I'm trying to use the warm start anotation in Minizinc to give a known suboptimal solution to a model.
I started by trying to execute this warm start example from the Minizinc documentation (the only one they provide):
array[1..3] of var 0..10: x;
array[1..3] of var 0.0..10.5: xf;
var bool: b;
array[1..3] of var set of 5..9: xs;
constraint b+sum(x)==1;
constraint b+sum(xf)==2.4;
constraint 5==sum( [ card(xs[i]) | i in index_set(xs) ] );
solve
:: warm_start_array( [ %%% Can be on the upper level
warm_start( x, [<>,8,4] ), %%% Use <> for missing values
warm_start( xf, array1d(-5..-3, [5.6,<>,4.7] ) ),
warm_start( xs, array1d( -3..-2, [ 6..8, 5..7 ] ) )
] )
:: seq_search( [
warm_start_array( [ %%% Now included in seq_search to keep order
warm_start( x, [<>,5,2] ), %%% Repeated warm_starts allowed but not specified
warm_start( xf, array1d(-5..-3, [5.6,<>,4.7] ) ),
warm_start( xs, array1d( -3..-2, [ 6..8, 5..7 ] ) )
] ),
warm_start( [b], [true] ),
int_search(x, first_fail, indomain_min)
] )
minimize x[1] + b + xf[2] + card( xs[1] intersect xs[3] );
The example runs, and it gets the optimal solution. However, the output displays warnings stating all the warm start anotations were ignored.
Warning, ignored search annotation: warm_start_array([warm_start([[xi(1), xi(2)], [i(5), i(2)]]), warm_start([[xf(0), xf(2)], [f(5.6), f(4.7)]]), warm_start([[xs(0), xs(1), xs(2)], [s(), s()]])])
Warning, ignored search annotation: warm_start([[xb(0)], [b(true)]])
Warning, ignored search annotation: warm_start_array([warm_start([[xi(1), xi(2)], [i(8), i(4)]]), warm_start([[xf(0), xf(2)], [f(5.6), f(4.7)]]), warm_start([[xs(0), xs(1), xs(2)], [s(), s()]])])
I didnt modified anything in the example, just copy-pasted it and ran it in the Minizinc IDE with the Geocode default solver. In case it is relevant, I'm using Windows. I have ran other models and used other search anotations without problems.
In the example there is two blocks of warm stars (one after solve and one inside seq_search). I'm not sure if both are necessary. I tried removing one, then the other, but the warnings still happen for all the remaining warm start anotations. Also I dont get why 'b' isnt refered in the fisrt block.
There is a similar example in git https://github.com/google/or-tools/issues/539 but it also produces the warnings.
If someone could point me out to a working example of warm_start it would be great.
Your usage of the warm_start annotations are correct, but warm start annotations are currently not supported in most solvers. At the time of writing I believe the warm start annotations are only supported by the Mixed Integer Programming interfaces (CoinBC, Gurobi, CPlex, XPress, and SCIP). Although we've been working on adding support for the annotation in Gecode and Chuffed, support for this annotation has not been included in any of the released versions.
Related
To solve a 5 parameter model, I need at least 5 data points to get a unique solution. For x and y data below:
import numpy as np
x = np.array([[-0.24155831, 0.37083184, -1.69002708, 1.4578805 , 0.91790011,
0.31648635, -0.15957368],
[-0.37541846, -0.14572825, -2.19695883, 1.01136142, 0.57288752,
0.32080956, -0.82986857],
[ 0.33815532, 3.1123936 , -0.29317028, 3.01493602, 1.64978158,
0.56301755, 1.3958912 ],
[ 0.84486735, 4.74567324, 0.7982888 , 3.56604097, 1.47633894,
1.38743513, 3.0679506 ],
[-0.2752026 , 2.9110031 , 0.19218081, 2.0691105 , 0.49240373,
1.63213241, 2.4235483 ],
[ 0.89942508, 5.09052174, 1.26048572, 3.73477373, 1.4302902 ,
1.91907482, 3.70126468]])
y = np.array([-0.81388378, -1.59719762, -0.08256274, 0.61297275, 0.99359647,
1.11315445])
I used only 6 data to fit a 8 parameter model (7 slopes and 1 intercept).
lr = LinearRegression().fit(x, y)
print(lr.coef_)
array([-0.83916772, -0.57249998, 0.73025938, -0.02065629, 0.47637768,
-0.36962192, 0.99128474])
print(lr.intercept_)
0.2978781587718828
Clearly, it's using some kind of assignment to reduce the degrees of freedom. I tried to look into the source code but couldn't found anything about that. What method do they use to find the parameter of under specified model?
You don't need to reduce the degrees of freedom, it simply finds a solution to the least squares problem min sum_i (dot(beta,x_i)+beta_0-y_i)**2. For example, in the non-sparse case it uses the linalg.lstsq module from scipy. The default solver for this optimization problem is the gelsd LAPACK driver. If
A= np.concatenate((ones_v, X), axis=1)
is the augmented array with ones as its first column, then your solution is given by
x=numpy.linalg.pinv(A.T*A)*A.T*y
Where we use the pseudoinverse precisely because the matrix may not be of full rank. Of course, the solver doesn't actually use this formula but uses singular value Decomposition of A to reduce this formula.
I need to compose a simple rmarkdown file, with text, code and the results of executed code included in a resulting PDF file. I would prefer if the source file is executable and self sifficient, voiding the need for a makefile.
This is the best I have been able to achieve, and it is far from good:
#!/usr/bin/env Rscript
library(knitr)
pandoc('hw_ch4.rmd', format='latex')
# TODO: how to NOT print the above commands to the resulting .pdf?
# TODO: how to avoid putting everyting from here on in ""s?
# TODO: how to avoid mentioning the file name above?
# TODO: how to render special symbols, such as tilde, miu, sigma?
# Unicode character (U+3BC) not set up for use with LaTeX.
# See the inputenc package documentation for explanation.
# nano hw_ch4.rmd && ./hw_ch4.rmd && evince hw_ch4.pdf
"
4E1. In the model definition below, which line is the likelihood?
A: y_i is the likelihood, based on the expectation and deviation.
4M1. For the model definition below, simulate observed heights from the prior (not the posterior).
A:
```{r}
points <- 10
rnorm(points, mean=rnorm(points, 0, 10), sd=runif(points, 0, 10))
```
4M3. Translate the map model formula below into a mathematical model definition.
A:
```{r}
flist <- alist(
y tilda dnorm( mu , sigma ),
miu tilda dnorm( 0 , 10 ),
sigma tilda dunif( 0 , 10 )
)
```
"
Result:
What I eventually came to use is the following header. At first it sounded neat, but later I realized
+ is indeed easy to compile in one step
- this is code duplication
- mixing executable script and presentation data in one file is a security risk.
Code:
#!/usr/bin/env Rscript
#<!---
library(rmarkdown)
argv <- commandArgs(trailingOnly=FALSE)
fname <- sub("--file=", "", argv[grep("--file=", argv)])
render(fname, output_format="pdf_document")
quit(status=0)
#-->
---
title:
author:
date: "compiled on: `r Sys.time()`"
---
The quit() line is supposed to guarantee that the rest of the file is treated as data. The <!--- and --> comments are to render the executable code as comments in the data interpretation. They are, in turn, hidden by the #s from the shell.
Trying to get some of my old code up and running in Pharo. Some method names are different but after some hardship I managed to find equivalents that work.
I am parsing my code and I'd like to check if the receiver or any of the arguments is aSymbol in an effort to match them to supported alternatives. I've managed to do this to selectors, by analysing RBMessageNode s
aNode selector == aSymbol ifTrue: [ aNode selector: replacementSymbol ].
How can this be done to arguments and receivers? Is there a comprehensive guide on RBParser somewhere?
By direct manipulation
Assuming that you are looking for cases like this:
aSymbol message: aSymbol message: aSymbol
For receiver you should do:
(aNode isMessage and: [
aNode receiver isVariable and: [
aNode receiver name = 'aSymbol' ]]) ifTrue: [
"do your job here" ]
Here is another example on how to replace #aSymbol arguments with #newSymbol:
messageNode arguments: (messageNode arguments collect: [ :arg |
(arg isLiteralNode and: [ arg value = #aSymbol ])
ifFalse: [ arg ]
ifTrue: [ | newNode |
newNode := #aNewSymbol asLiteralNode.
arg replaceSourceWith: newNode.
newNode ] ]).
methodClass compile: ast newSource
The replaceSourceWith: makes sure that just a source will be replaced, but for newSource to actually return a new source you also need to swap the nodes themselves, that's why I'm doing a collect on arguments and return the new ones where needed.
You can view help about RBParser in Word Menu > Help > Help Browser > Refactoring Framework.
You can also play around by inspecting
RBParser parseExpression: 'aSymbol message: aSymbol message: aSymbol'
and looking at its contents
By Parse Tree Transformation
You can use pattern code to match and replace certain code. For example to change the symbol argument of a perform: message you can do this:
ast := yourMethod parseTree.
rewriter := RBParseTreeRewriter new
replace: '`receiver perform: #aSymbol'
with: '`receiver perform: #newSelector'.
(rewriter executeTree: ast) ifTrue: [
yourMethod class compile: ast newSource ]
You can learn more about the pattern matching syntax in the help topic Word Menu > Help > Help Browser > Refactoring Framework > Refactoring Engine > RBPatternParser …. I thing that MatchTool from pharo catalog can greatly help you in testing the match expressions (it also has a dedicated help topic about the matching syntax) while RewriteTool can help you to preview how your code will be transformed.
I hope you can help me with a very simple model I'm running right now in Rjags.
The data I have are as follows:
> print(data)
$R
225738 184094 66275 24861 11266
228662 199379 70308 27511 12229
246808 224814 78255 30447 13425
254823 236063 83099 33148 13961
263772 250706 89182 35450 14750
272844 262707 96918 37116 15715
280101 271612 102604 38692 16682
291493 283018 111125 40996 18064
310474 299315 119354 44552 19707
340975 322054 126901 47757 21510
347597 332946 127708 49103 21354
354252 355994 130561 51925 22421
366818 393534 140628 56562 23711
346430 400629 146037 59594 25313
316438 399545 150733 62414 26720
303294 405876 161793 67060 29545
$N
9597000 8843000 9154000 9956000 11329000
9854932 9349814 9532373 10195193 11357751
9908897 9676950 9303113 10263930 11141510
9981879 9916245 9248586 10270193 10903446
10086567 10093723 9307104 10193818 10660101
10242793 10190641 9479080 10041145 10453320
10434789 10222806 9712544 9835154 10411620
10597293 10238784 10014422 9611918 10489448
10731326 10270163 10229259 9559334 10502839
10805148 10339566 10393532 9625879 10437809
10804571 10459413 10466871 9800559 10292169
10696317 10611599 10477448 10030407 10085603
10540942 10860363 10539271 10245334 9850488
10411836 11053751 10569913 10435763 9797028
10336667 11152428 10652017 10613341 9850533
10283624 11172747 10826549 10719741 9981814
$n
[1] 16
$na
[1] 5
$pbeta
[1] 0.70 0.95
and the model is as follows:
cat('model{
## likelihoods ##
for(k in 1:na){ for(w in 1:n){ R[w,k] ~ dbin( theta[w,k], N[w,k] ) }}
for(k in 1:na){ for(w in 1:n){ theta[w,k] <- 0.5*beta[w,k]*0.5 }}
for(k in 1:na){
beta[1,k] ~ dunif(pbeta[1], pbeta[2])
beta.plus[1,k] <- beta[1,k]
for (w in 2:n){
beta.plus[w,k] ~ dunif(beta[(w-1),k], 0.95)
beta[w,k] <- beta.plus[w,k]} } }',
file='model1.bug')
######## initial random values for beta
bbb=bb.plus=matrix(rep(NA, 16*5), byrow=T, ncol=5);
for(k in 1:5){
bbb[1,k]=runif(1, 0.7,0.95);
for (w in 2:16){
bb.plus[w,k] = runif(1, bbb[w-1,k], 0.95);
bbb[w,k]=bb.plus[w,k]} }
## data & initial values
inits1 <- list('beta'= bbb )
jags_mod <- jags.model('model1.bug', data=data, inits=inits1, n.chains=1, n.adapt=1000)
update(jags_mod, n.iter=1000)
posts=coda.samples(model=jags_mod,variable.names=c('beta','theta'), n.iter=niter, thin=1000)
Super easy. This is actually a scaled down model from a more complex one which gives me exactly the same error message I get here.
Whenever I run this model, no problems at all.
You will notice that the priors for parameter beta are written in such a way to be increasing from 0.7 to 0.95.
Now I would like to "shut off" the likelihood for R by commenting out the first line of the model. I'd like to do so, to see how the parameter theta gets estimated in any case (basically I should find theta=beta/4 in this case, but that would be fine with me)
When I do that, I get an "Invalid parent" error for parameter beta, generally in the bottom rows (rows 15 or 16) of the matrix.
Actually it's more sophisticated than this: sometimes I get an error, and sometimes I don't (mostly, I do).
I don' t understand why this happens: shouldn't the values of beta generated independently from the presence/absence of a likelihood?
Sorry if this is a naive question, I really hope you can help me sort it out.
Thanks, best!
Emanuele
After playing around with the model a bit more I think I found the cause of your problem. One necessary aspect of the uniform distribution (i.e., unif(a,b)) is that a<b. When you are making the uniform distribution smaller and smaller within your model you are bringing a closer and closer to b. At times, it does not reach it, but other times a equals b and you get the invalid parent values error. For example, in your model if you include:
example ~ dunif(0.4,0.4)
You will get "Error in node example, Invalid parent values".
So, to solve this I think it will be easier to adjust how you specify your priors instead of assigning them randomly. You could do this with the beta distribution. At the first step, beta(23.48, 4.98) covers most of the range from 0.7 to 0.95, but we could truncate it to make sure it lies between that range. Then, as n increases you can lower 4.98 so that the prior shrinks towards 0.95. The model below will do this. After inspecting the priors, it does turn out that theta does equal beta/4.
data.list <- list( n = 16, na = 5,
B = rev(seq(0.1, 4.98, length.out = 16)))
cat('model{
## likelihoods ##
#for(k in 1:na){ for(w in 1:n){ R[w,k] ~ dbin( theta[w,k], N[w,k] ) }}
for(k in 1:na){ for(w in 1:n){ theta[w,k] <- 0.5*beta[w,k]*0.5 }}
for(k in 1:na){
for(w in 1:n){
beta[w,k] ~ dbeta(23.48, B[w]) T(0.7,0.95)
} } }',
file='model1.bug')
jags_mod <- jags.model('model1.bug', data=data.list,
inits=inits1, n.chains=1, n.adapt=1000)
update(jags_mod, n.iter=1000)
posts=coda.samples(model=jags_mod,
variable.names=c('beta','theta'), n.iter=10000, thin=10)
Looking at some of the output from this model we get
beta[1,1] theta[1,1]
[1,] 0.9448125 0.2362031
[2,] 0.7788794 0.1947198
[3,] 0.9498806 0.2374702
0.9448125/4
[1] 0.2362031
Since I don't really know what you are trying to use the model for I do not know if the beta distribution would suit your needs, but the above method will mimic what you are trying to do.
I wish to generate a lot of --enable-*/--disable-* options by something like:
COMPONENTS([a b c], [yes])
where the second argument is the default value of the automatic enable_* variable. My first attempt was to write an AC_ARG_ENABLE(...) within an m4_foreach_w, but so far, I'm only getting the first component to appear in the ./configure --help output.
If I add hand-written AC_ARG_ENABLEs, they work as usual.
Regardless, the --enable-*/--disable-* options work as they should, just the help text is missing.
Here's the full code to reproduce the problem:
AC_INIT([foo], 1.0)
AM_INIT_AUTOMAKE([foreign])
AC_DEFUN([COMPONENTS],
[
m4_foreach_w([component], [$1], [
AS_ECHO(["Processing [component] component with default enable=$2"])
AC_ARG_ENABLE([component],
[AS_HELP_STRING([--enable-[]component], [component] component)],
,
[enable_[]AS_TR_SH([component])=$2]
)
])
AC_ARG_ENABLE([x],
[AS_HELP_STRING([--enable-[]x], [component x])],
,
[enable_[]AS_TR_SH([x])=$2]
)
AC_ARG_ENABLE([y],
[AS_HELP_STRING([--enable-[]y], [component y])],
,
[enable_[]AS_TR_SH([y])=$2]
)
])
COMPONENTS([a b c], [yes])
for var in a b c x y; do
echo -n "\$enable_$var="
eval echo "\$enable_$var"
done
AC_CONFIG_FILES(Makefile)
AC_OUTPUT
And an empty Makefile.am. To verify that the options work:
$ ./configure --disable-a --disable-b --disable-d --disable-x
configure: WARNING: unrecognized options: --disable-d
...
Processing component a with default enable=yes
Processing component b with default enable=yes
Processing component c with default enable=yes
$enable_a=no
$enable_b=no
$enable_c=yes
$enable_x=no
$enable_y=yes
After I poked around in autoconf sources, I figured out this has to do with the m4_divert_once call in the implementation of AC_ARG_ENABLE:
# AC_ARG_ENABLE(FEATURE, HELP-STRING, [ACTION-IF-TRUE], [ACTION-IF-FALSE])
# ------------------------------------------------------------------------
AC_DEFUN([AC_ARG_ENABLE],
[AC_PROVIDE_IFELSE([AC_PRESERVE_HELP_ORDER],
[],
[m4_divert_once([HELP_ENABLE], [[
Optional Features:
--disable-option-checking ignore unrecognized --enable/--with options
--disable-FEATURE do not include FEATURE (same as --enable-FEATURE=no)
--enable-FEATURE[=ARG] include FEATURE [ARG=yes]]])])dnl
m4_divert_once([HELP_ENABLE], [$2])dnl
_AC_ENABLE_IF([enable], [$1], [$3], [$4])dnl
])# AC_ARG_ENABLE
# m4_divert_once(DIVERSION-NAME, CONTENT)
# ---------------------------------------
# Output CONTENT into DIVERSION-NAME once, if not already there.
# An end of line is appended for free to CONTENT.
m4_define([m4_divert_once],
[m4_expand_once([m4_divert_text([$1], [$2])])])
I'm guessing that the HELP-STRING argument is remembered in it's unexpanded form, so it is added just once for all components. Manually expanding the AC_HELP_STRING does what I want:
AC_DEFUN([COMPONENTS],
[
m4_foreach_w([comp], [$1], [
AS_ECHO(["Processing component 'comp' with default enable=$2"])
AC_ARG_ENABLE([comp],
m4_expand([AS_HELP_STRING([--enable-comp], enable component comp)]),
,
[enable_[]AS_TR_SH([comp])=$2]
)
])
])
COMPONENTS([a b c x y], [yes])
I couldn't find a way to properly quote components so that it appears as a string, after being used as the loop variable in m4_foreach_w, so I just renamed it to spare me the trouble.