Lado Direito Matricial

• Forward:

  Python Listing: ../../../Code/Gauss.py. def Gauss2_Forward(A,B=[]): det=1.0 for i in range( len(A) ): pivote=Gauss_Pivote(A,i) if (pivote!=i): if (B): Matrices_Rows_Swap(B,i,pivote) Matrices_Rows_Swap(A,i,pivote) det*=-1.0 if (A[i][i]==0.0): print "Gauss2_Forward: Matrix Singular at ",i,"x",i return 0.0 det*=A[i][i] fact=1.0/A[i][i] #Always work on b first if (B): Matrices_Row_Mult(B,i,fact) Matrices_Row_Mult(A,i,fact) for j in range( i+1,len(A) ): if (B): Matrices_Rows_Operation(B,j,-A[j][i],i) Matrices_Rows_Operation(A,j,-A[j][i],i) return det

• Backward:

  Python Listing: ../../../Code/Gauss.py. def Gauss2_Backward(A,B=[]): for i in range(len(A)-1,-1,-1): for j in range(i): if (B): Matrices_Rows_Operation(B,j,-A[j][i],i) Matrices_Rows_Operation(A,j,-A[j][i],i)

• Both:

  Python Listing: ../../../Code/Gauss.py. def Gauss2(A,X=[]): det=Gauss2_Forward(A,X) print "Gauss Forward, det",det if (det==0.0): exit() Gauss2_Backward(A,X) return det

• Test:

  Python Listing: ../../../Code/Gauss.py. def Gauss2_Test(A,B=[]): #Save for residual calc AA=Matrix_Copy(A) BB=Matrix_Copy(B) det=Gauss2(A,B) #B is our solution, calc residual R_B=Matrices_Mult(AA,B) R_B=Matrices_Sub(R_B,BB) residual=Matrix_Norm(R_B)/Matrix_Norm(BB) print "Matrix_Gauss_Test, Residual: %.6e" % residual return det