I have this code:
mm = np.array([[1, 4, 7, 8], [2, 2, 8, 4], [1, 13, 1, 5]])
mm = np.column_stack(mm)
mmCov = np.cov(mm, rowvar=0)
print("covariance\n", mmCov)
# my code to get correlations
mmResCor = np.zeros(shape=(3, 3))
for i in range(len(mmCov)):
for j in range(len(mmCov[i])):
mmResCor[i][j] = mmCov[i][j] / (math.sqrt(mmCov[i][i] * mmCov[j] [j]))
print("correlaciones a mano\n", mmResCor)
mmCor = np.corrcoef(mmCov, rowvar=0)
print("correlations\n", mmCor)
X = csr_matrix(mmCor)
XX = minimum_spanning_tree(X)
print("minimun spanning tree\n", XX)
first: each column represents a variable, with observations in the rows
numpy corrcoef use this relation with covariance matrix:
R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }
when I use numpy corrcoef I get this matrix
correlations
[[ 1. 0.8660254 -0.82603319]
[ 0.8660254 1. -0.99717646]
[-0.82603319 -0.99717646 1. ]]
but when I apply "my code" to get the same result...
mmResCor = np.zeros(shape=(3, 3))
for i in range(len(mmCov)):
for j in range(len(mmCov[i])):
mmResCor[i][j] = mmCov[i][j] / (math.sqrt(mmCov[i][i] * mmCov[j][j]))
I get this matrix
correlaciones a mano
[[ 1. 0.67082039 0. ]
[ 0.67082039 1. -0.5 ]
[ 0. -0.5 1. ]]
why do I get differents results if its suppose I am doing the same?
One more question:
When I apply minimun_spanning_tree I get this:
minimun spanning tree
(0, 2) -0.826033187631
(1, 2) -0.997176464953
Is there any way to represent these or can I save this result in some variables?
The np.corrcoef should take the data as the input. You're passing the covariance matrix as input. If you pass the data, you get the same result as your manual computation:
>>> np.corrcoef(mm, rowvar=0)
array([[ 1. , 0.67082039, 0. ],
[ 0.67082039, 1. , -0.5 ],
[ 0. , -0.5 , 1. ]])
Regarding the minimum spanning tree, I'm not sure what your question is, but the output XX is a sparse matrix which stores a matrix representation of the tree.
Related
I have two numpy arrays of shapes (4,4) and (9,4)
matrix1 = array([[ 72. , 72. , 72. , 72. ],
[ 72.00396729, 72.00396729, 72.00396729, 72.00396729],
[596.29998779, 596.29998779, 596.29998779, 596.29998779],
[708.83398438, 708.83398438, 708.83398438, 708.83398438]])
matrix2 = array([[ 72.02400208, 77.68997192, 115.6057663 , 105.64997101],
[120.98195648, 77.68997192, 247.19802856, 105.64997101],
[252.6330719 , 77.68997192, 337.25634766, 105.64997101],
[342.63256836, 77.68997192, 365.60125732, 105.64997101],
[ 72.02400208, 113.53997803, 189.65515137, 149.53997803],
[196.87202454, 113.53997803, 308.13119507, 149.53997803],
[315.3480835 , 113.53997803, 405.77023315, 149.53997803],
[412.86999512, 113.53997803, 482.0453186 , 149.53997803],
[ 72.02400208, 155.81002808, 108.98254395, 183.77003479]])
I need to compare all the rows of matrix2 with every row of matrix1. How can this be done without looping in the elements of matrix1?
If it is about element-wise comparison of the rows, then check this example:
# Generate sample arrays
a = np.random.randint(0, 5, size = (4, 3))
b = np.random.randint(-1, 6, size = (5, 3))
# Compare
a == b[:, None]
The last line does the comparison for you. The output array will have shape (num_of_b_rows, num_of_a_rows, common_num_of_cols): in this case, (5, 4, 3).
I am (re)building up my knowledge of numpy, having used it a little while ago.
I have a question about fancy indexing with multidimenional (in this case 2D) arrays.
Given the following snippet:
>>> a = np.arange(12).reshape(3,4)
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> i = np.array( [ [0,1], # indices for the first dim of a
... [1,2] ] )
>>> j = np.array( [ [2,1], # indices for the second dim
... [3,3] ] )
>>>
>>> a[i,j] # i and j must have equal shape
array([[ 2, 5],
[ 7, 11]])
Could someone explain in simple English, the logic being applied to give the results produced. Ideally, the explanation would be applicable for 3D and higher rank arrays being used to index an array.
Conceptually (in terms of restrictions placed on "rows" and "columns"), what does it mean to index using a 2D array?
Conceptually (in terms of restrictions placed on "rows" and "columns"), what does it mean to index using a 2D array?
It means you are constructing a 2d array R, such that R=A[B, C]. This means that the value for rij=abijcij.
So it means that the item located at R[0,0] is the item in A with as row index B[0,0] and as column index C[0,0]. The item R[0,1] is the item in A with row index B[0,1] and as column index C[0,1], etc.
So in this specific case:
>>> b = a[i,j]
>>> b
array([[ 2, 5],
[ 7, 11]])
b[0,0] = 2 since i[0,0] = 0, and j[0,0] = 2, and thus a[0,2] = 2. b[0,1] = 5 since i[0,0] = 1, and j[0,0] = 1, and thus a[1,1] = 5. b[1,0] = 7 since i[0,0] = 1, and j[0,0] = 3, and thus a[1,3] = 7. b[1,1] = 11 since i[0,0] = 2, and j[0,0] = 3, and thus a[2,3] = 11.
So you can say that i will determine the "row indices", and j will determine the "column indices". Of course this concept holds in more dimensions as well: the first "indexer" thus determines the indices in the first index, the second "indexer" the indices in the second index, and so on.
I have a 2D array, say
x = np.random.rand(10, 3)
array([[ 0.51158246, 0.51214272, 0.1107923 ],
[ 0.5210391 , 0.85308284, 0.63227215],
[ 0.57239625, 0.06276943, 0.1069803 ],
[ 0.71627613, 0.66454443, 0.56771438],
[ 0.24595493, 0.01007568, 0.84959605],
[ 0.99158904, 0.25034553, 0.00144037],
[ 0.43292656, 0.9247424 , 0.5123086 ],
[ 0.07224077, 0.57230282, 0.88522979],
[ 0.55665913, 0.20119776, 0.58865823],
[ 0.55129624, 0.26226446, 0.63070611]])
Then I find the indexes of maximum elements along the columns:
indexes = np.argmax(x, axis=0)
array([5, 6, 7])
So far so good.
But how do I actually get those elements? That is, how do I get ?some_operation?(x, indexes) == [0.99158904, 0.9247424, 0.88522979]?
Note that I need both the indexes and the associated values.
The best I could come up with was x[indexes, range(x.shape[1])], but it looks kinda complicated and inefficient. Is there a more idiomatic way?
You can use np.amax to find max value along an axis.
Using your example (x is the original array in your post):
In[1]: np.argmax(x, axis=0)
Out[1]:
array([5, 6, 7], dtype=int64)
In[2]: np.amax(x, axis=0)
Out[2]:
array([ 0.99158904, 0.9247424 , 0.88522979])
Documentation link
I have a numpy array (N,M) where some of the columns should be one-hot encoded. Please help to make a one-hot encoding using numpy and/or tensorflow.
Example:
[
[ 0.993, 0, 0.88 ]
[ 0.234, 1, 1.00 ]
[ 0.235, 2, 1.01 ]
.....
]
The 2nd column here ( with values 3 and 2 ) should be one hot-encoded, I know that there are only 3 distinct values ( 0, 1, 2 ).
The resulting array should look like:
[
[ 0.993, 0.88, 0, 0, 0 ]
[ 0.234, 1.00, 0, 1, 0 ]
[ 0.235, 1.01, 1, 0, 0 ]
.....
]
Like that I would be able to feed this array into the tensorflow.
Please notice that 2nd column was removed and it's one-hot version was appended in the end of each sub-array.
Any help would be highly appreciated.
Thanks in advance.
Update:
Here is what I have right now:
Well, not exactly...
1. I have more than 3 columns in the array...but I still want to do it only with 2nd..
2. First array is structured, ie it's shape is (N,)
Here is what I have:
def one_hot(value, max_value):
value = int(value)
a = np.zeros(max_value, 'uint8')
if value != 0:
a[value] = 1
return a
# data is structured array with the shape of (N,)
# it has strings, ints, floats inside..
# was get by np.genfromtxt(dtype=None)
unique_values = dict()
unique_values['categorical1'] = 1
unique_values['categorical2'] = 2
for row in data:
row[col] = unique_values[row[col]]
codes = np.zeros((data.shape[0], len(unique_values)))
idx = 0
for row in data:
codes[idx] = one_hot(row[col], len(unique_values)) # could be optimised by not creating new array every time
idx += 1
data = np.c_[data[:, [range(0, col), range(col + 1, 32)]], codes[data[:, col].astype(int)]]
Also trying to concatenate via:
print data.shape # shape (5000,)
print codes.shape # shape (5000,3)
data = np.concatenate((data, codes), axis=1)
Here's one approach -
In [384]: a # input array
Out[384]:
array([[ 0.993, 0. , 0.88 ],
[ 0.234, 1. , 1. ],
[ 0.235, 2. , 1.01 ]])
In [385]: codes = np.array([[0,0,0],[0,1,0],[1,0,0]]) # define codes here
In [387]: codes
Out[387]:
array([[0, 0, 0], # encoding for 0
[0, 1, 0], # encoding for 1
[1, 0, 0]]) # encoding for 2
# Slice out the second column and append one-hot encoded array
In [386]: np.c_[a[:,[0,2]], codes[a[:,1].astype(int)]]
Out[386]:
array([[ 0.993, 0.88 , 0. , 0. , 0. ],
[ 0.234, 1. , 0. , 1. , 0. ],
[ 0.235, 1.01 , 1. , 0. , 0. ]])
If you want to evaluate a 1-d array for multiple arguments efficiently i.e. without for-loop, you can do this:
x = array([1, 2, 3])
def gen_1d_arr(x):
arr = array([2 + x, 2 - x,])
return arr
gen_1d_arr(x).T
and you get:
array([[ 3, 1],
[ 4, 0],
[ 5, -1]])
Okay, but how do you do this for 2-d array like below:
def gen_2d_arr(x):
arr = array([[2 + x, 2 - x,],
[2 * x, 2 / x]])
return arr
and obtain this?:
array([[[ 3. , 1. ],
[ 2. , 2. ]],
[[ 4. , 0. ],
[ 4. , 1. ]],
[[ 5. , -1. ],
[ 6. , 0.66666667]]])
Also, is this generally possible for n-d arrays?
Look at what you get with your function
In [274]: arr = np.array([[2 + x, 2 - x,],
[2 * x, 2 / x]])
In [275]: arr
Out[275]:
array([[[ 3. , 4. , 5. ],
[ 1. , 0. , -1. ]],
[[ 2. , 4. , 6. ],
[ 2. , 1. , 0.66666667]]])
In [276]: arr.shape
Out[276]: (2, 2, 3)
The 3 comes from x. The middle 2 comes from [2+x, 2-x] pairs, and the 1st 2 from the outer list.
Looks like what you want is a (3,2,2) array. One option is to apply a transpose or axis swap to arr.
arr.transpose([2,0,1])
The basic operation of np.array([arr1,arr2]) is to construct a new array with a new dimension in front, i.e. with shape (2, *arr1(shape)).
There are other operations that combine arrays. np.concatenate and its variants hstack, vstack, dstack, column_stack, join arrays. .reshape() and [None,...], atleast_nd etc add dimensions. Look at the code of the stack functions to get some ideas on how to combine arrays using these tools.
On the question of efficiency, my time tests show that concatenate operations are generally faster than np.array. Often np.array converts its inputs to lists, and reparses the values. This gives it more power in cooercing arrays to specific dtypes, but at the expense of time. But I'd only worry about this with large arrays where construction time is significant.