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==========================================
Solving linear systems of equations
==========================================
Real systems:
Square system: Ax=b
============================
A=[[-0.283885 1.55783 -1.26756 2.36508]
[1.36446 0.56497 -0.300385 1.22804]
[0.906001 -0.596145 -1.0746 0.234136]
[1.24942 -1.19732 2.36476 -0.732016]]
b=[-2.10553 -0.923457 -1.89227 -0.664315]
x=[0.567745 2.89152 0.0468522 -2.70159]
Square system: AX=B
============================
A=[[-0.869443 -0.900489 1.44132 0.51065]
[-0.0504762 -0.227649 -1.48058 1.10323]
[0.799682 -1.83729 1.07507 0.910165]
[1.02849 0.0511841 -0.396638 1.12342]]
B=[[1.46072 0.494639]
[-0.269572 0.721932]
[-1.00539 0.246282]
[1.87195 0.672038]]
X=[[-0.288243 -0.198088]
[2.51547 0.22125]
[1.57136 0.0793743]
[2.37036 0.797498]]
Square system (chol): Ax=b
============================
A=[[1.9913 3.6961 -1.14807 -1.17394]
[3.6961 7.64716 -2.29094 -1.23612]
[-1.14807 -2.29094 4.73466 -1.62202]
[-1.17394 -1.23612 -1.62202 4.42265]]
b=[-0.859404 0.075397 -0.172018 -1.20035]
x=[-11.9288 4.92971 -1.42876 -2.58393]
Square system (Chol): AX=B
============================
A=[[5.31846 -3.62451 0.639575 2.35781]
[-3.62451 2.72182 -0.509437 -1.27826]
[0.639575 -0.509437 0.187849 0.342553]
[2.35781 -1.27826 0.342553 1.91344]]
B=[[-0.115989 0.1234]
[-0.49744 -0.421365]
[0.312621 0.419113]
[0.897405 1.27429]]
X=[[-13.745 -10.3588]
[-16.9402 -12.3473]
[-12.7432 -8.06913]
[8.37061 6.62646]]
Overdetermined system: Ax=b
============================
A=[[-0.32882 -0.901661]
[1.36355 -1.76627]
[1.18344 0.480208]
[-0.675009 0.0332149]]
b=[-0.256686 -1.22057 0.878319 -0.5088]
x=[0.2637 0.769654]
Overdetermined system: AX=B
============================
A=[[0.867379 -0.673021]
[0.716969 0.170602]
[-0.417785 -1.21233]
[0.954855 -0.0915031]]
B=[[0.797619 0.750496 1.35716]
[0.914909 -0.330124 0.395377]
[0.496313 -0.532099 -0.234376]
[-1.18677 1.35402 -2.93901]]
X=[[-0.00493739 0.820064 -0.533252]
[-0.445897 -0.00281812 -0.160925]]
Underdetermined system: Ax=b
============================
A=[[-0.609542 -0.942463 0.191133 1.03981]
[-0.245957 -0.255721 0.610152 0.528111]]
b=[-0.613556 -0.407417]
x=[0.146367 0.17172 -0.279479 -0.297248]
Underdetermined system: AX=B
============================
A=[[0.614165 -0.703154 1.84956 -0.905295]
[-0.46485 0.522814 0.911948 -0.661143]]
B=[[0.35102 0.408726 1.18826]
[-0.156875 0.518324 0.506951]]
X=[[0.185859 -0.158099 0.0745981]
[-0.210747 0.178063 -0.0863754]
[0.0571189 0.248651 0.463066]
[0.0187346 -0.189039 -0.248804]]
Complex systems:
Square system: Ax=b
============================
A=[[-0.553286+0.0173776i 0.544018-0.639508i -0.367446+0.689669i -0.303096+0.899195i]
[0.166865+0.139432i -0.0358186+0.726389i 0.826762-0.540905i -0.0308906-0.182278i]
[-0.304968+1.67774i 0.0141512-1.15327i 0.0171929-0.304334i 0.540058-0.207293i]
[0.214558-0.605614i 0.878131-0.401499i 0.475183+0.136609i -0.6724-0.329522i]]
b=[2.25393-0.170705i -0.25516+1.69291i 0.49826-0.550361i 0.338276-0.300265i]
x=[1.46343-0.862356i 1.79686-0.0956254i -0.309463+0.118249i 0.076739-2.36142i]
Square system: AX=B
============================
A=[[0.559865+0.00183951i -0.293208+0.663596i -0.37374+0.405477i 0.158062+0.51012i]
[0.242933+0.543132i 0.89475+0.303812i 0.301014+0.506654i 1.00245-0.229429i]
[-0.612738+0.588127i -1.0207-0.951271i 0.960425+0.975944i 0.0881398-0.58438i]
[1.65792-0.393007i -1.04226-0.386231i 0.335689+0.747608i 0.126475-0.189326i]]
B=[[-0.618709+0.491061i -0.253027-0.541688i]
[1.16609-0.145443i -0.934058+0.686608i]
[0.983717-0.213724i -1.25157-0.584849i]
[-0.731866+0.217072i -1.01874+0.76928i]]
X=[[-0.647035-0.0797186i -0.444017+0.365443i]
[-0.432648+0.234662i -0.390796-0.940388i]
[0.353828+0.766879i -2.21001+0.264831i]
[1.97228+0.188757i -0.392537+2.74235i]]
Square system (chol): Ax=b
============================
A=[[0.642759-0.111856i 1.3799+0.875182i 0.523224-0.163564i -0.545654+0.469629i]
[1.3799+0.875182i 0.255661-0.122812i 1.65199-2.6126i -1.57054+0.633755i]
[0.523224-0.163564i 1.65199-2.6126i -1.56583-1.12734i 0.155171-0.735735i]
[-0.545654+0.469629i -1.57054+0.633755i 0.155171-0.735735i 0.969467+2.25502i]]
b=[-1.18005-1.24755i 0.926539-0.38808i 1.65558-0.23692i 1.54007+0.101457i]
x=[-1.42493-2.6008i 0.105342-0.046747i -1.4517+0.626622i -0.821244-0.105259i]
Square system (Chol): AX=B
============================
A=[[-0.0148067-1.02659i 1.44002+1.05624i -0.391971+0.107885i 0.333963+1.06198i]
[1.44002+1.05624i -1.43101+1.62274i 1.29331+0.372876i -1.12338+0.0113861i]
[-0.391971+0.107885i 1.29331+0.372876i 2.73332+0.4951i 1.14373-0.476184i]
[0.333963+1.06198i -1.12338+0.0113861i 1.14373-0.476184i -1.31052-1.55123i]]
B=[[-0.158393-0.157269i -0.63153-0.612888i]
[0.0125424-0.0270121i 0.460076-0.878953i]
[-0.300359+0.101718i 0.378644-0.988922i]
[0.158826-0.502674i 0.249059-0.589429i]]
X=[[0.389139+0.0892948i -1.01639+0.828168i]
[-0.0375853-0.165545i -1.34917-0.264449i]
[-0.297581-0.00326746i 0.608098+0.173997i]
[0.343503+0.561919i 0.255098-0.318909i]]
Overdetermined system: Ax=b
============================
A=[[0.887644+0.582224i 0.0900309-0.997146i]
[-0.0248339+0.78084i 0.977005+0.114152i]
[0.15159-0.305971i -0.140535+0.87207i]
[-0.415223+0.745347i 0.389236-0.558537i]]
b=[0.276085+0.862114i -1.06655+0.16668i 0.259354-0.144917i 0.117112+0.628333i]
x=[0.0665721+0.196317i -0.59465+0.275673i]
Overdetermined system: AX=B
============================
A=[[-0.659098-1.48735i 0.58196+0.342779i]
[0.0430125-0.665631i 0.461418+0.702588i]
[-0.370575-0.431749i 0.110563+1.34271i]
[-1.12362-1.24675i -0.00076101-0.48476i]]
B=[[1.40989+0.195876i -0.737889-0.424932i 1.11931-0.181617i]
[0.425358+0.748408i -0.269236+0.0084679i 1.26684+1.15784i]
[0.410579-0.438732i -0.051776-0.741508i -0.0620548-0.988024i]
[0.463633+0.247649i -0.261667+1.31094i 0.316112-0.582709i]]
X=[[-0.438722+0.436199i -0.163013-0.328491i -0.0390137+0.650818i]
[-0.0363226-0.179313i -0.684569-0.174871i 0.057899+0.0385157i]]
Underdetermined system: Ax=b
============================
A=[[-0.0698983+0.088161i 0.778473+0.593819i -0.8982-0.0189115i -1.17379+0.928384i]
[-0.195936+0.710242i -0.139549+1.08637i 0.499634+1.05246i -0.0335779+0.71951i]]
b=[0.176255+1.29583i -1.17782-0.117682i]
x=[0.0430714+0.304995i 0.300008+0.787028i -0.457362+0.0316862i 0.209836-0.296065i]
Underdetermined system: AX=B
============================
A=[[-0.733434+0.604719i -0.384603-1.29524i -0.899498-0.59834i -0.271117-0.21665i]
[0.890914+0.570106i -0.583197-0.457921i 0.563629+0.130534i 0.238394+0.0181737i]]
B=[[1.17187-0.961501i -0.0316097+0.348813i 0.294257-0.531736i]
[0.746982+1.05226i -0.0338086-0.340333i 0.714624+0.369524i]]
X=[[0.3885+0.326178i -0.0743608-0.164814i 0.326415+0.038784i]
[-0.451728+0.726351i 0.0349013-0.0602447i -0.125941+0.433723i]
[0.209724+1.11027i -0.0723079-0.245307i 0.355353+0.450711i]
[0.105905+0.42722i -0.0273786-0.0925306i 0.149089+0.172091i]]
|
