i1 : kk = ZZ/101; |
i2 : A = matrix"1,2,3,4;1,3,6,10;19,7,11,13" ** kk o2 = | 1 2 3 4 | | 1 3 6 10 | | 19 7 11 13 | 3 4 o2 : Matrix kk <--- kk |
i3 : A = mutableMatrix A o3 = | 1 2 3 4 | | 1 3 6 10 | | 19 7 11 13 | o3 : MutableMatrix |
i4 : (P,L,U) = LU A o4 = ({0, 1, 2}, | 1 . . |, | 1 2 3 4 |) | 1 1 . | | . 1 3 6 | | 19 -31 1 | | . . 47 22 | o4 : Sequence |
i5 : matrix L * matrix U == matrix A o5 = true |
i6 : kk = RR o6 = RR o6 : Ring |
i7 : A = matrix"1,2,3,4,5,6;1,3,6,12,13,16;19,7,11,47,48,21" ** kk o7 = | 1 2.000000 3.000000 4.000000 5.000000 6.000000 | | 1 3.000000 6.000000 12.000000 13.000000 16.000000 | | 19.000000 7.000000 11.000000 47.000000 48.000000 21.000000 | 3 6 o7 : Matrix RR <--- RR |
i8 : A = mutableMatrix(A, Dense=>true) o8 = | 1 2.000000 3.000000 4.000000 5.000000 6.000000 | | 1 3.000000 6.000000 12.000000 13.000000 16.000000 | | 19.000000 7.000000 11.000000 47.000000 48.000000 21.000000 | o8 : MutableMatrix |
i9 : (P,L,U) = LU A o9 = ({2, 1, 0}, | 1 . . |, | 19.000000 7.000000 11.000000 | 0.052632 1 . | | . 2.631579 5.421053 | 0.052632 0.620000 1 | | . . -0.940000 ------------------------------------------------------------------------ 47.000000 48.000000 21.000000 |) 9.526316 10.473684 14.894737 | -4.380000 -4.020000 -4.340000 | o9 : Sequence |
i10 : Q = mutableZero(kk, numrows A, numrows A) o10 = 0 o10 : MutableMatrix |
i11 : for i from 0 to numrows A - 1 do Q_(i,P_i) = 1.0 |
i12 : matrix Q * matrix L * matrix U == matrix A o12 = true |
i13 : kk = CC o13 = CC o13 : Ring |
i14 : A = mutableZero(kk,1000,900, Dense=>true) o14 = 0 o14 : MutableMatrix |
i15 : for i from 1 to 10000 do A_(random 1000, random 900) = random 1.0 + ii * random 1.0; |
i16 : time (P,L,U) = LU A; -- used 2.40815 seconds |