Related
I have three numpy arrays each with different lengths:
A.shape = (3401,)
B.shape = (2200,)
C.shape = (4103,)
I would like to average the three arrays to produce a new array with size of the largest array (in this case C):
D.shape = (4103,)
Problem is, I don't think I can do this without adding "fake" data to A and B, by interpolation.
How can I perform interpolation on the first two numpy arrays so that they are of the same length as array C?
Do I even need to interpolate here?
First thing that comes to mind is zoom from scipy:
The array is zoomed using spline interpolation of the requested order.
Code:
import numpy as np
from scipy.ndimage import zoom
A = np.random.rand(3401)
B = np.random.rand(2200)
C = np.ones(4103)
for arr in [A, B]:
zoom_rate = C.shape[0] / arr.shape[0]
arr = zoom(arr, zoom_rate)
print(arr.shape)
Output:
(4103,)
(4103,)
I think the simplest option is to do the following:
D = np.concatenate([np.average([A[:2200], B, C[:2200]], axis=0),
np.average([A[2200:3401], C[2200:3401]], axis=0),
C[3401:]])
I have a Multi-index dataframe with multiple test result values.
For further data analysis I want to add the derivation to the dataframe.
I tried to either calculate it via a lambda function directly after I grouped the dataframe. Grouping (mean values) is required due to the noise in the sampling.
Later I want to delete the rows from my dataframes where the derivative is <= 0.
The simplified Multi-index dataframe looks like this:
arrays = [['LS13', 'LS13', 'LS13', 'LS13','LS14','LS14','LS14','LS14','LS14','LS14','LS14','LS14'],[0, 2, 2.5, 3,0,2,5,5.5,6,6.5,7,7.5]]
index = pd.MultiIndex.from_arrays(arrays, names=('File', 'Flow Rate Setpoint [l/s]'))
df = pd.DataFrame({('Flow Rate [l/s]','mean') : [-0.057,2.089,2.496,3.011,0.056,2.070,4.995,5.519,6.011,6.511,7.030,7.499],('Time [s]','mean') : [42.225,104.909,165.676,226.446,42.225,104.918,469.560,530.328,591.100,651.864,712.660,773.034],('Shear Stress [Pa]','mean') : [-0.698,5.621,7.946,11.278,-0.774,6.557,40.610,48.370,54.685,58.414,58.356,56.254]},index=index)
if I run my code:
import numpy as np
xls = ['LS13', 'LS14']
gradient = [pd.Series(np.gradient(df.loc[(i),('Shear Stress [Pa]','mean')],df.loc[(i),('Time [s]','mean')])) for i in xls]
now I want to concat gradient to df on axis = 1, Title could be df['Gradient''values'].
So my pd.Series looks like:
Gradient
values
0 0.100808
1 0.069048
2 0.04654
3 0.054801
0 0.116941
1 0.087431
2 0.149521
3 0.115805
4 0.082639
5 0.030213
6 -0.017938
7 -0.034806
next step would be to remove/drop the rows where ['Gradient','values'] <= 0, in my example ['LS14','7':'7.5']
When I tried to concatenate both Dataframe df and Series gradient (I'm aware that the indexes are different)
merged = pd.concat([pd.DataFrame(df),pd.Series(gradient)], axis=1 , ignore_index = True)
Errors are usually one of the following:
ValueError: Buffer dtype mismatch, expected 'Python object' but got
'long long'
TypeError: cannot concatenate object of type "<class 'list'>"; only
pd.Series, pd.DataFrame, and pd.Panel (deprecated) objs are valid
I would also assume there is an easier way to get this done with an lambda function and just apply it in place.
merged = pd.concat([df, pd.Series([gradient], name=('Gradient','value'))], axis=1)
I would have expected that to work, but I also get a miss match error:
ValueError: Buffer dtype mismatch, expected 'Python object' but got 'long long'
when I try:
df[("Gradient","value")] =pd.Series([pd.Series(np.gradient(df.loc[(i),('Shear Stress [Pa]','mean')],df.loc[(i),('Time [s]','mean')])) for i in xls])
The 'Gradient','value' column gets correctly added to the dataframe but the values are again NaN.
You can try groupby().apply():
def get_gradients(x):
gradients = np.gradient(x[('Shear Stress [Pa]', 'mean')],x[('Time [s]', 'mean')] )
return pd.Series(gradients, index=x.index)
df[('Gradient','Value')] = (df.groupby('File', group_keys=False)
.apply(get_gradients)
)
Given the following data:
DC,Mode,Mod,Ven,TY1,TY2,TY3,TY4,TY5,TY6,TY7,TY8
Intra,S,Dir,C1,False,False,False,False,False,True,True,False
Intra,S,Co,C1,False,False,False,False,False,False,False,False
Intra,M,Dir,C1,False,False,False,False,False,False,True,False
Inter,S,Co,C1,False,False,False,False,False,False,False,False
Intra,S,Dir,C2,False,True,True,True,True,True,True,False
Intra,S,Co,C2,False,False,False,False,False,False,False,False
Intra,M,Dir,C2,False,False,False,False,False,False,False,False
Inter,S,Co,C2,False,False,False,False,False,False,False,False
Intra,S,Dir,C3,False,False,False,False,True,True,False,False
Intra,S,Co,C3,False,False,False,False,False,False,False,False
Intra,M,Dir,C3,False,False,False,False,False,False,False,False
Inter,S,Co,C3,False,False,False,False,False,False,False,False
Intra,S,Dir,C4,False,False,False,False,False,True,False,True
Intra,S,Co,C4,True,True,True,True,False,True,False,True
Intra,M,Dir,C4,False,False,False,False,False,True,False,True
Inter,S,Co,C4,True,True,True,False,False,True,False,True
Intra,S,Dir,C5,True,True,False,False,False,False,False,False
Intra,S,Co,C5,False,False,False,False,False,False,False,False
Intra,M,Dir,C5,True,True,False,False,False,False,False,False
Inter,S,Co,C5,False,False,False,False,False,False,False,False
Imports:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
To reproduce my DataFrame, copy the data then use:
df = pd.read_clipboard(sep=',')
I'd like to create a plot conveying the same information as my example, but not necessarily with the same shape (I'm open to suggestions). I'd also like to hover over the color and have the appropriate Ven displayed (e.g. C1, not 1).:
Edit 2018-10-17:
The two solutions provided so far, are helpful and each accomplish a different aspect of what I'm looking for. However, the key issue I'd like to resolve, which wasn't explicitly stated prior to this edit, is the following:
I would like to perform the plotting without converting Ven to an int; this numeric transformation isn't practical with the real data. So the actual scope of the question is to plot all categorical data with two categorical axes.
The issue I'm experiencing is the data is categorical and the y-axis is multi-indexed.
I've done the following to transform the DataFrame:
# replace False witn nan
df = df.replace(False, np.nan)
# replace True with a number representing Ven (e.g. C1 = 1)
def rep_ven(row):
return row.iloc[4:].replace(True, int(row.Ven[1]))
df.iloc[:, 4:] = df.apply(rep_ven, axis=1)
# drop the Ven column
df = df.drop(columns=['Ven'])
# set multi-index
df_m = df.set_index(['DC', 'Mode', 'Mod'])
Plotting the transformed DataFrame produces:
plt.figure(figsize=(20,10))
heatmap = plt.imshow(df_m)
plt.xticks(range(len(df_m.columns.values)), df_m.columns.values)
plt.yticks(range(len(df_m.index)), df_m.index)
plt.show()
This plot isn't very streamlined, there are four axis values for each Ven. This is a subset of data, so the graph would be very long with all the data.
Here's my solution. Instead of plotting I just apply a style to the DataFrame, see https://pandas.pydata.org/pandas-docs/stable/style.html
# Transform Ven values from "C1", "C2" to 1, 2, ..
df['Ven'] = df['Ven'].str[1]
# Given a specific combination of dc, mode, mod, ven,
# do we have any True cells?
g = df.groupby(['DC', 'Mode', 'Mod', 'Ven']).any()
# Let's drop any rows with only False values
g = g[g.any(axis=1)]
# Convert True, False to 1, 0
g = g.astype(int)
# Get the values of the ven index as an int array
# Note: we don't want to drop the ven index!!
# Otherwise styling won't work
ven = g.index.get_level_values('Ven').values.astype(int)
# Multiply 1 and 0 with Ven value
g = g.mul(ven, axis=0)
# Sort the index
g.sort_index(ascending=False, inplace=True)
# Now display the dataframe with styling
# first we get a color map
import matplotlib
cmap = matplotlib.cm.get_cmap('tab10')
def apply_color_map(val):
# hide the 0 values
if val == 0:
return 'color: white; background-color: white'
else:
# for non-zero: get color from cmap, convert to hexcode for css
s = "color:white; background-color: " + matplotlib.colors.rgb2hex(cmap(val))
return s
g
g.style.applymap(apply_color_map)
The available matplotlib colormaps can be seen here: Colormap reference, with some additional explanation here: Choosing a colormap
Explanation: Remove rows where TY1-TY8 are all nan to create your plot. Refer to this answer as a starting point for creating interactive annotations to display Ven.
The below code should work:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
df = pd.read_clipboard(sep=',')
# replace False witn nan
df = df.replace(False, np.nan)
# replace True with a number representing Ven (e.g. C1 = 1)
def rep_ven(row):
return row.iloc[4:].replace(True, int(row.Ven[1]))
df.iloc[:, 4:] = df.apply(rep_ven, axis=1)
# drop the Ven column
df = df.drop(columns=['Ven'])
idx = df[['TY1','TY2', 'TY3', 'TY4','TY5','TY6','TY7','TY8']].dropna(thresh=1).index.values
df = df.loc[idx,:].sort_values(by=['DC', 'Mode','Mod'], ascending=False)
# set multi-index
df_m = df.set_index(['DC', 'Mode', 'Mod'])
plt.figure(figsize=(20,10))
heatmap = plt.imshow(df_m)
plt.xticks(range(len(df_m.columns.values)), df_m.columns.values)
plt.yticks(range(len(df_m.index)), df_m.index)
plt.show()
I have a data that looks like a sigmoidal plot but flipped relative to the vertical line.
But the plot is a result of plotting 1D data instead of some sort of function.
My goal is to find the x value when the y value is at 50%. As you can see, there is no data point when y is exactly at 50%.
Interpolate comes to my mind. But I'm not sure if interpolate enable me to find the x value when the y value is 50%. So my question is 1) can you use interpolate to find the x when the y is 50%? or 2)do you need to fit the data to some sort of a function?
Below is what I currently have in my code
import numpy as np
import matplotlib.pyplot as plt
my_x = [4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66]
my_y_raw=np.array([0.99470977497817203, 0.99434995886145172, 0.98974611323163653, 0.961630837657524, 0.99327633558441175, 0.99338952769251909, 0.99428263292577534, 0.98690514212711611, 0.99111667721533181, 0.99149418924880861, 0.99133773062680464, 0.99143506380003499, 0.99151080464011454, 0.99268261743308517, 0.99289757252812316, 0.99100207861144063, 0.99157171773324027, 0.99112571824824358, 0.99031608691035722, 0.98978104266076905, 0.989782674787969, 0.98897835092187614, 0.98517540405423909, 0.98308943666187076, 0.96081810781994603, 0.85563541881892147, 0.61570811548079107, 0.33076276040577052, 0.14655134838124245, 0.076853147122142126, 0.035831324928136087, 0.021344669212790181])
my_y=my_y_raw/np.max(my_y_raw)
plt.plot(my_x, my_y,color='k', markersize=40)
plt.scatter(my_x,my_y,marker='*',label="myplot", color='k', edgecolor='k', linewidth=1,facecolors='none',s=50)
plt.legend(loc="lower left")
plt.xlim([4,102])
plt.show()
Using SciPy
The most straightforward way to do the interpolation is to use the SciPy interpolate.interp1d function. SciPy is closely related to NumPy and you may already have it installed. The advantage to interp1d is that it can sort the data for you. This comes at the cost of somewhat funky syntax. In many interpolation functions it is assumed that you are trying to interpolate a y value from an x value. These functions generally need the "x" values to be monotonically increasing. In your case, we swap the normal sense of x and y. The y values have an outlier as #Abhishek Mishra has pointed out. In the case of your data, you are lucky and you can get away with the the leaving the outlier in.
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
my_x = [4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,
48,50,52,54,56,58,60,62,64,66]
my_y_raw=np.array([0.99470977497817203, 0.99434995886145172,
0.98974611323163653, 0.961630837657524, 0.99327633558441175,
0.99338952769251909, 0.99428263292577534, 0.98690514212711611,
0.99111667721533181, 0.99149418924880861, 0.99133773062680464,
0.99143506380003499, 0.99151080464011454, 0.99268261743308517,
0.99289757252812316, 0.99100207861144063, 0.99157171773324027,
0.99112571824824358, 0.99031608691035722, 0.98978104266076905,
0.989782674787969, 0.98897835092187614, 0.98517540405423909,
0.98308943666187076, 0.96081810781994603, 0.85563541881892147,
0.61570811548079107, 0.33076276040577052, 0.14655134838124245,
0.076853147122142126, 0.035831324928136087, 0.021344669212790181])
# set assume_sorted to have scipy automatically sort for you
f = interp1d(my_y_raw, my_x, assume_sorted = False)
xnew = f(0.5)
print('interpolated value is ', xnew)
plt.plot(my_x, my_y_raw,'x-', markersize=10)
plt.plot(xnew, 0.5, 'x', color = 'r', markersize=20)
plt.plot((0, xnew), (0.5,0.5), ':')
plt.grid(True)
plt.show()
which gives
interpolated value is 56.81214249272691
Using NumPy
Numpy also has an interp function, but it doesn't do the sort for you. And if you don't sort, you'll be sorry:
Does not check that the x-coordinate sequence xp is increasing. If xp
is not increasing, the results are nonsense.
The only way I could get np.interp to work was to shove the data in to a structured array.
import numpy as np
import matplotlib.pyplot as plt
my_x = np.array([4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,
48,50,52,54,56,58,60,62,64,66], dtype = np.float)
my_y_raw=np.array([0.99470977497817203, 0.99434995886145172,
0.98974611323163653, 0.961630837657524, 0.99327633558441175,
0.99338952769251909, 0.99428263292577534, 0.98690514212711611,
0.99111667721533181, 0.99149418924880861, 0.99133773062680464,
0.99143506380003499, 0.99151080464011454, 0.99268261743308517,
0.99289757252812316, 0.99100207861144063, 0.99157171773324027,
0.99112571824824358, 0.99031608691035722, 0.98978104266076905,
0.989782674787969, 0.98897835092187614, 0.98517540405423909,
0.98308943666187076, 0.96081810781994603, 0.85563541881892147,
0.61570811548079107, 0.33076276040577052, 0.14655134838124245,
0.076853147122142126, 0.035831324928136087, 0.021344669212790181],
dtype = np.float)
dt = np.dtype([('x', np.float), ('y', np.float)])
data = np.zeros( (len(my_x)), dtype = dt)
data['x'] = my_x
data['y'] = my_y_raw
data.sort(order = 'y') # sort data in place by y values
print('numpy interp gives ', np.interp(0.5, data['y'], data['x']))
which gives
numpy interp gives 56.81214249272691
As you said, your data looks like a flipped sigmoidal. Can we make the assumption that your function is a strictly decreasing function? If that is the case, we can try the following methods:
Remove all the points where the data is not strictly decreasing.For example, for your data that point will be near 0.
Use the binary search to find the location where y=0.5 should be put in.
Now you know two (x, y) pairs where your desired y=0.5 should lie.
You can use simple linear interpolation if (x, y) pairs are very close.
Otherwise, you can see what is the approximation of sigmoid near those pairs.
You might not need to fit any functions to your data. Simply find the following two elements:
The largest x for which y<50%
The smallest x for which y>50%
Then use interpolation and find the x*. Below is the code
my_x = np.array([4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66])
my_y=np.array([0.99470977497817203, 0.99434995886145172, 0.98974611323163653, 0.961630837657524, 0.99327633558441175, 0.99338952769251909, 0.99428263292577534, 0.98690514212711611, 0.99111667721533181, 0.99149418924880861, 0.99133773062680464, 0.99143506380003499, 0.99151080464011454, 0.99268261743308517, 0.99289757252812316, 0.99100207861144063, 0.99157171773324027, 0.99112571824824358, 0.99031608691035722, 0.98978104266076905, 0.989782674787969, 0.98897835092187614, 0.98517540405423909, 0.98308943666187076, 0.96081810781994603, 0.85563541881892147, 0.61570811548079107, 0.33076276040577052, 0.14655134838124245, 0.076853147122142126, 0.035831324928136087, 0.021344669212790181])
tempInd1 = my_y<.5 # This will only work if the values are monotonic
x1 = my_x[tempInd1][0]
y1 = my_y[tempInd1][0]
x2 = my_x[~tempInd1][-1]
y2 = my_y[~tempInd1][-1]
scipy.interp(0.5, [y1, y2], [x1, x2])
I can create a simple columnar diagram in a matplotlib according to the 'simple' dictionary:
import matplotlib.pyplot as plt
D = {u'Label1':26, u'Label2': 17, u'Label3':30}
plt.bar(range(len(D)), D.values(), align='center')
plt.xticks(range(len(D)), D.keys())
plt.show()
But, how do I create curved line on the text and numeric data of this dictionarie, I do not know?
ΠΆ_OLD = {'10': 'need1', '11': 'need2', '12': 'need1', '13': 'need2', '14': 'need1'}
Like the picture below
You may use numpy to convert the dictionary to an array with two columns, which can be plotted.
import matplotlib.pyplot as plt
import numpy as np
T_OLD = {'10' : 'need1', '11':'need2', '12':'need1', '13':'need2','14':'need1'}
x = list(zip(*T_OLD.items()))
# sort array, since dictionary is unsorted
x = np.array(x)[:,np.argsort(x[0])].T
# let second column be "True" if "need2", else be "False
x[:,1] = (x[:,1] == "need2").astype(int)
# plot the two columns of the array
plt.plot(x[:,0], x[:,1])
#set the labels accordinly
plt.gca().set_yticks([0,1])
plt.gca().set_yticklabels(['need1', 'need2'])
plt.show()
The following would be a version, which is independent on the actual content of the dictionary; only assumption is that the keys can be converted to floats.
import matplotlib.pyplot as plt
import numpy as np
T_OLD = {'10': 'run', '11': 'tea', '12': 'mathematics', '13': 'run', '14' :'chemistry'}
x = np.array(list(zip(*T_OLD.items())))
u, ind = np.unique(x[1,:], return_inverse=True)
x[1,:] = ind
x = x.astype(float)[:,np.argsort(x[0])].T
# plot the two columns of the array
plt.plot(x[:,0], x[:,1])
#set the labels accordinly
plt.gca().set_yticks(range(len(u)))
plt.gca().set_yticklabels(u)
plt.show()
Use numeric values for your y-axis ticks, and then map them to desired strings with plt.yticks():
import matplotlib.pyplot as plt
import pandas as pd
# example data
times = pd.date_range(start='2017-10-17 00:00', end='2017-10-17 5:00', freq='H')
data = np.random.choice([0,1], size=len(times))
data_labels = ['need1','need2']
fig, ax = plt.subplots()
ax.plot(times, data, marker='o', linestyle="None")
plt.yticks(data, data_labels)
plt.xlabel("time")
Note: It's generally not a good idea to use a line graph to represent categorical changes in time (e.g. from need1 to need2). Doing that gives the visual impression of a continuum between time points, which may not be accurate. Here, I changed the plotting style to points instead of lines. If for some reason you need the lines, just remove linestyle="None" from the call to plt.plot().
UPDATE
(per comments)
To make this work with a y-axis category set of arbitrary length, use ax.set_yticks() and ax.set_yticklabels() to map to y-axis values.
For example, given a set of potential y-axis values labels, let N be the size of a subset of labels (here we'll set it to 4, but it could be any size).
Then draw a random sample data of y values and plot against time, labeling the y-axis ticks based on the full set labels. Note that we still use set_yticks() first with numerical markers, and then replace with our category labels with set_yticklabels().
labels = np.array(['A','B','C','D','E','F','G'])
N = 4
# example data
times = pd.date_range(start='2017-10-17 00:00', end='2017-10-17 5:00', freq='H')
data = np.random.choice(np.arange(len(labels)), size=len(times))
fig, ax = plt.subplots(figsize=(15,10))
ax.plot(times, data, marker='o', linestyle="None")
ax.set_yticks(np.arange(len(labels)))
ax.set_yticklabels(labels)
plt.xlabel("time")
This gives the exact desired plot:
import matplotlib.pyplot as plt
from collections import OrderedDict
T_OLD = {'10' : 'need1', '11':'need2', '12':'need1', '13':'need2','14':'need1'}
T_SRT = OrderedDict(sorted(T_OLD.items(), key=lambda t: t[0]))
plt.plot(map(int, T_SRT.keys()), map(lambda x: int(x[-1]), T_SRT.values()),'r')
plt.ylim([0.9,2.1])
ax = plt.gca()
ax.set_yticks([1,2])
ax.set_yticklabels(['need1', 'need2'])
plt.title('T_OLD')
plt.xlabel('time')
plt.ylabel('need')
plt.show()
For Python 3.X the plotting lines needs to explicitly convert the map() output to lists:
plt.plot(list(map(int, T_SRT.keys())), list(map(lambda x: int(x[-1]), T_SRT.values())),'r')
as in Python 3.X map() returns an iterator as opposed to a list in Python 2.7.
The plot uses the dictionary keys converted to ints and last elements of need1 or need2, also converted to ints. This relies on the particular structure of your data, if the values where need1 and need3 it would need a couple more operations.
After plotting and changing the axes limits, the program simply modifies the tick labels at y positions 1 and 2. It then also adds the title and the x and y axis labels.
Important part is that the dictionary/input data has to be sorted. One way to do it is to use OrderedDict. Here T_SRT is an OrderedDict object sorted by keys in T_OLD.
The output is:
This is a more general case for more values/labels in T_OLD. It assumes that the label is always 'needX' where X is any number. This can readily be done for a general case of any string preceding the number though it would require more processing,
import matplotlib.pyplot as plt
from collections import OrderedDict
import re
T_OLD = {'10' : 'need1', '11':'need8', '12':'need11', '13':'need1','14':'need3'}
T_SRT = OrderedDict(sorted(T_OLD.items(), key=lambda t: t[0]))
x_val = list(map(int, T_SRT.keys()))
y_val = list(map(lambda x: int(re.findall(r'\d+', x)[-1]), T_SRT.values()))
plt.plot(x_val, y_val,'r')
plt.ylim([0.9*min(y_val),1.1*max(y_val)])
ax = plt.gca()
y_axis = list(set(y_val))
ax.set_yticks(y_axis)
ax.set_yticklabels(['need' + str(i) for i in y_axis])
plt.title('T_OLD')
plt.xlabel('time')
plt.ylabel('need')
plt.show()
This solution finds the number at the end of the label using re.findall to accommodate for the possibility of multi-digit numbers. Previous solution just took the last component of the string because numbers were single digit. It still assumes that the number for plotting position is the last number in the string, hence the [-1]. Again for Python 3.X map output is explicitly converted to list, step not necessary in Python 2.7.
The labels are now generated by first selecting unique y-values using set and then renaming their labels through concatenation of the strings 'need' with its corresponding integer.
The limits of y-axis are set as 0.9 of the minimum value and 1.1 of the maximum value. Rest of the formatting is as before.
The result for this test case is: