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# j9ac9k/gauss.py

Last active Oct 3, 2021
Gaussian Elimination in Python
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 def gauss(A): m = len(A) assert all([len(row) == m + 1 for row in A[1:]]), "Matrix rows have non-uniform length" n = m + 1 for k in range(m): pivots = [abs(A[i][k]) for i in range(k, m)] i_max = pivots.index(max(pivots)) + k # Check for singular matrix assert A[i_max][k] != 0, "Matrix is singular!" # Swap rows A[k], A[i_max] = A[i_max], A[k] for i in range(k + 1, m): f = A[i][k] / A[k][k] for j in range(k + 1, n): A[i][j] -= A[k][j] * f # Fill lower triangular matrix with zeros: A[i][k] = 0 # Solve equation Ax=b for an upper triangular matrix A x = [] for i in range(m - 1, -1, -1): x.insert(0, A[i][m] / A[i][i]) for k in range(i - 1, -1, -1): A[k][m] -= A[k][i] * x return x

### FedericoIbarra commented Mar 12, 2019

 No sirve

### NotNikita commented Apr 10, 2020

 Danke, sir.

### gizemika commented May 17, 2020

 hi , thank you for code but I could not do this which is for 4 or more unknown equations . could you help me ?

### j9ac9k commented May 18, 2020

 hi , thank you for code but I could not do this which is for 4 or more unknown equations . could you help me ? Haven't touched this in ages, can you provide a working example? This has handled arbitrary sized equations.

### githubsourav commented Jul 4, 2020 • edited Loading

 def GaussElim(M,V): # Get a Matrix A and Vector B ``````import numpy as np A=np.array(M) B=np.array(V) Adim=A.shape; # Dimension of A Matrix Bdim=B.shape; print(Adim,Bdim) NumRow=Adim NumCol=Adim # How many Number of Rows and Columns Solve_x=np.zeros((NumRow,1)); # Check for Consistencey of the Solution if NumRow==NumCol: print("Number of Equation is Equal to Number of Variables:- Good \/Checked") if Bdim==NumRow: print("Size of the Vector is Consistent with Number of Variables:-Good \/Checked") # When no solution due to inconsistency `````` else: print("Size of the Vector is Note Correct") Solve_x="NaN" ``````b=B.reshape((NumRow,1)) # Reshaping the Vector B into b as a Column vector # NumPy arrays by default row vector # Joining A and b CatAB_stack=np.hstack((A,b)) # Horizontally stacking or Concatinating # the M and V # or Use Numpy Concatenate command as follows CatAB_concat=np.concatenate((A,b),axis=1); ####################################################################### ## Forward Elimination # Getting the size of the new concatenated matrix R=NumRow; # Getting Number of Rows - Redundant NumRow C=CatAB_stack.shape; # Getting Number of Columns (NumCol+1) CatAB=CatAB_concat; # Initializig the CatAB - Continuously changing # Forward Eliminated Matrix # range defines like this range(Start Index, Max number of loop, interval) for j in range(NumRow-1): # for j running from 0 to NumRow-2 for i in range(j+1, NumRow): # for i running from j+1 to NumRow CatAB[i,j:C]=CatAB[i,j:C]-(CatAB[j,j:C]*(CatAB[i,j]/CatAB[j,j])); ####################################################################### ## Backward Substitution Solve_x=np.zeros((R,1)) # Initializing the solution vector Solve_x[R-1]=CatAB[R-1,C-1]/CatAB[R-1,R-1]; # Solve the last variable -1 to satisfy the index "Matlab-1=C" # Reverse Looping range(Starting Number,Last Number,- negative increment) for i in range(NumRow-1,-1,-1): var=0 for j in range(i+1, C-1): var+=CatAB[i,j]*Solve_x[j] Solve_x[i]=(CatAB[i,C-1]-var)/CatAB[i,i] return [Solve_x,CatAB] ``````

### nopeva commented Jul 28, 2021 • edited Loading

 hi , thank you for code but I could not do this which is for 4 or more unknown equations . could you help me ? Haven't touched this in ages, can you provide a working example? This has handled arbitrary sized equations. Thanks for the code. I am having trouble with singular matrices when using it with bigger matrices and have found the following article which deals with this specific problem for gaussian elimination. It seems to be an easy extension, I wonder if you could give help me with it given I am not familiar with the method: "When a row of zeros, say the ith, is encountered in the transform of A, the diagonal element of that row is changed to 1, and in the augmented portion of the matrix all other rows are changed to 0, the ith row being unchanged".