I'm looking forward to assign a specific count of persons to a specific shift. For example I got six persons and three different shifts. Now I have to assign exact two persons to every shift. I tried something like this but..
NOTE: this won't work, so please edit as fast as possible to misslead people, I even removed the "." after it so nobody is copying it:
person(a)
person(b)
person(c)
person(d)
person(e)
person(f)
shift("mor")
shift("aft")
shift("nig")
shiftCount(2).
{ assign(P,S) : shift(S)} = 1 :- person(P).
% DO NOT COPY THIS! SEE RIGHT ANSWER DOWN BELOW
:- #count{P : assign(P,"mor")} = K, shiftCount(K).
:- #count{P : assign(P,"aft")} = K, shiftCount(K).
:- #count{P : assign(P,"nig")} = K, shiftCount(K).
#show assign/2.
Is this possible to count the number of assigned shifts, so I can assign exactly as many people as a given number?
The output of the code above (when the "." are inserted) is:
clingo version 5.5.0
Reading from stdin
Solving...
Answer: 1
assign(a,"nig") assign(b,"aft") assign(c,"mor") assign(d,"mor")
assign(e,"mor") assign(f,"mor")
SATISFIABLE
Models : 1+
Calls : 1
Time : 0.021s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)
CPU Time : 0.000s
Here you can defently see, that the morning ("mor") shift is used more than two times, as difined in the shiftCount. What do I need to change to get the wanted result?
Replace your 3 lines constraints with
{assign(P,S): person(P)} == K :- shift(S), shiftCount(K).
or alternatively if you want to use the constraint writing:
:- {assign(P,S): person(P)} != K, shift(S), shiftCount(K).
First line states: For a given shiftCount K and for every shift S: the number of assignments over all people P for this shift S is K.
The constraint reads: it can not be the case for a shiftCount K and a shift S that the number of assignments over all people P to the shift S is not K.
Please do not alter your question / sample code dramatically since this may leads to the case that this answer won't work anymore.
From q for mortals, i'm struggling to understand how to read this, and understand it logically.
1 2 3,/:\:10 20
I understand the result is a cross product when in full form: raze 1 2 3,/:\:10 20.
But reading from left to right, I'm currently lost at understanding what this yields (in my head)
\:10 20
combined with 1 2 3,/: ??
Help in understanding how to read this clearly (in words or clear logic) would be appreciated.
I found myself saying the following in my head whilst I program the syntax in q. q works from right to left.
Internal Monologue -> Join the string on the right onto each of the strings on the left
code -> "ABC",\:"-D"
result -> "A-D"
"B-D"
"C-D"
I think that's an easy way to understand it. 'join' can be replaced with whatever...
Internal Monologue -> Does the string on the right match any of the strings on the left
code -> ("Cat";"Dog";"CAT";"dog")~\:"CAT"
result -> 0010b
Each-right is the same concept and combining them is straightforward also;
Internal Monologue -> Does each of the strings on the right match each of the strings on the left
code -> ("Cat";"Dog";"CAT";"dog")~\:/:("CAT";"Dog")
result -> 0010b
0100b
So in your example 1 2 3,/:\:10 20 - you're saying 'Join each of the elements on the right to each of the elements on the left'
Hope this helps!!
EDIT To add a real world example.... - consider the following table
q)show tab:([] upper syms:10?`2; names:10?("Robert";"John";"Peter";"Jenny"); amount:10?til 10)
syms names amount
--------------------
CF "Peter" 8
BP "Robert" 1
IC "John" 9
IN "John" 5
NM "Peter" 4
OJ "Jenny" 6
BJ "Robert" 6
KH "John" 1
HJ "Peter" 8
LH "John" 5
q)
I you want to get all records where the name is Robert, you can do; select from tab where names like "Robert"
But if you want to get the results where the name is either Robert or John, then it is a perfect scenario to use our each-left and each-right.
Consider the names column - it's a list of strings (a list where each element is a list of chars). What we want to ask is 'does any of the strings in the names column match any of the strings we want to find'... that translates to (namesList)~\:/:(list;of;names;to;find). Here's the steps;
q)(tab`names)~\:/:("Robert";"John")
0100001000b
0011000101b
From that result we want a compiled list of booleans where each element is true of it is true for Robert OR John - for example, if you look at index 1 of both lists, it's 1b for Robert and 0b for John - in our result, the value at index 1 should be 1b. Index 2 should be 1b, index3 should be 1b, index4 should be 0b etc... To do this, we can apply the any function (or max or sum!). The result is then;
q)any(tab`names)~\:/:("Robert";"John")
0111001101b
Putting it all together, we get;
q)select from tab where any names~\:/:("Robert";"John")
syms names amount
--------------------
BP "Robert" 1
IC "John" 9
IN "John" 5
BJ "Robert" 6
KH "John" 1
LH "John" 5
q)
Firstly, q is executed (and hence generally read) right to left. This means that it's interpreting the \: as a modifier to be applied to the previous function, which itself is a simple join modified by the /: adverb. So the way to read this is "Apply join each-right to each of the left-hand arguments."
In this case, you're applying the two adverbs to the join - \:10 20 on its own has no real meaning here.
I find it helpful to also look at the converse case 1 2 3,\:/:10 20, running that code produces a 2x6 matrix, which I'd describe more like "apply join each-left to each of the right hand arguments" ... I hope that makes sense.
An alternative syntax which also might help is ,/:\:[1 2 3;10 20] - this might be useful as it makes it very clear what the function you're applying is, and is equivalent to your in-place notation.
I know this is very commom question. But I havenot still known why in my case as follows. Give me your idea about this issue:
Question: I want to count the number of user who appear in list < 3.
- First I created the "calculated Field"
- Here is my function:
If COUNT([User]) < 3 then [User] END
Finally, I count this Meseasure again to gain the final result.
Here's my example:
User
a
a
a
a
b
b
c
b
The result expected: 1 (only c)
Thanks all
Place your IF statement inside the COUNT().
So I've spent hours trying to work out exactly how this code produces prime numbers.
lazy val ps: Stream[Int] = 2 #:: Stream.from(3).filter(i =>
ps.takeWhile{j => j * j <= i}.forall{ k => i % k > 0});
I've used a number of printlns etc, but nothings making it clearer.
This is what I think the code does:
/**
* [2,3]
*
* takeWhile 2*2 <= 3
* takeWhile 2*2 <= 4 found match
* (4 % [2,3] > 1) return false.
* takeWhile 2*2 <= 5 found match
* (5 % [2,3] > 1) return true
* Add 5 to the list
* takeWhile 2*2 <= 6 found match
* (6 % [2,3,5] > 1) return false
* takeWhile 2*2 <= 7
* (7 % [2,3,5] > 1) return true
* Add 7 to the list
*/
But If I change j*j in the list to be 2*2 which I assumed would work exactly the same, it causes a stackoverflow error.
I'm obviously missing something fundamental here, and could really use someone explaining this to me like I was a five year old.
Any help would be greatly appreciated.
I'm not sure that seeking a procedural/imperative explanation is the best way to gain understanding here. Streams come from functional programming and they're best understood from that perspective. The key aspects of the definition you've given are:
It's lazy. Other than the first element in the stream, nothing is computed until you ask for it. If you never ask for the 5th prime, it will never be computed.
It's recursive. The list of prime numbers is defined in terms of itself.
It's infinite. Streams have the interesting property (because they're lazy) that they can represent a sequence with an infinite number of elements. Stream.from(3) is an example of this: it represents the list [3, 4, 5, ...].
Let's see if we can understand why your definition computes the sequence of prime numbers.
The definition starts out with 2 #:: .... This just says that the first number in the sequence is 2 - simple enough so far.
The next part defines the rest of the prime numbers. We can start with all the counting numbers starting at 3 (Stream.from(3)), but we obviously need to filter a bunch of these numbers out (i.e., all the composites). So let's consider each number i. If i is not a multiple of a lesser prime number, then i is prime. That is, i is prime if, for all primes k less than i, i % k > 0. In Scala, we could express this as
nums.filter(i => ps.takeWhile(k => k < i).forall(k => i % k > 0))
However, it isn't actually necessary to check all lesser prime numbers -- we really only need to check the prime numbers whose square is less than or equal to i (this is a fact from number theory*). So we could instead write
nums.filter(i => ps.takeWhile(k => k * k <= i).forall(k => i % k > 0))
So we've derived your definition.
Now, if you happened to try the first definition (with k < i), you would have found that it didn't work. Why not? It has to do with the fact that this is a recursive definition.
Suppose we're trying to decide what comes after 2 in the sequence. The definition tells us to first determine whether 3 belongs. To do so, we consider the list of primes up to the first one greater than or equal to 3 (takeWhile(k => k < i)). The first prime is 2, which is less than 3 -- so far so good. But we don't yet know the second prime, so we need to compute it. Fine, so we need to first see whether 3 belongs ... BOOM!
* It's pretty easy to see that if a number n is composite then the square of one of its factors must be less than or equal to n. If n is composite, then by definition n == a * b, where 1 < a <= b < n (we can guarantee a <= b just by labeling the two factors appropriately). From a <= b it follows that a^2 <= a * b, so it follows that a^2 <= n.
Your explanations are mostly correct, you made only two mistakes:
takeWhile doesn't include the last checked element:
scala> List(1,2,3).takeWhile(_<2)
res1: List[Int] = List(1)
You assume that ps always contains only a two and a three but because Stream is lazy it is possible to add new elements to it. In fact each time a new prime is found it is added to ps and in the next step takeWhile will consider this new added element. Here, it is important to remember that the tail of a Stream is computed only when it is needed, thus takeWhile can't see it before forall is evaluated to true.
Keep these two things in mind and you should came up with this:
ps = [2]
i = 3
takeWhile
2*2 <= 3 -> false
forall on []
-> true
ps = [2,3]
i = 4
takeWhile
2*2 <= 4 -> true
3*3 <= 4 -> false
forall on [2]
4%2 > 0 -> false
ps = [2,3]
i = 5
takeWhile
2*2 <= 5 -> true
3*3 <= 5 -> false
forall on [2]
5%2 > 0 -> true
ps = [2,3,5]
i = 6
...
While these steps describe the behavior of the code, it is not fully correct because not only adding elements to the Stream is lazy but every operation on it. This means that when you call xs.takeWhile(f) not all values until the point when f is false are computed at once - they are computed when forall wants to see them (because it is the only function here that needs to look at all elements before it definitely can result to true, for false it can abort earlier). Here the computation order when laziness is considered everywhere (example only looking at 9):
ps = [2,3,5,7]
i = 9
takeWhile on 2
2*2 <= 9 -> true
forall on 2
9%2 > 0 -> true
takeWhile on 3
3*3 <= 9 -> true
forall on 3
9%3 > 0 -> false
ps = [2,3,5,7]
i = 10
...
Because forall is aborted when it evaluates to false, takeWhile doesn't calculate the remaining possible elements.
That code is easier (for me, at least) to read with some variables renamed suggestively, as
lazy val ps: Stream[Int] = 2 #:: Stream.from(3).filter(i =>
ps.takeWhile{p => p * p <= i}.forall{ p => i % p > 0});
This reads left-to-right quite naturally, as
primes are 2, and those numbers i from 3 up, that all of the primes p whose square does not exceed the i, do not divide i evenly (i.e. without some non-zero remainder).
In a true recursive fashion, to understand this definition as defining the ever increasing stream of primes, we assume that it is so, and from that assumption we see that no contradiction arises, i.e. the truth of the definition holds.
The only potential problem after that, is the timing of accessing the stream ps as it is being defined. As the first step, imagine we just have another stream of primes provided to us from somewhere, magically. Then, after seeing the truth of the definition, check that the timing of the access is okay, i.e. we never try to access the areas of ps before they are defined; that would make the definition stuck, unproductive.
I remember reading somewhere (don't recall where) something like the following -- a conversation between a student and a wizard,
student: which numbers are prime?
wizard: well, do you know what number is the first prime?
s: yes, it's 2.
w: okay (quickly writes down 2 on a piece of paper). And what about the next one?
s: well, next candidate is 3. we need to check whether it is divided by any prime whose square does not exceed it, but I don't yet know what the primes are!
w: don't worry, I'l give them to you. It's a magic I know; I'm a wizard after all.
s: okay, so what is the first prime number?
w: (glances over the piece of paper) 2.
s: great, so its square is already greater than 3... HEY, you've cheated! .....
Here's a pseudocode1 translation of your code, read partially right-to-left, with some variables again renamed for clarity (using p for "prime"):
ps = 2 : filter (\i-> all (\p->rem i p > 0) (takeWhile (\p->p^2 <= i) ps)) [3..]
which is also
ps = 2 : [i | i <- [3..], and [rem i p > 0 | p <- takeWhile (\p->p^2 <= i) ps]]
which is a bit more visually apparent, using list comprehensions. and checks that all entries in a list of Booleans are True (read | as "for", <- as "drawn from", , as "such that" and (\p-> ...) as "lambda of p").
So you see, ps is a lazy list of 2, and then of numbers i drawn from a stream [3,4,5,...] such that for all p drawn from ps such that p^2 <= i, it is true that i % p > 0. Which is actually an optimal trial division algorithm. :)
There's a subtlety here of course: the list ps is open-ended. We use it as it is being "fleshed-out" (that of course, because it is lazy). When ps are taken from ps, it could potentially be a case that we run past its end, in which case we'd have a non-terminating calculation on our hands (a "black hole"). It just so happens :) (and needs to ⁄ can be proved mathematically) that this is impossible with the above definition. So 2 is put into ps unconditionally, so there's something in it to begin with.
But if we try to "simplify",
bad = 2 : [i | i <- [3..], and [rem i p > 0 | p <- takeWhile (\p->p < i) bad]]
it stops working after producing just one number, 2: when considering 3 as the candidate, takeWhile (\p->p < 3) bad demands the next number in bad after 2, but there aren't yet any more numbers there. It "jumps ahead of itself".
This is "fixed" with
bad = 2 : [i | i <- [3..], and [rem i p > 0 | p <- [2..(i-1)] ]]
but that is a much much slower trial division algorithm, very far from the optimal one.
--
1 (Haskell actually, it's just easier for me that way :) )
I'm looking for a function or solution to the following:
For the chart in SQL Reporting i need to multiply values from a Column A. For summation i would use =SUM(COLUMN_A) for the chart. But what can i use for multiplication - i was not able to find a solution so far?
Currently i am calculating the value of the stacked column as following:
=ROUND(SUM(Fields!Value_Is.Value)/SUM(Fields!StartValue.Value),3)
Instead of SUM i need something to multiply the values.
Something like that:
=ROUND(MULTIPLY(Fields!Value_Is.Value)/MULTIPLY(Fields!StartValue.Value),3)
EDIT #1
Okay tried to get this thing running.
The expression for the chart looks like this:
=Exp(Sum(Log(IIf(Fields!Menge_Ist.Value = 0, 10^-306, Fields!Menge_Ist.Value)))) / Exp(Sum(Log(IIf(Fields!Startmenge.Value = 0, 10^-306, Fields!Startmenge.Value))))
If i calculate my 'needs' manually i have to get the following result:
In my SQL Report i get the following result:
To make it easier, these are the raw values:
and you have the possibility to group the chart by CW, CQ or CY
(The values from the first pictures are aggregated Sum values from the raw values by FertStufe)
EDIT #2
Tried your expression, which results in this:
Just to make it clear:
The values in the column
=Value_IS / Start_Value
in the first picture are multiplied against each other
0,9947 x 1,0000 x 0,59401 = 0,58573
Diffusion Calenderweek 44 Sums
Startvalue: 1900,00 Value Is: 1890,00 == yield:0,99474
Waffer unbestrahlt Calenderweek 44 Sums
Startvalue: 620,00 Value Is: 620,00 == yield 1,0000
Pellet Calenderweek 44 Sums
Startvalue: 271,00 Value Is: 160,00 == yield 0,59041
yield Diffusion x yield Wafer x yield Pellet = needed Value in chart = 0,58730
EDIT #3
The raw values look like this:
The chart ist grouped - like in the image - on these fields
CY (Calendar year), CM (Calendar month), CW (Calendar week)
You can download the data as xls here:
https://www.dropbox.com/s/g0yrzo3330adgem/2013-01-17_data.xls
The expression i use (copy / past from the edit window)
=Exp(Sum(Log(Fields!Menge_Ist.Value / Fields!Startmenge.Value)))
I've exported the whole report result to excel, you can get it here:
https://www.dropbox.com/s/uogdh9ac2onuqh6/2013-01-17_report.xls
it's actually a workaround. But I am pretty sure is the only solution for this infamous problem :D
This is how I did:
Exp(∑(Log(X))), so what you should do is:
Exp(Sum(Log(Fields!YourField.Value)))
Who said math was worth nothing? =D
EDIT:
Corrected the formula.
By the way, it's tested.
Addressing Ian's concern:
Exp(Sum(Log(IIf(Fields!YourField.Value = 0, 10^-306, Fields!YourField.Value))))
The idea is change 0 with a very small number. Just an idea.
EDIT:
Based on your updated question this is what you should do:
Exp(Sum(Log(Fields!Value_IS.Value / Fields!Start_Value.Value)))
I just tested the above code and got the result you hoped for.