If I have a dataframe:
myData = {'start': [1, 2, 3, 4, 5],
'end': [2, 3, 5,7,6],
'number': [1, 2, 7,9, 7]
}
df = pd.DataFrame(myData, columns=['start', 'end', 'number'])
df
And I need to do something like:
result = {'start': [1, 4, 5],
'end': [7,7,6],
'number': [10,9, 7]
}
df = pd.DataFrame(result, columns=['start', 'end', 'number'])
df
If number < 1, start = start(previous row), end = end(current row), then delete previous rows.
That is, to merge the rows, the difference between the end of the first and the beginning of the second is less than 1, rewrite the new beginning, merge the number and delete the first.
Can I do it without iteration?
enter image description here
You can use:
# identify when end - previous_start > 2
# and create a new group
group = df['end'].sub(df['start'].shift()).gt(2).cumsum()
# aggregate
out = df.groupby(group).agg({'start': 'first', 'end': 'last', 'number': 'sum'})
Output:
start end number
0 1 3 3
1 3 5 7
2 4 6 16
Given the following DataFrame:
pd.DataFrame({
'x': [0, 1],
'y': [0, 1],
'a_idx': [0, 1],
'a_val': [2, 3],
'b_idx': [4, 5],
'b_val': [6, 7],
})
What is the cleanest way to pivot the DataFrame based on the prefix of the idx and val columns if you have an indeterminate amount of unique prefixes (a, b, ... n), so as to obtain the following DataFrame?
pd.DataFrame({
'x': [0, 1, 0, 1],
'y': [0, 1, 0, 1],
'key': ['a','a','b','b'],
'idx': [0, 1, 4, 5],
'val': [2, 3, 6, 7]
})
I am not very knowledgeable in pandas, so my easiest solution was to go earlier in the data generation process and generate a subset of the result DataFrame for each prefix in SQL, and then concat the result sets into a final DataFrame. I'm curious however if there is a simple way to do this using the API of pandas.DataFrame. Is there such a thing?
Let's try wide_to_long with extras:
(pd.wide_to_long(df,stubnames=['a','b'],
i=['x','y'],
j='key',
sep='_',
suffix='\\w+'
)
.unstack('key').stack(level=0).reset_index()
)
Or manually with melt:
out = df.melt(['x', 'y'])
out = (out.join(out['variable'].str.split('_', expand=True))
.rename(columns={0: 'key'})
.pivot_table(index=['x', 'y', 'key'], columns=[1], values='value')
.reset_index()
)
Output:
key x y level_2 idx val
0 0 0 a 0 2
1 0 0 b 4 6
2 1 1 a 1 3
3 1 1 b 5 7
I have:
df = pd.DataFrame(
[
[22, 33, 44],
[55, 11, 22],
[33, 55, 11],
],
index=["abc", "def", "ghi"],
columns=list("abc")
) # size(3,3)
and:
unique = pd.Series([11, 22, 33, 44, 55]) # size(1,5)
then I create a new df based on unique and df, so that:
df_new = pd.DataFrame(index=unique, columns=df.columns) # size(5,3)
From this newly created df, I'd like to create a new boolean df based on unique and df, so that the end result is:
df_new = pd.DataFrame(
[
[0, 1, 1],
[1, 0, 1],
[1, 1, 0],
[0, 0, 1],
[1, 1, 0],
],
index=unique,
columns=df.columns
)
This new df is either true or false depending on whether the value is present in the original dataframe or not. For example, the first column has three values: [22, 55, 33]. In a df with dimensions (5,3), this first column would be: [0, 1, 1, 0, 1] i.e. [0, 22, 33, 0 , 55]
I tried filter2 = unique.isin(df) but this doesn't work, also notnull. I tried applying a filter but the dimensions returned were incorrect. How can I do this?
Use DataFrame.stack with DataFrame.reset_index, DataFrame.pivot, then check if not missing values by DataFrame.notna, cast to integers for True->1 and False->0 mapping and last remove index and columns names by DataFrame.rename_axis:
df_new = (df.stack()
.reset_index(name='v')
.pivot('v','level_1','level_0')
.notna()
.astype(int)
.rename_axis(index=None, columns=None))
print (df_new)
a b c
11 0 1 1
22 1 0 1
33 1 1 0
44 0 0 1
55 1 1 0
Helper Series is not necessary, but if there is more values or is necessary change order by helper Series use add DataFrame.reindex:
#added 66
unique = pd.Series([11, 22, 33, 44, 55,66])
df_new = (df.stack()
.reset_index(name='v')
.pivot('v','level_1','level_0')
.reindex(unique)
.notna()
.astype(int)
.rename_axis(index=None, columns=None))
print (df_new)
a b c
11 0 1 1
22 1 0 1
33 1 1 0
44 0 0 1
55 1 1 0
66 0 0 0
What is a generic, efficient algorithm to find the minimal subset of columns in a discrete-valued matrix that makes that rows unique.
For example, consider this matrix (with named columns):
a b c d
2 1 0 0
2 0 0 0
2 1 2 2
1 2 2 2
2 1 1 0
Each row in the matrix is unique. However, if we remove columns a and d we maintain that same property.
I could enumerate all possible combinations of the columns, however, that will quickly become intractable as my matrix grows. Is there a faster, optimal algorithm for doing this?
Actually, my original formulation wasn't very good. This is better as a set cover.
import pulp
# Input data
A = [
[2, 1, 0, 0],
[2, 0, 0, 0],
[2, 1, 2, 2],
[1, 2, 2, 2],
[2, 1, 1, 0]
]
# Preprocess the data a bit.
# Bikj = 1 if Aij != Akj, 0 otherwise
B = []
for i in range(len(A)):
Bi = []
for k in range(len(A)):
Bik = [int(A[i][j] != A[k][j]) for j in range(len(A[i]))]
Bi.append(Bik)
B.append(Bi)
model = pulp.LpProblem('Tim', pulp.LpMinimize)
# Variables turn on and off columns.
x = [pulp.LpVariable('x_%d' % j, cat=pulp.LpBinary) for j in range(len(A[0]))]
# The sum of elementwise absolute difference per element and row.
for i in range(len(A)):
for k in range(i + 1, len(A)):
model += sum(B[i][k][j] * x[j] for j in range(len(A[i]))) >= 1
model.setObjective(pulp.lpSum(x))
assert model.solve() == pulp.LpStatusOptimal
print([xi.value() for xi in x])
An observation: if M has unique rows without both columns i and j, then it has unique rows without column i and without column j independently (in other words, adding a column to a matrix with unique rows cannot make the rows not unique). Therefore, you should be able to find the minimum (not just minimal) solution by using a depth first search.
def has_unique_rows(M):
return len(set([tuple(i) for i in M])) == len(M)
def remove_cols(M, cols):
ret = []
for row in M:
new_row = []
for i in range(len(row)):
if i in cols:
continue
new_row.append(row[i])
ret.append(new_row)
return ret
def minimum_unique_rows(M):
if not has_unique_rows(M):
raise ValueError("M must have unique rows")
cols = list(range(len(M[0])))
def _cols_to_remove(M, removed_cols=(), max_removed_cols=()):
for i in set(cols) - set(removed_cols):
new_removed_cols = removed_cols + (i,)
new_M = remove_cols(M, new_removed_cols)
if not has_unique_rows(new_M):
continue
if len(new_removed_cols) > len(max_removed_cols):
max_removed_cols = new_removed_cols
return _cols_to_remove(M, new_removed_cols, max_removed_cols)
return max_removed_cols
removed_cols = _cols_to_remove(M)
return remove_cols(M, removed_cols), removed_cols
(note that my variable naming is terrible)
Here's it on your matrix
In [172]: rows = [
.....: [2, 1, 0, 0],
.....: [2, 0, 0, 0],
.....: [2, 1, 2, 2],
.....: [1, 2, 2, 2],
.....: [2, 1, 1, 0]
.....: ]
In [173]: minimum_unique_rows(rows)
Out[173]: ([[1, 0], [0, 0], [1, 2], [2, 2], [1, 1]], (0, 3))
I generated a random matrix (using sympy.randMatrix) which is shown below
⎡0 1 0 1 0 1 1⎤
⎢ ⎥
⎢0 1 1 2 0 0 2⎥
⎢ ⎥
⎢1 0 1 1 1 0 0⎥
⎢ ⎥
⎢1 2 2 1 1 2 2⎥
⎢ ⎥
⎢2 0 0 0 0 1 1⎥
⎢ ⎥
⎢2 0 2 2 1 1 0⎥
⎢ ⎥
⎢2 1 2 1 1 0 1⎥
⎢ ⎥
⎢2 2 1 2 1 0 1⎥
⎢ ⎥
⎣2 2 2 1 1 2 1⎦
(note that sorting the rows of M helps a lot in checking these things by hand)
In [224]: M1 = [[0, 1, 0, 1, 0, 1, 1], [0, 1, 1, 2, 0, 0, 2], [1, 0, 1, 1, 1, 0, 0], [1, 2, 2, 1, 1, 2, 2], [2, 0, 0, 0, 0, 1, 1], [2, 0, 2, 2, 1, 1, 0], [2, 1, 2, 1, 1, 0
, 1], [2, 2, 1, 2, 1, 0, 1], [2, 2, 2, 1, 1, 2, 1]]
In [225]: minimum_unique_rows(M1)
Out[225]: ([[1, 1, 1], [2, 0, 2], [1, 0, 0], [1, 2, 2], [0, 1, 1], [2, 1, 0], [1, 0, 1], [2, 0, 1], [1, 2, 1]], (0, 1, 2, 4))
Here's a brute-force check that it's the minimum answer (actually there are quite a few minimums).
In [229]: from itertools import combinations
In [230]: print([has_unique_rows(remove_cols(M1, r)) for r in combinations(range(7), 6)])
[False, False, False, False, False, False, False]
In [231]: print([has_unique_rows(remove_cols(M1, r)) for r in combinations(range(7), 5)])
[False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]
In [232]: print([has_unique_rows(remove_cols(M1, r)) for r in combinations(range(7), 4)])
[False, True, False, False, False, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, True, False, False, False, False, False, True, True]
Here is my greedy solution. (Yes, that fails your "optimal" criterion.) Randomly pick a row that can be safely thrown away and throw it away. Keep going until no more such rows. I'm sure the is_valid could be optimized.
rows = [
[2, 1, 0, 0],
[2, 0, 0, 0],
[2, 1, 2, 2],
[1, 2, 2, 2],
[2, 1, 1, 0]
]
col_names = [0, 1, 2, 3]
def is_valid(rows, col_names):
# it's valid if every row has a distinct "signature"
signatures = { tuple(row[col] for col in col_names) for row in rows }
return len(signatures) == len(rows)
import random
def minimal_distinct_columns(rows, col_names):
col_names = col_names[:]
random.shuffle(col_names)
for i, col in enumerate(col_names):
fewer_col_names = col_names[:i] + col_names[(i+1):]
if is_valid(rows, fewer_col_names):
return minimal_distinct_columns(rows, fewer_col_names)
return col_names
Since it's greedy, it doesn't get the best answer always, but it should be relatively speedy (and simple).
Although I'm sure there's better approaches, this fondly reminded me of some Genetic Algorithms stuff I did in the 90s. I wrote up a quick version using R's GA package.
library(GA)
matrix_to_minimize <- matrix(c(2,2,1,1,2,
1,0,1,2,1,
0,0,2,2,1,
0,0,2,2,0), ncol=4)
evaluate <- function(indices) {
if(all(indices == 0)) {
return(0)
}
selected_cols <- matrix_to_minimize[, as.logical(indices), drop=FALSE]
are_unique <- nrow(selected_cols) == nrow(unique(selected_cols))
if (are_unique == FALSE) {
return(0)
}
retval <- (1/sum(as.logical(indices)))
return(retval)
}
ga_results <- ga("binary", evaluate,
nBits=ncol(matrix_to_minimize),
popSize=10 * ncol(matrix_to_minimize), #why not
maxiter=1000,
run=10) #probably want to play with this
print("Best Solution: ")
print(ga_results#solution)
I don't know that it's good or optimal, but I bet it will provide a reasonably good answer in a reasonable amount of time? :)