How can I export data from MatLab to a .txt file without loosing precision?

Hello. I would like to know how can export data from MatLab to a .txt file without loosing precision. I would like to export this data so I can do some computations using a C++ code I have. I've done some research, and I have found out that MatLab's double type (default type) has around 16 decimal digits of precision. Here is the code I've written:

x = rand(4,1);
file = fopen('file.txt', 'w');
fprintf(file, '%.15f\n', x);
fclose(file);

I would like to know if this code is correct or if there is something I can improve. Thank you very much for your help!

Answer 1

[Jan]

Not only Matlab's double type uses about 16 digits, but this is the IEEE754 standard, which is available in all numerical software and usual processors. Besides Walter's suggestion to use '%.16g', which is more suitable e.g. for pi*1e14, the conversion to the decimal number as an ASCII file must reduce the precision. Example:

a = pi * 1e16;
fid = fopen('test.txt', 'w');
fprintf(fid, '%.16g', a);
fclose(fid);

fid = fopen('test.txt', 'r');
b = fscanf(fid, '%g');
fclose(fid);

a - b
>> 4

The conversion from the binary double format to the decimal text format includes a certain loss of precision already. When you want to deliver the values accurately, store them in binary format:

fid = fopen('test.bin', 'w');
fwrite(fid, a, 'double);
fclose(fid);

fid = fopen('test.bin', 'r');
b = fread(fid, 1, 'double);
fclose(fid);

a - b
>> 0

You can read the binary format from the C++ function also. And the import is faster than the conversion from the string.

[Reynaldo]

Awesome! so you suggest that it is better to export all my data in the binary format? I need to export 2GB of data. This approach is very interesting, I never though of this... Thank you!

[Reynaldo]

Jan, how can I read the binary format file on C++? If I store a 100 element random vector like this:

a = rand(100,1);
fid = fopen('test.bin', 'w');
fwrite(fid, a, 'double);
fclose(fid);

How can I store each element on a C++ array? Thanks!

[Jan]

@Reynaldo: The reading from C++ is very similar to the reading in Matlab. Look for the documentation of FREAD in C++, e.g. http://www.cplusplus.com/reference/cstdio/fread/ (this first link found by Google, but it seems quite clear). When you write 2GB, the binary format has the advantage of using less memory: 16 digits occupy up to 22 bytes (with 'e123' and a separator character), while the exact binary representation needs 8 bytes only.

[Tahariet Sharon]

How to save to txt without space or commas or tabs between the numbers? I want to generate a 100K digit random number, so I first generate the 100K individual random numbers. I just need the spaces to be removed upon exporting.

Answer 2

[Walter Roberson]

I suggest using a "%.16g" format.

[Reynaldo]

Thank you very much for your suggestion. I have one other question... if I use "%.40g" MatLab will write the number to file with 40 precision digits. I dont understand how is this possible since MatLab is only supposedly able to handle 16 decimal digit precision when using 64-bits. Does MatLab makes up the numbers after the 16th decimal digit? Thanks!

[Jan]

Again this is an effect of the conversion from binary to decimal: Most binary numbers do not have an exact decimal representation. And then the conversion can be calculated with much more than the the significant digits. See James Tursa's http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str.