Does a string hash exist which can ignore the order of chars in this string? Eg."helloword" and "wordhello" can map into the same bucket.
There is a number of different approaches you can take.
You can add the values of the characters together. (a + b + c is
equal to a + c + b.) Unfortunately, this is the least desirable
approach, since strings like "ac" and "bb" will generate the same
hash value.
To reduce the possibility of hash code collisions, you can XOR the
values together. (a ^ b ^ c is equal to a ^ c ^ b.) Unfortunately,
this will not give a very broad distribution of random bits, so it
will still give a high chance of collisions for different strings.
To even further reduce the possibility of hash code collisions, you
can multiply the values of the characters together. (a * b * c is
equal to a * c * b.)
If that's not good enough either, then you can sort all the
characters in the string before applying the default string hashing
function offered to you by whatever language it is that you are
using. (So, both "helloword" ad "wordhello" would become "dehlloorw"
before hashing, thus generating the same hash code.) The only disadvantage of this approach is that it is computationally more expensive than the others.
Although the other suggestions of multiplying or adding characters would work, notice that such a hash function is not secure at all.
The reason is that it will introduce a ton of collisions and one of the main properties a hash function has is the low probability of collisions.
For example, a + b + c is the same as c + b + a. However, it is also the same as a + a + d (since the sum of the ascii characters are the same). The same thing applies for multiplying or xor-ing the numbers.
In sum, if you want to achieve a hash function which ignores order, you can but it will introduce a ton of collisions which will potentially make your program faulty and insecure.
I have two vectors in Matlab, z and beta. Vector z is a 1x17:
1 0.430742139435890 0.257372971229541 0.0965909090909091 0.694329541928697 0 0.394960106863064 0 0.100000000000000 1 0.264704325268675 0.387774594078319 0.269207605609567 0.472226643323253 0.750000000000000 0.513121013402805 0.697062571025173
... and beta is a 17x1:
6.55269487769363e+26
0
0
-56.3867588816768
-2.21310778926413
0
57.0726052009847
0
3.47223691057151e+27
-1.00249317882651e+27
3.38202232046686
1.16425987969027
0.229504956512063
-0.314243264212449
-0.257394312588330
0.498644243389556
-0.852510642195370
I'm dealing with some singularity issues, and I noticed that if I want to compute the dot product of z*beta, I potentially get 2 different solutions. If I use the * command, z*beta = 18.5045. If I write a loop to compute the dot product (below), I get a solution of 0.7287.
summation=0;
for i=1:17
addition=z(1,i)*beta(i);
summation=summation+addition;
end
Any idea what's going on here?
Here's a link to the data: https://dl.dropboxusercontent.com/u/16594701/data.zip
The problem here is that addition of floating point numbers is not associative. When summing a sequence of numbers of comparable magnitude, this is not usually a problem. However, in your sequence, most numbers are around 1 or 10, while several entries have magnitude 10^26 or 10^27. Numerical problems are almost unavoidable in this situation.
The wikipedia page http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems shows a worked example where (a + b) + c is not equal to a + (b + c), i.e. demonstrating that the order in which you add up floating point numbers does matter.
I would guess that this is a homework assignment designed to illustrate these exact issues. If not, I'd ask what the data represents to suss out the appropriate approach. It would probably be much more productive to find out why such large numbers are being produced in the first place than trying to make sense of the dot product that includes them.
Is there an existing subset of the alphanumerics that is easier to read? In particular, is there a subset that has fewer characters that are visually ambiguous, and by removing (or equating) certain characters we reduce human error?
I know "visually ambiguous" is somewhat waffly of an expression, but it is fairly evident that D, O and 0 are all similar, and 1 and I are also similar. I would like to maximize the size of the set of alpha-numerics, but minimize the number of characters that are likely to be misinterpreted.
The only precedent I am aware of for such a set is the Canada Postal code system that removes the letters D, F, I, O, Q, and U, and that subset was created to aid the postal system's OCR process.
My initial thought is to use only capital letters and numbers as follows:
A
B = 8
C = G
D = 0 = O = Q
E = F
H
I = J = L = T = 1 = 7
K = X
M
N
P
R
S = 5
U = V = Y
W
Z = 2
3
4
6
9
This problem may be difficult to separate from the given type face. The distinctiveness of the characters in the chosen typeface could significantly affect the potential visual ambiguity of any two characters, but I expect that in most modern typefaces the above characters that are equated will have a similar enough appearance to warrant equating them.
I would be grateful for thoughts on the above – are the above equations suitable, or perhaps are there more characters that should be equated? Would lowercase characters be more suitable?
I needed a replacement for hexadecimal (base 16) for similar reasons (e.g. for encoding a key, etc.), the best I could come up with is the following set of 16 characters, which can be used as a replacement for hexadecimal:
0 1 2 3 4 5 6 7 8 9 A B C D E F Hexadecimal
H M N 3 4 P 6 7 R 9 T W C X Y F Replacement
In the replacement set, we consider the following:
All characters used have major distinguishing features that would only be omitted in a truly awful font.
Vowels A E I O U omitted to avoid accidentally spelling words.
Sets of characters that could potentially be very similar or identical in some fonts are avoided completely (none of the characters in any set are used at all):
0 O D Q
1 I L J
8 B
5 S
2 Z
By avoiding these characters completely, the hope is that the user will enter the correct characters, rather than trying to correct mis-entered characters.
For sets of less similar but potentially confusing characters, we only use one character in each set, hopefully the most distinctive:
Y U V
Here Y is used, since it always has the lower vertical section, and a serif in serif fonts
C G
Here C is used, since it seems less likely that a C would be entered as G, than vice versa
X K
Here X is used, since it is more consistent in most fonts
F E
Here F is used, since it is not a vowel
In the case of these similar sets, entry of any character in the set could be automatically converted to the one that is actually used (the first one listed in each set). Note that E must not be automatically converted to F if hexadecimal input might be used (see below).
Note that there are still similar-sounding letters in the replacement set, this is pretty much unavoidable. When reading aloud, a phonetic alphabet should be used.
Where characters that are also present in standard hexadecimal are used in the replacement set, they are used for the same base-16 value. In theory mixed input of hexadecimal and replacement characters could be supported, provided E is not automatically converted to F.
Since this is just a character replacement, it should be easy to convert to/from hexadecimal.
Upper case seems best for the "canonical" form for output, although lower case also looks reasonable, except for "h" and "n", which should still be relatively clear in most fonts:
h m n 3 4 p 6 7 r 9 t w c x y f
Input can of course be case-insensitive.
There are several similar systems for base 32, see http://en.wikipedia.org/wiki/Base32 However these obviously need to introduce more similar-looking characters, in return for an additional 25% more information per character.
Apparently the following set was also used for Windows product keys in base 24, but again has more similar-looking characters:
B C D F G H J K M P Q R T V W X Y 2 3 4 6 7 8 9
My set of 23 unambiguous characters is:
c,d,e,f,h,j,k,m,n,p,r,t,v,w,x,y,2,3,4,5,6,8,9
I needed a set of unambiguous characters for user input, and I couldn't find anywhere that others have already produced a character set and set of rules that fit my criteria.
My requirements:
No capitals: this supposed to be used in URIs, and typed by people who might not have a lot of typing experience, for whom even the shift key can slow them down and cause uncertainty. I also want someone to be able to say "all lowercase" so as to reduce uncertainty, so I want to avoid capital letters.
Few or no vowels: an easy way to avoid creating foul language or surprising words is to simply omit most vowels. I think keeping "e" and "y" is ok.
Resolve ambiguity consistently: I'm open to using some ambiguous characters, so long as I only use one character from each group (e.g., out of lowercase s, uppercase S, and five, I might only use five); that way, on the backend, I can just replace any of these ambiguous characters with the one correct character from their group. So, the input string "3Sh" would be replaced with "35h" before I look up its match in my database.
Only needed to create tokens: I don't need to encode information like base64 or base32 do, so the exact number of characters in my set doesn't really matter, besides my wanting to to be as large as possible. It only needs to be useful for producing random UUID-type id tokens.
Strongly prefer non-ambiguity: I think it's much more costly for someone to enter a token and have something go wrong than it is for someone to have to type out a longer token. There's a tradeoff, of course, but I want to strongly prefer non-ambiguity over brevity.
The confusable groups of characters I identified:
A/4
b/6/G
8/B
c/C
f/F
9/g/q
i/I/1/l/7 - just too ambiguous to use; note that european "1" can look a lot like many people's "7"
k/K
o/O/0 - just too ambiguous to use
p/P
s/S/5
v/V
w/W
x/X
y/Y
z/Z/2
Unambiguous characters:
I think this leaves only 9 totally unambiguous lowercase/numeric chars, with no vowels:
d,e,h,j,m,n,r,t,3
Adding back in one character from each of those ambiguous groups (and trying to prefer the character that looks most distinct, while avoiding uppercase), there are 23 characters:
c,d,e,f,h,j,k,m,n,p,r,t,v,w,x,y,2,3,4,5,6,8,9
Analysis:
Using the rule of thumb that a UUID with a numerical equivalent range of N possibilities is sufficient to avoid collisions for sqrt(N) instances:
an 8-digit UUID using this character set should be sufficient to avoid collisions for about 300,000 instances
a 16-digit UUID using this character set should be sufficient to avoid collisions for about 80 billion instances.
Mainly drawing inspiration from this ux thread, mentioned by #rwb,
Several programs use similar things. The list in your post seems to be very similar to those used in these programs, and I think it should be enough for most purposes. You can add always add redundancy (error-correction) to "forgive" minor mistakes; this will require you to space-out your codes (see Hamming distance), though.
No references as to particular method used in deriving the lists, except trial and error
with humans (which is great for non-ocr: your users are humans)
It may make sense to use character grouping (say, groups of 5) to increase context ("first character in the second of 5 groups")
Ambiguity can be eliminated by using complete nouns (from a dictionary with few look-alikes; word-edit-distance may be useful here) instead of characters. People may confuse "1" with "i", but few will confuse "one" with "ice".
Another option is to make your code into a (fake) word that can be read out loud. A markov model may help you there.
If you have the option to use only capitals, I created this set based on characters which users commonly mistyped, however this wholly depends on the font they read the text in.
Characters to use: A C D E F G H J K L M N P Q R T U V W X Y 3 4 6 7 9
Characters to avoid:
B similar to 8
I similar to 1
O similar to 0
S similar to 5
Z similar to 2
What you seek is an unambiguous, efficient Human-Computer code. What I recommend is to encode the entire data with literal(meaningful) words, nouns in particular.
I have been developing a software to do just that - and most efficiently. I call it WCode. Technically its just Base-1024 Encoding - wherein you use words instead of symbols.
Here are the links:
Presentation: https://docs.google.com/presentation/d/1sYiXCWIYAWpKAahrGFZ2p5zJX8uMxPccu-oaGOajrGA/edit
Documentation: https://docs.google.com/folder/d/0B0pxLafSqCjKOWhYSFFGOHd1a2c/edit
Project: https://github.com/San13/WCode (Please wait while I get around uploading...)
This would be a general problem in OCR. Thus for end to end solution where in OCR encoding is controlled - specialised fonts have been developed to solve the "visual ambiguity" issue you mention of.
See: http://en.wikipedia.org/wiki/OCR-A_font
as additional information : you may want to know about Base32 Encoding - wherein symbol for digit '1' is not used as it may 'confuse' the users with the symbol for alphabet 'l'.
Unambiguous looking letters for humans are also unambiguous for optical character recognition (OCR). By removing all pairs of letters that are confusing for OCR, one obtains:
!+2345679:BCDEGHKLQSUZadehiopqstu
See https://www.monperrus.net/martin/store-data-paper
It depends how large you want your set to be. For example, just the set {0, 1} will probably work well. Similarly the set of digits only. But probably you want a set that's roughly half the size of the original set of characters.
I have not done this, but here's a suggestion. Pick a font, pick an initial set of characters, and write some code to do the following. Draw each character to fit into an n-by-n square of black and white pixels, for n = 1 through (say) 10. Cut away any all-white rows and columns from the edge, since we're only interested in the black area. That gives you a list of 10 codes for each character. Measure the distance between any two characters by how many of these codes differ. Estimate what distance is acceptable for your application. Then do a brute-force search for a set of characters which are that far apart.
Basically, use a script to simulate squinting at the characters and see which ones you can still tell apart.
Here's some python I wrote to encode and decode integers using the system of characters described above.
def base20encode(i):
"""Convert integer into base20 string of unambiguous characters."""
if not isinstance(i, int):
raise TypeError('This function must be called on an integer.')
chars, s = '012345689ACEHKMNPRUW', ''
while i > 0:
i, remainder = divmod(i, 20)
s = chars[remainder] + s
return s
def base20decode(s):
"""Convert string to unambiguous chars and then return integer from resultant base20"""
if not isinstance(s, str):
raise TypeError('This function must be called on a string.')
s = s.translate(bytes.maketrans(b'BGDOQFIJLT7KSVYZ', b'8C000E11111X5UU2'))
chars, i, exponent = '012345689ACEHKMNPRUW', 0, 1
for number in s[::-1]:
i += chars.index(number) * exponent
exponent *= 20
return i
base20decode(base20encode(10))
base58:123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz
So I'm completely new to MATLAB and I'm trying to understand colon notation within mathematical operations. So, in this book I found this statement:
w(1:5)=j(1:5) + k(1:5);
I do not understand what it really does. I know that w(1:5) is pretty much iterating through the w array from index 1 through 5, but in the statement above, shouldn't all indexes of w be equal to j(5) + k(5) in the end? Or am I completely wrong on how this works? It'd be awesome if someone posted the equivalent in Java to that up there. Thanks in advance :-)
I am pretty sure this means
"The first 5 elements of w shall be the first 5 elements of j + the first 5 elements of k" (I am not sure if matlab arrays start with 0 or 1 though)
So:
w1 = j1+k1
w2 = j2+k2
w3 = j3+k3
w4 = j4+k4
w5 = j5+k5
Think "Vector addition" here.
w(1:5)=j(1:5) + k(1:5);
is the same that:
for i=1:5
w(i)=j(i)+k(i);
end
MATLAB uses vectors and matrices, and is heavily optimized to handle operations on them efficiently.
The expression w(1:5) means a vector consisting of the first 5 elements of w; the expression you posted adds two 5 element vectors (the first 5 elements of j and k) and assigns the result to the first five elements of w.
I think your problem comes from the way how do you call this statement. It is not an iteration, but rather simple assignment. Now we only need to understand what was assigned to what.
I will assume j,k, w are all vectors 1 by N.
j(1:5) - means elements from 1 to 5 of the vector j
j(1:5) + k(1:5) - will result in elementwise sum of both operands
w(1:5) = ... - will assign the result again elementwise to w
Writing your code using colon notation makes it less verbose and more efficient. So it is highly recommended to do so. Also, colon notation is the basic and very powerful feature of MATLAB. Make sure you understand it well, before you move on. MATLAB is very well documented so you can read on this topic here.
Perl
print 2 % -18;
-->
-16
Tcl
puts [expr {2 % -18}]
-->
-16
but VBScript
wscript.echo 2 mod -18
-->
2
Why the difference?
The wikipedia answer is fairly helpful here.
A short summary is that any integer can be defined as
a = qn + r
where all of these letters are integers, and
0 <= |r| < |n|.
Almost every programming language will require that (a/n) * n + (a%n) = a. So the definition of modulus will nearly always depend on the definition of integer division. There are two choices for integer division by negative numbers 2/-18 = 0 or 2/-18 = -1. Depending on which one is true for your language will usually change the % operator.
This is because 2 = (-1) * -18 + (-16) and 2 = 0 * -18 + 2.
For Perl the situation is complicated. The manual page says: "Note that when use integer is in scope, "%" gives you direct access to the modulus operator as implemented by your C compiler. This operator is not as well defined for negative operands, but it will execute faster. " So it can choose either option for Perl (like C) if use integer is in scope. If use integer is not in scope, the manual says " If $b is negative, then $a % $b is $a minus the smallest multiple of $b that is not less than $a (i.e. the result will be less than or equal to zero). "
Wikipedia's "Modulo operation" page explains it quite well. I won't try to do any better here, as I'm likely to make a subtle but important mistake.
The rub of it is that you can define "remainder" or "modulus" in different ways, and different languages have chosen different options to implement.
After dividing a number and a divisor, one of which is negative, you have at least two ways to separate them into a quotient and a remainder, such that quotient * divisor + remainder = number: you can either round the quotient towards negative infinity, or towards zero.
Many languages just choose one.
I can't resist pointing out that Common Lisp offers both.
python, of course, explicitly informs you
>>> divmod(2,-18)
(-1, -16)