代码如下：
import numpy as np
import scipy
from scipy import linalg
import time
import random
def mul(m,n,row,mid,column):
matrix=np.zeros((row,column))
for i in range(row):
for j in range(column):
for temp in range(mid):
matrix[i][j]+=m[i][temp]*n[temp][j]
return matrix
A=np.random.normal(size=(20,50))
B=scipy.linalg.toeplitz(range(50))
#9.1
def fun1(lam):
return mul(A,(B-int(lam)*np.eye(50)),20,50,50)
print("A+A=")
print(A+A)
print("A*A.T=")
print(mul(A,A.T,20,50,20))
print("A.T*A=")
print(mul(A.T,A,50,20,50))
print("A*B=")
print(mul(A,B,20,50,50))
lam=input("Please input lambda: ")
print("A*(B-lambda*I)=")
print(fun1(lam))
#9.2
b=np.ones((50,1))
x=linalg.solve(B,b)
print(x)
#9.3
print("The Frobenius norm of A: ")
print(np.linalg.norm(A))
print("The infinity norm of B: ")
print(np.linalg.norm(B,ord=np.inf))
print("The largest and smallest singular values of B: ")
print(np.max(B))
print(np.min(B))
#9.4
def power_iteration(Z):
b0=np.ones((20,1))
b=0.5*np.ones((20,1))
t=0
print("Before: "+str(time.clock()))
while (t<700 and (max(b-b0)>0.01 or max(b-b0)<-0.01)):
b0=b
b=mul(Z,b0,20,20,1)
b_norm=np.linalg.norm(b)
b=b/b_norm
t=t+1
print("After: "+str(time.clock()))
print("After "+str(t)+" times of iterations, ")
print(b)
Z=np.random.normal(size=(20,20))
power_iteration(Z)
#9.5
p=random.random()
C=np.zeros((20,20))
for i in range(400):
if random.random()<float(p):
C[i//20][i%20]=1
else:
C[i//20][i%20]=0
U,S,Vh=scipy.linalg.svd(C)
print("The largest singular value is :")
print(max(S))
print("n*p:")
print(20*p)
#9.6
arr=np.random.normal(size=(1,20))
z=random.random()
for i in range(0,20):
arr[0][i]=abs(arr[0][i]-z)
print("The closest value is :")
print(arr[0][np.argmin(arr)])
程序运行结果如下：
A+A= [[-7.23731138e-01 -2.93788813e-01 -7.00822984e-01 -2.53089335e+00 7.94091001e-01 -3.23122702e+00 4.98630984e-01 -3.07319030e+00 -3.52983683e-01 -2.43580733e+00 -7.39653827e-01 2.42842736e+00 2.33747057e+00 2.49311779e+00 1.11616696e+00 2.10070795e+00 1.07706753e+00 1.12230640e+00 -1.07547599e+00 1.18005492e+00 -1.18854663e+00 -2.03381447e-01 2.99235458e-01 2.42893501e+00 9.73695965e-01 1.79812647e+00 -2.36713662e+00 -1.20540029e+00 -5.42919215e-01 9.83848127e-01 1.86172938e+00 6.86295053e-01 -2.83746043e+00 -1.55130958e+00 9.74106177e-01 1.27044605e+00 -3.76400925e-01 1.36985894e+00 -6.66907630e-01 1.51029426e+00 2.85926855e+00 -4.49479642e+00 1.07013693e+00 3.27621854e+00 5.72084165e-01 -8.77659007e-01 3.29257611e+00 -1.47450969e-01 -7.99228760e-01 -6.52014527e-01] [-1.25767822e+00 -3.67422010e-01 -3.70872520e+00 -7.27806970e-01 -2.26652840e-01 -5.42535650e+00 -2.59967776e+00 8.85790043e-01 2.27788961e+00 1.07628151e+00 -4.65020640e+00 3.43251557e+00 6.20022837e-01 1.52778827e+00 6.08481008e-01 -1.99531305e-01 2.57534365e+00 1.67158835e+00 1.17389609e+00 -4.49115820e-01 -3.98771134e+00 -2.55434311e+00 -2.16678745e+00 2.28048057e+00 1.87792700e+00 2.25014498e+00 3.43853606e+00 2.11111175e+00 -1.20515748e+00 1.76868787e+00 -3.90719444e+00 4.05229907e+00 -2.97108121e+00 5.23807486e-02 -4.11362566e+00 -6.55919197e-01 -7.89493111e-01 3.02770170e+00 2.16423140e+00 1.90386658e+00 1.77076577e+00 -2.62519254e+00 2.22096985e+00 1.08307320e+00 -1.11602693e-01 2.91688662e+00 -1.05269857e+00 -1.31645317e+00 1.04393615e+00 -4.06062669e+00] [ 2.66758123e+00 1.41443371e-01 -7.52845477e-01 -1.05792575e+00 -3.25630696e+00 3.69431308e+00 -9.04303567e-01 2.04143234e-02 -2.00660223e+00 8.36868962e-01 -1.62780710e+00 1.02146362e+00 -1.49015810e+00 2.86876933e+00 1.76378457e+00 -3.28799562e+00 1.15587693e+00 1.45582590e+00 2.40425395e+00 -3.00850946e+00 9.16023356e-01 1.84744110e+00 1.92487256e+00 -3.79804097e-01 -2.93110118e+00 1.11451953e+00 2.32588709e+00 4.99670606e-01 1.16493986e-01 -1.14985648e-01 -6.35728918e-01 -5.07545463e-01 3.47883904e+00 -5.67429817e-01 -1.49328927e+00 -3.34352332e+00 1.27269690e+00 -1.98932267e+00 -1.82088990e+00 1.90353486e+00 1.37805589e+00 1.17538391e+00 3.65419636e+00 -2.18044861e+00 -8.52032834e-01 -3.15628543e-01 1.86842173e-01 -3.02810179e+00 -1.20265386e+00 2.16305270e+00] [-4.02624417e+00 1.18154114e+00 -2.91569460e+00 4.03849540e-01 1.84643918e+00 -1.52708148e+00 1.20852076e-01 2.65810793e+00 3.45141639e+00 3.14734347e+00 4.27457612e-01 9.50471787e-01 -1.11768824e+00 2.46454224e+00 -7.85682827e-01 -1.65132007e+00 1.13202787e-01 3.01005750e+00 -7.12937203e-01 -1.06471603e+00 2.89893172e+00 -3.69908373e-01 -1.02600751e+00 -2.20865742e+00 2.31964188e+00 -1.38610752e+00 9.03163986e-01 1.35557208e+00 8.43905344e-01 -2.96683824e-01 -3.13497252e+00 2.93605289e+00 1.61363131e+00 2.69006760e-01 -3.15017874e+00 6.62992704e-01 -1.17604581e+00 1.52351643e+00 1.84887054e+00 1.30380842e+00 1.50535216e+00 2.29493160e+00 -5.26221038e-01 -2.01844364e+00 -4.94985198e-01 -2.12281214e+00 1.58928300e+00 -2.17152001e-01 2.82730301e+00 -2.38523041e+00] [ 1.02631981e+00 1.62945298e+00 -1.38067460e+00 -1.07214971e-01 -2.48565567e+00 2.72770525e-01 -7.99876002e-02 -2.16190601e+00 -6.96392851e-01 1.66511511e+00 -4.32131520e-01 1.62909639e+00 -6.31833827e-01 -3.85426351e+00 -1.61327535e+00 -9.46602093e-01 -2.68494567e+00 4.70829455e-01 -3.19318891e+00 -1.99815619e+00 2.21281177e+00 2.05813725e+00 -1.89732676e+00 -8.38023327e-01 1.19542873e+00 -3.65053581e+00 -3.06948599e+00 6.25586409e-02 2.45503079e+00 1.06803437e+00 -1.30080433e+00 -1.67492869e+00 2.51363314e+00 1.63283491e-02 -1.81256684e-01 1.69902066e+00 -1.20439760e-01 -3.84558913e-01 -2.47274854e+00 -1.72258086e-01 1.88606592e+00 -3.36118227e+00 1.35057108e+00 8.75535124e-01 -1.22318202e-01 -1.73507064e+00 -1.41057985e+00 -9.35763259e-02 -3.26687887e+00 1.80030248e+00] [-1.04273658e+00 -2.95619975e+00 -2.79106822e+00 -1.05959582e-01 -6.57377515e-01 -4.95229447e-01 -4.86517913e+00 2.77511374e+00 1.20001508e+00 5.17234372e-01 -2.87298949e+00 -4.07874032e-01 -2.70301583e+00 4.35320933e-01 -1.44981791e+00 3.95975823e+00 9.51834643e-01 -2.90549142e-01 -9.25524342e-01 1.50648245e+00 6.21707037e-01 -2.01394775e+00 -2.19272177e+00 -3.46685752e+00 -1.71577182e+00 -8.29380393e-02 -2.66255466e+00 2.11257264e+00 1.03700333e+00 2.21356207e+00 -1.00225878e+00 5.51374840e+00 -1.08773068e+00 -1.60528667e+00 2.85662147e+00 -2.18069217e+00 1.46520844e+00 -2.53394844e-02 -1.63994532e+00 3.75731825e+00 -1.30977628e+00 4.14380398e+00 1.07185550e+00 2.91701228e-01 6.25254272e-01 5.20074831e-01 4.62830237e+00 1.98675008e+00 -1.84979397e-01 -2.97542044e+00] [ 1.97518657e+00 2.03570316e+00 1.64471942e+00 -1.38450494e+00 -1.82545681e+00 3.35925634e+00 1.20988012e+00 -2.13007131e+00 1.55880667e+00 1.27603541e+00 -1.13965289e+00 2.52555889e+00 8.36732468e-01 1.11981468e+00 -2.06633920e-01 2.50388512e+00 3.93047724e-02 8.56507713e-01 4.63664944e+00 -4.27549831e-01 -1.82966524e+00 -2.10047082e+00 2.02850480e+00 -4.23648357e-04 -1.58131452e+00 -1.80449489e-01 1.17626585e+00 -2.15067178e+00 1.68884719e+00 -1.00186568e+00 -1.68240042e+00 -9.94544691e-01 1.47182346e+00 3.03466668e-01 1.33101403e+00 -1.05514352e+00 6.55874899e-01 -1.98031591e+00 -5.84010449e-01 2.18843687e+00 -4.20938541e+00 2.46494817e-02 1.75094440e+00 -6.67977692e-01 -3.06367432e-01 -2.64145794e-01 5.22803053e+00 -9.23647802e-01 -1.03703895e+00 -3.30034479e+00] [-1.87187183e+00 -1.19828798e+00 -3.77540588e+00 -1.30895120e+00 1.62333090e-01 2.94077732e-01 -3.14987618e-01 3.79165630e+00 -1.54027646e+00 5.91188513e-01 5.24393817e-01 6.94156295e-01 6.40617940e-01 -2.15266634e+00 2.60156622e+00 -2.46220236e+00 -2.60687628e+00 2.73930659e+00 1.03270329e+00 -1.16892656e+00 2.45885458e-01 -1.65059438e+00 9.25202020e-01 7.95877539e-01 -1.67199919e+00 -8.24560289e-01 9.82765678e-01 -2.14310473e+00 1.13251794e-01 -2.58764557e+00 -1.39091229e+00 -4.23871793e+00 -3.77669247e+00 1.06094119e+00 -1.40821545e+00 1.54059249e-01 -3.22884218e+00 1.19293275e+00 -1.57954916e+00 -1.36599959e+00 -2.04677905e+00 5.89306789e-01 -2.35572634e+00 2.10520518e-01 -2.72249216e+00 9.34128571e-01 9.97067854e-03 1.66220437e+00 1.43953772e+00 -3.83228939e+00] [-2.97811684e-01 3.01490177e-01 -6.38410694e-01 -6.16716904e-01 -9.56363269e-01 1.26139812e+00 3.46425615e-01 -8.76422649e-01 2.50317000e+00 1.93618167e-01 2.06676873e+00 2.10637618e+00 -1.20997862e+00 -9.47309872e-01 -1.67495479e+00 2.07747089e+00 -2.57422938e+00 -1.35342030e+00 9.46817017e-01 3.27772516e+00 -2.74869812e+00 2.71458311e+00 1.59757289e+00 5.97534420e+00 1.24826362e+00 1.20058215e+00 -6.34845427e-01 -1.18471090e+00 -4.98142720e-01 1.15105170e+00 5.70700262e-01 1.24959616e+00 -7.23827515e-01 9.70885168e-01 -1.31485621e+00 -1.87161539e+00 -2.35960315e+00 -3.09933172e+00 -8.18867852e-01 3.66152575e+00 -5.76994336e-01 -3.03582208e-01 7.44864310e-01 -4.31097867e+00 -2.64178968e+00 8.07808725e-01 -1.46010208e+00 -8.70288947e-02 4.16877613e-01 -2.39949128e+00] [-1.63784347e+00 4.68160034e-02 2.93232982e+00 -1.65965429e+00 2.36149064e+00 8.87097439e-01 4.75113208e-01 -3.99602583e+00 -1.89538172e+00 1.35726462e-01 -2.19761677e+00 -2.01179675e+00 3.40246792e+00 -2.82995671e+00 -1.48039348e+00 4.50082998e-02 -1.33501741e+00 7.27676426e-01 2.12512886e+00 -6.58980954e-01 8.07712693e-01 -2.38608790e+00 1.02683028e+00 4.92653023e-01 2.92071691e+00 2.47109711e-01 -3.59391877e+00 -8.29698543e-01 1.53881694e+00 5.08702195e-01 1.48220481e+00 2.03533201e+00 9.41286198e-01 -1.81726495e+00 -1.19088288e+00 -1.95683100e+00 -1.98900841e+00 -2.71569556e-01 1.27483870e+00 -2.90052912e+00 3.46634197e+00 -3.88219219e+00 -3.46387286e+00 2.66268261e+00 4.25785956e+00 -4.49735227e-02 6.06972117e-01 -4.02209200e-01 -1.85257041e+00 9.85847362e-01] [-1.10714335e+00 1.75378122e+00 2.00838069e-01 -8.27408443e-01 -6.51880442e-01 2.10907822e+00 -1.06636510e-01 -1.52385395e+00 -4.33130526e+00 -4.82137504e-01 2.47480700e+00 -1.28734865e+00 2.82890558e+00 -2.39168058e+00 -1.91089415e-01 1.92605911e+00 -1.74854378e+00 1.25361116e+00 -1.74350853e-01 2.74903353e+00 -8.25200159e-01 -3.27392007e+00 -1.53385154e-01 2.28197069e+00 1.90801058e+00 -5.06325642e-01 2.24649011e+00 2.40188560e-01 4.05931665e-01 -4.24206344e-02 6.25088921e-01 -2.72373237e-01 -1.78683760e-01 -1.50768240e+00 6.99058525e-02 1.80149432e+00 1.01767591e+00 1.28893721e-01 2.15145162e+00 -3.55426380e-01 -6.01642461e-03 -7.34299803e-01 -9.03647241e-03 1.41335571e+00 -5.37294585e+00 -6.02428080e-01 2.72295256e-01 9.67432145e-01 1.09890570e+00 5.30612408e-01] [-1.85919087e-01 -6.59009793e-03 -4.32451773e-02 -7.14786159e-01 1.92378497e+00 -1.21474649e+00 -1.45242887e+00 -1.73485239e+00 -1.64072177e+00 1.15308301e+00 -1.86173712e-01 3.99212735e+00 5.75026610e-03 -1.72333327e+00 1.56739135e+00 7.24027379e-01 -2.61588843e+00 2.95579311e+00 2.34316055e+00 2.28174687e-01 -2.38509866e+00 -9.96368291e-01 1.32397835e+00 -1.26223388e+00 2.28643483e+00 -3.52578061e+00 -1.05971691e+00 1.09555923e+00 -1.37673873e+00 -3.27769709e+00 -2.76072255e+00 -2.05961275e+00 -1.31079154e+00 1.64657163e+00 -2.62582738e+00 8.70114034e-01 2.49300035e+00 -8.74405438e-01 -1.84917687e+00 -1.62925096e+00 1.43503224e+00 -2.22894895e+00 -1.24714827e+00 1.25629295e+00 -1.84996899e+00 -2.34978955e-01 6.50396404e-01 -4.00259986e-01 -2.75603806e-01 1.52036257e+00] [-9.44450241e-01 -5.40402858e-01 9.34111842e-01 1.77186942e+00 -3.13906282e+00 -4.21422365e+00 -2.09926825e+00 -2.02133593e+00 -3.86012846e+00 4.23254729e-01 1.91336933e+00 -2.84036923e+00 -7.28795495e-01 -2.96849915e+00 -3.76233312e-01 3.55333958e-01 2.47181426e+00 -2.43562280e+00 1.57209316e+00 -2.01904588e+00 -1.22582834e+00 -3.87446365e-02 -2.12171826e+00 -9.62810448e-01 -1.04003300e+00 2.37950164e+00 -1.79516169e+00 -2.63096656e+00 -6.97159944e-01 4.79486676e-01 3.75883551e+00 -2.87373092e-01 3.52481484e+00 -9.40713797e-01 2.52136563e+00 2.97843379e+00 -2.58847663e+00 1.64460385e+00 1.12787747e+00 1.28408398e-01 2.03125737e+00 2.60382523e+00 -3.35083849e-01 -1.47247934e+00 3.33917872e+00 2.16523300e+00 5.27273878e-01 -6.78790357e-01 1.64272162e+00 -1.72421787e+00] [ 1.59730505e+00 2.70076719e-02 9.83714903e-01 6.54368196e-01 -2.16529810e+00 -3.43538377e+00 1.51809267e+00 2.42311127e+00 1.84771262e+00 1.50798354e+00 6.22123534e-01 6.20519877e-01 7.93684810e-01 -3.53806095e-01 -5.54310755e-01 1.75679474e+00 2.22131867e+00 4.04161319e-01 4.33296312e-01 7.86328567e-01 -1.37836717e+00 -9.36651033e-02 -6.60053981e-01 4.77036203e-01 -1.44726984e+00 1.36768487e-02 -2.66849280e+00 1.38988406e-01 -1.00847772e+00 -3.76232383e+00 5.16850219e-01 1.14823739e+00 1.86574855e+00 1.31793464e+00 -2.08924085e+00 4.62381112e+00 3.49835000e+00 5.71824500e-01 6.97492740e-01 1.14526064e-01 4.85280092e+00 -2.68604726e+00 -2.23358222e-01 -2.14307151e+00 5.79120604e-01 2.75517951e+00 -1.37972664e+00 -2.53432017e+00 -6.36088837e-01 2.71429336e+00] [-1.56080913e+00 3.48005931e-01 1.17191182e+00 1.60264968e+00 -1.72208967e+00 8.41989314e-01 -1.67650000e+00 1.41255647e-01 7.22898039e-01 -1.64686940e+00 2.63029739e+00 -2.17176806e+00 -2.79569481e-01 -1.78690670e+00 -9.57730125e-01 1.23526659e+00 -1.69822718e-01 4.77448258e-01 1.89588867e+00 -1.29582139e+00 2.32436213e+00 7.18336057e-01 -1.84606769e+00 -1.10978873e+00 1.28385010e+00 -2.20334490e-01 -1.39705086e+00 -5.53438777e+00 1.39003757e+00 -2.70376510e+00 1.33648931e+00 -2.98442546e+00 -5.35181803e-01 9.23342843e-01 -3.36583832e+00 -5.27289695e-01 2.17835222e+00 1.03269824e+00 -2.17781644e+00 2.61155968e-01 2.34386967e+00 9.54320660e-01 -7.51752079e-02 8.24039056e-01 -9.18222611e-01 4.83473769e-01 -2.75046607e-01 2.01762156e+00 1.84799774e+00 2.40159976e-01] [ 1.79707139e+00 3.13354032e+00 -1.48976758e+00 1.32286753e+00 6.42781728e-01 -2.50962877e-01 1.24738374e+00 2.36424081e+00 2.74470231e+00 1.41150679e+00 -4.71768208e-01 1.84062422e+00 -3.26974071e-01 -1.55187947e+00 1.53291256e+00 -8.24369924e-01 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-2.56530298e+00 -4.44305995e+00 3.06126133e+00 -2.86997299e+00 -4.90201161e+00 -2.11982387e+00 5.14620250e+00 3.85599477e-01] [ 4.77905234e+00 5.60822834e+00 -2.51366200e+00 3.92868297e-01 9.78020228e+00 -1.13087818e+01 3.16279979e+00 1.13970300e+01 -3.00832624e+00 7.11464888e+00 7.74605836e+00 3.85414848e+01 -1.51639139e+01 8.03208083e+00 3.98919623e+00 4.28775854e+00 2.19942828e-01 6.49464992e+00 -3.88279448e-01 5.00145983e+00] [-2.84024583e-01 -5.54220561e+00 -5.57375979e+00 -7.76685057e+00 -2.15257595e+00 3.43505670e+00 -7.40515895e+00 -6.76609861e+00 -6.39586589e+00 6.28084926e+00 -2.56530298e+00 -1.51639139e+01 5.24315893e+01 9.11994869e+00 8.81272479e+00 -1.07645138e+01 9.22311715e+00 4.80925476e+00 -7.78703277e+00 -1.74649383e+01] [ 4.02039156e+00 7.65880848e+00 -9.24382040e-01 -5.79787825e-02 4.61770466e+00 -9.79699584e+00 -7.79876530e+00 -1.19599885e+01 -1.77976388e+00 -7.55914279e-01 -4.44305995e+00 8.03208083e+00 9.11994869e+00 4.42877662e+01 4.72781344e+00 -3.67309109e-01 1.33069779e+01 -1.05446058e-01 -4.82920243e-01 -6.64857106e+00] [-4.48606331e+00 -1.40590586e+01 -2.80493381e+00 -3.26124398e-01 4.53393960e+00 -5.45762006e+00 -3.18105727e+00 7.62947154e+00 -1.54950297e+00 1.97203669e+00 3.06126133e+00 3.98919623e+00 8.81272479e+00 4.72781344e+00 3.57611098e+01 5.61546633e+00 3.32207791e+00 8.40672249e+00 -1.16700344e+01 -1.67054350e+00] [-4.05665876e+00 -1.12993611e-01 9.87360008e-01 1.24473494e+01 1.10285162e+01 -3.90043374e+00 -5.31267570e+00 7.45228859e+00 -5.85127176e+00 -5.52953685e+00 -2.86997299e+00 4.28775854e+00 -1.07645138e+01 -3.67309109e-01 5.61546633e+00 4.42967719e+01 1.23584564e+00 3.44247513e+00 -8.29948131e-01 1.02245224e+00] [ 8.38049721e-01 3.94754936e+00 8.31549260e+00 3.65298907e+00 2.31756117e+00 6.85191595e+00 3.19434844e+00 -9.74805360e+00 -2.45404178e+00 -9.66117786e+00 -4.90201161e+00 2.19942828e-01 9.22311715e+00 1.33069779e+01 3.32207791e+00 1.23584564e+00 5.26694316e+01 4.18602384e+00 -7.35626297e+00 1.44038988e+01] [-9.08330041e+00 9.17552730e+00 9.79278322e+00 7.53197082e+00 7.76660079e+00 1.75687480e+01 6.32873036e+00 1.30055185e+01 -4.52832830e+00 -4.01599751e+00 -2.11982387e+00 6.49464992e+00 4.80925476e+00 -1.05446058e-01 8.40672249e+00 3.44247513e+00 4.18602384e+00 6.26631646e+01 -6.24949412e+00 -8.10946242e-01] [-1.13688116e+01 -9.62897786e+00 2.10672493e+00 -6.90397368e+00 -9.84301818e+00 -7.14092750e+00 5.97853355e+00 1.26892964e+00 -2.63980713e+00 -4.19404412e+00 5.14620250e+00 -3.88279448e-01 -7.78703277e+00 -4.82920243e-01 -1.16700344e+01 -8.29948131e-01 -7.35626297e+00 -6.24949412e+00 4.58760809e+01 2.53289163e+00] [-2.19620082e+00 -3.02100947e+00 1.05162925e+01 -6.34266659e-01 2.48904445e+00 1.36594168e+01 6.37893491e+00 -3.04468828e+00 1.42129404e+00 -2.13832064e+00 3.85599477e-01 5.00145983e+00 -1.74649383e+01 -6.64857106e+00 -1.67054350e+00 1.02245224e+00 1.44038988e+01 -8.10946242e-01 2.53289163e+00 5.64852106e+01]] A.T*A= [[13.53693553 2.76831502 5.67023715 ... -3.80604181 -7.32768733 6.97258655] [ 2.76831502 9.37041014 1.35891632 ... 2.65567126 -1.64983901 3.55144733] [ 5.67023715 1.35891632 20.31482493 ... -3.89980296 -0.69079531 8.69960118] ... 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8.23011786e+01 7.40129017e+01 6.05882270e+01 4.82281754e+01 3.73496453e+01 2.77483009e+01 1.90869241e+01 1.30161587e+01 7.62329578e+00 2.47546779e+00 -5.44087658e+00 -1.20491354e+01 -1.79636393e+01 -2.07194088e+01 -2.33034694e+01 -2.25780427e+01 -2.22787996e+01 -1.55161043e+01 -8.33031510e+00 -1.27874819e+00 8.04538495e+00] [-1.44596249e+02 -1.43574558e+02 -1.43431840e+02 -1.42157915e+02 -1.41879416e+02 -1.41340707e+02 -1.38114942e+02 -1.35747260e+02 -1.31727906e+02 -1.28091022e+02 -1.25808117e+02 -1.22971308e+02 -1.21506460e+02 -1.19396664e+02 -1.16082277e+02 -1.13011062e+02 -1.09326491e+02 -1.05309292e+02 -1.01430159e+02 -9.53886525e+01 -8.54515898e+01 -7.46740729e+01 -6.42127154e+01 -5.07933252e+01 -3.67592768e+01 -2.54771034e+01 -1.80866180e+01 -5.75057568e+00 8.99049644e+00 2.22834364e+01 3.58121467e+01 4.86571740e+01 6.05339553e+01 7.26995386e+01 8.16690154e+01 9.04121248e+01 1.03296992e+02 1.17061722e+02 1.28227298e+02 1.40437104e+02 1.49943579e+02 1.56503862e+02 1.62897780e+02 1.67344498e+02 1.70635725e+02 1.76803869e+02 1.82784176e+02 1.86896383e+02 1.89561502e+02 1.91733488e+02] [ 2.49545051e+02 2.40554656e+02 2.33282141e+02 2.23252774e+02 2.14160895e+02 2.07077800e+02 2.05017568e+02 1.97886942e+02 1.91797980e+02 1.84716525e+02 1.76197826e+02 1.64372549e+02 1.55447412e+02 1.48807442e+02 1.40547202e+02 1.31790767e+02 1.23566048e+02 1.16045414e+02 1.06367085e+02 9.73403702e+01 8.94295377e+01 8.31926820e+01 7.96028695e+01 7.82521867e+01 7.60947945e+01 7.31574515e+01 7.07955917e+01 7.02429691e+01 7.27265087e+01 7.64290045e+01 7.91301016e+01 8.30208103e+01 8.87292516e+01 9.36339018e+01 1.01346161e+02 1.06688506e+02 1.11506664e+02 1.18573320e+02 1.26102472e+02 1.32937621e+02 1.41704920e+02 1.50006097e+02 1.57975384e+02 1.65706055e+02 1.71503344e+02 1.77011674e+02 1.80264203e+02 1.87642323e+02 1.98630541e+02 2.05609807e+02]] Please input lambda: 2 A*(B-lambda*I)= [[ 1.91691297e+02 1.86884268e+02 1.82620428e+02 1.79078800e+02 1.67851225e+02 1.64768043e+02 1.50698458e+02 1.44429183e+02 1.28794689e+02 1.17610243e+02 1.00211012e+02 8.06001994e+01 6.66768523e+01 5.48443716e+01 4.70376069e+01 3.79855172e+01 3.30423169e+01 2.81073048e+01 2.65376205e+01 1.94391468e+01 1.81448605e+01 1.23082608e+01 6.75082798e+00 -1.34452044e-01 -1.00585845e+00 -3.18323846e+00 1.42720162e+00 -1.65649435e+00 -5.44633536e+00 -1.06433819e+01 -1.42076941e+01 -1.38569614e+01 -1.04716126e+01 -1.47336304e+01 -2.17862228e+01 -2.56356331e+01 -2.62714105e+01 -3.06766957e+01 -2.99290955e+01 -3.40623713e+01 -3.58571254e+01 -2.60895716e+01 -3.37358125e+01 -3.69530648e+01 -3.19838826e+01 -2.76970074e+01 -2.99077695e+01 -2.12156933e+01 -1.54593173e+01 -1.13011622e+01] [ 9.42811600e+01 9.27919573e+01 9.51668920e+01 8.75108800e+01 8.16068252e+01 8.11759754e+01 6.72953866e+01 5.01553311e+01 3.59944338e+01 2.67051337e+01 2.30169950e+01 8.69440056e-01 -6.95038464e+00 -1.78704447e+01 -2.54356437e+01 -3.25036567e+01 -4.33540883e+01 -4.79505460e+01 -5.12814783e+01 -5.23131950e+01 -5.18784438e+01 -6.04033677e+01 -7.04368222e+01 -8.66967764e+01 -9.58264285e+01 -1.03852925e+02 -1.10445450e+02 -1.11083623e+02 -1.07621840e+02 -1.11655329e+02 -1.05270402e+02 -1.16428045e+02 -1.08550516e+02 -1.13690910e+02 -1.11589455e+02 -1.21225338e+02 -1.27925861e+02 -1.39366645e+02 -1.43099062e+02 -1.45270354e+02 -1.45665042e+02 -1.40026108e+02 -1.46254487e+02 -1.44277837e+02 -1.41161334e+02 -1.42379599e+02 -1.33682904e+02 -1.29744737e+02 -1.29747168e+02 -1.21240710e+02] [ 8.06653710e+00 1.16436736e+01 1.37304045e+01 1.44750814e+01 1.60551334e+01 5.22987718e+00 9.64817074e+00 7.63882620e+00 8.60163043e+00 2.68734469e+00 2.91807517e+00 -3.59294825e+00 -3.92161560e+00 -1.26109902e+01 -1.29676833e+01 -7.61379638e+00 -1.50435578e+01 -1.71735188e+01 -1.84961329e+01 -1.10533016e+01 -1.59562760e+01 -1.69501119e+01 -1.52425205e+01 -9.22794842e+00 -3.34656000e+00 -6.99319054e+00 -6.69104841e+00 -1.02543514e+00 3.69680887e+00 8.38384988e+00 1.32451689e+01 1.68218322e+01 1.60327491e+01 2.67551583e+01 3.37897283e+01 4.02553837e+01 3.69110614e+01 4.27176759e+01 4.31045153e+01 3.81144729e+01 3.92778690e+01 4.14965140e+01 4.22090585e+01 5.48892568e+01 5.82259458e+01 6.15026134e+01 6.44975860e+01 7.13968154e+01 7.02275512e+01 6.63153745e+01] [ 1.44333385e+02 1.29021118e+02 1.24195413e+02 1.09037234e+02 9.61598588e+01 8.99450332e+01 7.71816719e+01 6.36498404e+01 5.45200642e+01 4.99390858e+01 5.09212638e+01 4.90879993e+01 5.07963809e+01 4.57366837e+01 4.99739843e+01 5.10410142e+01 4.78265640e+01 4.35929846e+01 4.89893123e+01 5.03014868e+01 4.62335187e+01 5.22969702e+01 5.53777724e+01 5.79591178e+01 5.26208566e+01 5.78362860e+01 5.56705870e+01 5.62449153e+01 5.91388906e+01 6.35056937e+01 6.92735124e+01 6.29970445e+01 6.70500765e+01 7.27389428e+01 8.07713768e+01 7.84212751e+01 8.23863761e+01 8.06368305e+01 8.27850095e+01 8.76524752e+01 9.30771435e+01 9.94191282e+01 1.11666777e+02 1.22059274e+02 1.27417647e+02 1.35432320e+02 1.35984258e+02 1.43644010e+02 1.46235720e+02 1.59911721e+02] [-2.54659848e+02 -2.43171082e+02 -2.26439602e+02 -2.15372384e+02 -2.00760480e+02 -1.93771099e+02 -1.83397763e+02 -1.71375255e+02 -1.65062084e+02 -1.60341301e+02 -1.49496648e+02 -1.43242601e+02 -1.31037299e+02 -1.18502332e+02 -1.15285047e+02 -1.12106721e+02 -1.07469981e+02 -1.10412306e+02 -1.06064007e+02 -1.09767948e+02 -1.18485981e+02 -1.20625560e+02 -1.16906212e+02 -1.20098958e+02 -1.25103876e+02 -1.22033948e+02 -1.28041571e+02 -1.39669675e+02 -1.50495647e+02 -1.55087121e+02 -1.57628717e+02 -1.63465832e+02 -1.75540562e+02 -1.78415793e+02 -1.83574414e+02 -1.90992155e+02 -1.93011137e+02 -1.96705901e+02 -1.98961153e+02 -2.08077833e+02 -2.17124605e+02 -2.16979739e+02 -2.30155057e+02 -2.36793014e+02 -2.42032619e+02 -2.46779643e+02 -2.55198981e+02 -2.66021411e+02 -2.72447112e+02 -2.90380175e+02] [ 2.30708412e+02 2.32338388e+02 2.28933569e+02 2.20217705e+02 2.14632408e+02 2.07676168e+02 2.04756795e+02 1.84962002e+02 1.77157713e+02 1.69661121e+02 1.65389207e+02 1.52388965e+02 1.43741105e+02 1.26956751e+02 1.15631194e+02 9.55611034e+01 8.78682710e+01 7.93617335e+01 6.99572383e+01 5.65602367e+01 4.79864998e+01 4.17853493e+01 3.11133703e+01 1.93440312e+01 1.08261320e+00 -1.87763247e+01 -3.45057503e+01 -6.02524745e+01 -7.80359294e+01 -9.70345090e+01 -1.09427147e+02 -1.32553872e+02 -1.37049362e+02 -1.48716506e+02 -1.66968400e+02 -1.72864452e+02 -1.89624410e+02 -1.99782711e+02 -2.09842293e+02 -2.28553690e+02 -2.33043411e+02 -2.49363583e+02 -2.53014422e+02 -2.57885200e+02 -2.63577984e+02 -2.68206781e+02 -2.76528910e+02 -2.73472958e+02 -2.68900077e+02 -2.63893465e+02] [-3.16538773e+01 -3.49701299e+01 -3.57991790e+01 -3.23452681e+01 -3.28641346e+01 -4.08341230e+01 -3.81107656e+01 -3.29869530e+01 -3.70220410e+01 -3.55266731e+01 -3.06223528e+01 -3.29385855e+01 -2.73752210e+01 -2.29470328e+01 -1.57894990e+01 -1.28755668e+01 -2.28265010e+00 5.06778809e+00 1.03117952e+01 2.90367928e+01 4.36721566e+01 5.53465454e+01 6.05206822e+01 7.38812279e+01 8.67933123e+01 9.51423263e+01 1.03355040e+02 1.17427674e+02 1.22183178e+02 1.35157762e+02 1.45120302e+02 1.52032051e+02 1.56170743e+02 1.65415983e+02 1.72768786e+02 1.84866307e+02 1.91811510e+02 2.03759796e+02 2.09695270e+02 2.13670592e+02 2.29004620e+02 2.29497406e+02 2.32522581e+02 2.41443918e+02 2.46916744e+02 2.52402592e+02 2.52174339e+02 2.68817972e+02 2.78499669e+02 2.89294243e+02] [-4.52085918e+02 -4.38713380e+02 -4.23288427e+02 -4.16682453e+02 -4.10390260e+02 -4.02596194e+02 -3.93767241e+02 -3.89968984e+02 -3.72940495e+02 -3.64915679e+02 -3.54101415e+02 -3.42999315e+02 -3.30979758e+02 -3.15579836e+02 -3.09880098e+02 -2.91760793e+02 -2.81022784e+02 -2.78382509e+02 -2.65950141e+02 -2.51990043e+02 -2.42815313e+02 -2.30083406e+02 -2.23474370e+02 -2.13235011e+02 -1.99861222e+02 -1.91474748e+02 -1.84872721e+02 -1.72354732e+02 -1.67362075e+02 -1.57298912e+02 -1.53721026e+02 -1.47489513e+02 -1.48806548e+02 -1.58275885e+02 -1.59377490e+02 -1.65918742e+02 -1.67360758e+02 -1.79836293e+02 -1.83924638e+02 -1.92578564e+02 -2.01704161e+02 -2.16193402e+02 -2.24512217e+02 -2.40698038e+02 -2.51174080e+02 -2.70962247e+02 -2.85235506e+02 -3.02075187e+02 -3.15377763e+02 -3.22191641e+02] [-1.54205022e+02 -1.54707551e+02 -1.53369387e+02 -1.53631229e+02 -1.54148448e+02 -1.58179437e+02 -1.57816295e+02 -1.56798851e+02 -1.61260270e+02 -1.57529375e+02 -1.57787565e+02 -1.54145442e+02 -1.45040981e+02 -1.40725523e+02 -1.36367060e+02 -1.38163623e+02 -1.29478589e+02 -1.29240294e+02 -1.31434847e+02 -1.32713254e+02 -1.22356605e+02 -1.26238358e+02 -1.20825237e+02 -1.19309324e+02 -1.02713215e+02 -8.95482417e+01 -7.33949400e+01 -5.91620460e+01 -4.73502964e+01 -3.69993158e+01 -2.32677377e+01 -1.02247066e+01 6.72024015e+00 1.92732231e+01 3.67775452e+01 5.12380290e+01 6.37581259e+01 7.41703605e+01 7.84630709e+01 7.97369838e+01 9.33913361e+01 1.01956762e+02 1.09443571e+02 1.23779534e+02 1.27079486e+02 1.25957239e+02 1.31360311e+02 1.31662296e+02 1.32746419e+02 1.37567694e+02] [-6.07431681e+01 -6.01209138e+01 -6.06526978e+01 -5.07746541e+01 -5.11693937e+01 -4.37071045e+01 -3.64201269e+01 -2.45988812e+01 -2.33454445e+01 -2.39178536e+01 -1.99900848e+01 -2.07790961e+01 -2.88083487e+01 -2.17884442e+01 -2.51804842e+01 -3.02287562e+01 -3.23265925e+01 -3.92021657e+01 -4.46848210e+01 -4.38607853e+01 -4.79465340e+01 -4.65640757e+01 -5.41744242e+01 -5.68108469e+01 -6.19168577e+01 -5.90004806e+01 -5.46695724e+01 -6.05378317e+01 -6.68400848e+01 -6.82048908e+01 -7.10646119e+01 -7.20217528e+01 -6.92963887e+01 -6.39652330e+01 -6.38362755e+01 -6.35058707e+01 -6.58660676e+01 -7.19648892e+01 -7.81642497e+01 -7.73669955e+01 -9.00125093e+01 -8.54762759e+01 -9.25890881e+01 -1.08874009e+02 -1.17964870e+02 -1.16899860e+02 -1.20834603e+02 -1.22501247e+02 -1.24128920e+02 -1.31897942e+02] [ 7.32351069e+01 6.73708918e+01 6.76743257e+01 6.76539010e+01 6.56022934e+01 6.03133747e+01 6.21102075e+01 6.30019066e+01 6.37599856e+01 5.35301403e+01 4.37103807e+01 4.30845283e+01 3.32929173e+01 3.56670524e+01 2.82283295e+01 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7.73291955e+00 7.77560149e+00 9.19565232e+00 1.42900110e+01 1.10905661e+01 1.96006508e+01 1.92447034e+01 2.20087224e+01 2.06493208e+01 1.69683690e+01 1.81207697e+01 1.70509875e+01 1.56874841e+01 2.08300199e+01 1.78648407e+01 2.24502332e+01 2.87123394e+01 2.98276952e+01 2.81759025e+01 3.17057832e+01 3.46878613e+01 3.92335090e+01 2.71830067e+01 2.75407700e+01 1.70607111e+01 1.62783107e+01 5.74132638e+00 -4.34012070e+00 -7.75051914e+00 -2.16544857e+01 -3.59528352e+01 -4.42215366e+01 -4.93926791e+01 -6.23911251e+01 -7.47721564e+01 -8.13370553e+01 -8.73076868e+01 -9.52822035e+01 -9.97912053e+01 -1.08362388e+02 -1.14289880e+02 -1.23543607e+02 -1.28317420e+02 -1.29805022e+02] [-9.50854891e+01 -9.75178101e+01 -9.08568139e+01 -9.31215284e+01 -9.05706544e+01 -8.71633399e+01 -8.63990794e+01 -8.40059457e+01 -7.85121756e+01 -6.85600462e+01 -5.66463305e+01 -4.94000505e+01 -3.58331555e+01 -2.35359275e+01 -1.71002763e+01 -3.68963814e+00 3.78854968e+00 1.65067681e+01 3.24891723e+01 4.25207188e+01 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4.56884746e+01 5.06740972e+01 5.61365178e+01 5.77351404e+01 7.07291314e+01 7.99876489e+01 8.78985186e+01 9.80290955e+01 1.13928501e+02 1.25577429e+02 1.37492978e+02 1.54466990e+02 1.65288299e+02 1.71803366e+02] [ 4.61305322e+02 4.49767614e+02 4.39101740e+02 4.27049777e+02 4.11377760e+02 3.92201503e+02 3.83456516e+02 3.62646615e+02 3.55473361e+02 3.34134210e+02 3.28422485e+02 3.08166889e+02 2.99944655e+02 2.83546510e+02 2.60359788e+02 2.42877767e+02 2.26506254e+02 2.08247091e+02 1.93932443e+02 1.88647378e+02 1.71379239e+02 1.63216518e+02 1.56383663e+02 1.44536596e+02 1.35499514e+02 1.27338740e+02 1.17655746e+02 1.09035764e+02 8.97178599e+01 8.01493284e+01 7.91492995e+01 5.95236040e+01 4.67466538e+01 3.60724596e+01 2.68083333e+01 1.64963126e+01 1.23382563e+01 7.37826084e+00 5.24398418e+00 -6.74896213e+00 -1.27428903e+01 -2.11223736e+01 -2.08911178e+01 -2.66129567e+01 -2.21518592e+01 -2.87422516e+01 -1.59391983e+01 -8.19609280e+00 -3.55131441e+00 7.81706305e+00] [-1.46579926e+02 -1.42695583e+02 -1.44563047e+02 -1.41162488e+02 -1.42139627e+02 -1.44027764e+02 -1.37256859e+02 -1.37398932e+02 -1.31345437e+02 -1.26737042e+02 -1.26362020e+02 -1.21599347e+02 -1.22151409e+02 -1.20601256e+02 -1.15839105e+02 -1.13624418e+02 -1.09659118e+02 -1.05171225e+02 -1.03592534e+02 -9.92842083e+01 -8.62920441e+01 -7.43579135e+01 -6.71707480e+01 -5.14079834e+01 -3.40074019e+01 -2.15854153e+01 -2.30321749e+01 -8.15560548e+00 1.04386286e+01 2.20476662e+01 3.64958296e+01 4.96254199e+01 6.02451533e+01 7.58956452e+01 8.18953827e+01 8.62703674e+01 1.02417129e+02 1.19660875e+02 1.27183070e+02 1.43140434e+02 1.52889773e+02 1.56670225e+02 1.64844981e+02 1.68499988e+02 1.67758808e+02 1.76991705e+02 1.84652276e+02 1.88343471e+02 1.90054635e+02 1.92943489e+02] [ 2.49246572e+02 2.38836776e+02 2.36038992e+02 2.22315288e+02 2.12152110e+02 2.02054937e+02 2.10087962e+02 1.96845278e+02 1.92790474e+02 1.86153770e+02 1.79504403e+02 1.61472409e+02 1.53162247e+02 1.50427711e+02 1.41043397e+02 1.31259052e+02 1.22861962e+02 1.18203109e+02 1.05715472e+02 9.62244876e+01 8.77555608e+01 8.05456388e+01 7.73637398e+01 7.90588962e+01 7.68747452e+01 7.25819683e+01 6.89863546e+01 6.72068068e+01 7.15075527e+01 7.74304030e+01 7.79404901e+01 8.12030777e+01 8.95330427e+01 9.08262927e+01 1.03716076e+02 1.07212691e+02 1.09258168e+02 1.18110825e+02 1.26796474e+02 1.31005473e+02 1.42171041e+02 1.50337987e+02 1.58214001e+02 1.67639436e+02 1.71792305e+02 1.79267473e+02 1.76138613e+02 1.84032225e+02 2.02639493e+02 2.03300198e+02]] [[ 2.04081633e-02] [ 2.22044605e-16] [-1.45008722e-16] [ 5.12062048e-16] [-3.67053327e-16] [-3.39864191e-17] [-3.54987407e-30] [ 5.80034886e-16] [-8.02079491e-16] [-1.11022302e-16] [ 6.57070770e-16] [-3.14940817e-16] [ 6.81994144e-16] [-7.59030027e-16] [ 5.70971841e-16] [-8.02079491e-16] [ 1.88058186e-16] [ 3.73992220e-16] [-3.53458759e-16] [ 2.67359830e-16] [-2.26576127e-18] [-1.67666334e-16] [ 2.94548966e-16] [-2.22044605e-16] [ 9.06304510e-18] [ 2.94548966e-17] [-5.55111512e-17] [-7.93016446e-18] [ 1.35945676e-16] [-1.01959257e-16] [ 1.01959257e-16] [-2.12981560e-16] [ 3.98773984e-16] [-5.89097931e-16] [ 4.24830239e-16] [-1.06490780e-16] [ 1.69932096e-17] [-9.40290929e-17] [ 2.28275448e-16] [-1.78995141e-16] [ 1.35945676e-17] [-8.94975704e-17] [ 1.23767210e-16] [ 6.93889390e-17] [-1.16403485e-16] [ 3.10126074e-17] [-1.65683793e-17] [ 4.81474271e-18] [-6.93889390e-18] [ 2.04081633e-02]] The Frobenius norm of A: 31.06805061446402 The infinity norm of B: 1225.0 The largest and smallest singular values of B: 49 0 Before: 3.9506172839506174e-07 After: 0.01792316049382716 After 43 times of iterations, [[ 0.10919909] [ 0.27309663] [ 0.12245504] [ 0.11803031] [ 0.16796074] [-0.2292228 ] [ 0.28540725] [ 0.19348954] [-0.11351762] [ 0.22428982] [ 0.20873818] [ 0.09676903] [ 0.03523509] [-0.6180005 ] [-0.10118833] [-0.11385458] [ 0.27129727] [ 0.09543988] [ 0.24485189] [-0.14056474]] The largest singular value is : 18.253473694650108 n*p: 17.740363498984454 The closest value is : 0.17927543585051764