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| from array import * | |
| import numpy as np | |
| import math | |
| def protudoMatVet(A, v): | |
| n=len(A) | |
| s=array('f', [0 for i in range(n)]) | |
| for i in range(n): #linhas | |
| for j in range(len(A[i])): #colunas | |
| s[i] += A[i][j] * v[j] | |
| return s | |
| def subtrairVetores(a,b): | |
| n=len(a) | |
| c = array('f', [0 for i in range(n)]) | |
| for i in range(n): | |
| c[i]=a[i]-b[i] | |
| return c | |
| def somarVetores(a,b): | |
| n=len(a) | |
| c = array('f', [0 for i in range(n)]) | |
| for i in range(n): | |
| c[i]=a[i]+b[i] | |
| return c | |
| def multiplicarVetores(a,b): | |
| n=len(a) | |
| c = array('f', [0 for i in range(n)]) | |
| for i in range(n): | |
| c[i]=a[i]*b[i] | |
| return c | |
| def norma(x): | |
| s=0; | |
| l=len(x) | |
| for i in range(l): | |
| s += x[i]**2 | |
| return math.sqrt(s) | |
| def calcularVetUnit(v): | |
| n= norma(v) | |
| u= array('f', [0 for i in range(len(v))]) | |
| for i in range(len(v)): | |
| u[i] = v[i]/float(n) | |
| return u | |
| def multiplicarEscVet(s, v): | |
| n= len(v) | |
| r = array('f', [0 for i in range(n)]) | |
| for i in range(n): | |
| r[i]=s*v[i] | |
| return r | |
| def prodInterno(u,v): | |
| l=len(u) | |
| p=0 | |
| for i in range(l): | |
| p += u[i]*v[i] | |
| return p | |
| def GMRES(A, b, x0, kmax): | |
| Ax0 = protudoMatVet(A,x0) | |
| r = subtrairVetores(b, Ax0) | |
| x=[] | |
| x.append(r) # definindo x0 | |
| q = [0] * (kmax+1) # initializes q, nothing more than it ... | |
| h = [ array('f', [0 for i in range(kmax)]) for j in range(kmax+1) ] # initializer h ... | |
| q[0] = calcularVetUnit(r) | |
| for k in range(kmax): | |
| y = protudoMatVet(A,q[k]) | |
| for j in range(k): | |
| h[j][k] = prodInterno(q[j], y) | |
| y = subtrairVetores(y, multiplicarEscVet(h[j][k], q[j])) | |
| h[k + 1][k]=norma(y) | |
| if h[k + 1][k] != 0 and k != kmax: | |
| q[k + 1] = calcularVetUnit(y) | |
| b = array('f', [0 for i in range(kmax + 1)]) | |
| b[0] = norma(r) | |
| ck = np.linalg.lstsq(h,b)[0] | |
| x.append(somarVetores((multiplicarVetores(q[k],ck)), x0)) | |
| return x |
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