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I have implemented a numpy function that:
takes as inputs:
a n (rows) x m (columns) array of floats.
a threshold (float)
for each row:
if the max value of the row is larger than or equal to threshold,
if this max value is not preceded in the same row by a min value lower than or equal to -threshold,
then this row is flagged True (larger than),
else this row is flagged False (not larger than)
returns then this n (rows) x 1 (column) array of booleans
What I have implemented works (at least on provided example), but I am far from being an expert in numpy, and I wonder if there is no more efficient way of handling this (possibly avoid the miscellaneous transpose & tile for instance?)
I would gladly accept any advice on how making this function more efficient and/or readable.
import numpy as np
import pandas as pd
# Test data
threshold=0.02 #2%
df = pd.DataFrame({'variation_1': [0.01, 0.02, 0.005, -0.02, -0.01, -0.01],
'variation_2': [-0.01, 0.08, 0.08, 0.01, -0.02, 0.01],
'variation_3': [0.005, -0.03, -0.03, 0.002, 0.025, -0.03],
})
data = df.values
Checking expected results:
In [75]: df
Out[75]:
variation_1 variation_2 variation_3 # Expecting
0 0.010 -0.01 0.005 # False (no value larger than threshold)
1 0.020 0.08 -0.030 # True (1st value equal to threshold)
2 0.005 0.08 -0.030 # True (2nd value larger than threshold)
3 -0.020 0.01 0.002 # False (no value larger than threshold)
4 -0.010 -0.02 0.025 # False (2nd value lower than -threshold)
5 -0.010 0.01 -0.030 # False (no value larger than threshold)
Current function.
def greater_than(data: np.ndarray, threshold: float) -> np.ndarray:
# Step 1.
# Filtering out from 'low_max' mask the rows which 'max' is not greater than or equal
# to 'threshold'. 'low_max' is reshaped like input array for use in next step.
data_max = np.amax(data, axis=1)
low_max = np.transpose([data_max >= threshold] * data.shape[1])
# Step 2.
# Filtering values preceding max of each row
max_idx = np.argmax(data, axis=1) # Get idx of max.
max_idx = np.transpose([max_idx] * data.shape[1]) # Reshape like input array.
# Create an array of index.
idx_array = np.tile(np.arange(data.shape[1]), (data.shape[0],1))
# Keep indices lower than index of max for each row, and filter out rows with
# a max too low vs 'threshold' (from step 1).
mask_max = (idx_array <= max_idx) & (low_max)
# Step 3.
# On a masked array re-using mask from step 2 to filter out unqualifying values,
# filter out rows with a 'min' preceding the 'max' and that are lower than or
# equal to '-threshold'.
data = np.ma.array(data, mask=~mask_max)
data_min = np.amin(data, axis=1)
mask_min = data_min > -threshold
# Return 'mask_min', filling masked values with 'False'.
return np.ma.filled(mask_min, False)
Results.
res = greater_than(data, threshold)
In [78]:res
Out[78]: array([False, True, True, False, False, False])
Thanks in advance for any advice!
lesser = data <= -threshold
greater = data >= threshold
idx_lesser = np.argmax(lesser, axis=1)
idx_greater = np.argmax(greater, axis=1)
has_lesser = np.any(lesser, axis=1)
has_greater = np.any(greater, axis=1)
outptut = has_greater * (has_lesser * (idx_lesser > idx_greater) + np.logical_not(has_lesser))
yields your expected output on your data and should be quite fast. Also, I'm not entirely sure I understand your explanation so if this doesn't work on your actual data let me know.
I want to concatenate two tensors checkerboard-ly in tensorflow2, like examples showed below:
example 1:
a = [[1,1],[1,1]]
b = [[0,0],[0,0]]
concated_a_and_b = [[1,0,1,0],[0,1,0,1]]
example 2:
a = [[1,1,1],[1,1,1],[1,1,1]]
b = [[0,0,0],[0,0,0],[0,0,0]]
concated_a_and_b = [[1,0,1,0,1,0],[0,1,0,1,0,1],[1,0,1,0,1,0]]
Is there a decent way in tensorflow2 to concatenate them like this?
A bit of background for this:
I first split a tensor c with a checkerboard mask into two halves a and b. A after some transformation I have to concat them back into oringnal shape and order.
What I mean by checkerboard-ly:
Step 1: Generate a matrix with alternated values
You can do this by first concatenating into [1, 0] pairs, and then by applying a final reshape.
Step 2: Reverse some rows
I split the matrix into two parts, reverse the second part and then rebuild the full matrix by picking alternatively from the first and second part
Code sample:
import math
import numpy as np
import tensorflow as tf
a = tf.ones(shape=(3, 4))
b = tf.zeros(shape=(3, 4))
x = tf.expand_dims(a, axis=-1)
y = tf.expand_dims(b, axis=-1)
paired_ones_zeros = tf.concat([x, y], axis=-1)
alternated_values = tf.reshape(paired_ones_zeros, [-1, a.shape[1] + b.shape[1]])
num_samples = alternated_values.shape[0]
middle = math.ceil(num_samples / 2)
is_num_samples_odd = middle * 2 != num_samples
# Gather first part of the matrix, don't do anything to it
first_elements = tf.gather_nd(alternated_values, [[index] for index in range(middle)])
# Gather second part of the matrix and reverse its elements
second_elements = tf.reverse(tf.gather_nd(alternated_values, [[index] for index in range(middle, num_samples)]), axis=[1])
# Pick alternatively between first and second part of the matrix
indices = np.concatenate([[[index], [index + middle]] for index in range(middle)], axis=0)
if is_num_samples_odd:
indices = indices[:-1]
output = tf.gather_nd(
tf.concat([first_elements, second_elements], axis=0),
indices
)
print(output)
I know this is not a decent way as it will affect time and space complexity. But it solves the above problem
def concat(tf1, tf2):
result = []
for (index, (tf_item1, tf_item2)) in enumerate(zip(tf1, tf2)):
item = []
for (subitem1, subitem2) in zip(tf_item1, tf_item2):
if index % 2 == 0:
item.append(subitem1)
item.append(subitem2)
else:
item.append(subitem2)
item.append(subitem1)
concated_a_and_b.append(item)
return concated_a_and_b
I want to calculate pairwise distance between a set of Tensor (e.g 4 Tensor). Each matrix is 2D Tensor. I don't know how to do this in vectorize format. I wrote following sudo-code to determine what I need:
E.shape => [4,30,30]
sum = 0
for i in range(4):
for j in range(4):
res = calculate_distance(E[i],E[j]) # E[i] is one the 30*30 Tensor
sum = sum + reduce_sum(res)
Here is my last try:
x_ = tf.expand_dims(E, 0)
y_ = tf.expand_dims(E, 1)
s = x_ - y_
P = tf.reduce_sum(tf.norm(s, axis=[-2, -1]))
This code works But I don't know how do this in a Batch. For instance when E.shape is [BATCH_SIZE * 4 * 30 * 30] my code doesn't work and Out Of Memory will happen. How can I do this efficiently?
Edit: After a day, I find a solution. it's not perfect but works:
res = tf.map_fn(lambda x: tf.map_fn(lambda y: tf.map_fn(lambda z: tf.norm(z - x), x), x), E)
res = tf.reduce_mean(tf.square(res))
Your solution with expand_dims should be okay if your batch size is not too large. However, given that your original pseudo code loops over range(4), you should probably expand axes 1 and 2, instead of 0 and 1.
You can check the shape of the tensors to ensure that you're specifying the correct axes. For example,
batch_size = 8
E_np = np.random.rand(batch_size, 4, 30, 30)
E = K.variable(E_np) # shape=(8, 4, 30, 30)
x_ = K.expand_dims(E, 1)
y_ = K.expand_dims(E, 2)
s = x_ - y_ # shape=(8, 4, 4, 30, 30)
distances = tf.norm(s, axis=[-2, -1]) # shape=(8, 4, 4)
P = K.sum(distances, axis=[-2, -1]) # shape=(8,)
Now P will be the sum of pairwise distances between the 4 matrices for each of the 8 samples.
You can also verify that the values in P is the same as what would be computed in your pseudo code:
answer = []
for batch_idx in range(batch_size):
s = 0
for i in range(4):
for j in range(4):
a = E_np[batch_idx, i]
b = E_np[batch_idx, j]
s += np.sqrt(np.trace(np.dot(a - b, (a - b).T)))
answer.append(s)
print(answer)
[149.45960605637578, 147.2815068236368, 144.97487402393705, 146.04866735065312, 144.25537059201062, 148.9300986019226, 146.61229889228133, 149.34259789169045]
print(K.eval(P).tolist())
[149.4595947265625, 147.281494140625, 144.97488403320312, 146.04867553710938, 144.25537109375, 148.9300994873047, 146.6123046875, 149.34259033203125]
Tensorflow allows to compute the Frobenius norm via tf.norm function. In case of 2D matrices, it's equivalent to 1-norm.
The following solution isn't vectorized and assumes that the first dimension in E is known statically:
E = tf.random_normal(shape=[5, 3, 3], dtype=tf.float32)
F = tf.split(E, E.shape[0])
total = tf.reduce_sum([tf.norm(tensor=(lhs-rhs), ord=1, axis=(-2, -1)) for lhs in F for rhs in F])
Update:
An optimized vectorized version of the same code:
E = tf.random_normal(shape=[1024, 4, 30, 30], dtype=tf.float32)
lhs = tf.expand_dims(E, axis=1)
rhs = tf.expand_dims(E, axis=2)
total = tf.reduce_sum(tf.norm(tensor=(lhs - rhs), ord=1, axis=(-2, -1)))
Memory concerns: upon evaluating this code,
tf.contrib.memory_stats.MaxBytesInUse() reports that the peak memory consumption is 73729792 = 74Mb, which indicates relatively moderate overhead (the raw lhs-rhs tensor is 59Mb). Your OOM is most likely caused by the duplication of BATCH_SIZE dimension when you compute s = x_ - y_, because your batch size is much larger than the number of matrices (1024 vs 4).
I have a list of lists with two values that represent a start time-point and an end time-point. I would like to count how much of the time range between the two points fall into bins.
The bins are between 0-300,300-500 and 500-1200.
I would also like to bin them between 0-50, 50-100, 100-150 and so on.
The question is similar to Python: Checking to which bin a value belongs, but different since it involves a two-points time-range which can fall into separate bins at the same time.
I have created the a for loop in the code below, which works. But I'm wondering if there is a faster more pythonic way to calculate this, perhaps using pandas or numpy.
import numpy
x = numpy.array([[100, 150],[100, 125],[290, 310],[277, 330],
[300, 400],[480, 510],[500, 600]])
d = {'0-300': [0], '300-500': [0], '500-1200':[0]}
import pandas as pd
df = pd.DataFrame(data=d)
for i in x:
start,end = i[0],i[1]
if start <= 300 and end <= 300: # checks if time ranges falls into only 1st bin
df['0-300'][0] += end - start
elif start <= 300 and end > 300: # checks if time ranges falls into 1st and 2ed bin
df['0-300'][0] += (300 - start)
df['300-500'][0] += (end - 300)
elif start >= 300 and end >= 300 and end <= 500: # checks if time ranges falls into only 2ed bin
df['300-500'][0] += end - start
elif start <= 500 and end > 500: # checks if time ranges falls into 2ed and 3ed bin
df['300-500'][0] += (500 - start)
df['500-1200'][0] += (end - 500)
elif start > 500: # checks if time ranges falls into only 3ed bin
df['500-1200'][0] += end - start
df:
0-300 300-500 500-1200
108 160 110
thanks for reading
For a generic number of bins, here's a vectorized way leveraging np.add.at to get the counts and then np.add.reduceat for getting binned summations -
bins = [0, 300, 500, 1200] # Declare bins
id_arr = np.zeros(bins[-1], dtype=int)
np.add.at(id_arr, x[:,0], 1)
np.add.at(id_arr, x[:,1], -1)
c = id_arr.cumsum()
out = np.add.reduceat(c, bins[:-1])
# Present in a dataframe format
col_names = [str(i)+'-' + str(j) for i,j in zip(bins[:-1], bins[1:])]
df_out = pd.DataFrame([out], columns=col_names)
Sample output -
In [524]: df_out
Out[524]:
0-300 300-500 500-1200
0 108 160 110
Here is one way of doing it
In [1]: counts = np.zeros(1200, dtype=int)
In [2]: for x_lower, x_upper in x: counts[x_lower:x_upper] += 1
In [3]: d['0-300'] = counts[0:300].sum()
In [4]: d['300-500'] = counts[300:500].sum()
In [5]: d['500-1200'] = counts[500:1200].sum()
In [6]: d
Out[6]: {'0-300': 108, '300-500': 160, '500-1200': 110}
However, in order to sum up the results for all bins, it will be better to wrap those 3 steps into a for loop.
In pygame, I have a surface:
im = pygame.image.load('foo.png').convert_alpha()
im = pygame.transform.scale(im, (64, 64))
How can I get a grayscale copy of the image, or convert the image data to grayscale? I have numpy.
Use a Surfarray, and filter it with numpy or Numeric:
def grayscale(self, img):
arr = pygame.surfarray.array3d(img)
#luminosity filter
avgs = [[(r*0.298 + g*0.587 + b*0.114) for (r,g,b) in col] for col in arr]
arr = numpy.array([[[avg,avg,avg] for avg in col] for col in avgs])
return pygame.surfarray.make_surface(arr)
After a lot of research, I came up with this solution, because answers to this question were too slow for what I wanted this feature to:
def greyscale(surface: pygame.Surface):
start = time.time() # delete me!
arr = pygame.surfarray.array3d(surface)
# calulates the avg of the "rgb" values, this reduces the dim by 1
mean_arr = np.mean(arr, axis=2)
# restores the dimension from 2 to 3
mean_arr3d = mean_arr[..., np.newaxis]
# repeat the avg value obtained before over the axis 2
new_arr = np.repeat(mean_arr3d[:, :, :], 3, axis=2)
diff = time.time() - start # delete me!
# return the new surface
return pygame.surfarray.make_surface(new_arr)
I used time.time() to calculate the time cost for this approach, so for a (800, 600, 3) array it takes: 0.026769161224365234 s to run.
As you pointed out, here is a variant preserving the luminiscence:
def greyscale(surface: pygame.Surface):
arr = pygame.surfarray.pixels3d(surface)
mean_arr = np.dot(arr[:,:,:], [0.216, 0.587, 0.144])
mean_arr3d = mean_arr[..., np.newaxis]
new_arr = np.repeat(mean_arr3d[:, :, :], 3, axis=2)
return pygame.surfarray.make_surface(new_arr)
The easiest way is to iterate over all the pixels in your image and call .get_at(...) and .set_at(...).
This will be pretty slow, so in answer to your implicit suggestion about using NumPy, look at http://www.pygame.org/docs/tut/surfarray/SurfarrayIntro.html. The concepts and most of the code are identical.