Find largest value from multiple colums in each group of row index in Python, arrange those values diagonally in matrix, and find determinant

I am new to Python. I want to find the largest values from all the columns for repetitive row indexes (i.e. 5 to 130), and also show its row and column index label in output.The largest values should be absolute. (Irrespective of + or - sign). There should not be duplicates for row indexes in different groups. After finding largest from each group,I want to arrange those values diagonally in square matrix. Then fill the remaining array with the corresponding values of indexes for each group from the main dataframe and find its Determinant.

df=pd.DataFrame(
    {'0_deg': [43, 50, 45, -17, 5, 19, 11, 32, 36, 41, 19, 11, 32, 36, 1, 19, 7, 1, 36, 10], 
     '10_deg': [47, 41, 46, -18, 4, 16, 12, 34, -52, 31, 16, 12, 34, -71, 2, 9, 52, 34, -6, 9], 
     '20_deg': [46, 43, -56, 29, 6, 14, 13, 33, 43, 6, 14, 13, 37, 43, 3, 14, 13, 25, 40, 8], 
     '30_deg': [-46, 16, -40, -11, 9, 15, 33, -39, -22, 21, 15, 63, -39, -22, 4, 6, 25, -39, -22, 7]
    }, index=[5, 10, 12, 101, 130, 5, 10, 12, 101, 130, 5, 10, 12, 101, 130, 5, 10, 12, 101, 130]
)

Data set :

Expected Output:

My code is showing only till output 1.

Actual Output:

Code:

df = pd.read_csv ('Matrixfile.csv')
df = df.set_index('Number')

def f(x):
    x1 = x.abs().stack()
    x2 = x.stack()
    x = x2.iloc[np.argsort(-x1)].head(1)
    return x

groups = (df.index == 5).cumsum()
df1 = df.groupby(groups).apply(f).reset_index(level=[1,2])
df1.columns = ['Number','Angle','Value']

print (df1)
df1.to_csv('Matrix_OP.csv', encoding='utf-8', index=True)

Solution

I am not sure about @piRSquared output from what I understood from your question. There might be some errors in there, for instance, in group 2, max(abs(values)) = 52 (underline in red in picture) but 41 is displayed on left...

Here is a less elegant way of doing it but maybe easier for you to understand :

import numpy as np

# INPUT
data_dict ={'0_deg': [43, 50, 45, -17, 5, 19, 11, 32, 36, 41, 19, 11, 32, 36, 1, 19, 7, 1, 36, 10], 
   '10_deg': [47, 41, 46, -18, 4, 16, 12, 34, -52, 31, 16, 12, 34, -71, 2, 9, 52, 34, -6, 9], 
   '20_deg': [46, 43, -56, 29, 6, 14, 13, 33, 43, 6, 14, 13, 37, 43, 3, 14, 13, 25, 40, 8], 
   '30_deg': [-46, 16, -40, -11, 9, 15, 33, -39, -22, 21, 15, 63, -39, -22, 4, 6, 25, -39, -22, 7],
   }

# Row idx of a group in this list
idx = [5, 10, 12, 101, 130]


# Getting some dimensions and sorting the data
row_idx_length = len(idx) 
group_length = len(data_dict['0_deg'])
number_of_groups = len(data_dict.keys())  
idx = idx*number_of_groups   
data_arr = np.zeros((group_length,number_of_groups),dtype=np.int32) 
#
col = 0
keys = []
for key in sorted(data_dict):
    data_arr[:,col] = data_dict[key]
    keys.append(key)
    col+=1
def get_extrema_value_group(arr):
    # function to find absolute extrema value of a 2d array
    extrema = 0
    for i in range(0, len(arr)):
        max_value = max(arr[i])
        min_value = min(arr[i])
        if (abs(min_value) > max_value) and (abs(extrema) < abs(min_value)):
            extrema = min_value
        elif (abs(min_value) < max_value) and (abs(extrema) < max_value):
            extrema = max_value         
    return extrema 

# For output 1
max_values = []  
for i in range(0,row_idx_length*number_of_groups,row_idx_length):
    # get the max value for the current group
    value = get_extrema_value_group(data_arr[i:i+row_idx_length])
    # get the row and column idx associated with the max value
    idx_angle_number = np.nonzero(abs(data_arr[i:i+row_idx_length,:])==value)
    print('Group number : ' + str(i//row_idx_length+1))
    print('Number : '+ str(idx[idx_angle_number[0][0]]))
    print('Angle : '+ keys[idx_angle_number[1][0]])
    print('Absolute extrema value : ' + str(value))   
    print('------')
    max_values.append(value)

# Arrange those values diagonally in square matrix for output 2
A = np.diag(max_values)   
print('A = ' + str(A))

# Fill A with desired values
for i in range(0,number_of_groups,1):
    A[i,0] = data_arr[i*row_idx_length+2,2]   # 20 deg 12
    A[i,1:3] = data_arr[i*row_idx_length+3,1] # x2 : 10 deg 101
    A[i,3] = data_arr[i*row_idx_length+1,1]   # 10 deg 10

# Final output
# replace the diagonal of A with max values
# get the idx of diag
A_di = np.diag_indices(number_of_groups)
# replace with max values
A[A_di] = max_values
print ('A = ' + str(A)) 

# Compute determinant of A
det_A = np.linalg.det(A)
print ('det(A) = '+str(det_A))

Output 1:

Group number : 1
Number : 12
Angle : 20_deg
Absolute extrema value : -56
------
Group number : 2
Number : 101
Angle : 10_deg
Absolute extrema value : -52
------
Group number : 3
Number : 101
Angle : 10_deg
Absolute extrema value : -71
------
Group number : 4
Number : 10
Angle : 10_deg
Absolute extrema value : 52
------

Output 2 :

A = [[-56  0  0  0]
     [ 0 -52  0  0]
     [ 0  0 -71  0]
     [ 0  0  0  52]]

Output 3 :

A = [[-56 -18 -18  41]
     [ 33 -52 -52  12]
     [ 37 -71 -71  12]
     [ 25  -6  -6  52]]

det(A) = -5.4731330578761246e-11