Develop Reference

Variable changing value without changing it in the code

I am working on a custom numeric class for big numbers like BigInteger. I have to create this method where it finds the prime factorization of a given number. The problem lies in that method, when I assign the current value of a number and it doesn't find a factorization soon(like after 2 or 3 iterations) the value unexpectedly changes. Here's the code
public ArrayList<String> factors(){
ArrayList<String> pList = new ArrayList<>();
FedNumbers in = this;
FedNumbers d = new FedNumbers("2");
FedNumbers zero = new FedNumbers("0");
FedNumbers squared = d.product(d);
while(d.compareTo(in)<=0){
System.out.println(in);
if(in.divideR(d).compareTo(zero)==0){
pList.add(d.toString());
in=in.divideQ(d);
}
else{
d.inc();
squared=d.product(d);
}
}
pList.add(in.toString());
return pList;
}
divideQ is a method that divides and returns the coefficient and divideR one that returns its residue. The squared variable exists because of the assumption that I can found its factorization before sqrt(n). product multiplies two values and returns its result.
Here's the output for in being 161 at the beginning:
161
161
151
141
141
131
121
121
111
111
111
101
[1]
It never enter the iteration, I tried the division with residue and compareTo together in a tester alone and it worked, cant get why the in value changes suddenly after two iterations with no reason to.
That's the in value or the current value that I'm trying to factorize, same thing happens with many other numbers and every time I check its only the in value changing randomly. When I divide and use divideQ or divideR separate or multiply it always works perfectly. Thanks for the help in advance

I think the source of your problem is here:
FedNumbers in = this;
I may be wrong, but could it be that you think that this copies the current object, i.e., the one for which you call factors(), creating in as a new object?
This is not so. Copying a reference simply establishes another reference to the same object. Throughout factors, this and in refer to the same object.
It should not be too difficult to add a copy constructor to your code.

Exception in thread "main" java.lang.Error: Unresolved compilation problems: The local variable xxx may not have been initialized

I can't understand it.
my error
Exception in thread "main" java.lang.Error: Unresolved compilation problems:
The local variable time may not have been initialized
The local variable time may not have been initialized
at earth.main(earth.java:15)
My coding
public class Earth {
public static void main(String[] args) {
// TODO Auto-generated method stub
int time ;
int distance;
int speed ;
distance = 150000000;
speed = 300000;
distance = speed * time;
System.out.println(+time);
}
}

you have declared int time; but you have not assigned a value to it, so the runtime will have no idea what to do once you try to do speed * time. The compiler detects this and gives you that error.
Try assigning a value to time, like you're doing withspeed.

Interesting, I can see you just started to learn programming, and you are confused about the relation between programming and math.
You expect programming something like math.
In math, you define an equation:
1500 = 3 * time
And you then derive answer time = 500.
Programming does NOT work that way. Programming does what machine does, which literally only:
fetch data from some memory
perform simple operation (for instance math operation + - * / )
store result back to some memory
In programming, an equal sign = is way different from its mathematical meaning.
In programming, = is called assignment, means where to store the calculated result. So when you write distance = speed * time;, it's NOT an math equation. To machine, it means:
fetch values from memory "speed" and memory "time"
perform math multiply on the two values
store the result back to memory "distance"
Obviously it's not what you want to do. And because your "time" didn't contain any value, the Java compiler complain on the first step "fetch value from 'time'".
Computer is stupid, it doesn't solve math problem for you, you have to write down your solution clearly.
What you really want is:
time = distance / speed;
fetch values from distance and speed
perform math divide on the two values
store result back to time
Good luck on your study :)

Try this for example:
int time = 10;
You need to initialize it to some
value before you try using it.
The other two variables you initialized already
but the time variable you didn't initialize.

Rule 1:
Run only 100% compiled code. Resolve all compiler errors before running your code.
Rule 2:
Local variables should be initialize before they are getting used. initialize your time variable with some value.
int time = ? ;

Are 0.0 and 1.0 considered magic numbers?

I know that -1, 0, 1, and 2 are exceptions to the magic number rule. However I was wondering if the same is true for when they are floats. Do I have to initialize a final variable for them or can I just use them directly in my program.
I am using it as a percentage in a class. If the input is less than 0.0 or greater than 1.0 then I want it set the percentage automatically to zero. So if (0.0 <= input && input <= 1.0).
Thank you

Those numbers aren't really exceptions to the magic number rule. The common sense rule (as far as there is "one" rule), when it isn't simplified to the level of dogma, is basically, "Don't use numbers in a context that doesn't make their meaning obvious." It just so happens that these four numbers are very commonly used in obvious contexts. That doesn't mean they're the only numbers where this applies, e.g. if I have:
long kilometersToMeters(int km) { return km * 1000L; }
there is really no point in naming the number: it's obvious from the tiny context that it's a conversion factor. On the other hand, if I do this in some low-level code:
sendCommandToDevice(1);
it's still wrong, because that should be a constant kResetCommand = 1 or something like it.
So whether 0.0 and 1.0 should be replaced by a constant completely depends on the context.

It really depends on the context. The whole point of avoiding magic numbers is to maintain the readability of your code. Use your best judgement, or provide us with some context so that we may use ours.
Magic numbers are [u]nique values with unexplained meaning or multiple occurrences which could (preferably) be replaced with named constants.
http://en.wikipedia.org/wiki/Magic_number_(programming)
Edit: When to document code with variables names vs. when to just use a number is a hotly debated topic. My opinion is that of the author of the Wiki article linked above: if the meaning is not immediately obvious and it occurs multiple times in your code, use a named constant. If it only occurs once, just comment the code.
If you are interested in other people's (strongly biased) opinions, read
What is self-documenting code and can it replace well documented code?

Usually, every rule has exceptions (and this one too). It is a matter of style to use some mnemonic names for these constants.
For example:
int Rows = 2;
int Cols = 2;
Is a pretty valid example where usage of raw values will be misleading.
The meaning of the magic number should be obvious from the context. If it is not - give the thing a name.

Attaching a name for something creates an identity. Given the definitions
const double Moe = 2.0;
const double Joe = 2.0;
...
double Larry = Moe;
double Harry = Moe;
double Garry = Joe;
the use of symbols for Moe and Joe suggests that the default value of Larry and Harry are related to each other in a way that the default value of Garry is not. The decision of whether or not to define a name for a particular constant shouldn't depend upon the value of that constant, but rather whether it will non-coincidentally appear multiple places in the code. If one is communicating with a remote device which requires that a particular byte value be sent to it to trigger a reset, I would consider:
void ResetDevice()
{
// The 0xF9 command is described in the REMOTE_RESET section of the
// Frobnitz 9000 manual
transmitByte(0xF9);
}
... elsewhere
myDevice.ResetDevice();
...
otherDevice.ResetDevice();
to be in many cases superior to
// The 0xF9 command is described in the REMOTE_RESET section of the
// Frobnitz 9000 manual
const int FrobnitzResetCode = 0xF9;
... elsewhere
myDevice.transmitByte(FrobnitzResetCode );
...
otherDevice.transmitByte(FrobnitzResetCode );
The value 0xF9 has no real meaning outside the context of resetting the Frobnitz 9000 device. Unless there is some reason why outside code should prefer to send the necessary value itself rather than calling a ResetDevice method, the constant should have no value to any code outside the method. While one could perhaps use
void ResetDevice()
{
// The 0xF9 command is described in the REMOTE_RESET section of the
// Frobnitz 9000 manual
int FrobnitzResetCode = 0xF9;
transmitByte(FrobnitzResetCode);
}
there's really not much point to defining a name for something which is in such a narrow context.
The only thing "special" about values like 0 and 1 is that used significantly more often than other constants like e.g. 23 in cases where they have no domain-specific identity outside the context where they are used. If one is using a function which requires that the first parameter indicates the number of additional parameters (somewhat common in C) it's better to say:
output_multiple_strings(4, "Bob", Joe, Larry, "Fred"); // There are 4 arguments
...
output_multiple_strings(4, "George", Fred, "James", Lucy); // There are 4 arguments
than
#define NUMBER_OF_STRINGS 4 // There are 4 arguments
output_multiple_strings(NUMBER_OF_STRINGS, "Bob", Joe, Larry, "Fred");
...
output_multiple_strings(NUMBER_OF_STRINGS, "George", Fred, "James", Lucy);
The latter statement implies a stronger connection between the value passed to the first method and the value passed to the second, than exists between the value passed to the first method and anything else in that method call. Among other things, if one of the calls needs to be changed to pass 5 arguments, it would be unclear in the second code sample what should be changed to allow that. By contrast, in the former sample, the constant "4" should be changed to "5".

How to reduce an algorithm into smaller parts so I can scale it?

I have updated this question(found last question not clear, if you want to refer to it check out the reversion history). The current answers so far do not work because I failed to explain my question clearly(sorry, second attempt).
Goal:
Trying to take a set of numbers(pos or neg, thus needs bounds to limit growth of specific variable) and find their linear combinations that can be used to get to a specific sum. For example, to get to a sum of 10 using [2,4,5] we get:
5*2 + 0*4 + 0*5 = 10
3*2 + 1*4 + 0*5 = 10
1*2 + 2*4 + 0*5 = 10
0*2 + 0*4 + 2*5 = 10
How can I create an algo that is scalable for large number of variables and target_sums? I can write the code on my own if an algo is given, but if there's a library avail, I'm fine with any library but prefer to use java.

One idea would be to break out of the loop once you set T[z][i] to true, since you are only basically modifying T[z][i] here, and if it does become true, it won't ever be modified again.
for i = 1 to k
for z = 0 to sum:
for j = z-x_i to 0:
if(T[j][i-1]):
T[z][i]=true;
break;
EDIT2: Additionally, if I am getting it right, T[z][i] depends on the array T[z-x_i..0][i-1]. T[z+1][i] depends on T[z+1-x_i..0][i-1]. So once you know if T[z][i] is true, you only need to check one additional element (T[z+1-x_i][i-1]) to know if T[z+1][i-1] will be true.
Let's say you represent the fact whether T[z][i] was updated by a variable changed. Then, you can simply say that T[z][i] = changed && T[z-1][i]. So you should be done in two loops instead of three. This should make it much faster.
Now, to scale it - Now that T[z,i] depends only on T[z-1,i] and T[z-1-x_i,i-1], so to populate T[z,i], you do not need to wait until the whole (i-1)th column is populated. You can start working on T[z,i] as soon as the required values are populated. I can't implement it without knowing the details, but you can try this approach.

I take it this is something like unbounded knapsack? You can dispense with the loop over c entirely.
for i = 1 to k
for z = 0 to sum
T[z][i] = z >= x_i cand (T[z - x_i][i - 1] or T[z - x_i][i])

Based on the original example data you gave (linear combination of terms) and your answer to my question in the comments section (there are bounds), would a brute force approach not work?
c0x0 + c1x1 + c2x2 +...+ cnxn = SUM
I'm guessing I'm missing something important but here it is anyway:
Brute Force Divide and Conquer:
main controller generates coefficients for say, half of the terms (or however many may make sense)
it then sends each partial set of fixed coefficients to a work queue
a worker picks up a partial set of fixed coefficients and proceeds to brute force its own way through the remaining combinations
it doesn't use much memory at all as it works sequentially on each valid set of coefficients
could be optimized to ignore equivalent combinations and probably many other ways
Pseudocode for Multiprocessing
class Controller
work_queue = Queue
solution_queue = Queue
solution_sets = []
create x number of workers with access to work_queue and solution_queue
#say for 2000 terms:
for partial_set in coefficient_generator(start_term=0, end_term=999):
if worker_available(): #generate just in time
push partial set onto work_queue
while solution_queue:
add any solutions to solution_sets
#there is an efficient way to do this type of polling but I forget
class Worker
while true: #actually stops when a stop work token is received
get partial_set from the work queue
for remaining_set in coefficient_generator(start_term=1000, end_term=1999):
combine the two sets (partial_set.extend(remaining_set))
if is_solution(full_set):
push full_set onto the solution queue

Java: micro-optimizing array manipulation

I am trying to make a Java port of a simple feed-forward neural network.
This obviously involves lots of numeric calculations, so I am trying to optimize my central loop as much as possible. The results should be correct within the limits of the float data type.
My current code looks as follows (error handling & initialization removed):
/**
* Simple implementation of a feedforward neural network. The network supports
* including a bias neuron with a constant output of 1.0 and weighted synapses
* to hidden and output layers.
*
* #author Martin Wiboe
*/
public class FeedForwardNetwork {
private final int outputNeurons; // No of neurons in output layer
private final int inputNeurons; // No of neurons in input layer
private int largestLayerNeurons; // No of neurons in largest layer
private final int numberLayers; // No of layers
private final int[] neuronCounts; // Neuron count in each layer, 0 is input
// layer.
private final float[][][] fWeights; // Weights between neurons.
// fWeight[fromLayer][fromNeuron][toNeuron]
// is the weight from fromNeuron in
// fromLayer to toNeuron in layer
// fromLayer+1.
private float[][] neuronOutput; // Temporary storage of output from previous layer
public float[] compute(float[] input) {
// Copy input values to input layer output
for (int i = 0; i < inputNeurons; i++) {
neuronOutput[0][i] = input[i];
}
// Loop through layers
for (int layer = 1; layer < numberLayers; layer++) {
// Loop over neurons in the layer and determine weighted input sum
for (int neuron = 0; neuron < neuronCounts[layer]; neuron++) {
// Bias neuron is the last neuron in the previous layer
int biasNeuron = neuronCounts[layer - 1];
// Get weighted input from bias neuron - output is always 1.0
float activation = 1.0F * fWeights[layer - 1][biasNeuron][neuron];
// Get weighted inputs from rest of neurons in previous layer
for (int inputNeuron = 0; inputNeuron < biasNeuron; inputNeuron++) {
activation += neuronOutput[layer-1][inputNeuron] * fWeights[layer - 1][inputNeuron][neuron];
}
// Store neuron output for next round of computation
neuronOutput[layer][neuron] = sigmoid(activation);
}
}
// Return output from network = output from last layer
float[] result = new float[outputNeurons];
for (int i = 0; i < outputNeurons; i++)
result[i] = neuronOutput[numberLayers - 1][i];
return result;
}
private final static float sigmoid(final float input) {
return (float) (1.0F / (1.0F + Math.exp(-1.0F * input)));
}
}
I am running the JVM with the -server option, and as of now my code is between 25% and 50% slower than similar C code. What can I do to improve this situation?
Thank you,
Martin Wiboe
Edit #1: After seeing the vast amount of responses, I should probably clarify the numbers in our scenario. During a typical run, the method will be called about 50.000 times with different inputs. A typical network would have numberLayers = 3 layers with 190, 2 and 1 neuron, respectively. The innermost loop will therefore have about 2*191+3=385 iterations (when counting the added bias neuron in layers 0 and 1)
Edit #1: After implementing the various suggestions in this thread, our implementation is practically as fast as the C version (within ~2 %). Thanks for all the help! All of the suggestions have been helpful, but since I can only mark one answer as the correct one, I will give it to #Durandal for both suggesting array optimizations and being the only one to precalculate the for loop header.

Some tips.
in your inner most loop, think about how you are traversing your CPU cache and re-arrange your matrix so you are accessing the outer most array sequentially. This will result in you accessing your cache in order rather than jumping all over the place. A cache hit can be two orders of magniture faster than a cache miss.
e.g restructure fWeights so it is accessed as
activation += neuronOutput[layer-1][inputNeuron] * fWeights[layer - 1][neuron][inputNeuron];
don't perform work inside the loop (every time) which can be done outside the loop (once). Don't perform the [layer -1] lookup every time when you can place this in a local variable. Your IDE should be able to refactor this easily.
multi-dimensional arrays in Java are not as efficient as they are in C. They are actually multiple layers of single dimensional arrays. You can restructure the code so you're only using a single dimensional array.
don't return a new array when you can pass the result array as an argument. (Saves creating a new object on each call).
rather than peforming layer-1 all over the place, why not use layer1 as layer-1 and using layer1+1 instead of layer.

Disregarding the actual math, the array indexing in Java can be a performance hog in itself. Consider that Java has no real multidimensional arrays, but rather implements them as array of arrays. In your innermost loop, you access over multiple indices, some of which are in fact constant in that loop. Part of the array access can be move outside of the loop:
final int[] neuronOutputSlice = neuronOutput[layer - 1];
final int[][] fWeightSlice = fWeights[layer - 1];
for (int inputNeuron = 0; inputNeuron < biasNeuron; inputNeuron++) {
activation += neuronOutputSlice[inputNeuron] * fWeightsSlice[inputNeuron][neuron];
}
It is possible that the server JIT performs a similar code invariant movement, the only way to find out is change and profile it. On the client JIT this should improve performance no matter what.
Another thing you can try is to precalculate the for-loop exit conditions, like this:
for (int neuron = 0; neuron < neuronCounts[layer]; neuron++) { ... }
// transform to precalculated exit condition (move invariant array access outside loop)
for (int neuron = 0, neuronCount = neuronCounts[layer]; neuron < neuronCount; neuron++) { ... }
Again the JIT may already do this for you, so profile if it helps.
Is there a point to multiplying with 1.0F that eludes me here?:
float activation = 1.0F * fWeights[layer - 1][biasNeuron][neuron];
Other things that could potentially improve speed at cost of readability: inline sigmoid() function manually (the JIT has a very tight limit for inlining and the function might be larger).
It can be slightly faster to run a loop backwards (where it doesnt change the outcome of course), since testing the loop index against zero is a little cheaper than checking against a local variable (the innermost loop is a potentical candidate again, but dont expect the output to be 100% identical in all cases, since adding floats a + b + c is potentially not the same as a + c + b).

For a start, don't do this:
// Copy input values to input layer output
for (int i = 0; i < inputNeurons; i++) {
neuronOutput[0][i] = input[i];
}
But this:
System.arraycopy( input, 0, neuronOutput[0], 0, inputNeurons );

First thing I would look into is seeing if Math.exp is slowing you down. See this post on a Math.exp approximation for a native alternative.

Replace the expensive floating point sigmoid transfer function with an integer step transfer function.
The sigmoid transfer function is a model of organic analog synaptic learning, which in turn seems to be a model of a step function.
The historical precedent for this is that Hinton designed the back-prop algorithm directly from the first principles of cognitive science theories about real synapses, which in turn were based on real analog measurements, which turn out to be sigmoid.
But the sigmoid transfer function seems to be an organic model of the digital step function, which of course cannot be directly implemented organically.
Rather than model a model, replace the expensive floating point implementation of the organic sigmoid transfer function with the direct digital implementation of a step function (less than zero = -1, greater than zero = +1).
The brain cannot do this, but backprop can!
This not only linearly and drastically improves performance of a single learning iteration, it also reduces the number of learning iterations required to train the network: supporting evidence that learning is inherently digital.
Also supports the argument that Computer Science is inherently cool.

Purely based upon code inspection, your inner most loop has to compute references to a three-dimensional parameter and its being done a lot. Depending upon your array dimensions could you possibly be having cache issues due to have to jump around memory with each loop iteration. Maybe you could rearrange the dimensions so the inner loop tries to access memory elements that are closer to one another than they are now?
In any case, profile your code before making any changes and see where the real bottleneck is.

I suggest using a fixed point system rather than a floating point system. On almost all processors using int is faster than float. The simplest way to do this is simply shift everything left by a certain amount (4 or 5 are good starting points) and treat the bottom 4 bits as the decimal.
Your innermost loop is doing floating point maths so this may give you quite a boost.

The key to optimization is to first measure where the time is spent. Surround various parts of your algorithm with calls to System.nanoTime():
long start_time = System.nanoTime();
doStuff();
long time_taken = System.nanoTime() - start_time;
I'd guess that while using System.arraycopy() would help a bit, you'll find your real costs in the inner loop.
Depending on what you find, you might consider replacing the float arithmetic with integer arithmetic.