We Keep Coding

Python: How to sum two signed int16 arrays into one without overflow

I have several int16 streams in strings and I want them sum together (without overflow) and return it as an int16 string. Background is mixing several wave files into one stream.
decodeddata1 = numpy.fromstring(data, numpy.int16)
decodeddata2 = numpy.fromstring(data2, numpy.int16)
newdata = decodeddata1 + decodeddata2
return newdata.tostring()
Is there a way doing this with numpy or is there another library?
Processing each single value in python is too slow and results in stutter.
The most important thing is performance, since this code is used in a callback method feeding the audio.
#edit:
test input data:
a = np.int16([20000,20000,-20000,-20000])
b = np.int16([10000,20000,-10000,-20000])
print a + b --> [ 30000 -25536 -30000 25536]
but I want to keep the maximum levels:
[ 30000 40000 -30000 -40000]

The obvious consequence of mixing two signals together with a dynamic range of -32768<x<32767 is a resulting signal of with range of -65537<x<65536 - which requires 17 bits to represent it.
To avoid clipping, you will need to gain-scale the inputs - the obvious way is to divide the sum (or both of the inputs) by 2.
numpy looks as thought it should be quite fast for this - at least faster than python's builtin variable-size integer type. If the additional arithmetic is a performance concern, you should consider your choice of language.

Why do I have such a distortion with pygame sndarray objects?

I'm using sndarray from pygame to play with basic sound synthesis. The problem is Whatever I do, I have an awful distortion on the generated sound.
In the code I'll provide at the end of the question, you'll see a bunch of code coming from here and there. Actually, the main stuff comes from a MIT's source I found on the interweb which is using Numeric to do mathematic stuff and handling arrays, and since I can't install it for now, I decided to use Numpy for this.
First, I thought the problem was coming from the Int format of my arrays, but if I cast the values to numpy.int16, I don't have sound anymore.
Plus, I can't find anything on google about that kind of behavior from pygame / sndarray.
Any idea ?
Thanks !
Code :
global_sample_rate = 44100
def sine_array_onecycle(hz, peak):
length = global_sample_rate / float(hz)
omega = numpy.pi * 2 / length
xvalues = numpy.arange(int(length)) * omega
return (peak * numpy.sin(xvalues))
def zipstereo(f):
return numpy.array(zip (f , f))
def make_sound(arr, n_samples = global_sample_rate):
return pygame.sndarray.make_sound( zipstereo( numpy.resize(numpy.array(arr), (n_samples,)) ) )
def sine(hz, peak):
snd = make_sound(sine_array_onecycle(hz, peak), global_sample_rate)
return snd
=> 'hope I didn't make any lame mistake, I'm pretty new in the world of python

Presuming you have some initialization code like
pygame.mixer.pre_init(44100, -16, 2) # 44.1kHz, 16-bit signed, stereo
sndarray expects you to be passing it 16-bit integer arrays, not float arrays.
Your "peak" value needs to make sense given the 16-bit integer representation. So, if your float array has values in the range -1.0 to +1.0, then you need to multiply by 2**15 to get it scaled appropriately.
To be clear, you may want a conversion like:
numpy.int16(float_array*(2**15))
My best guess of the situation is that you had a float array with a low peak value like 1.0, so when converting it to int16 most everything was getting converted to 0 or +/-1, which you wouldn't be able to hear. When passing the float array, you were probably just getting random bits (when interpreted as 16 bit integers) so then it sounded like harsh noise (I stumbled through this phase on my way to getting this working).

Process RGBA data efficiently using python?

I'm trying to process an RGBA buffer (list of chars), and run "unpremultiply" on each pixel. The algorithm is color_out=color*255/alpha.
This is what I came up with:
def rgba_unpremultiply(data):
for i in range(0, len(data), 4):
a = ord(data[i+3])
if a != 0:
data[i] = chr(255*ord(data[i])/a)
data[i+1] = chr(255*ord(data[i+1])/a)
data[i+2] = chr(255*ord(data[i+2])/a)
return data
It works but causes a major drawback in performance.
I'm wondering besides writing a C module, what are my options to optimize this particular function?

This is exactly the kind of code NumPy is great for.
import numpy
def rgba_unpremultiply(data):
a = numpy.fromstring(data, 'B') # Treat the string as an array of bytes
a = a.astype('I') # Cast array of bytes to array of uints, since temporary values needs to be larger than byte
alpha = a[3::4] # Every 4th element starting from index 3
alpha = numpy.where(alpha == 0, 255, alpha) # Don't modify colors where alpha is 0
a[0::4] = a[0::4] * 255 // alpha # Operates on entire slices of the array instead of looping over each element
a[1::4] = a[1::4] * 255 // alpha
a[2::4] = a[2::4] * 255 // alpha
return a.astype('B').tostring() # Cast back to bytes

How big is data? Assuming this is on python2.X Try using xrange instead of range so that you don't have to constantly allocate and reallocate a large list.
You could convert all the data to integers for working with them so you're not constantly converting to and from characters.
Look into using numpy to vectorize this: Link I suspect that simply storing the data as integers and using a numpy array will greatly improve the performance.
And another relatively simple thing you could do is write a little Cython:
http://wiki.cython.org/examples/mandelbrot
Basically Cython will compile your above function into C code with just a few lines of type hints. It greatly reduces the barrier to writing a C extension.

I don't have a concrete answer, but some useful pointers might be:
Python's array module
numpy
OpenCV if you have actual image data

There are some minor things you can do, but I do not think you can improve a lot.
Anyway, here's some hint:
def rgba_unpremultiply(data):
# xrange() is more performant then range, it does not precalculate the whole array
for i in xrange(0, len(data), 4):
a = ord(data[i+3])
if a != 0:
# Not sure about this, but maybe (c << 8) - c is faster than c*255
# So maybe you can arrange this to do that
# Check for performance improvement
data[i] = chr(((ord(data[i]) << 8) - ord(data[i]))/a)
data[i+1] = chr(255*ord(data[i+1])/a)
data[i+2] = chr(255*ord(data[i+2])/a)
return data
I've just make some dummy benchmark on << vs *, and it seems not to be markable differences, but I guess you can do better evaluation on your project.
Anyway, a c module may be a good thing, even if it does not seem to be "language related" the problem.

Fast way to read interleaved data?

I've got a file containing several channels of data. The file is sampled at a base rate, and each channel is sampled at that base rate divided by some number -- it seems to always be a power of 2, though I don't think that's important.
So, if I have channels a, b, and c, sampled at divders of 1, 2, and 4, my stream will look like:
a0 b0 c0 a1 a2 b1 a3 a4 b2 c1 a5 ...
For added fun, the channels can independently be floats or ints (though I know for each one), and the data stream does not necessarily end on a power of 2: the example stream would be valid without further extension. The values are sometimes big and sometimes little-endian, though I know what I'm dealing with up-front.
I've got code that properly unpacks these and fills numpy arrays with the correct values, but it's slow: it looks something like (hope I'm not glossing over too much; just giving an idea of the algorithm):
for sample_num in range(total_samples):
channels_to_sample = [ch for ch in all_channels if ch.samples_for(sample_num)]
format_str = ... # build format string from channels_to_sample
data = struct.unpack( my_file.read( ... ) ) # read and unpack the data
# iterate over data tuple and put values in channels_to_sample
for val, ch in zip(data, channels_to_sample):
ch.data[sample_num / ch.divider] = val
And it's slow -- a few seconds to read a 20MB file on my laptop. Profiler tells me I'm spending a bunch of time in Channel#samples_for() -- which makes sense; there's a bit of conditional logic there.
My brain feels like there's a way to do this in one fell swoop instead of nesting loops -- maybe using indexing tricks to read the bytes I want into each array? The idea of building one massive, insane format string also seems like a questionable road to go down.
Update
Thanks to those who responded. For what it's worth, the numpy indexing trick reduced the time required to read my test data from about 10 second to about 0.2 seconds, for a speedup of 50x.

The best way to really improve the performance is to get rid of the Python loop over all samples and let NumPy do this loop in compiled C code. This is a bit tricky to achieve, but it is possible.
First, you need a bit of preparation. As pointed out by Justin Peel, the pattern in which the samples are arranged repeats after some number of steps. If d_1, ..., d_k are the divisors for your k data streams and b_1, ..., b_k are the sample sizes of the streams in bytes, and lcm is the least common multiple of these divisors, then
N = lcm*sum(b_1/d_1+...+b_k/d_k)
will be the number of bytes which the pattern of streams will repeat after. If you have figured out which stream each of the first N bytes belongs to, you can simply repeat this pattern.
You can now build the array of stream indices for the first N bytes by something similar to
stream_index = []
for sample_num in range(lcm):
stream_index += [i for i, ch in enumerate(all_channels)
if ch.samples_for(sample_num)]
repeat_count = [b[i] for i in stream_index]
stream_index = numpy.array(stream_index).repeat(repeat_count)
Here, d is the sequence d_1, ..., d_k and b is the sequence b_1, ..., b_k.
Now you can do
data = numpy.fromfile(my_file, dtype=numpy.uint8).reshape(-1, N)
streams = [data[:,stream_index == i].ravel() for i in range(k)]
You possibly need to pad the data a bit at the end to make the reshape() work.
Now you have all the bytes belonging to each stream in separate NumPy arrays. You can reinterpret the data by simply assigning to the dtype attribute of each stream. If you want the first stream to be intepreted as big endian integers, simply write
streams[0].dtype = ">i"
This won't change the data in the array in any way, just the way it is interpreted.
This may look a bit cryptic, but should be much better performance-wise.

Replace channel.samples_for(sample_num) with a iter_channels(channels_config) iterator that keeps some internal state and lets you read the file in one pass. Use it like this:
for (chan, sample_data) in izip(iter_channels(), data):
decoded_data = chan.decode(sample_data)
To implement the iterator, think of a base clock with a period of one. The periods of the various channels are integers. Iterate the channels in order, and emit a channel if the clock modulo its period is zero.
for i in itertools.count():
for chan in channels:
if i % chan.period == 0:
yield chan

The grouper() recipe along with itertools.izip() should be of some help here.

What is the equivalent of 'fread' from Matlab in Python?

I have practically no knowledge of Matlab, and need to translate some parsing routines into Python. They are for large files, that are themselves divided into 'blocks', and I'm having difficulty right from the off with the checksum at the top of the file.
What exactly is going on here in Matlab?
status = fseek(fid, 0, 'cof');
fposition = ftell(fid);
disp(' ');
disp(['** Block ',num2str(iBlock),' File Position = ',int2str(fposition)]);
% ----------------- Block Start ------------------ %
[A, count] = fread(fid, 3, 'uint32');
if(count == 3)
magic_l = A(1);
magic_h = A(2);
block_length = A(3);
else
if(fposition == file_length)
disp(['** End of file OK']);
else
disp(['** Cannot read block start magic ! Note File Length = ',num2str(file_length)]);
end
ok = 0;
break;
end
fid is the file currently being looked at
iBlock is a counter for which 'block' you're in within the file
magic_l and magic_h are to do with checksums later, here is the code for that (follows straight from the code above):
disp(sprintf(' Magic_L = %08X, Magic_H = %08X, Length = %i', magic_l, magic_h, block_length));
correct_magic_l = hex2dec('4D445254');
correct_magic_h = hex2dec('43494741');
if(magic_l ~= correct_magic_l | magic_h ~= correct_magic_h)
disp(['** Bad block start magic !']);
ok = 0;
return;
end
remaining_length = block_length - 3*4 - 3*4; % We read Block Header, and we expect a footer
disp(sprintf(' Remaining Block bytes = %i', remaining_length));
What is going on with the %08X and the hex2dec stuff?
Also, why specify 3*4 instead of 12?
Really though, I want to know how to replicate [A, count] = fread(fid, 3, 'uint32'); in Python, as io.readline() is just pulling the first 3 characters of the file. Apologies if I'm missing the point somewhere here. It's just that using io.readline(3) on the file seems to return something it shouldn't, and I don't understand how the block_length can fit in a single byte when it could potentially be very long.
Thanks for reading this ramble. I hope you can understand kind of what I want to know! (Any insight at all is appreciated.)

Python Code for Reading a 1-Dimensional Array
When replacing Matlab with Python, I wanted to read binary data into a numpy.array, so I used numpy.fromfile to read the data into a 1-dimensional array:
import numpy as np
with open(inputfilename, 'rb') as fid:
data_array = np.fromfile(fid, np.int16)
Some advantages of using numpy.fromfile versus other Python solutions include:
Not having to manually determine the number of items to be read. You can specify them using the count= argument, but it defaults to -1 which indicates reading the entire file.
Being able to specify either an open file object (as I did above with fid) or you can specify a filename. I prefer using an open file object, but if you wanted to use a filename, you could replace the two lines above with:
data_array = numpy.fromfile(inputfilename, numpy.int16)
Matlab Code for a 2-Dimensional Array
Matlab's fread has the ability to read the data into a matrix of form [m, n] instead of just reading it into a column vector. For instance, to read data into a matrix with 2 rows use:
fid = fopen(inputfilename, 'r');
data_array = fread(fid, [2, inf], 'int16');
fclose(fid);
Equivalent Python Code for a 2-Dimensional Array
You can handle this scenario in Python using Numpy's shape and transpose.
import numpy as np
with open(inputfilename, 'rb') as fid:
data_array = np.fromfile(fid, np.int16).reshape((-1, 2)).T
The -1 tells numpy.reshape to infer the length of the array for that dimension based on the other dimension—the equivalent of Matlab's inf infinity representation.
The .T transposes the array so that it is a 2-dimensional array with the first dimension—the axis—having a length of 2.

From the documentation of fread, it is a function to read binary data. The second argument specifies the size of the output vector, the third one the size/type of the items read.
In order to recreate this in Python, you can use the array module:
f = open(...)
import array
a = array.array("L") # L is the typecode for uint32
a.fromfile(f, 3)
This will read read three uint32 values from the file f, which are available in a afterwards. From the documentation of fromfile:
Read n items (as machine values) from the file object f and append them to the end of the array. If less than n items are available, EOFError is raised, but the items that were available are still inserted into the array. f must be a real built-in file object; something else with a read() method won’t do.
Arrays implement the sequence protocol and therefore support the same operations as lists, but you can also use the .tolist() method to create a normal list from the array.

Really though, I want to know how to replicate [A, count] = fread(fid, 3, 'uint32');
In Matlab, one of fread()'s signatures is fread(fileID, sizeA, precision). This reads in the first sizeA elements (not bytes) of a file, each of a size sufficient for precision. In this case, since you're reading in uint32, each element is of size 32 bits, or 4 bytes.
So, instead, try io.readline(12) to get the first 3 4-byte elements from the file.

The first part is covered by Torsten's answer... you're going to need array or numarray to do anything with this data anyway.
As for the %08X and the hex2dec stuff, %08X is just the print format for those unit32 numbers (8 digit hex, exactly the same as Python), and hex2dec('4D445254') is matlab for 0x4D445254.
Finally, ~= in matlab is a bitwise compare; use == in Python.