I'm quite new to Matlab and I was trying to figure out a line in a code I'm trying to review and understand.
data(:,U==0)=[];
To give some context :
The class of the variable data is a double, and inside of it I have an array (matrix) of numbers :
For exemple :
data = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16; 1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16]
U is a double too, given by the standard deviation of the data :
U=std(data);
For the same exemple :
U = [4.7809 4.7809 4.7809 4.7809]
The question I am asking is about the first line of code I shared at the beginning, I think I understood a bit how arrays were working on Matlab, but I can't find any real documentation about what the "U==0" means here.
So what I'm really asking is how this line of code will affect my dataset if my variable "data" contains a lot more data in it?
If you have some piece of documentation to further understand the concepts behind this kind of operations on matrixes and arrays in Matlab I would be really grateful if you would share them with me.
Thank you so much in advance if you have some kind of solution or explanation.
Have a great day !
I'm new to working with files in C...just started this week. I would appreciate your help...
I'm working with files and structures in C. Running the program, I ask for information to fill in several fields.
here is the content of the file:
111 12 2 2022 12 0 13 2 2022 14 0 opolisttt listtt ttt
The correct should be:
111 12 2 2022 12 0 13 2 2022 14 0 opo lis ttt
For sure I'm doing something wrong, I just don't know what... Any help?
Problem solved: as #SergeBallesta wrote, I had to add 1 to all character arrays. I just had troubles when I used the full length of the array, then, no space for the null terminator.
Ok, I'm posting this fearing that it might be closed before anyone ever reads it - I'm quite used to that - but I'll give it a try... even pointing me to the right direction or some existing answer that does contain a specific answer would definitely do...
So, after this brief intro...
I'm currently writting a bytecode interpreter, in C, (stack-based VM) for a programming language I have designed.
If you want to have a look at the supported opcodes, feel free to check them out here: https://github.com/arturo-lang/arturo/blob/master/src/vm/opcodes.h
There is nothing really special about the stack machine. Values are being pushed and popped, and operators and functions work on them, pushing the evaluation result back to the stack. So far so good.
Now, I'm at the point where all the core functionality is in and I'm trying to give it an extra boost by doing further optimizations.
Here's an example (and hopefully a rather illustrative one).
Input:
fibo: $(x){
if x<2 {
return 1
} {
return [fibo x-1] + [fibo x-2]
}
}
i: 0
loop i<34 {
print "fibo(" + i + ") = " + [fibo i]
i: i+1
}
Bytecode produced:
|== Data Segment /======================>
0 : [Func ]= function <5,1>
1 : [Int ]= 34
2 : [String]= fibo(
3 : [String]= ) =
==/ Data Segment =======================|
|== Bytecode Listing /======================>
0 :0 JUMP [Dword] 31
1 :5 LLOAD0
2 :6 IPUSH2
3 :7 CMPLT
4 :8 JMPIFNOT [Dword] 20
5 :13 IPUSH1
6 :14 RET
7 :15 JUMP [Dword] 30
8 :20 LLOAD0
9 :21 IPUSH1
10 :22 SUB
11 :23 GCALL0
12 :24 LLOAD0
13 :25 IPUSH2
14 :26 SUB
15 :27 GCALL0
16 :28 ADD
17 :29 RET
18 :30 RET
19 :31 CPUSH0
20 :32 GSTORE0
21 :33 IPUSH0
22 :34 GSTORE1
23 :35 GLOAD1
24 :36 CPUSH1
25 :37 CMPLT
26 :38 JMPIFNOT [Dword] 61
27 :43 CPUSH2
28 :44 GLOAD1
29 :45 ADD
30 :46 CPUSH3
31 :47 ADD
32 :48 GLOAD1
33 :49 GCALL0
34 :50 ADD
35 :51 DO_PRINT
36 :52 GLOAD1
37 :53 IPUSH1
38 :54 ADD
39 :55 GSTORE1
40 :56 JUMP [Dword] 35
41 :61 END
==/ Bytecode Listing =======================|
For anyone who has worked with compilers, bytecode interpreters or even JVM, the code above should be familiar.
What I want?
Ideas - general or specific ones - about how to further optimize my bytecode.
For examples, every *2 (that is: IPUSH2 followed by a MUL instruction) is converted to: IPUSH1, SHL since it's a faster operation.
What else would you suggest? Is there anywhere a list of such things to optimize? Could you suggest something concrete?
Thanks in advance! :)
The example you give is not particularly good, because the performance gain for an interpreter is very low if it makes a shift instead of a multiplication. The overhead of executing a single byte code instruction at all outnumbers the gain of this particular optimization in a order of several magnitudes.
The highest performance gain for an interpreter is to minimize the number of instructions that need to be performed. For example, accumulate two succeeding additions or subtractions on the same register to a single operation when possible.
To be able to make this kind of optimizations, you should try to identify so-called Basic Blocks (these are blocks where either all or no instructions are executed, i.e. no jumps in or out of the block happens) and optimize the number of instructions in those blocks by substituting several instructions into a single one while maintaining the same code semantics.
If you really mean it, you can also try to write a gcc backend for your language to compile it to bytecode; this way you can benefit from gcc's sophisticated optimization methods on the intermediate code representation (RTL).
What is the preferred approach in J for selectively summing multiple axes of an array?
For instance, suppose that a is the following rank 3 array:
]a =: i. 2 3 4
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19
20 21 22 23
My goal is to define a dyad "sumAxes" to sum over multiple axes of my choosing:
0 1 sumAxes a NB. 0+4+8+12+16+20 ...
60 66 72 78
0 2 sumAxes a NB. 0+1+2+3+12+13+14+15 ...
60 92 124
1 2 sumAxes a NB. 0+1+2+3+4+5+6+7+8+9+10+11 ...
66 210
The way that I am currently trying to implement this verb is to use the dyad |: to first permute the axes of a, and then ravel the items of the necessary rank using ,"n (where n is the number axes I want to sum over) before summing the resulting items:
sumAxes =: dyad : '(+/ # ,"(#x)) x |: y'
This appears to work as I want, but as a beginner in J I am unsure if I am overlooking some aspect of rank or particular verbs that would enable a cleaner definition. More generally I wonder whether permuting axes, ravelling and summing is idiomatic or efficient in this language.
For context, most of my previous experience with array programming is with Python's NumPy library.
NumPy does not have J's concept of rank and instead expects the user to explicitly label the axes of an array to reduce over:
>>> import numpy
>>> a = numpy.arange(2*3*4).reshape(2, 3, 4) # a =: i. 2 3 4
>>> a.sum(axis=(0, 2)) # sum over specified axes
array([ 60, 92, 124])
As a footnote, my current implementation of sumAxes has the disadvantage of working "incorrectly" compared to NumPy when just a single axis is specified (as rank is not interchangeable with "axis").
Motivation
J has incredible facilities for handling arbitrarily-ranked arrays. But there's one facet of the language which is simultaneously almost universally useful as well as justified, but also somewhat antithetical to this dimensionality-agnostic nature.
The major axis (in fact, leading axes in general) are implicitly privileged. This is the concept that underlies, e.g. # being the count of items (i.e. the dimension of the first axis), the understated elegance and generality of +/ without further modification, and a host of other beautiful parts of the language.
But it's also what accounts for the obstacles you're meeting in trying to solve this problem.
Standard approach
So the general approach to solving the problem is just as you have it: transpose or otherwise rearrange the data so the axes that interest you become leading axes. Your approach is classic and unimpeachable. You can use it in good conscience.
Alternative approaches
But, like you, it niggles me a bit that we are forced to jump through such hoops in similar circumstances. One clue that we're kind of working against the grain of the language is the dynamic argument to the conjunction "(#x); usually arguments to conjunctions are fixed, and calculating them at runtime often forces us to use either explicit code (as in your example) or dramatically more complicated code. When the language makes something hard to do, it's usually a sign you're cutting against the grain.
Another is that ravel (,). It's not just that we want to transpose some axes; it's that we want to focus on one specific axis, and then run all the elements trailing it into a flat vector. Though I actually think this reflects more a constraint imposed by how we're framing the problem, rather than one in the notation. More on in the final section of this post.
With that, we might feel justified in our desire to address a non-leading axis directly. And, here and there, J provides primitives that allow us to do exactly that, which might be a hint that the language's designers also felt the need to include certain exceptions to the primacy of leading axes.
Introductory examples
For example, dyadic |. (rotate) has ranks 1 _, i.e. it takes a vector on the left.
This is sometimes surprising to people who have been using it for years, never having passed more than a scalar on the left. That, along with the unbound right rank, is another subtle consequence of J's leading-axis bias: we think of the right argument as a vector of items, and the left argument as a simple, scalar rotation value of that vector.
Thus:
3 |. 1 2 3 4 5 6
4 5 6 1 2 3
and
1 |. 1 2 , 3 4 ,: 5 6
3 4
5 6
1 2
But in this latter case, what if we didn't want to treat the table as a vector of rows, but as a vector of columns?
Of course, the classic approach is to use rank, to explicitly denote the the axis we're interested in (because leaving it implicit always selects the leading axis):
1 |."1 ] 1 2 , 3 4 ,: 5 6
2 1
4 3
6 5
Now, this is perfectly idiomatic, standard, and ubiquitous in J code: J encourages us to think in terms of rank. No one would blink an eye on reading this code.
But, as described at the outset, in another sense it can feel like a cop-out, or manual adjustment. Especially when we want to dynamically choose the rank at runtime. Notationally, we are now no longer addressing the array as a whole, but addressing each row.
And this is where the left rank of |. comes in: it's one of those few primitives which can address non-leading axes directly.
0 1 |. 1 2 , 3 4 ,: 5 6
2 1
4 3
6 5
Look ma, no rank! Of course, we now have to specify a rotation value for each axis independently, but that's not only ok, it's useful, because now that left argument smells much more like something which can be calculated from the input, in true J spirit.
Summing non-leading axes directly
So, now that we know J lets us address non-leading axes in certain cases, we simply have to survey those cases and identify one which seems fit for our purpose here.
The primitive I've found most generally useful for non-leading-axis work is ;. with a boxed left-hand argument. So my instinct is to reach for that first.
Let's start with your examples, slightly modified to see what we're summing.
]a =: i. 2 3 4
sumAxes =: dyad : '(< # ,"(#x)) x |: y'
0 1 sumAxes a
+--------------+--------------+---------------+---------------+
|0 4 8 12 16 20|1 5 9 13 17 21|2 6 10 14 18 22|3 7 11 15 19 23|
+--------------+--------------+---------------+---------------+
0 2 sumAxes a
+-------------------+-------------------+---------------------+
|0 1 2 3 12 13 14 15|4 5 6 7 16 17 18 19|8 9 10 11 20 21 22 23|
+-------------------+-------------------+---------------------+
1 2 sumAxes a
+-------------------------+-----------------------------------+
|0 1 2 3 4 5 6 7 8 9 10 11|12 13 14 15 16 17 18 19 20 21 22 23|
+-------------------------+-----------------------------------+
The relevant part of the definition of for dyads derived from ;.1 and friends is:
The frets in the dyadic cases 1, _1, 2 , and _2 are determined by the 1s in boolean vector x; an empty vector x and non-zero #y indicates the entire of y. If x is the atom 0 or 1 it is treated as (#y)#x. In general, boolean vector >j{x specifies how axis j is to be cut, with an atom treated as (j{$y)#>j{x.
What this means is: if we're just trying to slice an array along its dimensions with no internal segmentation, we can simply use dyad cut with a left argument consisting solely of 1s and a:s. The number of 1s in the vector (ie. the sum) determines the rank of the resulting array.
Thus, to reproduce the examples above:
('';'';1) <#:,;.1 a
+--------------+--------------+---------------+---------------+
|0 4 8 12 16 20|1 5 9 13 17 21|2 6 10 14 18 22|3 7 11 15 19 23|
+--------------+--------------+---------------+---------------+
('';1;'') <#:,;.1 a
+-------------------+-------------------+---------------------+
|0 1 2 3 12 13 14 15|4 5 6 7 16 17 18 19|8 9 10 11 20 21 22 23|
+-------------------+-------------------+---------------------+
(1;'';'') <#:,;.1 a
+-------------------------+-----------------------------------+
|0 1 2 3 4 5 6 7 8 9 10 11|12 13 14 15 16 17 18 19 20 21 22 23|
+-------------------------+-----------------------------------+
Et voila. Also, notice the pattern in the left hand argument? The two aces are exactly at the indices of your original calls to sumAxe. See what I mean by the fact that providing a value for each dimension smelling like a good thing, in the J spirit?
So, to use this approach to provide an analog to sumAxe with the same interface:
sax =: dyad : 'y +/#:,;.1~ (1;a:#~r-1) |.~ - {. x -.~ i. r=.#$y' NB. Explicit
sax =: ] +/#:,;.1~ ( (] (-#{.#] |. 1 ; a: #~ <:#[) (-.~ i.) ) ##$) NB. Tacit
Results elided for brevity, but they're identical to your sumAxe.
Final considerations
There's one more thing I'd like to point out. The interface to your sumAxe call, calqued from Python, names the two axes you'd like "run together". That's definitely one way of looking at it.
Another way of looking at it, which draws upon the J philosophies I've touched on here, is to name the axis you want to sum along. The fact that this is our actual focus is confirmed by the fact that we ravel each "slice", because we do not care about its shape, only its values.
This change in perspective to talk about the thing you're interested in, has the advantage that it is always a single thing, and this singularity permits certain simplifications in our code (again, especially in J, where we usually talk about the [new, i.e. post-transpose] leading axis)¹.
Let's look again at our ones-and-aces vector arguments to ;., to illustrate what I mean:
('';'';1) <#:,;.1 a
('';1;'') <#:,;.1 a
(1;'';'') <#:,;.1 a
Now consider the three parenthesized arguments as a single matrix of three rows. What stands out to you? To me, it's the ones along the anti-diagonal. They are less numerous, and have values; by contrast the aces form the "background" of the matrix (the zeros). The ones are the true content.
Which is in contrast to how our sumAxe interface stands now: it asks us to specify the aces (zeros). How about instead we specify the 1, i.e. the axis that actually interests us?
If we do that, we can rewrite our functions thus:
xas =: dyad : 'y +/#:,;.1~ (-x) |. 1 ; a: #~ _1 + #$y' NB. Explicit
xas =: ] +/#:,;.1~ -#[ |. 1 ; a: #~ <:###$#] NB. Tacit
And instead of calling 0 1 sax a, you'd call 2 xas a, instead of 0 2 sax a, you'd call 1 xas a, etc.
The relative simplicity of these two verbs suggests J agrees with this inversion of focus.
¹ In this code I'm assuming you always want to collapse all axes except 1. This assumption is encoded in the approach I use to generate the ones-and-aces vector, using |..
However, your footnote sumAxes has the disadvantage of working "incorrectly" compared to NumPy when just a single axis is specified suggests sometimes you want to only collapse one axis.
That's perfectly possible and the ;. approach can take arbitrary (orthotopic) slices; we'd only need to alter the method by which we instruct it (generate the 1s-and-aces vector). If you provide a couple examples of generalizations you'd like, I'll update the post here. Probably just a matter of using (<1) x} a: #~ #$y or ((1;'') {~ (e.~ i.###$)) instead of (-x) |. 1 ; a:#~<:#$y.
Can you help me here? I'm a complete newbie and was given this homework using Goldbach Conjecture in C. I tried to research on my own but with no luck finding a similar requirement. I understand how it works but not sure how to code via C Programming or what would be the most efficient way I can do this where I can define a start and finish and have an output like on the example below using C:
#define START 700
#define FINISH 1100
Output will show every even number greater than 2 is the sum of two primes:
700 = 17 + 683
702 = 11 + 691
704 = 3 + 701
:
:
1098 = 5 + 1093
1100 = 3 + 1097
Any inputs or sample code to start this would really help.
Thanks in advance..