Hi list, I am new here, and not that experienced with mathematical methods such as Linear Programming. I am trying to solve a problem (related to audio alignment) for which, on stack exchange, I have been told to use LP. Please check my original question:
http://math.stackexchange.com/questions/276492/stretching-of-a-set-of-numbers-to-align-to-a-reference I have then studied it the whole afternoon, and it opened me a world, this is so useful! But the absolute value in my problem is giving me a big headache and I don't fully understand the suggestion I got. If you have read the formulation of the problem in the link above, here follows the modeling I am trying to plug into gplk: please try to follow my solution. As this is the first time I try gplk I am going to use numbers, then of course my program will use runtime data. I want to find the alignment S from the following points: Q0 = 3 Q1 = 5 Q2 = 8 Q3 = 12 with reference points R0 = 2 R1 = 5 R2 = 7 R3 = 11 where the segments Si-Si+1 can't move more than 50% of the original length 1 <= S1 - S0 <= 3 (original length Q0-Q1 = 2) 1.5 <= S2 - S1 <= 4.5 (original length Q1-Q2 = 3) 2 <= S3 - S2 <= 6 (original length Q2-Q3 = 4) The problem is a minimization problem with min: |r0 - s0| + |r1 - s1| + |r2 - s2| + |r3 - s3| for each one of the absolute values i we need introduce one variable Zi and two contraints Zi >= Ri - Si Zi >= -Ri + Si (this is what I have understood by the answer on SE, and to get it I have also read the page http://lpsolve.sourceforge.net/5.1/absolute.htm : paragraph "minimization and sign is positive or maximization and sign is negative") To create the matrix A I use just my relationships over the segment lengths: since these are inequalities, I introduce for each "i" two new variables called SLi (stretch low) and SHi (stretch high), and so I can remove the >= and <= by adding constraints. for each i from 0 to 2: Lower bound of the length of the segment Si+1 - Si >= Qi - alpha * (Qi+1 - Qi) Si+1 - Si = SLi (Stretch lower) Introduces constraint SLi >= Qi - alpha * (Qi+1 - Qi) Upper bound of the length of the segment Si+1 - Si <= Qi + beta * (Qi+1 - Qi) Si+1 - Si <= SHi Introduces constraint SHi <= Qi + beta * (Qi+1 - Qi) Since all the Q values are known, the constraint on SLi and SHi sems very simple. Now my problem arrives: for what I got, each one of the new variables just introduced creates a row, while each of the original unknowns is a column. S0 S1 S2 S3 Variable -1 1 0 0 0 Sl0 -1 1 0 0 0 Sh0 0 -1 1 0 0 Sl1 0 -1 1 0 0 Sh1 0 0 -1 1 0 Sl2 0 0 -1 1 0 Sh2 At this point I am stuck: I have an objective function made of the Zs introduced before, and I know the constraints on them. But those Zs do not show up in the A matrix, so… stuck, and I don't know if any of the above is correct. Thanks in advance for your precious help. Alessandro _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk
