I am struggling to understand why the np.convolve method returns an N+M-1 set. I would appreciate your help.
Suppose I have two discrete probability distributions with values of [1,2] and [10,12] and probabilities of [.5,0.2] and [.5,0.4] respectively.
Using numpy's convolve function I get:
>>In[]: np.convolve([.5,0.2],[.5,0.4])
>>Out[]: array([[0.25, 0.3 , 0.08])
However I don't understand why the resulting probability distribution only has 3 datapoints. To my understanding the sum of my input variables can have the following values: [11,12,13,14] so I would expect 4 datapoints to reflect the probabilities of each of these occurrences.
What am I missing?
I have managed to find the answer to my own question after understanding convolution a bit better. Posting it here for anyone wondering:
Effectively, the convolution of the two "signals" or probability functions in my example above is not correctly done as it is nowhere reflected that the events [1,2] of the first distribution and [10,12] of the second do not coincide.
Simply taking np.convolve([.5,0.2],[.5,0.4]) assumes the probabilities corresponding to the same events (e.g. [1,2] [1,2]).
Correct approach would be to bring the two series into alignment under a common X axis as in x \in [1,12] as below:
>>In[]: vector1 = [.5,0.2, 0,0,0,0,0,0,0,0,0,0]
>>In[]: vector2 = [0,0,0,0,0,0,0,0,0,.5, 0,0.4]
>>In[]: np.convolve(vector1, vector2)
>>Out[]: array([0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.25, 0.1 ,
0.2 , 0.08, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. ])
which gives the correct values for 11,12,13,14
Related
I seem to be stuck with something seemlingy trivial: I need to access elements in a numpy.matrix. But the matrix doesn't behave as I expect:
>>> mymatrix
matrix([[0.02700243, 0. , 0. , ..., 0. , 0. ,
0. ]])
>>> type(mymatrix)
<class 'numpy.matrix'>
>>> mymatrix.shape
(1, 10000)
>>> mymatrix[0]
matrix([[0.02700243, 0. , 0. , ..., 0. , 0. ,
0. ]])
>>> mymatrix[0][0]
matrix([[0.02700243, 0. , 0. , ..., 0. , 0. ,
0. ]])
>>> mymatrix[0][0][0]
matrix([[0.02700243, 0. , 0. , ..., 0. , 0. ,
0. ]])
i.e. no matter whether I take the matrix itself, or the [0] element of the matrix or the [0][0] element of the [0][0][0], i always get the same object ... How is that possible?
According to NumPy Manual:
A matrix is a specialized 2-D array that retains its 2-D nature
through operations
And:
It is no longer recommended to use this class, even for linear
algebra. Instead use regular arrays. The class may be removed in the
future.
Maybe you could consider using a regular array instead. You can return your matrix as an array using:
mymatrix.A
mymatrix.A[0]
mymatrix.A[0][0]
You need to transpose your matrix to index the first element in a matrix with this shape.
Try:
mymatrix.T[0]
I have got a set of histograms from numpy.histogram:
probas, years = zip(*[np.histogram(r, bins= bin_values) for r in results])
results is an array of shape(9, 10000) The bin values are the years from 2029 and 2066. The probas array has a shape (9,37) and the years array (9,38). So years[:,:-1] has a shape of (9,37).
I can obtaint he cumulative histogram data using:
probas = np.cumsum(probas, axis=1)
I can then normalize it to [0,1]:
probas = np.asarray(probas)
probas = probas/np.max(probas, axis = 0)
I then try and interpolate that cumulative distribution using scipy:
inverse_pdfs = [scipy.interpolate.interp1d(probas[i], years[i,:-1]) for i in range(probas.shape[0])]
When I plot the third histogram of the data set as a plt.plot() and that from the inverse_pdfs using:
i = 2
plt.plot(years[i,:-1], probas[i], color="orange")
probability_range = np.arange(0.,1.01,0.01)
plt.plot([inverse_pdfs[i](p) for p in probability_range], probability_range, color="blue")
I obtain:
As you can see the match is pretty good for most of the years after 2042, but before that it is very bad.
Any suggestion on how to improve that match, or where the problem comes from, would be very welcome.
For information, the data used to train the interpolator on the third histogram are:
years[2,:-1]: [2029. 2030. 2031. 2032. 2033. 2034. 2035. 2036. 2037. 2038. 2039. 2040.
2041. 2042. 2043. 2044. 2045. 2046. 2047. 2048. 2049. 2050. 2051. 2052.
2053. 2054. 2055. 2056. 2057. 2058. 2059. 2060. 2061. 2062. 2063. 2064.
2065.]
probas[2]:[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0.0916 0.2968 0.4888 0.6666 0.8335 0.9683 1.
1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
1. 1. 1. 1. 1. 1. 1. ]
I am really new to Python and scikit-learn (sklearn) and I am trying to load this dataset which consists of 7 columns of attributes and 1 column of the data classification (class/data target). But there's this one attribute which consists of data [1,2,3,4,5] which actually marks a stage of something, thus making it a nominal, not numeric. But of course python recognizes it as a numerical data (int64), when in fact I want it to be treated as a nominal data (object). How do I change the column type to nominal?
I have done the following.
print(data.dtypes)
data["col_name"]=data["col_name"].astype(numpy.object)
print(data.dtypes)
In the first print, it still recognizes my data["col_name"] as an int64, but after the astype line, it has changed it object. But it doesn't make any difference to the data, since when I try to use matplotlib and create a histogram, it still recognizes both the X and Y as numbers instead of object.
Also I have read about the One Hot Encoding and Label Encoding on the documentation, but I figured they are not what I need in my case. I wonder if I have misunderstood something or maybe there's another solution.
Thanks
Reading through the documents for sklearn. This package has thorough documentation. In particular the Preprocessing section on encoding categorical features:
In regards to keeping categorical features represented in an array of integers, ie [1,2,3,4,5], we have this:
Such integer representation can not be used directly with scikit-learn
estimators, as these expect continuous input, and would interpret the
categories as being ordered, which is often not desired (i.e. the set
of browsers was ordered arbitrarily). One possibility to convert
categorical features to features that can be used with scikit-learn
estimators is to use a one-of-K or one-hot encoding, which is
implemented in OneHotEncoder. This estimator transforms each
categorical feature with m possible values into m binary features,
with only one active.
So what you can to do is convert your array into 5 new columns (this case, since you have 5 possible values) using one-hot encoding.
Here is some working code. The input is a column of categorical parameters [1,2,3,4,5], the ouput is a matrix, 5 columns, 1 for each of the 5 possible choices:
from sklearn.preprocessing import OneHotEncoder
enc = OneHotEncoder()
enc.fit([[1],[2],[3],[4],[5]])
OneHotEncoder(categorical_features='all', dtype='numpy.float64', handle_unknown='error', n_values='auto', sparse=True)
print enc.transform([[1],[2],[3],[4],[5]]).toarray()
Output:
[[ 1. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0.]
[ 0. 0. 1. 0. 0.]
[ 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 1.]]
Say your categorical parameters were in this order: [1,3,2,5,4,3,2,1,3,4,2]. You would get this output:
[[ 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0.]
[ 0. 1. 0. 0. 0.]
[ 0. 0. 0. 0. 1.]
[ 0. 0. 0. 1. 0.]
[ 0. 0. 1. 0. 0.]
[ 0. 1. 0. 0. 0.]
[ 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0.]
[ 0. 0. 0. 1. 0.]
[ 0. 1. 0. 0. 0.]]
So this 1 column will convert into 5 columns.
print(data.dtypes)
data["col_name"]=data["col_name"].astype(str)
print(data.dtypes)
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn import svm
digits = datasets.load_digits()
print(digits.data)
classifier = svm.SVC(gamma=0.4, C=100)
x, y = digits.data[:-1], digits.target[:-1]
x = x.reshape(1,-1)
y = y.reshape(-1,1)
print((x))
classifier.fit(x, y)
###
print('Prediction:', classifier.predict(digits.data[-3]))
###
plt.imshow(digits.images[-1], cmap=plt.cm.gray_r, interpolation='nearest')
plt.show()
I have reshaped the x and y as well. Still I'm getting an error saying :
Found input variables with inconsistent numbers of samples: [1, 1796]
Y has 1-d array with 1796 elements whereas x has many. How does it show 1 for x?
Actually scrap what I suggested below:
This link describes the general dataset API. The attribute data is a 2d array of each image, already flattened:
import sklearn.datasets
digits = sklearn.datasets.load_digits()
digits.data.shape
#: (1797, 64)
This is all you need to provide, no reshaping required. Similarly, the attribute data is a 1d array of each label:
digits.data.shape
#: (1797,)
No reshaping necessary. Just split into training and testing and run with it.
Try printing x.shape and y.shape. I feel that you're going to find something like: (1, 1796, ...) and (1796, ...) respectively. When calling fit for classifiers in scikit it expects two identically shaped iterables.
The clue, why are the arguments when reshaping different ways around:
x = x.reshape(1, -1)
y = y.reshape(-1, 1)
Maybe try:
x = x.reshape(-1, 1)
Completely unrelated to your question, but you're predicting on digits.data[-3] when the only element left out of the training set is digits.data[-1]. Not sure if that was intentional.
Regardless, it could be good to check your classifier over more results using the scikit metrics package. This page has an example of using it over the digits dataset.
The reshaping will transform your 8x8 matrix to a 1-dimensional vector, which can be used as a feature. You need to reshape the entire X vector, not only those of the training data, since the one's you will use for prediction need to have the same format.
The following code shows how:
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn import svm
digits = datasets.load_digits()
classifier = svm.SVC(gamma=0.4, C=100)
x, y = digits.images, digits.target
#only reshape X since its a 8x8 matrix and needs to be flattened
n_samples = len(digits.images)
x = x.reshape((n_samples, -1))
print("before reshape:" + str(digits.images[0]))
print("After reshape" + str(x[0]))
classifier.fit(x[:-2], y[:-2])
###
print('Prediction:', classifier.predict(x[-2]))
###
plt.imshow(digits.images[-2], cmap=plt.cm.gray_r, interpolation='nearest')
plt.show()
###
print('Prediction:', classifier.predict(x[-1]))
###
plt.imshow(digits.images[-1], cmap=plt.cm.gray_r, interpolation='nearest')
plt.show()
It will output:
before reshape:[[ 0. 0. 5. 13. 9. 1. 0. 0.]
[ 0. 0. 13. 15. 10. 15. 5. 0.]
[ 0. 3. 15. 2. 0. 11. 8. 0.]
[ 0. 4. 12. 0. 0. 8. 8. 0.]
[ 0. 5. 8. 0. 0. 9. 8. 0.]
[ 0. 4. 11. 0. 1. 12. 7. 0.]
[ 0. 2. 14. 5. 10. 12. 0. 0.]
[ 0. 0. 6. 13. 10. 0. 0. 0.]]
After reshape[ 0. 0. 5. 13. 9. 1. 0. 0. 0. 0. 13. 15. 10. 15. 5.
0. 0. 3. 15. 2. 0. 11. 8. 0. 0. 4. 12. 0. 0. 8.
8. 0. 0. 5. 8. 0. 0. 9. 8. 0. 0. 4. 11. 0. 1.
12. 7. 0. 0. 2. 14. 5. 10. 12. 0. 0. 0. 0. 6. 13.
10. 0. 0. 0.]
And a correct prediction for the last 2 images, which weren't used for training - you can decide however to make a bigger split between testing and training set.
I want to plot a 2D map of a sillicon wafer dies. Hence only the center portion have values and corners have the value 0. I'm using matplotlib's plt.imshow to obtain a simple map as follows:
data = np.array([[ 0. , 0. , 1. , 1. , 0. , 0. ],
[ 0. , 1. , 1. , 1. , 1. , 0. ],
[ 1. , 2. , 0.1, 2. , 2. , 1. ],
[ 1. , 2. , 2. , 0.1, 2. , 1. ],
[ 0. , 1. , 1. , 1. , 1. , 0. ],
[ 0. , 0. , 1. , 1. , 0. , 0. ]])
plt.figure(1)
plt.imshow(data ,interpolation='none')
plt.colorbar()
And I obtain the following map:
Is there any way to remove the dark blue areas where the values are zeros while retaining the shape of the 'wafer' (the green, red and lighter blue areas)? Meaning the corners would be whitespaces while the remainder retains the color configuration.
Or is there a better function I could use to obtain this?
There are two ways to get rid of the dark blue corners:
You can flag the data with zero values:
data[data == 0] = np.nan
plt.imshow(data, interpolation = 'none', vmin = 0)
Or you can create a masked array for imshow:
data_masked = np.ma.masked_where(data == 0, data)
plt.imshow(data_masked, interpolation = 'none', vmin = 0)
The two solutions above both solve your problem, although the use of masks is a bit more general.
If you want to retain the exact color configuration you need to manually set the vmin/vmax arguments for plotting the image. Passing vmin = 0 to plt.imshow above makes sure that the discarded zeros still show up on the color bar.