ALNP4

#1. DEF

A1=matrix(RDF, 5, [-0.960238943936,0.455472711421,-0.932352706004,0.818261532564,0.0334939638739,-0.360989451003,0.776221564231,-0.834685169725,-0.0503182064317,-0.255305378654,
-0.212877475579,0.98088751552,-0.984269407259,-0.149618905993,-0.99891975969,-0.616798752504,0.518510564469,0.557800915264,-0.94449964861,-0.540931124822,0.918389729,
-0.47034724669,-0.180871136883,0.605537477656,-0.756221380381]).transpose()
show(A1)

print '\n============================\n'
#1.1 si r>1 no converge, el menor r indica el metodo mas rapido
print ' \nRadio espectral jacobi: '
show(radio_espectral(matriz_jacobi(A1)))
print ' \nRadio espectral gauss seidel: '
show(radio_espectral(matriz_gauss_seidel(A1)))
print ' \nRadio espectral relajacion: '
show(radio_espectral(matriz_relajacion(A1,1.1)))

print '\n============================\n'
#1.2
print ' \nRadio espectral ej2: '
radio_espectral(A1)

print '\n============================\n'
#Si Ra >=1 no converge, en el ejemplo es 1.1, no converge

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#Ej2.1
#Reordenamos teniendo en cuenta los elementos mayores de cada fila de coef

A2 = (matrix(QQ,5,[[20,2,3,1,4],[5,17,3,1,4],[5,2,18,1,4],[5,2,3,16,4],[5,2,3,1,19]]))
show(A2)
b2 = vector(QQ,[200,140,170,230,110])
show(b2)

#2.2
print ' \n\nEj2.2: '
for i in range(21):
    Lw = matriz_relajacion(A2, i/10.)
    print 'parametro: %.2f; radio espectral: %s'%(i/10., radio_espectral(Lw))

print '\n\n\n'

#######################################
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valor_inicial = 0.9    ### aqui fijamos el valor previo al encontrado en la lista anterior

### no hay que modificar el resto

for w in [valor_inicial, valor_inicial+0.01..valor_inicial+0.2]:
    Lw = matriz_relajacion(A2, w)
    print 'parametro: %.3f; radio espectral: %s'%(w, radio_espectral(Lw))

#######################################
#######################################

#2.3
print ' \nGauss Seidel: '
show(metodo_descomposicion(A2, b2, tol =0.0001, metodo = 'Gauss-Seidel'))
print ' \nJacobi: '
show(metodo_descomposicion(A2, b2, tol =0.0001, metodo = 'Jacobi'))
print ' \nRelajacion: '
show(metodo_descomposicion(A2, b2, tol =0.0001, w=1.70, metodo = 'relajacion'))

#sumar las 3 cantidades de iteraciones

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#3
A1=matrix(RDF, 5, [-0.960238943936,0.455472711421,-0.932352706004,0.818261532564,0.0334939638739,-0.360989451003,0.776221564231,-0.834685169725,-0.0503182064317,-0.255305378654,
-0.212877475579,0.98088751552,-0.984269407259,-0.149618905993,-0.99891975969,-0.616798752504,0.518510564469,0.557800915264,-0.94449964861,-0.540931124822,0.918389729,
-0.47034724669,-0.180871136883,0.605537477656,-0.756221380381]).transpose()
show(A1)

b31 = vector(RDF,[1,0,0,0,0,0,0,0,0,2])
b32 = vector(RDF,[1,0,0,0,0,0,0,0,0,2])

#3.1
metodo_descomposicion(A3,b31,tol = 0, metodo = 'Gauss-Seidel')
#se toma el mayor valor

#3.2
#mismo vector pero cogemos el valor pedido