1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
|
==========================================
Solving linear systems of equations
==========================================
Real systems:
Square system: Ax=b
============================
A=[[0.764873 1.36468 0.251912 -0.129499]
[-1.13073 0.355365 -0.902459 0.28002]
[0.452336 -0.556704 -0.946328 -0.439783]
[-0.451817 1.00977 0.403829 -0.0494359]]
b=[-0.235643 -0.268905 -1.53793 1.67876]
x=[-1.54905 0.193275 1.69682 -1.99214]
Square system: AX=B
============================
A=[[1.02093 0.369076 1.02917 -0.116042]
[1.25461 0.611692 -1.37943 1.18937]
[1.00032 -0.0799272 -0.534532 -0.105928]
[-1.12474 -0.101654 1.51576 0.103149]]
B=[[-0.86184 0.14747]
[-0.420697 -1.17376]
[0.297823 0.114017]
[-0.286478 0.522963]]
X=[[0.0313881 0.224382]
[-1.60349 -1.39614]
[-0.280874 0.419199]
[0.112094 -0.0193503]]
Square system (chol): Ax=b
============================
A=[[0.666387 0.804845 0.480441 -0.478744]
[0.804845 1.84129 -0.0446662 0.407226]
[0.480441 -0.0446662 1.08701 -1.01069]
[-0.478744 0.407226 -1.01069 1.57378]]
b=[1.05107 -0.627135 -1.64426 1.41366]
x=[131.231 -68.3216 -19.6875 45.854]
Square system (Chol): AX=B
============================
A=[[1.20338 -1.4805 1.46096 -1.74008]
[-1.4805 4.02725 -2.78482 0.441944]
[1.46096 -2.78482 4.06821 0.16804]
[-1.74008 0.441944 0.16804 6.42739]]
B=[[-0.205583 0.924263]
[-0.0438112 1.29568]
[-0.612381 -0.298188]
[1.48153 -0.074446]]
X=[[2.79392 9.62892]
[0.150627 2.03561]
[-1.09228 -2.2416]
[1.0051 2.51388]]
Overdetermined system: Ax=b
============================
A=[[-0.132568 0.299621]
[0.271843 -1.29917]
[-0.295757 -0.884113]
[0.558465 -1.33417]]
b=[0.607251 -0.761232 0.793751 -1.06072]
x=[-2.33904 -0.0382135]
Overdetermined system: AX=B
============================
A=[[0.310015 0.178929]
[-0.200339 -0.492694]
[0.142131 -0.3124]
[1.49336 0.235794]]
B=[[-0.764755 1.43945 0.452514]
[0.673211 -0.793485 1.01024]
[0.249099 -0.331153 0.0648304]
[-0.390933 0.77596 -1.42904]]
X=[[-0.122448 0.374918 -0.715873]
[-1.35987 1.77997 -1.03591]]
Underdetermined system: Ax=b
============================
A=[[1.17414 -0.351737 -0.25974 -0.208985]
[-1.83818 -0.890961 1.55045 -0.301503]]
b=[-0.239394 -0.611282]
x=[-0.11157 0.396945 -0.263743 0.178387]
Underdetermined system: AX=B
============================
A=[[-0.412196 -0.95487 -1.07691 -0.415946]
[1.10352 -0.0547612 2.28626 -1.13048]]
B=[[0.378676 0.289082 1.83316]
[-1.53426 1.31029 -0.145683]]
X=[[-0.215085 0.157984 -0.0958426]
[0.0671544 -0.413286 -1.03805]
[-0.432702 0.234639 -0.436917]
[0.26888 -0.510292 -0.79802]]
Complex systems:
Square system: Ax=b
============================
A=[[-0.093321+0.28428i -0.588264+1.18731i -0.17659+1.26968i 0.0145848+0.68688i]
[-0.806121+0.623665i 0.849613-0.857419i 0.438768-0.24119i -0.777352-0.566061i]
[-0.869934-0.703924i 0.0682477-0.995181i 0.000363858-1.35847i -1.63595+0.769185i]
[0.704778+0.0975581i -0.685392-0.413759i -0.00599554-0.239655i 0.738196-0.527364i]]
b=[-1.12676-0.697522i 1.26072-1.13755i -0.0444372-0.480627i -1.55569+0.72902i]
x=[0.599421-0.442476i 2.45107-0.559037i -2.80418+0.323737i -0.787787+0.715033i]
Square system: AX=B
============================
A=[[0.415023+0.38752i 0.152014+0.190999i -0.117702-1.64864i -0.151134+0.76442i]
[0.885893+1.49547i -0.0139722-0.183752i -0.309757+0.322777i -0.737179-0.994019i]
[0.795048-0.675515i 0.474554-0.316045i -0.187205+1.46323i -0.172383+0.61953i]
[-0.579474-0.369294i 0.180024+0.14861i 0.41336-0.0811581i 0.475768-0.141198i]]
B=[[0.159679+0.374208i 0.864439-1.24452i]
[0.837619-1.19847i -1.25025+0.457809i]
[0.595088+0.598712i -0.265076+0.366291i]
[-0.394214+0.917501i -0.420762-0.553852i]]
X=[[-0.324133-0.814008i -0.85555-0.684366i]
[0.699022+2.53139i -1.32323-0.599889i]
[-0.0839363+0.00645343i 0.109773-0.297755i]
[0.145261-0.467575i -0.55961-1.91009i]]
Square system (chol): Ax=b
============================
A=[[1.62944+0.555332i 1.63957-1.07315i 1.21494+0.342534i -0.761262-0.617118i]
[1.63957-1.07315i -0.207272+1.04483i 0.96635+0.443342i -2.43698+0.0999023i]
[1.21494+0.342534i 0.96635+0.443342i 1.11042-1.1402i -0.450344+0.370951i]
[-0.761262-0.617118i -2.43698+0.0999023i -0.450344+0.370951i -0.3612-1.07726i]]
b=[0.937537-2.03659i 0.19452-0.206761i 0.247784+0.825422i 0.153154+1.07945i]
x=[-1.27531+0.908553i 1.61837-0.52723i -0.224481+0.919612i -0.799434+2.28745i]
Square system (Chol): AX=B
============================
A=[[-3.0662-0.954436i -2.75557+1.37065i -0.266927+3.15779i -1.97066+1.86958i]
[-2.75557+1.37065i -1.82767+3.72907i 1.02925+1.35399i 0.692073+1.16706i]
[-0.266927+3.15779i 1.02925+1.35399i 3.2581-1.95395i 2.11046+0.693208i]
[-1.97066+1.86958i 0.692073+1.16706i 2.11046+0.693208i 1.89491+1.57558i]]
B=[[-0.227327+0.0951244i -0.16277-0.685912i]
[0.239203-0.122535i 0.443924+0.124224i]
[-0.753627+0.300013i 0.261094+0.761865i]
[1.85046-0.0196291i 0.578384-0.181877i]]
X=[[-0.546819-0.382327i -1.1951+0.00444406i]
[0.318522+0.432441i 0.463628+0.0439242i]
[-1.0685-0.354589i -0.527186+0.771971i]
[1.01061-0.277068i -0.0631567+0.171764i]]
Overdetermined system: Ax=b
============================
A=[[0.0348912-0.842404i 0.670827+1.02865i]
[0.282421-0.434695i 0.816629+0.306487i]
[0.0141931-0.990653i 0.236073-0.572607i]
[1.13339+1.28962i 1.14966-0.826234i]]
b=[0.24925+1.07171i -0.0219854+0.126539i 0.968325-0.285063i -1.33972+0.652463i]
x=[-0.325411+0.77611i 0.110888+0.220972i]
Overdetermined system: AX=B
============================
A=[[0.0682392+0.294786i -1.15494-0.191964i]
[0.277154+0.401626i -0.00129113+1.18853i]
[-0.192581-0.128696i -0.547807+0.021772i]
[-1.76261-1.16233i -0.877805-0.107337i]]
B=[[-0.0850079-1.11724i -0.06137+0.113727i 0.262203-0.144847i]
[-0.344417+0.983163i -2.18995+0.157849i -1.00492-0.417426i]
[0.605962-0.578442i -0.518596+0.0568115i -0.381524+0.0541465i]
[0.845162+0.50678i -0.368323+1.62214i -0.215193-0.551352i]]
X=[[-0.667677-0.0635872i -0.569895-0.792786i 0.181962-0.0466279i]
[0.449553+0.499784i 0.435347+0.723123i -0.183203+0.492896i]]
Underdetermined system: Ax=b
============================
A=[[0.39806+1.02531i 0.918554+1.3219i 0.0366897-0.444846i -0.630533-0.781426i]
[0.136734+1.19397i 0.502892+0.155139i 0.836414+0.111108i 0.749081+0.270285i]]
b=[-0.361354+1.60678i 0.644921+0.525162i]
x=[0.412428-0.0962262i 0.489975+0.515621i 0.135787-0.0464523i 0.109421-0.394122i]
Underdetermined system: AX=B
============================
A=[[1.09542+0.679409i -0.464532+0.324864i 0.84955+0.90871i -0.525668-0.556375i]
[0.0101851+1.17529i 0.225441+1.35615i -1.28271+0.343133i -0.214564-0.913887i]]
B=[[0.58863-1.15171i 0.292171+0.90123i 0.430405-0.445413i]
[-1.68994+0.912746i 0.2313+0.470384i -1.274-0.509279i]]
X=[[-0.0425619-0.156767i 0.256629+0.134454i -0.070459-0.0681732i]
[-0.158429+1.09168i 0.152653-0.362265i -0.52063+0.527672i]
[0.353559-0.772808i 0.0987215+0.161894i 0.412771-0.182161i]
[0.227353-0.131776i -0.234354-0.00776177i 0.234925-0.00335474i]]
|
