Created
November 7, 2016 12:15
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Algoritmo de Arnoldi
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| def Arnoldi(A,b): | |
| n=len(A) | |
| # Build S set | |
| q=[[] for j in range(n+1)] | |
| S=[[] for j in range(n+1)] | |
| q[0]=b | |
| for i in range(n): | |
| S[i]=multiply(A,q[i]) | |
| tmp=[0 for l in range(len(S[i]))] | |
| for j in range(0,i): | |
| tmp=subtract(tmp,Proj(q[j],S[i])) | |
| q[i+1]=addition(S[i], tmp) # ui = vi - proj(uj, vi) | |
| # Build orthogonal with GramSchmidt | |
| n=len(S) | |
| u=[[] for j in range(n)] | |
| u[0]=S[0] | |
| for i in range(1,n): | |
| tmp=[0 for l in range(len(S[i]))] | |
| for j in range(0,i): | |
| tmp=subtract(tmp,Proj(u[j],S[i])) | |
| u[i]=addition(S[i], tmp) | |
| # Build Hessenber Matrix | |
| n=len(S) | |
| H=[[0 for j in range(n)] for i in range(n)] | |
| i=0 | |
| while (i+1) < n: | |
| H[i+1][i]=norm(u[i]) # Subdiagonal | |
| j=0 | |
| while j<=i: | |
| H[j][i]=internProduct(u[j],u[j]) | |
| H[j][i]=internProduct(S[i],u[j])*(1/float(H[j][i])) # hj,n = qj * vi | |
| j += 1 | |
| i+=1 | |
| return H |
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