Convert decimal number to vector - matlab

In matlab I want to convert this:
12345.6788993442355456789
into a vector
[1 2 3 4 5 6 7 8 8 9 9 3 4 4 2 3 5 5 4 5 6 7 8 9]
I have found several solutions to convert a integer into a vector using commands like scanf, num2str,... but those don't fit with non-integers, and some solutions have problems with numbers with a large number of decimal places...
That kind of conversion is needed because I want to see and use all of the digits of the number.

What input source are you getting those numbers from? And are all those digits significant? Your example numbers are already beyond the relative precision of the double numeric type. The eps function will tell you how much roundoff you're getting.
>> sprintf('%.20f', 12345.6788993442355456789)
ans =
12345.67889934423500000000
>> eps(12345.6788993442355456789)
ans =
1.818989403545857e-012
>> sprintf('%.20f', 23432.23432345678911111111111100998)
ans =
23432.23432345678900000000
>> eps(23432.23432345678911111111111100998)
ans =
3.637978807091713e-012
When you type a number in to Matlab source code, it's treated as a literal of type double. So many of those digits are lost as soon as you enter them. See this question for more discussion: In MATLAB, are variables REALLY double-precision by default?.
If you really want to preserve all those digits, you need to avoid storing them in doubles in the first place. Start off with the full number in a string, and then parse it.
function out = parseLongDecimal(str)
ixDot = find(str == '.');
if isempty(ixDot)
out.whole = arrayfun(#str2double, str);
out.fraction = [];
else
out.whole = arrayfun(#str2double, str(1:ixDot-1));
out.fraction = arrayfun(#str2double, str(ixDot+1:end));
end
That will preserve all the digits.
>> xAsStr = '23432.23432345678911111111111100998'; % as a string literal, not numeric
>> parseLongDecimal(xAsStr)
ans =
whole: [2 3 4 3 2]
fraction: [2 3 4 3 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 1 1 0 0 9 9 8]
Depending on your use case, you could also just throw it in a Java BigDecimal object and work with it there.
>> jx = java.math.BigDecimal(xAsStr)
jx =
23432.23432345678911111111111100998

Also using num2str, you can do:
sol=arrayfun(#str2num,(sprintf('%f',23432.23432)),'UniformOutput',0)
horzcat(sol{:})
ans =
2 3 4 3 2 2 3 4 3
Do you want to keep the information about where is the comma?

Not familiar with Matlab syntax but if you
convert the number to a string
loop through each character and add the digit to the vector if the character is not the decimal point
that would work. There are probably more efficient ways to do this.

Related

Convert 3d matrix to String and back to 3d matrix using Matlab

I am currently working on a stenography assignment on how to embed secret image to a cover image using Wang's algorithm. Basically i just want to change for eg:
3d matrix
A(:,:,1) = [5 7 8; 0 1 9; 4 3 6];
A(:,:,2) = [1 0 4; 3 5 6; 9 8 7];
A(:,:,3) = [7 9 3; 4 5 9; 1 9 9];
To
Str = '578019436104356987793459199'
and also vice-versa if anybody can help out.
Another way is to just use sprintf. You first need to transpose each slice independently, so the call to permute as per Ander's answer will get to that point. After you can just supply a single format string of %d (integer) and the actual permuted matrix and it will unroll all elements column-wise and concatenate all of the numbers together. The additional advantage is that you no longer need to assume that only one digit occupies each matrix element:
str = sprintf('%d', permute(A, [2 1 3]));
Example
>> str = sprintf('%d', permute(A, [2 1 3]))
str =
578019436104356987793459199
>> class(str)
ans =
char
However, to reconstruct the matrix, you will have to assume that there's one element per matrix. In this case, you could use the undocumented sprintfc function that can output one cell per character, then convert the characters to numbers with str2double. Finally, reshape your matrix and undo the transpose:
A2 = permute(reshape(str2double(sprintfc('%c', str)), size(A)), [2 1 3]);
Example
>> A2 = permute(reshape(str2double(sprintfc('%c', str)), size(A)), [2 1 3])
A2(:,:,1) =
5 7 8
0 1 9
4 3 6
A2(:,:,2) =
1 0 4
3 5 6
9 8 7
A2(:,:,3) =
7 9 3
4 5 9
1 9 9
Because of the order of the unrolling of MATLAB matrices, your problem is slightly less straightforward than it may seem. You need to use reshape and permute to make it work.
str=arrayfun(#num2str,reshape(permute(A,[2 1 3]),[],1,1)).';
A2=permute(reshape(arrayfun(#str2double,str),[size(A)]),[2 1 3]);
isequal(A2,A)
This of course assumes what #Sardar comments in your question: all numbers have single digits (i.e. are integers range 0-9)

Removing third dimension of matrix

Lets say I have matrix such that A(:,:,1)=[1,2,3;2,3,4], A(:,:,2)=[3,4,5;4,5,6].
How is the easiest way of accessing and plotting the vectors (1,2,3),(2,3,4),(3,4,5),(4,5,6). I tried creating B=[A(:,:,1);A(:,:,2)], but i need a procedure to arbitrary number of A's.
Hope this isn't trivial and I've formulated myself satisfactory.
You should think 'vertically'. This will allow you to use colon indexing:
>> A(:,:,1) = [1,2,3;2,3,4].'; %'// NOTE: transpose of your original
>> A(:,:,2) = [3,4,5;4,5,6].'; %'// NOTE: transpose of your original
>> A(:,:)
ans =
1 2 3 4
2 3 4 5
3 4 5 6
The colon indexing with two colons works for any dimension A:
>> A(:,:,:,:,1,1) = [1 2 3; 2 3 4].'; %'
>> A(:,:,:,:,2,1) = [3 4 5; 4 5 6].'; %'
>> A(:,:,:,:,1,2) = [5 6 7; 6 7 8].'; %'
>> A(:,:,:,:,2,2) = [7 8 9; 8 9 0].'; %'
>> A(:,:)
ans =
1 2 3 4 5 6 7 8
2 3 4 5 6 7 8 9
3 4 5 6 7 8 9 0
Colon indexing in MATLAB is quite interesting and really powerful once you master it. For example, if you use fewer colons than there are dimensions in the array (like above), MATLAB will automatically concatenate the remainder of the data along the dimension equal to the colon count.
So, if A has 48 dimensions, but you index with just 2 colons: you'll get a 2D array, that is the concatenation of the remaining 46 dimensions along the 2nd dimension.
In general: if A has N dimensions, but you index with just M ≤ N colons: you'll get an M-D array, that is the concatenation of the remaining N-M dimensions along the Mth dimension.
So as long as you are free to define your A to contain vectors on the columns rather than the rows (you should advise everyone to do this, as virtually everything in MATLAB is a bit faster that way), I think this is the fastest and most elegant way to do what you want.
If not, well, then just reshape like Dan :)
Assuming the order does not matter, here is how you can do it for vectors of length 3:
B = reshape(shiftdim(A,2), [], 3)
plot(B')
For vectors of arbitrary dimensions, replace 3 by size(A,2)

Find the increasing and decreasing trend in a curve MATLAB

a=[2 3 6 7 2 1 0.01 6 8 10 12 15 18 9 6 5 4 2].
Here is an array i need to extract the exact values where the increasing and decreasing trend starts.
the output for the array a will be [2(first element) 2 6 9]
a=[2 3 6 7 2 1 0.01 6 8 10 12 15 18 9 6 5 4 2].
^ ^ ^ ^
| | | |
Kindly help me to get the result in MATLAB for any similar type of array..
You just have to find where the sign of the difference between consecutive numbers changes.
With some common sense and the functions diff, sign and find, you get this solution:
a = [2 3 6 7 2 1 0.01 6 8 10 12 15 18 9 6 5 4 2];
sda = sign(diff(a));
idx = [1 find(sda(1:end-1)~=sda(2:end))+2 ];
result = a(idx);
EDIT:
The sign function messes things up when there are two consecutive numbers which are the same, because sign(0) = 0, which is falsely identified as a trend change. You'd have to filter these out. You can do this by first removing the consecutive duplicates from the original data. Since you only want the values where the trend change starts, and not the position where it actually starts, this is easiest:
a(diff(a)==0) = [];
This is a great place to use the diff function.
Your first step will be to do the following:
B = [0 diff(a)]
The reason we add the 0 there is to keep the matrix the same length because of the way the diff function works. It will start with the first element in the matrix and then report the difference between that and the next element. There's no leading element before the first one so is just truncates the matrix by one element. We add a zero because there is no change there as it's the starting element.
If you look at the results in B now it is quite obvious where the inflection points are (where you go from positive to negative numbers).
To pull this out programatically there are a number of things you can do. I tend to use a little multiplication and the find command.
Result = find(B(1:end-1).*B(2:end)<0)
This will return the index where you are on the cusp of the inflection. In this case it will be:
ans =
4 7 13

Matlab How to easily loop round array

Hi i'm looking for a way to take a slice of an array from the near the end to near the beginning. I know I could do this in two parts, then add them, but it seems like such a commonly desired operation I thought matlab probably already has it built in but I couldn't find any information in my search.
To clarify I would like to be able to say:
y = 1:10
y(-3:3) or y(8:3)
returns:
8 9 10 1 2 3
Thanks in advance.
there actually is a way to do it (without splitting it up in a concatenation of the negative and positive part of indices): use the modulo operator on your desired range:
>> y = 1:10;
>> y(mod([-3:3]-1,numel(y))+1)
ans =
7 8 9 10 1 2 3
This result consists of 7 numbers (opposing your desired [8 9 10 1 2 3]), which is logical because -3:3 actually spans 7 numbers.
The number 0 would correspond to y(end) with this method, -1 would correspond to y(end-1), etc.
You can try this:
y = 1:10;
n = 3;
y([end-n+1:end 1:n]);
This returns
ans =
8 9 10 1 2 3

MATLAB Concatenate matrices with unequal dimensions

Is there any easy way to concatenate matrices with unequal dimensions using zero padding?
short = [1 2 3]';
long = [4 5 6 7]';
desiredResult = horzcat(short, long);
I would like something like:
desiredResult =
1 4
2 5
3 6
0 7
Matrices in MATLAB are automatically grown and padded with zeroes when you assign to indices outside the current bounds of the matrix. For example:
>> short = [1 2 3]';
>> long = [4 5 6 7]';
>> desiredResult(1:numel(short),1) = short; %# Add short to column 1
>> desiredResult(1:numel(long),2) = long; %# Add long to column 2
>> desiredResult
desiredResult =
1 4
2 5
3 6
0 7
EDIT:
I have edited my earlier solution so that you won't have to supply a maxLength parameter to the function. The function calculates it before doing the padding.
function out=joinUnevenVectors(varargin)
%#Horizontally catenate multiple column vectors by appending zeros
%#at the ends of the shorter vectors
%#
%#SYNTAX: out = joinUnevenVectors(vec1, vec2, ... , vecN)
maxLength=max(cellfun(#numel,varargin));
out=cell2mat(cellfun(#(x)cat(1,x,zeros(maxLength-length(x),1)),varargin,'UniformOutput',false));
The convenience of having it as a function is that you can easily join multiple uneven vectors in a single line as joinUnevenVectors(vec1,vec2,vec3,vec4) and so on, without having to manually enter it in each line.
EXAMPLE:
short = [1 2 3]';
long = [4 5 6 7]';
joinUnevenVectors(short,long)
ans =
1 4
2 5
3 6
0 7
Matlab automatically does padding when writing to a non-existent element of a matrix.
Therefore, another very simple way of doing this is the following:
short=[1;2;3];
long=[4;5;6;7];
short(1:length(long),2)=long;