LU factorization of a square QD matrix
[L,U] = lu(A)
square matrix of QD real numbers, of size [n,n].
Upper triangular square matrix of QD real numbers, of size [n,n].
square matrix of QD real numbers, of size [m,n], Lower triangular after some rows permutations.
[L,U]= lu(A)
computes the matrices L
L and
U
such that A = L*U
, with U
Upper triangular, and L
Lower triangular after some rows permutations.
The implementation for matrices of QD numbers is restricted to square matrices.
:
--> A = qdrand(4,4) A = [d1] 0.2113249 0.6653811 0.8782165 0.7263507 0.7560439 0.6283918 0.068374 0.1985144 0.0002211 0.8497452 0.5608486 0.5442573 0.3303271 0.685731 0.6623569 0.2320748 [d2] 10^-17 * 0.9179115 -2.5457833 2.8569193 -0.0895016 -0.5581342 4.4783202 0.079312 1.0642382 0.0007956 -0.7443819 1.1313369 -5.3577353 -1.362032 -2.042491 3.8557987 -0.7230452 [d3] 10^-34 * -3.1771128 5.926026 -28.470856 0.4634389 0.9909281 11.387791 0.278016 0.5853533 -0.0069856 4.883837 2.3716206 -9.5272717 1.8738568 -11.904973 23.61867 6.6879229 [d4] 10^-51 * -5.5450448 -2.4259894 143.85887 -1.9487679 6.3859594 39.266399 -1.5289045 4.2949033 -0.04034 29.550156 -11.818576 -34.428087 -7.5784425 -15.544252 63.266317 -34.142348 --> [L,U] = lu(A) U = [d1] 0.2113249 0.6653811 0.8782165 0.7263507 0. -1.7521009 -3.0735666 -2.4001053 0. 0. -0.9294872 -0.6195676 0. 0. 0. -0.3587091 [d2] 10^-17 * 0.9179115 -2.5457833 2.8569193 -0.0895016 0. 9.1176704 4.0771268 7.7802232 0. 0. 1.9475187 -5.3156318 0. 0. 0. -0.8330074 [d3] 10^-34 * -3.1771128 5.926026 -28.470856 0.4634389 0. 44.225787 -30.388578 -51.514873 0. 0. -15.231586 6.9457524 0. 0. 0. -4.9963616 [d4] 10^-51 * -5.5450448 -2.4259894 143.85887 -1.9487679 0. -173.8784 90.755608 -325.22583 0. 0. 60.278397 32.035422 0. 0. 0. 40.514566 L = [d1] 1. 0. 0. 0. 3.5776379 1. 0. 0. 0.0010464 -0.4845891 1. 0. 1.5631246 0.2022387 0.0955482 1. [d2] 10^-17 * 0. 0. 0. 0. 13.646401 0. 0. 0. 0.0086084 -0.8552402 0. 0. -6.5616244 0.5924347 0.6097856 0. [d3] 10^-34 * 0. 0. 0. 0. 101.23008 0. 0. 0. -0.0090916 -1.1613989 0. 0. 42.858922 0.3631728 2.6062432 0. [d4] 10^-51 * 0. 0. 0. 0. 252.9254 0. 0. 0. 0.0413223 -8.8502451 0. 0. -290.23453 0.7679612 -16.352271 0. --> L*U - A ans = [d1] 10^-65 * 0. 0. 0. 0. 6.5282028 1.4243352 0.0890209 0.6528203 0.0018546 -2.8486703 -0.2373892 0. 1.3056406 1.186946 0. 0. [d2] zeros(4,4) [d3] zeros(4,4) [d4] zeros(4,4)