SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br

Eliminação do Gauss
Quando Pedro me fala sobre Paulo
Sei mais do Pedro do que do Paulo
Sigmund Freud
< Matriz Inversa | Atividades | Interpolação >

Atividades 7:

  1. Arquivo N01.py: Representa em Python as matrices como Python lists of lists:
    \(\underline{\underline{\textbf{A}}}_0=\left(\begin{array}{cccc}1& 1& 1& 1\\1&-1& 1&-1\\ 1& 1&-1&-1\\-1& 1& 1&-1\\\end{array}\right),\) \(\underline{\underline{\textbf{A}}}_1=\left(\begin{array}{cccc}1& 2& 4& 8\\1&-1& 1&-1\\1&-2& 4&-8\\1& 1& 1& 1\\\end{array}\right),\)
    \(\underline{\underline{\textbf{A}}}_2=\left(\begin{array}{cccc}1& 1& 1& 1\\1&-1& 1&-1\\1& 2& 4& 8\\1& 3& 9&27\\ \end{array}\right),\) \(\underline{\underline{\textbf{A}}}_3=\left(\begin{array}{cccc}1& 1& 1& 1\\1& 2& 4& 8\\1& 3& 9&27\\1& 4&16&64\\\end{array}\right),\)
    Python Listing: N01.py. 
    from Matrix import *

#Lista de matrices
A=[
    [
        [ -1.0, 1.0, 1.0, 1.0,],
        [  1.0,-1.0, 1.0, 1.0,],
        [  1.0, 1.0,-1.0, 1.0,],
        [  1.0, 1.0, 1.0,-1.0,],
    ],
    Matrix_Vandermonte([ 2.0,-1.0,-2.0, 1.0 ]),
    Matrix_Vandermonte([ 1.0,-1.0, 2.0, 3.0 ]),
    Matrix_Vandermonte([ 1.0, 2.0, 3.0, 4.0 ]),
]
  2. Arquivo N02py: Encontre as inversas das matrizes no item anterior.
    Python Listing: N02.py. 
    from Matrix import *
from Gauss import *

from N01 import *

for i in range( len(A) ):
    print i,":"

    Matrix_Print(A[i])
    AA=Inverse(A[i])
    Matrix_Print(AA)

    0 :
[
    [-1.000000,1.000000,1.000000,1.000000]
    [1.000000,-1.000000,1.000000,1.000000]
    [1.000000,1.000000,-1.000000,1.000000]
    [1.000000,1.000000,1.000000,-1.000000]
]
Gauss Forward, det -16.0
Matrix_Gauss_Test, Residual: 0.000000e+00
[
    [-0.250000,0.250000,0.250000,0.250000]
    [0.250000,-0.250000,0.250000,0.250000]
    [0.250000,0.250000,-0.250000,0.250000]
    [0.250000,0.250000,0.250000,-0.250000]
]
1 :
[
    [1.000000,2.000000,4.000000,8.000000]
    [1.000000,-1.000000,1.000000,-1.000000]
    [1.000000,-2.000000,4.000000,-8.000000]
    [1.000000,1.000000,1.000000,1.000000]
]
Gauss Forward, det 72.0
Matrix_Gauss_Test, Residual: 2.127425e-16
[
    [-0.166667,0.666667,-0.166667,0.666667]
    [-0.083333,-0.666667,0.083333,0.666667]
    [0.166667,-0.166667,0.166667,-0.166667]
    [0.083333,0.166667,-0.083333,-0.166667]
]
2 :
[
    [1.000000,1.000000,1.000000,1.000000]
    [1.000000,-1.000000,1.000000,-1.000000]
    [1.000000,2.000000,4.000000,8.000000]
    [1.000000,3.000000,9.000000,27.000000]
]
Gauss Forward, det -48.0
Matrix_Gauss_Test, Residual: 7.351626e-17
[
    [1.500000,0.250000,-1.000000,0.250000]
    [0.250000,-0.458333,0.333333,-0.125000]
    [-1.000000,0.250000,1.000000,-0.250000]
    [0.250000,-0.041667,-0.333333,0.125000]
]
3 :
[
    [1.000000,1.000000,1.000000,1.000000]
    [1.000000,2.000000,4.000000,8.000000]
    [1.000000,3.000000,9.000000,27.000000]
    [1.000000,4.000000,16.000000,64.000000]
]
Gauss Forward, det 12.0
Matrix_Gauss_Test, Residual: 5.594315e-16
[
    [4.000000,-6.000000,4.000000,-1.000000]
    [-4.333333,9.500000,-7.000000,1.833333]
    [1.500000,-4.000000,3.500000,-1.000000]
    [-0.166667,0.500000,-0.500000,0.166667]
]
    Output from: /usr/bin/python N02.py
  3. Arquivo N03py: Gere matrices de Vandermonte regulares de ordem 5,6,7,8,9 e 10 e encontre suas inversas.
    Python Listing: N03.py. 
    from Matrix import *
from Gauss import *

v=[0.0]
for i in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]:
    v.append( 1.0*i )
    A=Matrix_Vandermonte(v)
    print "Ordem",i+1,":"

    AA=Inverse(A)

    Ordem 2 :
Gauss Forward, det 1.0
Matrix_Gauss_Test, Residual: 0.000000e+00
Ordem 3 :
Gauss Forward, det 2.0
Matrix_Gauss_Test, Residual: 0.000000e+00
Ordem 4 :
Gauss Forward, det 12.0
Matrix_Gauss_Test, Residual: 5.909070e-16
Ordem 5 :
Gauss Forward, det 288.0
Matrix_Gauss_Test, Residual: 2.123877e-15
Ordem 6 :
Gauss Forward, det 34560.0
Matrix_Gauss_Test, Residual: 3.431676e-14
Ordem 7 :
Gauss Forward, det 24883200.0
Matrix_Gauss_Test, Residual: 3.373950e-13
Ordem 8 :
Gauss Forward, det 1.25411328e+11
Matrix_Gauss_Test, Residual: 2.793467e-12
Ordem 9 :
Gauss Forward, det 5.05658474496e+15
Matrix_Gauss_Test, Residual: 1.127236e-11
Ordem 10 :
Gauss Forward, det 1.83493347225e+21
Matrix_Gauss_Test, Residual: 7.379216e-11
Ordem 11 :
Gauss Forward, det 6.6586065841e+27
Matrix_Gauss_Test, Residual: 8.298242e-10
Ordem 12 :
Gauss Forward, det 2.65790267296e+35
Matrix_Gauss_Test, Residual: 4.848438e-09
Ordem 13 :
Gauss Forward, det 1.27313963299e+44
Matrix_Gauss_Test, Residual: 3.850929e-08
Ordem 14 :
Gauss Forward, det 7.92786697562e+53
Matrix_Gauss_Test, Residual: 6.818547e-04
Ordem 15 :
Gauss Forward, det 6.91138269044e+64
Matrix_Gauss_Test, Residual: 2.825255e-01
Ordem 16 :
Gauss Forward, det 9.03784344483e+76
Matrix_Gauss_Test, Residual: 1.966895e-05
    Output from: /usr/bin/python N03.py
< Matriz Inversa | Atividades | Interpolação >
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