=================================
Test of LU factorization routines
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Real matrix
X = [[1.45728 1.30289 0.432204 1.28131 1.19487]
 [-1.13848 -0.505866 0.563233 0.00583875 0.284213]
 [1.12252 0.746416 0.917611 -0.0358695 -0.281477]
 [0.937431 -0.697447 -0.403519 -0.453088 1.51511]
 [0.308753 1.02252 0.457302 -1.72459 1.09403]]
L = [[1 0 0 0 0]
 [0.643273 1 0 0 0]
 [0.770284 0.167481 1 0 0]
 [0.211869 -0.486131 0.0492414 1 0]
 [-0.781232 -0.333423 0.963949 -0.527983 1]]
U = [[1.45728 1.30289 0.432204 1.28131 1.19487]
 [0 -1.53556 -0.681544 -1.27732 0.746484]
 [0 0 0.698836 -0.808916 -1.32689]
 [0 0 0 -2.57717 1.2691]
 [0 0 0 0 3.4157]]
p = [0 3 2 4 4]
P = [[1 0 0 0 0]
 [0 0 0 1 0]
 [0 0 1 0 0]
 [0 0 0 0 1]
 [0 1 0 0 0]]
X = P^T * L * U = [[1.45728 1.30289 0.432204 1.28131 1.19487]
 [-1.13848 -0.505866 0.563233 0.00583875 0.284213]
 [1.12252 0.746416 0.917611 -0.0358695 -0.281477]
 [0.937431 -0.697447 -0.403519 -0.453088 1.51511]
 [0.308753 1.02252 0.457302 -1.72459 1.09403]]
Complex matrix
X = [[-1.01415+0.298065i 0.219153-0.139473i -0.138344+1.18493i -0.192308-0.464038i -0.369841-0.242392i]
 [-0.781279+0.220548i 0.191044+0.93052i 0.4894-0.0572022i 1.38394+1.46117i -0.846777-0.175999i]
 [1.15323-0.319662i -0.0200631-0.358544i -1.33716-0.619299i -0.120173+1.04821i -0.292145+0.410116i]
 [0.181756-0.235722i -0.998818-0.958855i -0.214406+0.297753i -0.0550264+0.808222i -1.49255+0.7828i]
 [-0.866433-0.637334i 0.11692-0.622633i 0.555327+0.957725i 0.532925-0.19296i -0.170349+1.34399i]]
L = [[1+0i 0+0i 0+0i 0+0i 0+0i]
 [-0.00626336+0.276667i 1+0i 0+0i 0+0i 0+0i]
 [0.595316-0.78192i -0.451637+0.108356i 1+0i 0+0i 0+0i]
 [0.46362-0.595579i -0.795211-0.425091i 0.149505+0.165003i 1+0i 0+0i]
 [-0.687585+0.874716i 0.615003+0.236628i -0.182117+0.296757i 0.138947-0.0895202i 1+0i]]
U = [[-0.866433-0.637334i 0.11692-0.622633i 0.555327+0.957725i 0.532925-0.19296i -0.170349+1.34399i]
 [0+0i -1.17035-0.995103i 0.054044+0.15011i -0.105074+0.65957i -1.12178+0.838348i]
 [0+0i 0+0i -1.17713+1.11094i -0.334675+0.37681i -1.73512-0.67551i]
 [0+0i 0+0i 0+0i 1.00007+2.34675i -2.66873-0.323459i]
 [0+0i 0+0i 0+0i 0+0i 1.53792+1.43101i]]
p = [4 3 4 3 4]
P = [[0 0 0 0 1]
 [0 0 0 1 0]
 [1 0 0 0 0]
 [0 1 0 0 0]
 [0 0 1 0 0]]
X = P^T * L * U = [[-1.01415+0.298065i 0.219153-0.139473i -0.138344+1.18493i -0.192308-0.464038i -0.369841-0.242392i]
 [-0.781279+0.220548i 0.191044+0.93052i 0.4894-0.0572022i 1.38394+1.46117i -0.846777-0.175999i]
 [1.15323-0.319662i -0.0200631-0.358544i -1.33716-0.619299i -0.120173+1.04821i -0.292145+0.410116i]
 [0.181756-0.235722i -0.998818-0.958855i -0.214406+0.297753i -0.0550264+0.808222i -1.49255+0.7828i]
 [-0.866433-0.637334i 0.11692-0.622633i 0.555327+0.957725i 0.532925-0.19296i -0.170349+1.34399i]]