Cálculo Numérico, Semestre 2017.2, Prova Teste

from math import *


def f_1(x):
    return x*log(x)-x

def f_2(x):
    return x**2*cos(x)

def f_3(x):
    return x-sin(x)-1.0

def f_4(x):
    return x**3-3.0*x**2+x-2

def f_5(x):
    return -2.0-cos(x)+e**x

def df_1(x):
    return log(x)

def df_2(x):
    return 2.0*x*cos(x)-x**2*sin(x)

def df_3(x):
    return 1.0-cos(x)

def df_4(x):
    return 3.0*x**2-6.0*x+1.0

def df_5(x):
    return sin(x)+e**x

fs=[f_1,f_2,f_3,f_4,f_5]

xs=[
    0.25,1.0/3.0,0.5, 1.0, 2.0, 3.0,4.0
]

titles=["x","f\_1(x)","f\_2(x)","f\_3(x)","f\_4(x)","f\_5(x)"]

print '\\begin{tabular}{cccccc}'
print ' & '.join(titles)+'\\\\'

for x in xs:
    text=[ "%.6f" % x  ]
    for f in fs:
        text.append( "%.6f" % f(x) )
    print " & ".join(text)+'\\\\'
print '\end{tabular}'

\begin{tabular}{cccccc}
x & f\_1(x) & f\_2(x) & f\_3(x) & f\_4(x) & f\_5(x)\\
0.250000 & -0.596574 & 0.060557 & -0.997404 & -1.921875 & -1.684887\\
0.333333 & -0.699537 & 0.104995 & -0.993861 & -1.962963 & -1.549345\\
0.500000 & -0.846574 & 0.219396 & -0.979426 & -2.125000 & -1.228861\\
1.000000 & -1.000000 & 0.540302 & -0.841471 & -3.000000 & 0.177980\\
2.000000 & -0.613706 & -1.664587 & 0.090703 & -4.000000 & 5.805203\\
3.000000 & 0.295837 & -8.909932 & 1.858880 & 1.000000 & 19.075529\\
4.000000 & 1.545177 & -10.458298 & 3.756802 & 18.000000 & 53.251794\\
\end{tabular}

from math import *
from Residual import *
from Derivatives import *
from N01 import *




dfs=[df_1,df_2,df_3,df_4,df_5]

titles=["$x$","$df_{ana}$","$df_{num}$","$r_a$","$r_r$"]


for i in range( len(dfs) ):
    print "f_"+str(i+1)

    print '\\begin{tabular}{lllll}'
    print ' & '.join(titles)+'\\\\'
    
    f=fs[i]
    df=dfs[i]
    
    for x in xs:
        text=[ "%.6f" % x ]
        df_ana=df(x)
        df_num=d_f(f,x,1.0E-6)
        
        r_abs=R_Abs(df_ana,df_num)
        r_rel=R_Rel(df_ana,df_num)
        
        print '%.6f & %.6f & %.6f & %.6e & %.6e\\\\' % (x,df_ana,df_num,r_abs,r_rel)

    print '\end{tabular}'

Warning! Unable to pipe system command: cd /usr/local/Slides/1_Disciplines/1_CN/9_Tests/2017.2.0; /usr/bin/python N02.py

from math import *

from N01 import *

from Isolate import *
from Bisection import Bisection
from False_Position import False_Position
from Newton_Raphson import Newton_Raphson


ass=[2.0,1.0,1.0,2.0,0.5,]
bss=[3.0,2.0,3.0,3.0,1.0,]

fs=[f_1,f_2,f_3,f_4,f_5]
names=["f_1","f_2","f_3","f_4","f_5"]

print "\n\nEx 3\n"

print "\nBisection\n"

eps=1.0E-3

for n in range( len(fs) ):
    f=fs[n]
    a=ass[n]
    b=bss[n]
    name=names[n]
    
    xs=Bisection(f,a,b,eps)

    x=xs[ len(xs)-1 ]
    text=[
        name,
        "%.6f" %a,"%.6f" %b,
        "%d" %len(xs),
        "%.6f" %x,
        "%.6e" % f(x)
    ]
    print "\t".join(text)

print "\nFalse Position\n"

for n in range( len(fs) ):
    f=fs[n]
    a=ass[n]
    b=bss[n]
    name=names[n]
    
    xs=False_Position(f,a,b,eps)

    x=xs[ len(xs)-1 ]
    text=[
        name,
        "%.6f" %a,"%.6f" %b,
        "%d" %len(xs),
        "%.6f" %x,
        "%.6e" % f(x)
    ]
    print "\t".join(text)
    
print "\nNewton Raphson\n"

dfs=[df_1,df_2,df_3,df_4,df_5]

for n in range( len(fs) ):
    f=fs[n]
    df=dfs[n]
    
    x0=ass[n]
    name=names[n]
    
    xs=Newton_Raphson(f,df,x0,eps)

    x=xs[ len(xs)-1 ]
    text=[
        name,
        "%.6f" %a,"%.6f" %b,
        "%d" %len(xs),
        "%.6f" %x,
        "%.6e" % f(x)
    ]
    print "\t".join(text)

\begin{tabular}{cccccc}
x & f\_1(x) & f\_2(x) & f\_3(x) & f\_4(x) & f\_5(x)\\
0.250000 & -0.596574 & 0.060557 & -0.997404 & -1.921875 & -1.684887\\
0.333333 & -0.699537 & 0.104995 & -0.993861 & -1.962963 & -1.549345\\
0.500000 & -0.846574 & 0.219396 & -0.979426 & -2.125000 & -1.228861\\
1.000000 & -1.000000 & 0.540302 & -0.841471 & -3.000000 & 0.177980\\
2.000000 & -0.613706 & -1.664587 & 0.090703 & -4.000000 & 5.805203\\
3.000000 & 0.295837 & -8.909932 & 1.858880 & 1.000000 & 19.075529\\
4.000000 & 1.545177 & -10.458298 & 3.756802 & 18.000000 & 53.251794\\
\end{tabular}


Ex 3


Bisection

f_1    2.000000    3.000000    4    2.718750    4.682119e-04
f_2    1.000000    2.000000    10    1.570801    -1.099099e-05
f_3    1.000000    3.000000    10    1.934570    9.628553e-06
f_4    2.000000    3.000000    11    2.893311    1.868976e-04
f_5    0.500000    1.000000    9    0.948730    -2.861739e-04

False Position

f_1    2.000000    3.000000    2    2.717749    -5.326417e-04
f_2    1.000000    2.000000    6    1.570618    4.407991e-04
f_3    1.000000    3.000000    2    1.933856    -9.587618e-04
f_4    2.000000    3.000000    4    2.893280    -7.936443e-05
f_5    0.500000    1.000000    2    0.948698    -3.956837e-04

Newton Raphson

f_1    0.500000    1.000000    5    2.718282    2.911449e-12
f_2    0.500000    1.000000    7    -1.570796    -1.680804e-08
f_3    0.500000    1.000000    6    1.934563    1.545697e-11
f_4    0.500000    1.000000    8    2.893289    1.306660e-07
f_5    0.500000    1.000000    5    0.948815    9.193482e-10