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Numeric Methods
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‎Aasen.py‎

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import string
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import funciones
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def metodoAasen(aa,bb,nn):
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global aux,P,T,I,P_aux,b_aux,pvt,L,Lt,Pt,A,b,n
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A = aa[:]
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b = bb[:]
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n = nn
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aux=0.0
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P= [ [ 0 for i in range(n) ] for j in range(n) ]
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T,I,P_aux,b_aux,pvt,L,Lt,Pt = [],[],[],[],[],[],[],[]
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for i in range(n+1):
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if i!=n:
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T.append([])
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I.append([])
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pvt.append(i)
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L.append([])
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Lt.append([])
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Pt.append([])
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b_aux.append(0.0)
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P_aux.append(0.0)
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for j in range(n+1):
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if i!=n and j !=n:
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T[i].append(0.0)
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Lt[i].append(0.0)
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Pt[i].append(0.0)
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if i==j:
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I[i].append(1.0)
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L[i].append(1.0)
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else:
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I[i].append(0.0)
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L[i].append(0.0)
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a=[ [ 0 for i in range(n+1) ] for j in range(n+1) ]
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a=funciones.paso(A,n)
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#PIVOTACION
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alfa,beta,h,l,v = [],[],[],[],[]
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smax=0.0
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iq=0
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iaux=0
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suma=0.0
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aux=0.0
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a=[ [ 0 for i in range(n+1) ] for j in range(n+1) ]
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a=funciones.paso(A,n)
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for i in range (n+1):
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alfa.append(0.0)
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beta.append(0.0)
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h.append(0.0)
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for i in range (n+2):
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l.append(0.0)
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v.append(0.0)
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### EMPIEZA ################
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for j in range(1,n+1):
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if j == 1:
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h[j]=a[1][1]
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elif j==2:
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h[1]= beta[1]
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h[2]= a[2][2]
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else :
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l[0]=0.0
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l[1]=0.0
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for k in range(2,j):
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l[k]=L[j][k]
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l[j]=1.0
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h[j]=a[j][j]
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for k in range(1,j):
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h[k]=beta[k-1]*l[k-1] + alfa[k]*l[k] + beta[k]*l[k+1]
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h[j] = h[j] - l[k]*h[k]
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if j==1 or j==2:
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alfa[j]=h[j]
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else:
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alfa[j]=h[j] - beta[j-1]*L[j][j-1]
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if j<=n-1:
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smax=0.0
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iq = j
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for k in range (j+1,n+1):
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suma=0.0
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for e in range (1,j+1):
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suma -= L[k][e]*h[e]
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v[k]=a[k][j] +suma
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if (abs(v[k])>=smax):###posible >=
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smax=abs(v[k])
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iq=k
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aux=v[j+1]
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v[j+1]=v[iq]
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v[iq]=aux
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for k in range (2,j+1):
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aux= L[j+1][k]
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L[j+1][k]=L[iq][k]
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L[iq][k]=aux
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iaux = pvt[j+1]
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pvt[j+1] = pvt[iq]
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pvt[iq] = iaux
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for k in range(j+1,n+1):
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aux=a[j+1][k]
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a[j+1][k]=a[iq][k]
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a[iq][k]=aux
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for k in range(j+1,n+1):
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aux=a[k][j+1]
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a[k][j+1]=a[k][iq]
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a[k][iq]=aux
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beta[j]=v[j+1]
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if j<=n-2:
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for k in range(j+2,n+1):
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L[k][j+1]=v[k]
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if (v[j+1]!= 0.0):
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for k in range (j+2,n+1):
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L[k][j+1]= L[k][j+1]/v[j+1]
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for j in range (n-1):
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T[j][j]=alfa[j+1]
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T[j+1][j]=beta[j+1]
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T[j][j+1]=beta[j+1]
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T[n-1][n-1]=alfa[n]
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for i in range (1,n+1):
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P_aux[i]=I[pvt[i]]
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for i in range (n):
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for j in range (n):
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P[i][j]= P_aux[i+1][j+1]
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#FIN PIVOTE
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for i in range(n):
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b_aux[i]=b[pvt[i+1]-1]
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#LZ = b_aux
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j = 0
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z = []
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for i in range(n):
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z.append(0.0)
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while j < n:
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res = b_aux[j]
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for k in range (j):
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res -= L[j+1][k+1] *z[k]
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res /= float(L[j+1][j+1])
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z[j]=res
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j+=1
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# GAUS Tw =Z
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a = []
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for i in range(n):
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a.append([])
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for j in range(n):
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a[i].append(float(T[i][j]))
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for i in range(n):
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a[i].append(z[i])
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maxi = 0
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pos_maxi=-1
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P1 = []
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h1=0.0
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for i in range(n):
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P1.append(i)
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for i in range(n-1):
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maxi = 0
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pos_maxi=-1
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for p in range(i,n):
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if maxi< abs(a[p][i]):
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maxi = abs(a[p][i])
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pos_maxi = p
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a[i], a[pos_maxi] = a[pos_maxi], a[i]
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P1[i], P1[pos_maxi] = P1[pos_maxi], P1[i]
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for j in range(i+1, n):
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h1 = a[j][i]/float(a[i][i])
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for k in range(i, n+1):
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a[j][k] -= float((h1)*(a[i][k]))
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w = []
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for i in range(n):
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w.append(0.0)
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j = n-1
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while j>=0:
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res = a[j][n]
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for k in range (j+1, n):
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res -= a[j][k] *w[k]
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res /= float(a[j][j])
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w[j] = res
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j-=1
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#LY = w
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for i in range(n):
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for j in range(n):
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Lt[i][j]=L[j+1][i+1]
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j = n-1
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y = []
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for i in range(n):
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y.append(0.0)
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while j >=0:
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res2 = 0.0
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for k in range (j+1,n):
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res2 += Lt[j][k]*y[k]
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y[j] = float(w[j]-res2)/Lt[j][j]
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j-=1
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#X = P(t)y
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x = []
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for i in range(n):
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x.append(0.0)
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for i in range(n):
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for j in range(n):
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Pt[i][j]=P[j][i]
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for i in range(n):
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aux=0.0
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for j in range(n):
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aux+= Pt[i][j]*y[j]
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x[i]=aux
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print "\n Resolucion por Algoritmo de Aasen "
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print " -------------------------------------------------"
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print " Matriz P"
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funciones.imprimeMatriz(P)
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print " Matriz L"
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funciones.imprimeMatriz(funciones.transMatriz(Lt,n))
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print " Matriz T"
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funciones.imprimeMatriz(T)
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print " Como A.x = b, en P.A.Pt = L.T.Lt:"
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return x

‎Cholesky.py‎

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import math
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import funciones
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def metodoCholesky(A,B,n):
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#creamos matriz nula G
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G = [[0.0]*n]*n
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#creamos matriz nula G_T
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for i in range(n):
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suma = A[i][i]
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for k in range(i):
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suma = suma - A[k][i]**2
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if suma < 0: #no es definida positiva
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return ["NULL","NULL"]
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A[i][i] = math.sqrt(suma)
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for j in range(i+1, n):
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suma = A[i][j]
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for k in range(i):
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suma = suma - A[k][i]*A[k][j]
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A[i][j] = suma / A[i][i]
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for j in range(n):
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for i in range(n):
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if(i > j):
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A[i][j] = 0.0
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G = A
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Gt = funciones.transMatriz(G,n)
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print "\n Resolucion por Algoritmo Cholesky "
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print " -------------------------------------------------"
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print "\n Matriz G Triangular Superior"
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funciones.imprimeMatriz(G)
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print "\n Matriz Gt Triangular Inferior"
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funciones.imprimeMatriz(Gt)
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y = funciones.solucionL(Gt,B,n) #Ly = b "obtenemos y"
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x = funciones.solucionU(G,y,n) #Ux = y "obtenemos x"
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return [y,x]

‎ConditionNumber.py‎

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import numpy as np
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import numpy.linalg as LA
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from Tkinter import *
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import tkMessageBox
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class ConditionNumber:
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def __init__(self,A,dim):
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self.A = A
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self.n = dim
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self.graphics()
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def graphics(self):
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self.mGui = Toplevel()
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self.mGui.geometry('400x140+450+300')
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self.mGui.title('Numero de Condicion de una Matriz')
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mbotonTrivial = Button(self.mGui, text = 'K_1(A)',
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command = self.cond_1).place(x=20, y = 20)
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mbotonParcial = Button(self.mGui, text = 'K_2(A)',
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command = self.cond_2).place(x=20, y = 60)
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mbotonParcial = Button(self.mGui, text = 'K_inf(A)',
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command = self.cond_inf).place(x=20, y = 100)
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def norm_1(self,A):
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n = self.n
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ret = -np.inf
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for j in range(n):
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tmp = 0
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for i in range(n):
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tmp += abs(A[i][j])
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if(tmp > ret):
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ret = tmp
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return ret
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def norm_2(self,A):
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ret = LA.norm(A,2)
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return ret
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def norm_inf(self,A):
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n = self.n
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ret = -np.inf
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for i in range(n):
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tmp = 0
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for j in range(n):
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tmp += abs(A[i][j])
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if(tmp > ret):
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ret = tmp
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return ret
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def cond_1(self):
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ret = 0
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out = 'Numero de Condicion\n\n'
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if(np.isfinite(LA.cond(self.A))):
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Ainv = LA.inv(self.A)
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ret = self.norm_1(self.A)*self.norm_1(Ainv)
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out += 'K(A) = ' + str(ret) + '\n'
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else:
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out += 'Matriz Singular'
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text = Text(self.mGui)
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text.insert(INSERT, out)
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text.insert(END, '...')
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text.place(x=100,y=20)
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return ret
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def cond_2(self):
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ret = 0
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out = 'Numero de Condicion\n\n'
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if(np.isfinite(LA.cond(self.A))):
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Ainv = LA.inv(self.A)
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A = self.A
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ret = self.norm_2(self.A)*self.norm_2(Ainv)
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out += 'K(A) = ' + str(ret) + '\n'
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else:
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out += 'Matriz Singular'
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text = Text(self.mGui)
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text.insert(INSERT, out)
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text.insert(END, '...')
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text.place(x=100,y=20)
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return ret
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def cond_inf(self):
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ret = 0
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out = 'Numero de Condicion\n\n'
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if(np.isfinite(LA.cond(self.A))):
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Ainv = LA.inv(self.A)
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ret = self.norm_inf(self.A)*self.norm_inf(Ainv)
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out += 'K(A) = ' + str(ret) + '\n'
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else:
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out += 'Matriz Singular'
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text = Text(self.mGui)
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text.insert(INSERT, out)
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text.insert(END, '...')
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text.place(x=100,y=20)
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return ret

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