I have discovered an inconsistency for uint64 when using vectors in Matlab. It seems as an array of uint64 is not exact for all 64 bits. This did not give the output I expected,
p=uint64([0;0]);
p(1)=13286492335502040542
p =
13286492335502041088
0
However
q = uint64(13286492335502040542)
q =
13286492335502040542
does. It is also working with
p(1)=uint64(13286492335502040542)
p =
13286492335502040542
0
Working with unsigned integers one expect a special behaviour and usually also perfect precision. This seems weird and even a bit uncanny. I do not see this problem with smaller numbers. Maybe anyone knows more? I do not expect this to be an unknown problem, so I guess there must be some explanation to it. I would be good to know why this happen and when, to be able to avoid it. As usual this kind of issues is mentioned nowhere in the documentation.
Matlab 2014a, windows 7.
EDIT
It is worth mentioning that I can see the same behaviour when defining arrays directly.
p=uint64([13286492335502040542;13286492335502040543])
p =
13286492335502041088
13286492335502041088
This is the root to why I ask this question. I have hard to see workaround for this case.
While it might be surprising, this is a floating point precision issue. :-)
The thing is, all numeric literals are by default of type double in MATLAB; that's why:
13286492335502040542 == 13286492335502041088
will return true; the floating point representation in double precision of 13286492335502040542 is 13286492335502041088. Since p has the class uint64, all assignments done to it will cast the right-hand-side to its class.
On another hand, the uint64(13286492335502040542) "call" will be optimized by the MATLAB interpreter to avoid the overhead of calling the uint64 function for the double argument, and will convert the literal directly to its unsigned integer representation (which is exact).
On a third hand [sic], the function call optimization doesn't apply to
p = uint64([13286492335502040542;13286492335502040543])
because the argument of uint64 is not a literal, but the result of an expression, i.e. the result of the vertcat operator applied to two double operands. In this case the MATLAB interpreter is not smart enough to figure out that the two function calls should "commute" (concatenation of uint should be the same as uint of concatenation), so it evaluates the concatenation (which gives an array of equal double because FP precision), then converts the two similar double values to uint64.
TLDR: the difference between
p = uint64(13286492335502040542);
and
u = 13286492335502040542; p = uint64(u);
is a side effect of function call optimization.
Matlab, unless told otherwise reads numbers as double, then casts to the relevant datatype. The Matlab double datatype allows for 51 bits for the floating point fraction, giving the possibility to store 52 bit integers without loss of prepossession (mantissa). Notice that 13286492335502041088 is just 13286492335502040543 with the last 12 bits set to zero.
the solution as you said, is to convert the literals directly uint64(13286492335502040543).
p=uint64([13286492335502040542;13286492335502040543]) does not work because it creates a double array and then converts it to uint64
This issue is mentioned in the uint64 documentation, under 'More About', although it doesn't mention that laterals are read as doubles unless otherwise specified.
I agree this seems weird and I don't have an explanation. I do have a workaround:
p=[uint64(13286492335502040542);uint64(13286492335502040543)]
i.e., cast the separate values to uint64s.
Related
The value is absolute integer, not a floating point to be doubted, also, it is not about an overflow since a double value can hold until 2^1024.
fprintf('%f',realmax)
179769313486231570000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
The problem I am facing in nchoosek function that it doesn't produce exact values
fprintf('%f\n',nchoosek(55,24));
2488589544741302.000000
While it is a percentage error of 2 regarding that binomian(n,m)=binomial(n-1,m)+binomial(n-1,m-1) as follows
fprintf('%f',nchoosek(55-1,24)+nchoosek(55-1,24-1))
2488589544741301.000000
Ps: The exact value is 2488589544741300
this demo shows
What is wrong with MATLAB?
Your understanding of the realmax function is wrong. It's the maximum value which can be stored, but with such large numbers you have a floating point precision error far above 1. The first integer which can not be stored in a double value is 2^53+1, try 2^53==2^53+1 for a simple example.
If the symbolic toolbox is available, the easiest to implement solution is using it:
>> nchoosek(sym(55),sym(24))
ans =
2488589544741300
There is a difference between something that looks like an integer (55) and something that's actually an integer (in terms of variable type).
The way you're calculating it, your values are stored as floating point (which is what realmax is pointing you to - the largest positive floating point number - check intmax('int64') for the largest possible integer value), so you can get floating point errors. An absolute difference of 2 in a large value is not that unexpected - the actual percentage error is tiny.
Plus, you're using %f in your format string - e.g. asking it to display as floating point.
For nchoosek specifically, from the docs, the output is returned as a nonnegative scalar value, of the same type as inputs n and k, or, if they are different types, of the non-double type (you can only have different input types if one is a double).
In Matlab, when you type a number directly into a function input, it generally defaults to a float. You have to force it to be an integer.
Try instead:
fprintf('%d\n',nchoosek(int64(55),int64(24)));
Note: %d not %f, converting both inputs to specifically integer. The output of nchoosek here should be of type int64.
I don't have access to MATLAB, but since you're obviously okay working with Octave I'll post my observations based on that.
If you look at the Octave source code using edit nchoosek or here you'll see that the equation for calculating the binomial coefficient is quite simple:
A = round (prod ((v-k+1:v)./(1:k)));
As you can see, there are k divisions, each with the possibility of introducing some small error. The next line attempts to be helpful and warn you of the possibility of loss of precision:
if (A*2*k*eps >= 0.5)
warning ("nchoosek", "nchoosek: possible loss of precision");
So, if I may slightly modify your final question, what is wrong with Octave? I would say nothing is wrong. The authors obviously knew of the possibility of imprecision and included a check to warn users when that possibility arises. So the function is working as intended. If you require greater precision for your application than the built-in function provides, it looks as though you'll need to code (or find) something that calculates the intermediate results with greater precision.
for i=1:30
Name(i,1)=sprintf('String_%i',i);
end
I'm just confused what is not working here, this script seems very straightforward, wnat to build a list of strings with numbering from 1 to 30. getting error
Subscripted assignment dimension mismatch.
Matlab do not really have strings, they have char arrays. As in almost any programming language Matlab cannot define a variable without knowing how much memory to allocate. The java solution would look like this:
String str[] = {"I","am","a","string"};
Similar to the c++ solution:
std::string str[] = {"I","am","another","string"};
The c solution looks different, but is generally the same solution as in c++:
const char* str[] = {"I","am","a","c-type","string"};
However, despite the appearances these are all fundamentally the same in the sense to that they all knows how much data to allocate even though they would not be initiated. In particular you can for example write:
String str[3];
// Initialize element with an any length string.
The reason is that the memory stored in each element is stored by its reference in java and by a pointer in c and c++. So depending on operating system, each element is either 4 (32-bit) or 8 (64-bit) bytes.
However, in Matlab matrices data is stored by value. This makes it impossible to store a N char arrays in a 1xN or Nx1 matrix. Each element in the matrix is only allowed to be of the same size as a char and be of type char. This means that if you work with strings you need to use the data structure cell (as also suggested by Benoit_11) which stores a reference to any Matlab object in each element.
k = 1:30;
Name = cell(length(k),1);
for i=k
Name{i,1}=sprintf('String_%i',i);
end
Hope that the explanation makes sense to you. I assumed that according to your attempt you have at least some programming experience from at least one other language than matlab.
Typically in Matlab colours are represented by three element vectors of RGB intensity values, with precision uint8 (range 0 - 255) or double (range 0 - 1). Matlabs functions such as imshow work with either representation making both easy to use in a program.
It is equally easy however to introduce a bug when assigning colour values from a matrix of one type, to that of another (because the value is converted silently, but not re-scaled to the new range). Having just spent a number of hours finding such a bug, I would like to make sure it is never introduced again.
How do I make Matlab display a warning when type conversion takes place?
Ideally it would only be when the conversion is between double and uint8. It should also be difficult to deactivate (i.e. the option is not reset when loading a workspace, or when matlab crashes).
A possible solution is to define your own uint8 function that casts to uint8 and issues a warning if some value has been truncated.
You should place this function in a folder where it shadows the builtin uint8 funciton. For example, your user folder is a good choice, as it usually appears the first in path.
Or, as noted by Sam Roberts, if you want this function to be called only when converting from double into uint8 (not when converting from any other type into uint8), put it in a folder named #double within your path.
function y = uint8(x)
y = builtin('uint8', x);
if any(x(:)>255) || any(x(:)<0)
warning('MATLAB:castTruncation', 'Values truncated during conversion to uint8')
end
The warning is on by default. You can switch it on or off with the commands warning('on','MATLAB:castTruncation') and warning('off','MATLAB:castTruncation') (thanks to CitizenInsane for the suggestion).
The default type is uint64 but the below apparently requires larger support where you can see that the number 536870915 (100000000000000000000000000011 in binary, 30 bits' length) is not supported by the above bitget command. So
How to get bitget command working with large inputs like the below?
Input
hhhh=sparse([],[],[],2^40+1,1);
hhhh(536870915)=1;
bitget(str2num(dec2bin(find(hhhh)-1)),2,'uint64')
Output
Error using bitget
Double inputs must have integer values in the range of ASSUMEDTYPE.
You pass the output of dec2bin(find(hhhh)-1) to str2num. This directly converts the string of ones and zeros into a double: 9.999999999999999e+28. I'm guessing that's not what you want.
If you're just trying to get the second bit of 536870915, why not use:
bitget(find(hhhh)-1,2,'uint64')
On the other hand, I think that you could also use this (probably slower, but maybe it'll work with the rest of your code if you're already converting to string representation):
b = dec2bin(find(hhhh)-1);
str2double(b(end-1))
It seems like you're trying to combine two approaches.
The find function within matlab returns indices where the given locigal argument evaluates true.
Thus I'm wondering, why the return values (for the indices) are of type double and not uint32 or uint64 like the biggest index into a matrix could be.
Another strange thing which might be connected to that here is, that running
[~,max_num_of_elem]=computer
returns the maximal number of elements allowed for a matrix in the variable max_num_of_elem which is also of type double.
I can only guess, but probably because a wide range of functions only support double. Run
setdiff(methods('double'), methods('uint32'))
to see what functions are defined for double and not for uint32 on your version of MATLAB.
Also there is the overflow issue with integer data types in MATLAB that can introduce some hard to detect bugs.