In our model we need a set of equations
model.y[k] = model.F(model.x[k]) (where k is in a proper Set)
with piecewise function F(x) defined on a fixed set of domain variable (breakpoints), but with unknown, variable (!), values at these breakpoints.
I implemented the case via SOSConstraint(..., sos=2) and it works (I tested by SCIP solver).
Now we want to try other implementations of pw-functions (LOG, BIGM_BIN, DCC, DLOG, etc.) mentioned in Pyomo pyomo.core.base.piecewise.Piecewise code. But it seems that this class requires fixed numerical values for F(x) at all breakpoints. If a function passed by f_rule argument to Piecewise constructor returns Pyomo expression with variable, then I get the following error:
ERROR: evaluating object as numeric value: ...
Can somebody give an advice or an a reference to some example of a "variable" piecewise-function ?
E.g., regarding "LOG" representation (from Vielma etc.) I see the code of _LOGPiecewise function in pyomo/core/base/piecewise.py module. And I do not see any reasons to forbidden to use variables as "y"-values of pw-expression being constructed ...
Updated
I've succeeded to modify pyomo.core.base.piecewise module to use variables as values of pw-function. Frankly speaking, these "modifications" were just commenting of some fragments in piecewise.py...
But, for my problem, I did not get any speed up in comparison with SOSConstraint (for SCIP solver !).
Can anybody give the benefit of experience: what pw-models were faster SOSConstraint or LOG, BIGM_BIN, DCC, DLOG for other problems ?
Related
What the title says. How can I print the solution values of the subproblem variables when using the default implementation of the benders decomposition from scip.
For printing the variables I use the function SCIPprintSol(sub_scip, sol, pFile, false) together with SCIPgetBestSol(sub_scip) to get the best solution. I already tried SCIPprintBestSol(sub_scip, pFile, false) but that function gives no output at all.
Is there any function that can give me the output I want to have or do I use any of the functions not in the right way and therefore get no real output?
Context: I'm using Maxima on a platform that also uses KaTeX. For various reasons related to content management, this means that we are regularly using Maxima functions to generate the necessary KaTeX commands.
I'm currently trying to develop a group of functions that will facilitate generating different sets of strings corresponding to KaTeX commands for various symbols related to vectors.
Problem
I have written the following function makeKatexVector(x), which takes a string, list or list-of-lists and returns the same type of object, with each string wrapped in \vec{} (i.e. makeKatexVector(string) returns \vec{string} and makeKatexVector(["a","b"]) returns ["\vec{a}", "\vec{b}"] etc).
/* Flexible Make KaTeX Vector Version of List Items */
makeKatexVector(x):= block([ placeHolderList : x ],
if stringp(x) /* Special Handling if x is Just a String */
then placeHolderList : concat("\vec{", x, "}")
else if listp(x[1]) /* check to see if it is a list of lists */
then for j:1 thru length(x)
do placeHolderList[j] : makelist(concat("\vec{", k ,"}"), k, x[j] )
else if listp(x) /* check to see if it is just a list */
then placeHolderList : makelist(concat("\vec{", k, "}"), k, x)
else placeHolderList : "makeKatexVector error: not a list-of-lists, a list or a string",
return(placeHolderList));
Although I have my doubts about the efficiency or elegance of the above code, it seems to return the desired expressions; however, I would like to modify this function so that it can distinguish between single- and multi-character strings.
In particular, I'd like multi-character strings like x_1 to be returned as \vec{x}_1 and not \vec{x_1}.
In fact, I'd simply like to modify the above code so that \vec{} is wrapped around the first character of the string, regardless of how many characters there may be.
My Attempt
I was ready to tackle this with brute force (e.g. transcribing each character of a string into a list and then reassembling); however, the real programmer on the project suggested I look into "Regular Expressions". After exploring that endless rabbit hole, I found the command regex_subst; however, I can't find any Maxima documentation for it, and am struggling to reproduce the examples in the related documentation here.
Once I can work out the appropriate regex to use, I intend to implement this in the above code using an if statement, such as:
if slength(x) >1
then {regex command}
else {regular treatment}
If anyone knows of helpful resources on any of these fronts, I'd greatly appreciate any pointers at all.
Looks like you got the regex approach working, that's great. My advice about handling subscripted expressions in TeX, however, is to avoid working with names which contain underscores in Maxima, and instead work with Maxima expressions with indices, e.g. foo[k] instead of foo_k. While writing foo_k is a minor convenience in Maxima, you'll run into problems pretty quickly, and in order to straighten it out you might end up piling one complication on another.
E.g. Maxima doesn't know there's any relation between foo, foo_1, and foo_k -- those have no more in common than foo, abc, and xyz. What if there are 2 indices? foo_j_k will become something like foo_{j_k} by the preceding approach -- what if you want foo_{j, k} instead? (Incidentally the two are foo[j[k]] and foo[j, k] when represented by subscripts.) Another problematic expression is something like foo_bar_baz. Does that mean foo_bar[baz], foo[bar_baz] or foo_bar_baz?
The code for tex(x_y) yielding x_y in TeX is pretty old, so it's unlikely to go away, but over the years I've come to increasing feel like it should be avoided. However, the last time it came up and I proposed disabling that, there were enough people who supported it that we ended up keeping it.
Something that might be helpful, there is a function texput which allows you to specify how a symbol should appear in TeX output. For example:
(%i1) texput (v, "\\vec{v}");
(%o1) "\vec{v}"
(%i2) tex ([v, v[1], v[k], v[j[k]], v[j, k]]);
$$\left[ \vec{v} , \vec{v}_{1} , \vec{v}_{k} , \vec{v}_{j_{k}} ,
\vec{v}_{j,k} \right] $$
(%o2) false
texput can modify various aspects of TeX output; you can take a look at the documentation (see ? texput).
While I didn't expect that I'd work this out on my own, after several hours, I made some progress, so figured I'd share here, in case anyone else may benefit from the time I put in.
to load the regex in wxMaxima, at least on the MacOS version, simply type load("sregex");. I didn't have this loaded, and was trying to work through our custom platform, which cost me several hours.
take note that many of the arguments in the linked documentation by Dorai Sitaram occur in the reverse, or a different order than they do in their corresponding Maxima versions.
not all the "pregexp" functions exist in Maxima;
In addition to this, escaping special characters varied in important ways between wxMaxima, the inline Maxima compiler (running within Ace editor) and the actual rendered version on our platform; in particular, the inline compiler often returned false for expressions that compiled properly in wxMaxima and on the platform. Because I didn't have sregex loaded on wxMaxima from the beginning, I lost a lot of time to this.
Finally, the regex expression that achieved the desired substitution, in my case, was:
regex_subst("\vec{\\1}", "([[:alpha:]])", "v_1");
which returns vec{v}_1 in wxMaxima (N.B. none of my attempts to get wxMaxima to return \vec{v}_1 were successful; escaping the backslash just does not seem to work; fortunately, the usual escaped version \\vec{\\1} does return the desired form).
I have yet to adjust the code for the rest of the function, but I doubt that will be of use to anyone else, and wanted to be sure to post an update here, before anyone else took time to assist me.
Always interested in better methods / practices or any other pointers / feedback.
I have a nested structure with some fields labeled as L1, L2 etc. I try to access a substructure within the structure using the following code.
lfield = lfidcalc(le);
substruct = bmstruct.(lfield);
Since le changes its value in every iteration, lfield also changes its value from L1 to L9.
However, when I try to build this code to generate a C++ executable, I get the following error.
Non-constant expression or empty matrix. This expression must be
constant because its value determines the size or class of some
expression. In this context, the value of the string must be known.
Can anybody please try to help me sort out this problem?
I'm not sure exactly what's causing the error message you're seeing, but in any case MATLAB Coder does not support accessing the fields of a structure using dynamic field names.
Perhaps that is the direct cause of what you're seeing, perhaps not: but in either case you have a problem.
Not all correct matlab code can be converted to C/C++. Especially this kind of (very handy) code. Have you put '%#eml' on the second line of your function? It indicates that you will generate code. From matlab website: " We use the %#eml directive to turn on the MATLAB M-Lint code analyzer and check the function code for errors and recommend corrections."
I noticed that Z3 can do allsmt from some paper. In my project, I have to search for deterministic variables in a SMT formula. By deterministic I mean the variable can only take one int value to make the formula satisfiable. Is there a c++/c API function which can do this task?
The best I can do so far is to call the solver.check() function many times for the negation of each variable I am interested in. Is there a faster way to do this by using the API?
Basically, I want to do allsmt and predicate abstraction/projection.
There is no specialized API for checking if all models of a given variable have to agree on the same value. You can implement more or less efficient algorithms on top of Z3 to solve this question.
Here is a possible algorithm:
Get a model M from Z3.
For the variables you are interested in assert: Not (And([(M.eval(x) == x) for x in Vars]))
Recheck satisfiability. If the new state is unsatisfiable, then the remaining variales in Vars must have the same value. Otherwise, remove variables from Vars that evaluate to a new value different from the old M.eval(x), and repeat (2) until Vars is either empty or the context is unsatisfiable.
We would like to have user defined formulas in our c++ program.
e.g. The value v = x + ( y - (z - 2)) / 2. Later in the program the user would define x,y and z -> the program should return the result of the calculation. Somewhen later the formula may get changed, so the next time the program should parse the formula and add the new values. Any ideas / hints how to do something like this ? So far I just came to the solution to write a parser to calculate these formulas - maybe any ideas about that ?
If it will be used frequently and if it will be extended in the future, I would almost recommend adding either Python or Lua into your code. Lua is a very lightweight scripting language which you can hook into and provide new functions, operators etc. If you want to do more robust and complicated things, use Python instead.
You can represent your formula as a tree of operations and sub-expressions. You may want to define types or constants for Operation types and Variables.
You can then easily enough write a method that recurses through the tree, applying the appropriate operations to whatever values you pass in.
Building your own parser for this should be a straight-forward operation:
) convert the equation from infix to postfix notation (a typical compsci assignment) (I'd use a stack)
) wait to get the values you want
) pop the stack of infix items, dropping the value for the variable in where needed
) display results
Using Spirit (for example) to parse (and the 'semantic actions' it provides to construct an expression tree that you can then manipulate, e.g., evaluate) seems like quite a simple solution. You can find a grammar for arithmetic expressions there for example, if needed... (it's quite simple to come up with your own).
Note: Spirit is very simple to learn, and quite adapted for such tasks.
There's generally two ways of doing it, with three possible implementations:
as you've touched on yourself, a library to evaluate formulas
compiling the formula into code
The second option here is usually done either by compiling something that can be loaded in as a kind of plugin, or it can be compiled into a separate program that is then invoked and produces the necessary output.
For C++ I would guess that a library for evaluation would probably exist somewhere so that's where I would start.
If you want to write your own, search for "formal automata" and/or "finite state machine grammar"
In general what you will do is parse the string, pushing characters on a stack as you go. Then start popping the characters off and perform tasks based on what is popped. It's easier to code if you force equations to reverse-polish notation.
To make your life easier, I think getting this kind of input is best done through a GUI where users are restricted in what they can type in.
If you plan on doing it from the command line (that is the impression I get from your post), then you should probably define a strict set of allowable inputs (e.g. only single letter variables, no whitespace, and only certain mathematical symbols: ()+-*/ etc.).
Then, you will need to:
Read in the input char array
Parse it in order to build up a list of variables and actions
Carry out those actions - in BOMDAS order
With ANTLR you can create a parser/compiler that will interpret the user input, then execute the calculations using the Visitor pattern. A good example is here, but it is in C#. You should be able to adapt it quickly to your needs and remain using C++ as your development platform.