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So my question is how I should save a large amount of simulation data to a file using Python (or update new data rows to the existing file).
Lets say I have NN=1000 particles, and I want to save the position and velocity data of each particle (x y z, vx vy vz). The data is in format [x1,y1,z1,vx1,vy1,vz1, x2,y2,z2,vx2,vy2,vz2, ...] and so on.
Simulation is working well, but I believe the methods I use for saving and keeping these information saved is not really optimal for me.
Pseudo code similar to my code
T_max = 1000 # for example
dt = 0.1 # time step
T = 0 # current time
iterations = int(T_max/dt) # number of iterations we are doing
NN = 1000 # Number of particles
ZZ = np.zeros( (iterations, 2+NN*6 ) ) # Here I generate whole data matrix at the beginning.
# ^ might not be the best idea as the system needs to keep everything in memory for the whole time
# So I guess saving could be done in chunks?
ZZ[0][0], ZZ[0][1] = T , dt
# ZZ[0][2:] = initialize_system(NN=NN) # so lets initialize the system.
# However, for this post I do this differently due to simplicity. See below
ZZ[0][2:] = np.random.uniform(-100,100,NN*6)
i = 0
while i < iteration:
T += dt
Z[i+1][0], Z[i+1][1] = T, dt
#Z[i+1][2:] = rk4(EOM_function, posvel=Z[i][2:])
# ^ Using this I would calculate new positions based on previous ones.
Z[i+1][2:] = np.random.uniform(-100,100,NN*6) #This is just for example here.
i += 1
# Now the simulation data is basically done, so one would need to save
# This one feels slow, as it takes 181s to save and is size of 1046246KB
np.savetxt('test1.txt', ZZ)
#other method with a bit less accuracy as I don't need to have all decimals saved
np.savetxt('test2.txt', ZZ, fmt='%1.6f') # Takes 125s and size is 426698KB
# Both of the above are kinda slow so I also tried to save to npy format
np.save('test.npy', ZZ) # It took 8.9s and size 164118KB
so this np.save() method seems to be fast, but I read somewhere that I can not append data to it. So this would not work if I keep saving the data in parts while calculating new positions.
So back to my question. How should/could I save the data efficiently (fast and memory friendly). I keep having some memory issues when NN and T_max gets larger because with this method I keep this whole ZZ all the time in memory.
So I guess I should calculate ZZ in parts, i.e. iterations/10 parts but then I should append this data to an existing file, and tests I have made felt slow. Any suggestions?
EDIT: feel free to ask more specifying questions as I feel like I forgot to explain something.
That highly depends on what you intend to use the output for. If it's stored for further calculations, .npy or some other binary format is always the way to go as it is faster, takes less space, and doesn't lose precision between loads and saves, instead of serializing it into a human readable format. If you need it to be readable, you might as well just output row by row to a csv file or something.
If you want to do it with binary, h5py allows you to extend a dataset after saving and append more stuff to it.
import numpy as np
import h5py
T_max = 10**4 # for example
dt = 0.1 # time step
T = 0 # current time
iterations = int(T_max/dt) # number of iterations we are doing
NN = 1000 # Number of particles
chunk_size = 10**3
ZZ = np.zeros( (chunk_size, 2+NN*6 ) )
ZZ[0][0], ZZ[0][1] = T , dt
# ZZ[0][2:] = initialize_system(NN=NN) # so lets initialize the system.
# However, for this post I do this differently due to simplicity. See below
ZZ[0][2:] = np.random.uniform(-100,100,NN*6)
with h5py.File("test.h5", "a") as f:
dset = f.create_dataset('ZZ', (0,2+NN*6), maxshape=(None,2+NN*6), dtype='float64', chunks=(chunk_size,2+NN+6))
for chunk in range(0, iterations, chunk_size):
for i in range(0, chunk_size - 1):
T += dt
ZZ[i + 1][0], ZZ[i + 1][1] = T, dt
#Z[i+1][2:] = rk4(EOM_function, posvel=Z[i][2:])
# ^ Using this I would calculate new positions based on previous ones.
ZZ[i + 1][2:] = np.random.uniform(-100,100,NN*6) #This is just for example here.
# Expand the file here to allow for more data.
dset.resize(dset.shape[0] + chunk_size, axis=0)
dset[chunk: chunk + chunk_size ] = ZZ
# update and initialize next chunk. the next chunk's first row should be the last row of the previous chunk + iteration
T += dt
ZZ[0][0], ZZ[0][1] = T, dt
#Z[0][2:] = rk4(EOM_function, posvel=Z[-1][2:])
# ^ Using this I would calculate new positions based on previous ones.
ZZ[0][2:] = np.random.uniform(-100,100,NN*6) #This is just for example here.
print(dset.shape)
This takes 70 seconds on the save step on my computer, generating a 45GB file, for a dataset that is 100 times your original code.
The above code is more general in case you are streaming your data and don't know your final size. If you know it from the start, you can replace the initial create_dataset with
dset = f.create_dataset('ZZ', (iterations,2+NN*6), dtype='float64')
and remove the dset.resize(dset.shape[0] + chunk_size, axis=0)
You'll probably also want to read it back in chunks afterwards for other processing, in which case you can follow the docs here: https://docs.h5py.org/en/latest/high/dataset.html#reading-writing-data
Okay so I'm continuing my question / providing possible answer to it based on the answer of EricChen1248. EDIT: Answer provided by EricChen1248 works now and is way better than this my code part. See his code
I do not yet still understand completely how this f.create_dataset () truly works (i.e. when does it write data to file in the loop etc).
Using the code provided by Eric, it created and saved the data files fastly, but when I read the file as follows
hf = h5py.File('temp/test.h5', 'r')
ZZ = np.array(hf['ZZ'])
hf.close()
and plotted the first column (time T column, which should increase by timestep dt after each iteration) I get the following figure
plt.plot(ZZ[:,0])
time T column plotted
and as can be seen, it grows to a time of 100, and then goes to zero. This happens after the first 'chunk_size' has been passed. I started to read docs provided by Eric, and using his code as reference I managed to write something like this
import numpy as np
import h5py
T_max = 10**4
dt = 0.1
T = 0
NN = 1000
iterations = int(T_max/dt)
chunk_size = 10**3
with h5py.File('temp/data12.h5', 'a') as hf:
dset = hf.create_dataset("ZZ", (chunk_size, 2+NN*6),maxshape=(None,2+NN*6) ,chunks=(chunk_size, 2+NN*6), dtype='f8' )
# ^ first I create data set equals to one chunk_size
# Here I initialize the system. Columns ; 0=T , 1=dt, 2=arbitrary data point, 3=sin(column2)
# all the rest columns are random numbers just to fill some numbers in
dset[0,0], dset[0,1] = T, dt
#dset[0,2:] = np.random.uniform(0,1,NN*6)
dset[0,2] = 1
dset[0,3] = np.sin(dset[0,2])
dset[0,4:] = np.random.uniform(0,1,NN*6 -2)
print('starts')
# Main difference down there is that I use dataset (dset)
# as a data matrix to be filled instead of matrix ZZ as in my question.
i = 0
#for j, s in enumerate(dset.iter_chunks()):
for j, s in enumerate(range(0, iterations, chunk_size )):
print(j, s)
while i < iterations and i < chunk_size*(j+1) -1:
#for i in range(chunk_size*j, chunk_size*(j+1)-1):
T += dt
dset[i+1,0], dset[i+1,1] = T, dt
#dset[i+1,2:] = np.sin(dset[i,2:]+dt)
dset[i+1,2] = dset[i,2] + dt
dset[i+1,3] = np.sin(dset[i,2]+dt)
dset[i+1,4:] = dset[i,4:] + np.random.uniform(-1,1,NN*6-2)
i+=1
print(dset.shape)
dset.resize(dset.shape[0] + chunk_size, axis=0)
This code runs in 1min 50s , and saves a file of size 4.47GB so I am happy with the speed, and what I'm really happy is that it do not use so much memory while iterating (I used to get into problem with huge RAM usage).
When I read the data file provided by my code (similarly as above) I get following image for time Time T column plotted, my code version and it grows nicely to T=10e4 as should be. It still generated one more chunk_size block to the end of dataset which is full of zeros. That I need to get rid of. One more proof that the code works and saves data without weird problems is this sinusoidal plot plt.plot(ZZ[500:1500,0] , ZZ[500:1500,3]). Sinusoidal image proof Note that the plot is limited for T ~ [50,150] so one could still see something there (if plotted the whole thing, one could not see lines well).
I believe this is not the best way to write this code, but it is the way I got this working. So if someone sees improvements, please let me know. Also, I am curious to know why the code provided by Eric did not work, at least for me.
EDIT : fixed typos
I have a load of 3 hour MP3 files, and every ~15 minutes a distinct 1 second sound effect is played, which signals the beginning of a new chapter.
Is it possible to identify each time this sound effect is played, so I can note the time offsets?
The sound effect is similar every time, but because it's been encoded in a lossy file format, there will be a small amount of variation.
The time offsets will be stored in the ID3 Chapter Frame MetaData.
Example Source, where the sound effect plays twice.
ffmpeg -ss 0.9 -i source.mp3 -t 0.95 sample1.mp3 -acodec copy -y
Sample 1 (Spectrogram)
ffmpeg -ss 4.5 -i source.mp3 -t 0.95 sample2.mp3 -acodec copy -y
Sample 2 (Spectrogram)
I'm very new to audio processing, but my initial thought was to extract a sample of the 1 second sound effect, then use librosa in python to extract a floating point time series for both files, round the floating point numbers, and try to get a match.
import numpy
import librosa
print("Load files")
source_series, source_rate = librosa.load('source.mp3') # 3 hour file
sample_series, sample_rate = librosa.load('sample.mp3') # 1 second file
print("Round series")
source_series = numpy.around(source_series, decimals=5);
sample_series = numpy.around(sample_series, decimals=5);
print("Process series")
source_start = 0
sample_matching = 0
sample_length = len(sample_series)
for source_id, source_sample in enumerate(source_series):
if source_sample == sample_series[sample_matching]:
sample_matching += 1
if sample_matching >= sample_length:
print(float(source_start) / source_rate)
sample_matching = 0
elif sample_matching == 1:
source_start = source_id;
else:
sample_matching = 0
This does not work with the MP3 files above, but did with an MP4 version - where it was able to find the sample I extracted, but it was only that one sample (not all 12).
I should also note this script takes just over 1 minute to process the 3 hour file (which includes 237,426,624 samples). So I can imagine that some kind of averaging on every loop would cause this to take considerably longer.
Trying to directly match waveforms samples in the time domain is not a good idea. The mp3 signal will preserve the perceptual properties but it is quite likely the phases of the frequency components will be shifted so the sample values will not match.
You could try trying to match the volume envelopes of your effect and your sample.
This is less likely to be affected by the mp3 process.
First, normalise your sample so the embedded effects are the same level as your reference effect. Constructing new waveforms from the effect and the sample by using the average of the peak values over time frames that are just short enough to capture the relevant features. Better still use overlapping frames. Then use cross-correlation in the time domain.
If this does not work then you could analyze each frame using an FFT this gives you a feature vector for each frame. You then try to find matches of the sequence of features in your effect with the sample. Similar to https://stackoverflow.com/users/1967571/jonnor suggestion. MFCC is used in speech recognition but since you are not detecting speech FFT is probably OK.
I am assuming the effect playing by itself (no background noise) and it is added to the recording electronically (as opposed to being recorded via a microphone). If this is not the case the problem becomes more difficult.
This is an Audio Event Detection problem. If the sound is always the same and there are no other sounds at the same time, it can probably be solved with a Template Matching approach. At least if there is no other sounds with other meanings that sound similar.
The simplest kind of template matching is to compute the cross-correlation between your input signal and the template.
Cut out an example of the sound to detect (using Audacity). Take as much as possible, but avoid the start and end. Store this as .wav file
Load the .wav template using librosa.load()
Chop up the input file into a series of overlapping frames. Length should be same as your template. Can be done with librosa.util.frame
Iterate over the frames, and compute cross-correlation between frame and template using numpy.correlate.
High values of cross-correlation indicate a good match. A threshold can be applied in order to decide what is an event or not. And the frame number can be used to calculate the time of the event.
You should probably prepare some shorter test files which have both some examples of the sound to detect as well as other typical sounds.
If the volume of the recordings is inconsistent you'll want to normalize that before running detection.
If cross-correlation in the time-domain does not work, you can compute the melspectrogram or MFCC features and cross-correlate that. If this does not yield OK results either, a machine learning model can be trained using supervised learning, but this requires labeling a bunch of data as event/not-event.
To follow up on the answers by #jonnor and #paul-john-leonard, they are both correct, by using frames (FFT) I was able to do Audio Event Detection.
I've written up the full source code at:
https://github.com/craigfrancis/audio-detect
Some notes though:
To create the templates, I used ffmpeg:
ffmpeg -ss 13.15 -i source.mp4 -t 0.8 -acodec copy -y templates/01.mp4;
I decided to use librosa.core.stft, but I needed to make my own implementation of this stft function for the 3 hour file I'm analysing, as it's far too big to keep in memory.
When using stft I tried using a hop_length of 64 at first, rather than the default (512), as I assumed that would give me more data to work with... the theory might be true, but 64 was far too detailed, and caused it to fail most of the time.
I still have no idea how to get cross-correlation between frame and template to work (via numpy.correlate)... instead I took the results per frame (the 1025 buckets, not 1024, which I believe relate to the Hz frequencies found) and did a very simple average difference check, then ensured that average was above a certain value (my test case worked at 0.15, the main files I'm using this on required 0.55 - presumably because the main files had been compressed quite a bit more):
hz_score = abs(source[0:1025,x] - template[2][0:1025,y])
hz_score = sum(hz_score)/float(len(hz_score))
When checking these scores, it's really useful to show them on a graph. I often used something like the following:
import matplotlib.pyplot as plt
plt.figure(figsize=(30, 5))
plt.axhline(y=hz_match_required_start, color='y')
while x < source_length:
debug.append(hz_score)
if x == mark_frame:
plt.axvline(x=len(debug), ymin=0.1, ymax=1, color='r')
plt.plot(debug)
plt.show()
When you create the template, you need to trim off any leading silence (to avoid bad matching), and an extra ~5 frames (it seems that the compression / re-encoding process alters this)... likewise, remove the last 2 frames (I think the frames include a bit of data from their surroundings, where the last one in particular can be a bit off).
When you start finding a match, you might find it's ok for the first few frames, then it fails... you will probably need to try again a frame or two later. I found it easier having a process that supported multiple templates (slight variations on the sound), and would check their first testable (e.g. 6th) frame and if that matched, put them in a list of potential matches. Then, as it progressed on to the next frames of the source, it could compare it to the next frames of the template, until all frames in the template had been matched (or failed).
This might not be an answer, it's just where I got to before I start researching the answers by #jonnor and #paul-john-leonard.
I was looking at the Spectrograms you can get by using librosa stft and amplitude_to_db, and thinking that if I take the data that goes in to the graphs, with a bit of rounding, I could potentially find the 1 sound effect being played:
https://librosa.github.io/librosa/generated/librosa.display.specshow.html
The code I've written below kind of works; although it:
Does return quite a few false positives, which might be fixed by tweaking the parameters of what is considered a match.
I would need to replace the librosa functions with something that can parse, round, and do the match checks in one pass; as a 3 hour audio file causes python to run out of memory on a computer with 16GB of RAM after ~30 minutes before it even got to the rounding bit.
import sys
import numpy
import librosa
#--------------------------------------------------
if len(sys.argv) == 3:
source_path = sys.argv[1]
sample_path = sys.argv[2]
else:
print('Missing source and sample files as arguments');
sys.exit()
#--------------------------------------------------
print('Load files')
source_series, source_rate = librosa.load(source_path) # The 3 hour file
sample_series, sample_rate = librosa.load(sample_path) # The 1 second file
source_time_total = float(len(source_series) / source_rate);
#--------------------------------------------------
print('Parse Data')
source_data_raw = librosa.amplitude_to_db(abs(librosa.stft(source_series, hop_length=64)))
sample_data_raw = librosa.amplitude_to_db(abs(librosa.stft(sample_series, hop_length=64)))
sample_height = sample_data_raw.shape[0]
#--------------------------------------------------
print('Round Data') # Also switches X and Y indexes, so X becomes time.
def round_data(raw, height):
length = raw.shape[1]
data = [];
range_length = range(1, (length - 1))
range_height = range(1, (height - 1))
for x in range_length:
x_data = []
for y in range_height:
# neighbours = []
# for a in [(x - 1), x, (x + 1)]:
# for b in [(y - 1), y, (y + 1)]:
# neighbours.append(raw[b][a])
#
# neighbours = (sum(neighbours) / len(neighbours));
#
# x_data.append(round(((raw[y][x] + raw[y][x] + neighbours) / 3), 2))
x_data.append(round(raw[y][x], 2))
data.append(x_data)
return data
source_data = round_data(source_data_raw, sample_height)
sample_data = round_data(sample_data_raw, sample_height)
#--------------------------------------------------
sample_data = sample_data[50:268] # Temp: Crop the sample_data (318 to 218)
#--------------------------------------------------
source_length = len(source_data)
sample_length = len(sample_data)
sample_height -= 2;
source_timing = float(source_time_total / source_length);
#--------------------------------------------------
print('Process series')
hz_diff_match = 18 # For every comparison, how much of a difference is still considered a match - With the Source, using Sample 2, the maximum diff was 66.06, with an average of ~9.9
hz_match_required_switch = 30 # After matching "start" for X, drop to the lower "end" requirement
hz_match_required_start = 850 # Out of a maximum match value of 1023
hz_match_required_end = 650
hz_match_required = hz_match_required_start
source_start = 0
sample_matched = 0
x = 0;
while x < source_length:
hz_matched = 0
for y in range(0, sample_height):
diff = source_data[x][y] - sample_data[sample_matched][y];
if diff < 0:
diff = 0 - diff
if diff < hz_diff_match:
hz_matched += 1
# print(' {} Matches - {} # {}'.format(sample_matched, hz_matched, (x * source_timing)))
if hz_matched >= hz_match_required:
sample_matched += 1
if sample_matched >= sample_length:
print(' Found # {}'.format(source_start * source_timing))
sample_matched = 0 # Prep for next match
hz_match_required = hz_match_required_start
elif sample_matched == 1: # First match, record where we started
source_start = x;
if sample_matched > hz_match_required_switch:
hz_match_required = hz_match_required_end # Go to a weaker match requirement
elif sample_matched > 0:
# print(' Reset {} / {} # {}'.format(sample_matched, hz_matched, (source_start * source_timing)))
x = source_start # Matched something, so try again with x+1
sample_matched = 0 # Prep for next match
hz_match_required = hz_match_required_start
x += 1
#--------------------------------------------------
I think this code takes too long to execute, so maybe there are better ways to do this. I'm not looking for an answer related to parallelising the for loops, or using more than one processor.
What I'm trying to do is to read values from "file" using "np.genfromtxt(file)". I have 209*500*16 of these files. I want to extract the minimum value of the highest 1000 values of the 209 loop, and putting these 500 values in 16 different files. If the files are missing or the data hasn't the adequate size, the info is written to the "missing_all" file.
The questions are:
Is this the best method to open a file?
Is this the best method to write to files?
How can I make this code faster?
Code:
import numpy as np
import os.path
output_filename2 = '/home/missing_all.txt'
target2 = open(output_filename2, 'w')
for w in range(16):
group = 1200 + 50*w
output_filename = '/home/veto_%s.txt' %(group)
target = open(output_filename, 'w')
for z in range(1,501):
sig_b = np.zeros((209*300))
y = 0
for index in range(1,210):
file = '/home/BandNo_%s_%s/%s_209.dat' %(group,z,index)
if not os.path.isfile(file):
sig_b[y:y+300] = 0
y = y + 300
target2.write('%s %s %s\n' % (group,z,index))
continue
data = np.genfromtxt(file)
if (data.shape[0] < 300):
sig_b[y:y+300] = 0
y = y + 300
target2.write('%s %s %s\n' % (group,z,index))
continue
sig_b[y:y+300] = np.sort(data[:,4])[::-1][0:300]
y = y + 300
sig_b = np.sort(sig_b[:])[::-1][0:1000]
target.write('%s\n' % (sig_b[-1]))
Profiler
You can use a profiler to figure out what parts of your script take the most time. This way you know exactly what takes the most time and can optimize those lines instead of blindly trying to optimize your code. The time invested to figure out how the profiler works will pay for itself easily later on.
Some possible slow-downs
Here are some guesses, but they really are only guesses.
You open() only 17 files, so it probably doesn't matter how exactly you do this.
I don't know much about writing-performance. Using file.write() seems fine to me.
genfromtextfile probably takes quite a while (depends on your input files), is loadtxt an alternative for you? The docs states you can use it for data without holes.
Using a binary file format instead of text could speed up reading the file.
You sort your array on every iteration. Is there a way to sort it only at the end?
Usually asking the file system something is not very fast, i.e. os.path.isfile(file) is potentially slow. You could try creating a dict of all the children of the parent directory and use that cached version.
Similarly, if most of your files exist, using exceptions can be faster:
try:
data = np.genfromtxt(file)
except FileNotFoundError: # not sure if this is the correct exception
sig_b[y:y+300] = 0
y += 300
target2.write('%s %s %s\n' % (group,z,index))
continue
I didn't try to understand your code in detail. Maybe you can reduce the necessary work by using a smarter algorithm?
PS: I like that you try to put all equal signs on the same column. Unfortunately here it makes it harder to read your code.
I am trying to write my own custom audio filter for moviepy.
I am looking at audio_fadein as an example, but I am having trouble understanding the expected type of (t) the input variable.
Could anyone explain what the expected type of t is? Or where in the moviepy code I can look to see what libraries this t comes from or is used by? Thank you for any help, it is greatly appreciated.
#audio_video_fx
def audio_fadein(clip, duration):
"""Return an audio (or video) clip that is first mute, then the
sound arrives progressively over ``duration`` seconds."""
def fading(gf,t):
gft = gf(t)
if np.isscalar(t):
factor = min(1.0 * t / duration, 1)
factor = np.array([factor,factor])
else:
factor = np.minimum(1.0 * t / duration, 1)
factor = np.vstack([factor,factor]).T
return factor * gft
return clip.fl(fading, keep_duration = True)
The format of t was an array of 2000 equidistant values.
These values were actually all times since the start of the clip, and the 2000 were just giving a window of times, presumably so that in the audio processing you could look at more values than just the current 'moment'.
This array case is handled by the 'else' clause. I am not sure when this function receives t as a simple scalar value.
I am trying to make a video from a large number of images using MoviePy. The approach works fine for small numbers of images, but the process is killed for large numbers of images. At about 500 images added, the Python process is using all about half of the volatile memory available. There are many more images than that.
How should I address this? I want the processing to complete and I don't mind if the processing takes a bit longer, but it would be good if I could limit the memory and CPU usage in some way. With the current approach, the machine becomes almost unusable while processing.
The code is as follows:
import os
import time
from moviepy.editor import *
def ls_files(
path = "."
):
return([fileName for fileName in os.listdir(path) if os.path.isfile(
os.path.join(path, fileName)
)])
def main():
listOfFiles = ls_files()
listOfTileImageFiles = [fileName for fileName in listOfFiles \
if "_tile.png" in fileName
]
numberOfTiledImages = len(listOfTileImageFiles)
# Create a video clip for each image.
print("create video")
videoClips = []
imageDurations = []
for imageNumber in range(0, numberOfTiledImages):
imageFileName = str(imageNumber) + "_tile.png"
print("add image {fileName}".format(
fileName = imageFileName
))
imageClip = ImageClip(imageFileName)
duration = 0.1
videoClip = imageClip.set_duration(duration)
# Determine the image start time by calculating the sum of the durations
# of all previous images.
if imageNumber != 0:
videoStartTime = sum(imageDurations[0:imageNumber])
else:
videoStartTime = 0
videoClip = videoClip.set_start(videoStartTime)
videoClips.append(videoClip)
imageDurations.append(duration)
fullDuration = sum(imageDurations)
video = concatenate(videoClips)
video.write_videofile(
"video.mp4",
fps = 30,
codec = "mpeg4",
audio_codec = "libvorbis"
)
if __name__ == "__main__":
main()
If I understood correctly, you want to use the different images as the frames of your video.
In this case you should use ImageSequenceClip() (it's in the library, but not yet in the web docs, see here for the doc).
Basically, you just write
clip = ImageSequenceClip("some/directory/", fps=10)
clip.write_videofile("result.mp4")
And it will read the images in the directory in alpha-numerical order, while keeping only one frame at a time in the memory.
While I am at it, you can also provide a list of filenames or a list of numpy arrays to ImageSequenceClip.
Note that if you just want to transform images into a video, and not anything else fancy like adding titles or compositing with another video, then you can do it directly with ffmpeg. From memory the command should be:
ffmpeg -i *_tile.png -r 10 -o result.mp4