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1 >> umfpack_demo |
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2 |
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3 Enter the printing level for UMFPACK's output statistics: |
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4 0: none, 1: errors only, 2: statistics, 4: print some of outputs |
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5 5: print all output [default is 1]: |
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6 |
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7 -------------------------------------------------------------- |
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8 Factor and solve a small system, Ax=b, using default parameters |
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9 Solving Ax=b via UMFPACK: |
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10 Solving Ax=b via MATLAB: |
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11 Difference between UMFPACK and MATLAB solution: 0 |
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12 |
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13 -------------------------------------------------------------- |
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14 |
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15 Factorizing [L, U, P, Q, R] = umfpack (A) |
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16 |
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17 P * (R\A) * Q - L*U should be zero: |
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18 norm (P*(R\A)*Q - L*U, 1) = 6.80012e-16 (exact) 6.80012e-16 (estimated) |
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19 |
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20 Solution to Ax=b via UMFPACK factorization: |
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21 x = Q * (U \ (L \ (P * (R \ b)))) |
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22 |
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23 UMFPACK flop count: 2354 |
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24 |
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25 Factorizing [L, U, P] = lu (A (:, q)) |
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26 If you are using a version of MATLAB prior to V6.0, then the |
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27 following statement (q = colamd (A)) may fail. Either download |
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28 colamd from http://www.cise.ufl.edu/research/sparse, upgrade to |
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29 MATLAB V6.0 or later, or replace the statement with |
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30 q = colmmd (A) ; |
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31 |
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32 Solution to Ax=b via MATLAB factorization: |
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33 x = U \ (L \ (P * b)) ; x (q) = x ; |
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34 Difference between UMFPACK and MATLAB solution: 7.10543e-15 |
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35 |
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36 MATLAB LU flop count: 3164 |
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37 |
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38 -------------------------------------------------------------- |
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39 Solve A'x=b: |
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40 Solving A'x=b via UMFPACK: |
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41 Solving A'x=b via MATLAB: |
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42 Difference between UMFPACK and MATLAB solution: 2.66454e-15 |
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43 |
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44 -------------------------------------------------------------- |
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45 Compute C = A', and compute the LU factorization of C. |
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46 Factorizing A' can sometimes be better than factorizing A itself |
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47 (less work and memory usage). Solve C'x=b; the solution is the |
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48 same as the solution to Ax=b for the original A. |
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49 |
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50 P * (R\C) * Q - L*U should be zero: |
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51 norm (P*(R\C)*Q - L*U, 1) = 1.94289e-16 (exact) 5.55112e-17 (estimated) |
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52 |
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53 Solution to Ax=b via UMFPACK, using the factors of C: |
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54 x = R \ (P' * (L' \ (U' \ (Q' * b)))) ; |
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55 Solution to Ax=b via MATLAB: |
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56 Difference between UMFPACK and MATLAB solution: 7.10543e-15 |
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57 |
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58 -------------------------------------------------------------- |
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59 |
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60 Solve AX=B, where B is n-by-10, and sparse |
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61 Difference between UMFPACK and MATLAB solution: 6.72949e-14 |
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62 |
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63 -------------------------------------------------------------- |
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64 |
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65 Solve AX=B, where B is n-by-10, and sparse, using umfpack_btf |
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66 Difference between UMFPACK and MATLAB solution: 8.51541e-14 |
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67 |
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68 -------------------------------------------------------------- |
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69 |
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70 Solve A'X=B, where B is n-by-10, and sparse |
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71 Difference between UMFPACK and MATLAB solution: 7.99291e-14 |
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72 |
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73 -------------------------------------------------------------- |
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74 det(A): -4.07453e-05 UMFPACK determinant: -4.07453e-05 |
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75 >> |
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76 >> diary off |
