w,b) found by gradient descent: ({w_final:8.4f},{b_final:8.4f})")
Iteration    0: Cost 7.93e+04  dj_dw: -6.500e+02, dj_db: -4.000e+02   w:  6.500e+00, b: 4.00000e+00
Iteration 1000: Cost 3.41e+00  dj_dw: -3.712e-01, dj_db:  6.007e-01   w:  1.949e+02, b: 1.08228e+02
Iteration 2000: Cost 7.93e-01  dj_dw: -1.789e-01, dj_db:  2.895e-01   w:  1.975e+02, b: 1.03966e+02
Iteration 3000: Cost 1.84e-01  dj_dw: -8.625e-02, dj_db:  1.396e-01   w:  1.988e+02, b: 1.01912e+02
Iteration 4000: Cost 4.28e-02  dj_dw: -4.158e-02, dj_db:  6.727e-02   w:  1.994e+02, b: 1.00922e+02
Iteration 5000: Cost 9.95e-03  dj_dw: -2.004e-02, dj_db:  3.243e-02   w:  1.997e+02, b: 1.00444e+02
Iteration 6000: Cost 2.31e-03  dj_dw: -9.660e-03, dj_db:  1.563e-02   w:  1.999e+02, b: 1.00214e+02
Iteration 7000: Cost 5.37e-04  dj_dw: -4.657e-03, dj_db:  7.535e-03   w:  1.999e+02, b: 1.00103e+02
Iteration 8000: Cost 1.25e-04  dj_dw: -2.245e-03, dj_db:  3.632e-03   w:  2.000e+02, b: 1.00050e+02
Iteration 9000: Cost 2.90e-05  dj_dw: -1.082e-03, dj_db:  1.751e-03   w:  2.000e+02, b: 1.00024e+02
(w,b) found by gradient descent: (199.9929,100.0116)
w_final
199.99285075131766
b_final
100.011567727362
 np.arange(len(J_hist[1000:]))
array([   0,    1,    2, ..., 8997, 8998, 8999])
J_hist[1000:]
[3.4125109319154174,
 3.4075339615520726,
 3.4025642498421234,
 3.3976017861991608,
 3.3926465600524,
 3.3876985608460113,
 3.3827577780401223,
 3.3778242011100392,
 3.37289781954613,
 3.367978622854467,
 3.3630666005563263,
 3.358161742188174,
 3.353264037301804,
 3.348373475464178,
 3.3434900462575907,
 3.3386137392793622,
 3.333744544142247,
 3.3288824504740164,
 3.3240274479172975,
 3.319179526130373,
 3.31433867478602,
 3.3095048835726657,
 3.3046781421931897,
 3.2998584403659352,
 3.2950457678240683,
 3.290240114315667,
 3.2854414696039216,
 3.2806498234668764,
 3.275865165697401,
 3.2710874861033212,
 3.266316774507336,
 3.261553020747037,
 3.2567962146747838,
 3.2520463461576252,
 3.2473034050776732,
 3.2425673813314084,
 3.2378382648303865,
 3.2331160455007186,
 3.2284007132832904,
 3.223692258133517,
 3.2189906700216535,
 3.214295938932412,
 3.209608054865089,
 3.204927007833841,
 3.200252787867142,
 3.1955853850080693,
 3.1909247893141415,
 3.186270990857514,
 3.1816239797248214,
 3.1769837460170907,
 3.172350279849788,
 3.1677235713527,
 3.16310361067029,
 3.158490387961093,
 3.1538838933981594,
 3.1492841171689037,
 3.1446910494748352,
 3.1401046805321284,
 3.135525000570744,
 3.1309519998352693,
 3.1263856685845015,
 3.1218259970911504,
 3.117272975642429,
 3.11272659453956,
 3.108186844097903,
 3.10365371464715,
 3.0991271965307154,
 3.094607280106324,
 3.0900939557459446,
 3.0855872138351903,
 3.0810870447741032,
 3.0765934389762064,
 3.072106386869655,
 3.067625878896016,
 3.0631519055111207,
 3.0586844571846203,
 3.054223524399916,
 3.049769097654613,
 3.0453211674598286,
 3.040879724340739,
 3.036444758836324,
 3.032016261499277,
 3.0275942228961528,
 3.0231786336070874,
 3.0187694842263766,
 3.0143667653613875,
 3.0099704676337558,
 3.0055805816786347,
 3.00119709814459,
 2.996820007694243,
 2.992449301003424,
 2.9880849687619087,
 2.9837270016726674,
 2.97937539045276,
 2.9750301258322214,
 2.9706911985550035,
 2.966358599378348,
 2.9620323190731908,
 2.957712348423575,
 2.953398678227285,
 2.949091299295567,
 2.944790202452743,
 2.940495378536765,
 2.936206818398955,
 2.931924512903808,
 2.9276484529294367,
 2.9233786293668778,
 2.9191150331208293,
 2.914857655108877,
 2.9106064862620995,
 2.9063615175249096,
 2.90212273985456,
 2.8978901442218676,
 2.8936637216105865,
 2.8894434630176526,
 2.885229359453147,
 2.8810214019403677,
 2.876819581515622,
 2.8726238892281297,
 2.868434316140496,
 2.864250853328098,
 2.860073491879459,
 2.855902222895912,
 2.851737037492091,
 2.847577926795407,
 2.8434248819460874,
 2.8392778940975587,
 2.8351369544159173,
 2.8310020540800975,
 2.8268731842822388,
 2.8227503362270365,
 2.8186335011320143,
 2.814522670227773,
 2.8104178347572795,
 2.806318985976677,
 2.8022261151546015,
 2.7981392135725653,
 2.7940582725246617,
 2.7899832833178166,
 2.785914237271539,
 2.7818511257181373,
 2.77779394000235,
 2.7737426714817293,
 2.769697311526311,
 2.76565785151871,
 2.761624282854264,
 2.757596596940634,
 2.753574785198297,
 2.7495588390599024,
 2.7455487499708995,
 2.741544509389043,
 2.7375461087845703,
 2.7335535396401065,
 2.7295667934509513,
 2.7255858617245337,
 2.721610735980633,
 2.7176414077517803,
 2.713677868582396,
 2.70972011002953,
 2.7057681236624123,
 2.701821901062663,
 2.6978814338240595,
 2.6939467135527417,
 2.6900177318670173,
 2.6860944803975206,
 2.682176950786979,
 2.6782651346903776,
 2.6743590237748984,
 2.6704586097197365,
 2.666563884216295,
 2.6626748389682704,
 2.6587914656911997,
 2.654913756112791,
 2.6510417019729715,
 2.6471752950233878,
 2.6433145270279583,
 2.63945938976262,
 2.635609875015228,
 2.6317659745855457,
 2.6279276802855907,
 2.6240949839388854,
 2.620267877381224,
 2.6164463524601738,
 2.612630401035191,
 2.60882001497762,
 2.605015186170629,
 2.601215906509361,
 2.597422167900566,
 2.593633962262954,
 2.5898512815269963,
 2.5860741176348876,
 2.5823024625405218,
 2.5785363082096873,
 2.5747756466197433,
 2.571020469759903,
 2.567270769630955,
 2.5635265382453083,
 2.559787767627146,
 2.5560544498122124,
 2.5523265768477907,
 2.548604140792952,
 2.5448871337181913,
 2.5411755477056905,
 2.537469374849053,
 2.533768607253344,
 2.530073237035558,
 2.52638325632365,
 2.5226986572574615,
 2.519019431988079,
 2.515345572678102,
 2.511677071501515,
 2.5080139206437826,
 2.5043561123018296,
 2.500703638683789,
 2.497056492009247,
 2.4934146645092006,
 2.4897781484257164,
 2.486146936012548,
 2.4825210195345155,
 2.4789003912678376,
 2.4752850434997966,
 2.4716749685291957,
 2.46807015866589,
 2.46447060623093,
 2.4608763035566334,
 2.457287242986589,
 2.453703416875383,
 2.4501248175888346,
 2.4465514375039277,
 2.442983269008734,
 2.4394203045023666,
 2.435862536395175,
 2.4323099571082762,
 2.4287625590742548,
 2.425220334736461,
 2.4216832765493344,
 2.4181513769782312,
 2.4146246284996296,
 2.4111030236009796,
 2.4075865547805897,
 2.4040752145476896,
 2.4005689954225744,
 2.3970678899364284,
 2.3935718906312182,
 2.390080990059745,
 2.386595180786016,
 2.383114455384297,
 2.379638806440345,
 2.376168226550228,
 2.372702708321022,
 2.3692422443706516,
 2.365786827327556,
 2.3623364498311763,
 2.3588911045315886,
 2.355450784089657,
 2.3520154811766756,
 2.3485851884751305,
 2.3451598986776694,
 2.341739604487863,
 2.3383242986199373,
 2.3349139737986553,
 2.331508622759344,
 2.3281082382481375,
 2.324712813021514,
 2.321322339846591,
 2.3179368115012076,
 2.3145562207733343,
 2.311180560461945,
 2.3078098233762563,
 2.30444400233589,
 2.3010830901711126,
 2.297727079722494,
 2.2943759638412833,
 2.291029735388923,
 2.2876883872373894,
 2.284351912268903,
 2.281020303376362,
 2.2776935534626928,
 2.274371655441451,
 2.271054602236327,
 2.2677423867813506,
 2.2644350020210045,
 2.2611324409099987,
 2.2578346964132208,
 2.2545417615058256,
 2.2512536291734704,
 2.2479702924117033,
 2.244691744226397,
 2.241417977633784,
 2.2381489856601484,
 2.2348847613418443,
 2.231625297725593,
 2.228370587868132,
 2.225120624836327,
 2.2218754017072255,
 2.218634911567877,
 2.2153991475154458,
 2.212168102657224,
 2.2089417701105214,
 2.2057201430026483,
 2.202503214470976,
 2.1992909776628493,
 2.196083425735718,
 2.1928805518568018,
 2.189682349203448,
 2.1864888109630334,
 2.183299930332582,
 2.1801157005193144,
 2.1769361147401867,
 2.1737611662222185,
 2.1705908482020946,
 2.1674251539265432,
 2.1642640766520986,
 2.1611076096450224,
 2.15795574618153,
 2.1548084795475098,
 2.1516658030388336,
 2.1485277099609896,
 2.145394193629265,
 2.142265247368767,
 2.1391408645141885,
 2.136021038410157,
 2.132905762410877,
 2.1297950298801616,
 2.1266888341916568,
 2.1235871687286156,
 2.120490026883905,
 2.1173974020601136,
 2.1143092876693728,
 2.111225677133439,
 2.1081465638836554,
 2.105071941361052,
 2.1020018030160617,
 2.0989361423087174,
 2.0958749527087157,
 2.0928182276950484,
 2.0897659607564503,
 2.086718145390985,
 2.0836747751063642,
 2.080635843419612,
 2.0776013438571983,
 2.074571269955143,
 2.0715456152589113,
 2.068524373323161,
 2.0655075377123877,
 2.0624951019998896,
 2.059487059768802,
 2.0564834046115057,
 2.053484130129518,
 2.0504892299340494,
 2.0474986976452003,
 2.0445125268928077,
 2.041530711315742,
 2.038553244562165,
 2.0355801202894965,
 2.032611332164592,
 2.0296468738633022,
 2.0266867390708017,
 2.0237309214816013,
 2.020779414799092,
 2.0178322127362094,
 2.014889309014802,
 2.01195069736592,
 2.009016371529871,
 2.006086325255993,
 2.003160552302867,
 2.0002390464378976,
 1.997321801437852,
 1.9944088110884546,
 1.9915000691845917,
 1.988595569530015,
 1.9856953059376923,
 1.9827992722295154,
 1.9799074622365413,
 1.9770198697984813,
 1.9741364887644,
 1.9712573129921345,
 1.9683823363485624,
 1.9655115527094034,
 1.9626449559593937,
 1.9597825399923057,
 1.9569242987104816,
 1.9540702260255203,
 1.9512203158576344,
 1.9483745621360915,
 1.9455329587988581,
 1.942695499792889,
 1.9398621790738722,
 1.9370329906061428,
 1.9342079283633562,
 1.9313869863273618,
 1.9285701584892319,
 1.9257574388485352,
 1.9229488214136352,
 1.9201443002016894,
 1.9173438692386826,
 1.9145475225591013,
 1.9117552542062457,
 1.9089670582321099,
 1.9061829286972212,
 1.9034028596711572,
 1.9006268452315997,
 1.8978548794652974,
 1.8950869564674286,
 1.8923230703417846,
 1.8895632152007935,
 1.8868073851655645,
 1.8840555743656453,
 1.8813077769392428,
 1.878563987032887,
 1.8758241988019926,
 1.8730884064103055,
 1.87035660403003,
 1.8676287858419174,
 1.8649049460352924,
 1.862185078807907,
 1.8594691783659552,
 1.85675723892397,
 1.854049254705223,
 1.851345219941089,
 1.848645128871501,
 1.8459489757449323,
 1.8432567548179017,
 1.8405684603556471,
 1.8378840866315196,
 1.8352036279274606,
 1.8325270785333965,
 1.8298544327480077,
 1.8271856848779207,
 1.8245208292384134,
 1.8218598601526925,
 1.8192027719525867,
 1.8165495589778478,
 1.8139002155767514,
 1.8112547361057687,
 1.8086131149294817,
 1.8059753464208401,
 1.803341424960808,
 1.8007113449387844,
 1.79808510075221,
 1.7954626868066532,
 1.792844097515881,
 1.7902293273020318,
 1.78761837059495,
 1.7850112218329697,
 1.7824078754623822,
 1.7798083259375819,
 1.77721256772102,
 1.7746205952833016,
 1.7720324031030823,
 1.769447985667044,
 1.7668673374698827,
 1.7642904530144579,
 1.761717326811438,
 1.759147953379632,
 1.7565823272458836,
 1.7540204429449089,
 1.751462295019411,
 1.7489078780200729,
 1.7463571865056304,
 1.7438102150425374,
 1.7412669582054303,
 1.7387274105764998,
 1.7361915667462797,
 1.7336594213128358,
 1.73113096888231,
 1.72860620406864,
 1.7260851214935966,
 1.7235677157868667,
 1.7210539815859498,
 1.7185439135360734,
 1.7160375062903341,
 1.7135347545098139,
 1.7110356528629596,
 1.7085401960263709,
 1.7060483786843244,
 1.7035601955287452,
 1.701075641259325,
 1.6985947105835264,
 1.6961173982166333,
 1.6936436988814605,
 1.6911736073084986,
 1.6887071182361537,
 1.6862442264103228,
 1.6837849265846034,
 1.681329213520194,
 1.6788770819860743,
 1.6764285267587202,
 1.6739835426223646,
 1.6715421243685622,
 1.669104266796815,
 1.6666699647140555,
 1.664239212934623,
 1.6618120062808357,
 1.6593883395820843,
 1.6569682076757115,
 1.6545516054062444,
 1.652138527625929,
 1.6497289691945825,
 1.6473229249793078,
 1.6449203898549272,
 1.6425213587034375,
 1.6401258264146046,
 1.6377337878854554,
 1.635345238020602,
 1.632960171731907,
 1.630578583938836,
 1.6282004695681471,
 1.6258258235540328,
 1.6234546408380819,
 1.6210869163692216,
 1.6187226451038308,
 1.616361822005583,
 1.6140044420454933,
 1.6116505002019037,
 1.6092999914605386,
 1.6069529108143537,
 1.6046092532636582,
 1.6022690138160431,
 1.5999321874864234,
 1.5975987692968634,
 1.5952687542768906,
 1.5929421374630774,
 1.5906189138993043,
 1.5882990786366733,
 1.585982626733636,
 1.5836695532556258,
 1.5813598532754276,
 1.5790535218729636,
 1.5767505541353755,
 1.5744509451568602,
 1.5721546900388066,
 1.5698617838900035,
 1.567572221825921,
 1.5652859989694847,
 1.563003110450553,
 1.5607235514062854,
 1.5584473169807624,
 1.556174402325217,
 1.5539048025979285,
 1.5516385129641963,
 1.5493755285964275,
 1.5471158446741222,
 1.5448594563837705,
 1.5426063589188308,
 1.5403565474797043,
 1.5381100172740463,
 1.5358667635162564,
 1.533626781427843,
 1.5313900662371887,
 1.5291566131797654,
 1.5269264174979456,
 1.524699474440873,
 1.522475779264901,
 1.520255327233093,
 1.51803811361555,
 1.5158241336891256,
 1.5136133827377607,
 1.511405856052038,
 1.5092015489296404,
 1.5070004566749475,
 1.5048025745992417,
 1.5026078980206394,
 1.5004164222641405,
 1.4982281426614503,
 1.496043054551199,
 1.4938611532786708,
 1.49168243419608,
 1.4895068926624404,
 1.4873345240433435,
 1.4851653237113676,
 1.4829992870456001,
 1.4808364094321556,
 1.4786766862635359,
 1.4765201129392729,
 1.474366684865467,
 1.4722163974549,
 1.4700692461271443,
 1.4679252263082538,
 1.4657843334312441,
 1.463646562935595,
 1.4615119102673775,
 1.4593803708794242,
 1.4572519402312574,
 1.4551266137889225,
 1.453004387025065,
 1.45088525541893,
 1.4487692144564601,
 1.446656259630086,
 1.4445463864388597,
 1.4424395903882805,
 1.4403358669906043,
 1.4382352117645019,
 1.436137620235172,
 1.4340430879344495,
 1.43195161040052,
 1.4298631831781898,
 1.427777801818768,
 1.4256954618799715,
 1.423616158926086,
 1.4215398885278132,
 1.4194666462623688,
 1.4173964277132174,
 1.415329228470643,
 1.4132650441310104,
 1.411203870297291,
 1.409145702578773,
 1.4070905365912179,
 1.4050383679568126,
 1.4029891923040174,
 1.4009430052676994,
 1.3988998024891177,
 1.3968595796159702,
 1.3948223323021787,
 1.3927880562079595,
 1.3907567470000353,
 1.3887284003513123,
 1.3867030119410846,
 1.3846805774548796,
 1.3826610925845944,
 1.3806445530283473,
 1.3786309544906261,
 1.37662029268193,
 1.3746125633192727,
 1.3726077621259465,
 1.3706058848312033,
 1.3686069271707617,
 1.3666108848865361,
 1.364617753726538,
 1.3626275294450223,
 1.3606402078025064,
 1.3586557845656568,
 1.3566742555072377,
 1.3546956164062718,
 1.3527198630478918,
 1.3507469912234076,
 1.3487769967302792,
 1.3468098753719793,
 1.3448456229582688,
 1.3428842353049881,
 1.3409257082339119,
 1.3389700375730968,
 1.337017219156566,
 1.3350672488245074,
 1.3331201224231588,
 1.331175835804773,
 1.329234384827643,
 1.3272957653561517,
 1.3253599732607455,
 1.3234270044178347,
 1.3214968547096886,
 1.319569520024975,
 1.3176449962579895,
 1.3157232793092075,
 1.3138043650850635,
 1.3118882494978095,
 1.309974928465819,
 1.30806439791351,
 1.3061566537709282,
 1.3042516919743812,
 1.302349508465887,
 1.3004500991935006,
 1.2985534601110136,
 1.296659587178417,
 1.2947684763613327,
 1.2928801236313876,
 1.290994524966104,
 1.2891116763487125,
 1.2872315737684674,
 1.285354213220384,
 1.283479590705395,
 1.2816077022302463,
 1.2797385438074165,
 1.2778721114552822,
 1.2760084011979709,
 1.274147409065569,
 1.2722891310937656,
 1.2704335633239912,
 1.2685807018037523,
 1.2667305425859943,
 1.2648830817296013,
 1.2630383152990985,
 1.2611962393648586,
 1.2593568500028798,
 1.25752014329508,
 1.2556861153287238,
 1.2538547621972091,
 1.2520260799992444,
 1.250200064839556,
 1.2483767128284062,
 1.246556020081602,
 1.2447379827208493,
 1.2429225968734208,
 1.2411098586721325,
 1.239299764255558,
 1.2374923097679744,
 1.2356874913590599,
 1.2338853051842307,
 1.2320857474045877,
 1.2302888141867179,
 1.2284945017028241,
 1.2267028061306955,
 1.2249137236537586,
 1.2231272504608803,
 1.2213433827465896,
 1.2195621167108983,
 1.2177834485594536,
 1.2160073745033246,
 1.214233890759172,
 1.2124629935491698,
 1.2106946791009705,
 1.20892894364779,
 1.2071657834282215,
 1.2054051946864932,
 1.2036471736721954,
 1.2018917166404846,
 1.2001388198518725,
 1.198388479572395,
 1.1966406920735004,
 1.1948954536321668,
 1.193152760530591,
 1.1914126090566306,
 1.1896749955033932,
 1.1879399161695128,
 1.186207367358945,
 1.1844773453810713,
 1.182749846550515,
 1.1810248671875265,
 1.17930240361755,
 1.1775824521714267,
 1.1758650091853928,
 1.1741500710009298,
 1.1724376339649383,
 1.1707276944296472,
 1.1690202487526256,
 1.1673152932965862,
 1.1656128244296982,
 1.1639128385254875,
 1.1622153319625963,
 1.1605203011250547,
 1.1588277424021574,
 1.1571376521884815,
 1.1554500268837704,
 1.15376486289319,
 1.1520821566268833,
 1.150401904500526,
 1.1487241029347557,
 1.1470487483556762,
 1.1453758371944749,
 1.1437053658874488,
 1.142037330876294,
 1.140371728607763,
 1.1387085555338181,
 1.1370478081116455,
 1.1353894828034976,
 1.133733576076895,
 1.1320800844044623,
 1.1304290042639669,
 1.1287803321382546,
 1.1271340645154038,
 1.1254901978886067,
 1.1238487287561205,
 1.122209653621252,
 1.1205729689925636,
 1.1189386713836014,
 1.1173067573129924,
 1.1156772233045027,
 1.1140500658869255,
 1.112425281594152,
 1.110802866965032,
 1.1091828185435935,
 1.10756513287884,
 1.1059498065247835,
 1.104336836040472,
 1.1027262179900998,
 1.1011179489427017,
 1.0995120254723296,
 1.09790844415816,
 1.0963072015841706,
 1.0947082943395892,
 1.0931117190183115,
 1.0915174722193979,
 1.089925550546888,
 1.088335950609625,
 1.086748669021485,
 1.0851637024013003,
 1.0835810473728023,
 1.0820007005646266,
 1.0804226586104457,
 1.078846918148629,
 1.0772734758225808,
 1.0757023282807339,
 1.0741334721761047,
 1.0725669041668058,
 1.071002620915807,
 1.069440619090837,
 1.0678808953645933,
 1.0663234464145748,
 1.0647682689231859,
 1.0632153595775682,
 1.0616647150697145,
 1.060116332096571,
 1.0585702073597147,
 1.057026337565733,
 1.0554847194257944,
 1.0539453496560622,
 1.0524082249772952,
 1.0508733421153125,
 1.049340697800398,
 1.0478102887678598,
 1.0462821117575114,
 1.0447561635141844,
 1.0432324407873335,
 1.041710940331041,
 1.040191658904375,
 1.0386745932709511,
 1.0371597401991184,
 1.0356470964619875,
 1.034136658837413,
 1.0326284241077668,
 1.0311223890603904,
 1.0296185504870623,
 1.0281169051843762,
 1.026617449953529,
 1.0251201816004454,
 1.0236250969356342,
 1.0221321927744187,
 1.0206414659364906,
 1.019152913246478,
 1.0176665315333766,
 1.0161823176309357,
 1.014700268377637,
 1.0132203806163864,
 1.0117426511946892,
 1.010267076964861,
 1.0087936547834966,
 1.0073223815120849,
 1.0058532540164724,
 1.0043862691671812,
 1.0029214238393325,
 1.0014587149124454,
 0.9999981392707153,
 0.9985396938028983,
 0.9970833754022091,
 0.99562918096646,
 0.9941771073979384,
 0.9927271516034573,
 0.9912793104944122,
 0.9898335809865442,
 0.9883899600002313,
 0.9869484444603742,
 0.9855090312962311,
 0.9840717174416118,
 0.9826364998347301,
 0.9812033754183948,
 0.9797723411397214,
 0.978343393950438,
 0.9769165308065633,
 0.9754917486685946,
 0.9740690445015885,
 0.9726484152749199,
 0.9712298579623377,
 0.9698133695420526,
 0.9683989469967724,
 0.9669865873134529,
 0.9655762874835606,
 0.9641680445028672,
 0.9627618553716659,
 0.961357717094345,
 0.959955626679996,
 0.9585555811418633,
 0.9571575774975649,
 0.9557616127691551,
 0.9543676839829662,
 0.9529757881696965,
 0.9515859223643464,
 0.950198083606228,
 0.9488122689390448,
 0.9474284754107594,
 0.9460467000735591,
 0.9446669399841504,
 0.943289192203318,
 0.9419134537962062,
 0.9405397218323366,
 0.9391679933852926,
 0.9377982655331222,
 0.9364305353580523,
 0.9350647999465929,
 0.9337010563894155,
 0.9323393017815624,
 0.9309795332222555,
 0.9296217478149463,
 0.928265942667261,
 0.9269121148911093,
 0.92556026160266,
 0.9242103799221932,
 0.9228624669741721,
 0.9215165198873739,
 0.9201725357945696,
 0.9188305118329926,
 0.9174904451438306,
 0.9161523328724968,
 0.9148161721685155,
 0.9134819601857576,
 0.9121496940820248,
 0.9108193710193233,
 0.9094909881638846,
 0.9081645426860162,
 0.9068400317601364,
 0.905517452564816,
 0.904196802282702,
 0.9028780781006494,
 0.901561277209408,
 0.9002463968040625,
 0.8989334340836768,
 0.8976223862513415,
 0.8963132505143621,
 0.8950060240840181,
 0.8937007041756968,
 0.8923972880087769,
 0.8910957728068012,
 0.8897961557973054,
 0.8884984342118918,
 0.887202605286179,
 0.8859086662598021,
 0.8846166143764344,
 0.88332644688375,
 0.8820381610335799,
 0.8807517540815355,
 0.8794672232873175,
 0.8781845659147811,
 0.8769037792314756,
 0.8756248605092222,
 0.8743478070236623,
 0.8730726160544332,
 0.8717992848851553,
 0.870527810803368,
 0.8692581911007052,
 0.8679904230725347,
 0.8667245040183496,
 0.8654604312415366,
 0.8641982020493466,
 0.862937813753032,
 0.8616792636677018,
 0.8604225491124966,
 0.8591676674103519,
 0.8579146158881235,
 0.8566633918766202,
 0.8554139927104751,
 0.8541664157283086,
 0.8529206582725051,
 0.8516767176894023,
 0.8504345913291713,
 0.84919427654588,
 0.8479557706974297,
 0.8467190711456148,
 0.8454841752559574,
 0.8442510803980122,
 0.8430197839450063,
 0.8417902832740182,
 0.8405625757661197,
 0.8393366588059579,
 0.8381125297821685,
 0.8368901860871673,
 0.8356696251170724,
 0.8344508442718771,
 0.8332338409553929,
 0.8320186125752782,
 0.8308051565426767,
 0.8295934702728918,
 0.8283835511846916,
 0.8271753967007793,
 0.8259690042476352,
 0.824764371255315,
 0.8235614951577938,
 0.8223603733927707,
 0.8211610034015532,
 0.8199633826293484,
 0.8187675085249783,
 0.8175733785410062,
 0.8163809901337584,
 0.8151903407632113,
 0.8140014278930503,
 0.8128142489907524,
 0.8116288015273257,
 0.8104450829775762,
 0.8092630908200424,
 0.8080828225368222,
 0.8069042756136928,
 0.8057274475402256,
 0.8045523358095301,
 0.8033789379183327,
 0.8022072513672126,
 0.8010372736601552,
 0.7998690023050057,
 0.7987024348130486,
 0.7975375686993745,
 0.7963744014825843,
 0.7952129306848713,
 0.7940531538321492,
 ...]

fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12,4))
ax1.plot(J_hist[:100])
ax2.plot(1000 + np.arange(len(J_hist[1000:])), J_hist[1000:])
ax1.set_title("Cost vs. iteration(start)");  ax2.set_title("Cost vs. iteration (end)")
ax1.set_ylabel('Cost')            ;  ax2.set_ylabel('Cost') 
ax1.set_xlabel('iteration step')  ;  ax2.set_xlabel('iteration step') 
plt.show()


吴恩达471机器学习入门课程1第1周_第2张图片

print(f"1000 sqft house prediction {w_final*1.0 + b_final:0.1f} Thousand dollars")
print(f"1200 sqft house prediction {w_final*1.2 + b_final:0.1f} Thousand dollars")
print(f"2000 sqft house prediction {w_final*2.0 + b_final:0.1f} Thousand dollars")
1000 sqft house prediction 300.0 Thousand dollars
1200 sqft house prediction 340.0 Thousand dollars
2000 sqft house prediction 500.0 Thousand dollars

你可能感兴趣的:(机器学习,机器学习,python,人工智能)