SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br
Provas
Liberdade é um prato facil de comer.
Mas deficil de digerir
Mas deficil de digerir
Jean-Jaques Rousseau
< 2017.2.2
| 2017.2.Subst |
2018.1.1 >
Cálculo Numérico, Semestre 2017.2, Prova Substituitiva
- N01.py:
Python Listing: N01.py.
from math import * from Matrix import * from Gauss import * print "Question a" vs=[ [ 0.0, 1.0, sqrt(2.0), sqrt(3.0), ], [ 0.0,-1.0, sqrt(2.0),-sqrt(3.0), ], [ 0.0,-1.0,-sqrt(2.0), sqrt(3.0), ], [ 0.0, 1.0,-sqrt(2.0),-sqrt(3.0), ], ] Vs=[] for i in range( len(vs) ): Vs.append( Matrix_Vandermonte(vs[i]) ) print "V_%d=" % i, Matrix_Print(Vs[i]) print "Question b" for i in range( len(vs) ): for j in range( len(vs) ): w=Matrix_Mult_Vector(Vs[i],vs[j]) print "V_%d v_%d=" % (i,j), Vector_Print(w) def Det_V(v): det=1.0 for i in range( len(v) ): for j in range(i+1,len(v) ): det*=(v[j]-v[i]) return det print "Question c" text=[ "i", "Anal", "Num", "Abs", "Rel", ] print "\t".join(text) for i in range( len(vs) ): det_anal=Det_V(vs[i]) det_num=Gauss_Forward(Vs[i]) text=[ "%d" % i, "%.6f" % det_anal, "%.6f" % det_num, "%.6e" % abs(det_anal-det_num), "%.6e" % abs( (det_anal-det_num)/det_anal), ] print "\t".join(text) def C(): text=[ "i", "Anal", "Num", "Abs", "Rel", ] print "\\begin{tabular}{|r|rrrr|}" print "\\hline" print " & ".join(text)+"\\\\" print "\\hline" for i in range( len(vs) ): det_anal=Det_V(vs[i]) det_num=Gauss_Forward(Vs[i]) text=[ "%d" % i, "%.6f" % det_anal, "%.6f" % det_num, "%.6e" % abs(det_anal-det_num), "%.6e" % abs( (det_anal-det_num)/det_anal), ] print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" #C()Question a V_0= [ [1.000000,0.000000,0.000000,0.000000] [1.000000,1.000000,1.000000,1.000000] [1.000000,1.414214,2.000000,2.828427] [1.000000,1.732051,3.000000,5.196152] ] V_1= [ [1.000000,0.000000,0.000000,0.000000] [1.000000,-1.000000,1.000000,-1.000000] [1.000000,1.414214,2.000000,2.828427] [1.000000,-1.732051,3.000000,-5.196152] ] V_2= [ [1.000000,0.000000,0.000000,0.000000] [1.000000,-1.000000,1.000000,-1.000000] [1.000000,-1.414214,2.000000,-2.828427] [1.000000,1.732051,3.000000,5.196152] ] V_3= [ [1.000000,0.000000,0.000000,0.000000] [1.000000,1.000000,1.000000,1.000000] [1.000000,-1.414214,2.000000,-2.828427] [1.000000,-1.732051,3.000000,-5.196152] ] Question b V_0 v_0= [0.000000,4.146264,9.141620,14.974691] V_0 v_1= [0.000000,-1.317837,-3.484766,-6.489410] V_0 v_2= [0.000000,-0.682163,0.656339,3.025309] V_0 v_3= [0.000000,-2.146264,-6.313193,-11.510590] V_1 v_0= [0.000000,-1.317837,9.141620,-6.489410] V_1 v_1= [0.000000,4.146264,-3.484766,14.974691] V_1 v_2= [0.000000,-2.146264,0.656339,-11.510590] V_1 v_3= [0.000000,-0.682163,-6.313193,3.025309] V_2 v_0= [0.000000,-1.317837,-3.484766,14.974691] V_2 v_1= [0.000000,4.146264,9.141620,-6.489410] V_2 v_2= [0.000000,-2.146264,-6.313193,3.025309] V_2 v_3= [0.000000,-0.682163,0.656339,-11.510590] V_3 v_0= [0.000000,4.146264,-3.484766,-6.489410] V_3 v_1= [0.000000,-1.317837,9.141620,14.974691] V_3 v_2= [0.000000,-0.682163,-6.313193,-11.510590] V_3 v_3= [0.000000,-2.146264,0.656339,3.025309] Question c i Anal Num Abs Rel 0 0.236073 0.236073 4.163336e-16 1.763582e-15 1 13.620334 13.620334 0.000000e+00 0.000000e+00 2 -8.721354 -8.721354 0.000000e+00 0.000000e+00 3 -5.135052 -5.135052 2.664535e-15 5.188916e-16Output from: /usr/bin/python N01.py - N02.py:
Python Listing: N02.py.
from math import * from Derivatives import * print "Question a" def f0(x): return x*e**x def f1(x): return x*sin(x) def f2(x): return x*cos(x) def f3(x): return log(1.0+x) def f4(x): return x*sqrt(1.0+x) def df0(x): return (x+1.0)*e**x def df1(x): return sin(x)+x*cos(x) def df2(x): return cos(x)-x*sin(x) def df3(x): return 1.0/(x+1.0) def df4(x): u=sqrt(1.0+x) return u+0.5*x/u def d2f0(x): return (x+2.0)*e**x def d2f1(x): return 2.0*cos(x)-x*sin(x) def d2f2(x): return -2.0*sin(x)-x*cos(x) def d2f3(x): return -1.0/( (1.0+x)**2 ) def d2f4(x): u=sqrt(1.0+x) return 1.0/u-0.25*x/(u**3) print "Question b" fs=[f0,f1,f2,f3,f4] dfs=[df0,df1,df2,df3,df4] d2fs=[d2f0,d2f1,d2f2,d2f3,d2f4] xs=[0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9] for i in range( len(fs) ): text=[ "2","x","\tf"+str(i), "\tf_ana'","\tf_num'","\tr'", ] print "\t".join(text) f=fs[i] df=dfs[i] d2f=d2fs[i] for x in xs: ana1=df(x) num1=d_f(f,x) text=[ "%d" % i, "%.6f" % x, "%.6f" % f(x), "%.6f" % ana1, "%.6f" % num1, "%.6e" % abs( (ana1-num1)/ana1 ), ] print "\t".join(text) print "Question c" for i in range( len(fs) ): text=[ "2","x","\tf"+str(i), "\tf_ana''","\tf_num''","\tr''", ] print "\t".join(text) f=fs[i] df=dfs[i] d2f=d2fs[i] for x in xs: ana2=d2f(x) num2=d2_f(f,x) text=[ "%d" % i, "%.6f" % x, "%.6f" % f(x), "%.6f" % ana2, "%.6f" % num2, "%.6e" % abs( (ana2-num2)/ana2 ), ] print "\t".join(text) def B(): for i in range( len(fs) ): text=[ "$n$","$x$","$f$", "$f'_{a}$","$f'_{n}$","$r'_1$", ] print "\\begin{tabular}{|cccccc|}" print "\\hline" print " & ".join(text)+"\\\\" print "\\hline" f=fs[i] df=dfs[i] for x in xs: ana1=df(x) num1=d_f(f,x) text=[ "%d" % i, "%.6f" % x, "%.6f" % f(x), "%.6f" % ana1, "%.6f" % num1, "%.6e" % abs( (ana1-num1)/ana1 ), ] print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" text=[ "$i$","$x$","$f$", "$f''_{a}$","$f''_{n}$","$r_2$", ] print "\\begin{tabular}{|cccccc|}" print "\\hline" print " & ".join(text)+"\\\\" print "\\hline" f=fs[i] df=dfs[i] d2f=d2fs[i] for x in xs: ana2=d2f(x) num2=d2_f(f,x) text=[ "%d" % i, "%.6f" % x, "%.6f" % f(x), "%.6f" % ana2, "%.6f" % num2, "%.6e" % abs( (ana2-num2)/ana2 ), ] print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" #B()Question a Question b 2 x f0 f_ana' f_num' r' 0 0.100000 0.110517 1.215688 1.215688 6.380672e-12 0 0.200000 0.244281 1.465683 1.465683 1.639789e-12 0 0.300000 0.404958 1.754816 1.754816 2.238393e-12 0 0.400000 0.596730 2.088555 2.088555 3.817324e-11 0 0.500000 0.824361 2.473082 2.473082 1.846312e-11 0 0.600000 1.093271 2.915390 2.915390 5.776546e-11 0 0.700000 1.409627 3.423380 3.423380 4.320925e-12 0 0.800000 1.780433 4.005974 4.005974 1.321213e-11 0 0.900000 2.213643 4.673246 4.673246 3.407115e-11 2 x f1 f_ana' f_num' r' 1 0.100000 0.009983 0.199334 0.199334 3.243913e-12 1 0.200000 0.039734 0.394683 0.394683 1.011143e-11 1 0.300000 0.088656 0.582121 0.582121 2.424665e-11 1 0.400000 0.155767 0.757843 0.757843 1.852670e-11 1 0.500000 0.239713 0.918217 0.918217 1.704358e-12 1 0.600000 0.338785 1.059844 1.059844 3.935964e-11 1 0.700000 0.450952 1.179607 1.179607 1.029501e-11 1 0.800000 0.573885 1.274721 1.274721 5.243453e-11 1 0.900000 0.704994 1.342776 1.342776 1.921312e-11 2 x f2 f_ana' f_num' r' 2 0.100000 0.099500 0.985021 0.985021 2.314963e-12 2 0.200000 0.196013 0.940333 0.940333 1.502368e-11 2 0.300000 0.286601 0.866680 0.866680 8.807943e-12 2 0.400000 0.368424 0.765294 0.765294 2.956615e-11 2 0.500000 0.438791 0.637870 0.637870 1.342495e-11 2 0.600000 0.495201 0.486550 0.486550 4.342989e-11 2 0.700000 0.535390 0.313890 0.313890 4.899005e-11 2 0.800000 0.557365 0.122822 0.122822 1.468325e-10 2 0.900000 0.559449 -0.083384 -0.083384 6.569261e-10 2 x f3 f_ana' f_num' r' 3 0.100000 0.095310 0.909091 0.909091 2.528625e-11 3 0.200000 0.182322 0.833333 0.833333 2.320450e-11 3 0.300000 0.262364 0.769231 0.769231 8.504211e-11 3 0.400000 0.336472 0.714286 0.714286 5.651122e-11 3 0.500000 0.405465 0.666667 0.666667 5.651130e-11 3 0.600000 0.470004 0.625000 0.625000 5.096013e-11 3 0.700000 0.530628 0.588235 0.588235 5.451110e-11 3 0.800000 0.587787 0.555556 0.555556 9.336891e-11 3 0.900000 0.641854 0.526316 0.526316 6.206241e-11 2 x f4 f_ana' f_num' r' 4 0.100000 0.104881 1.096482 1.096482 8.126986e-12 4 0.200000 0.219089 1.186732 1.186732 4.682138e-12 4 0.300000 0.342053 1.271734 1.271734 5.735448e-11 4 0.400000 0.473286 1.352247 1.352247 6.649942e-12 4 0.500000 0.612372 1.428869 1.428869 1.195546e-11 4 0.600000 0.758947 1.502082 1.502082 9.051298e-12 4 0.700000 0.912688 1.572278 1.572278 2.013441e-11 4 0.800000 1.073313 1.639783 1.639783 2.414526e-11 4 0.900000 1.240564 1.704869 1.704869 3.845456e-11 Question c 2 x f0 f_ana'' f_num'' r'' 0 0.100000 0.110517 2.320859 2.320852 3.052283e-06 0 0.200000 0.244281 2.687086 2.687073 4.942697e-06 0 0.300000 0.404958 3.104675 3.104683 2.550923e-06 0 0.400000 0.596730 3.580379 3.580358 5.877094e-06 0 0.500000 0.824361 4.121803 4.121870 1.609384e-05 0 0.600000 1.093271 4.737509 4.737599 1.906504e-05 0 0.700000 1.409627 5.437132 5.437262 2.380699e-05 0 0.800000 1.780433 6.231515 6.231571 9.021104e-06 0 0.900000 2.213643 7.132849 7.132850 1.183194e-07 2 x f1 f_ana'' f_num'' r'' 1 0.100000 0.009983 1.980025 1.980026 2.674981e-07 1 0.200000 0.039734 1.920399 1.920398 7.399602e-07 1 0.300000 0.088656 1.822017 1.822025 4.529802e-06 1 0.400000 0.155767 1.686355 1.686346 5.421993e-06 1 0.500000 0.239713 1.515452 1.515475 1.510494e-05 1 0.600000 0.338785 1.311886 1.311895 7.082374e-06 1 0.700000 0.450952 1.078732 1.078734 2.160487e-06 1 0.800000 0.573885 0.819529 0.819511 2.125655e-05 1 0.900000 0.704994 0.538226 0.538236 1.933104e-05 2 x f2 f_ana'' f_num'' r'' 2 0.100000 0.099500 -0.299167 -0.299170 1.056548e-05 2 0.200000 0.196013 -0.593352 -0.593352 3.716872e-07 2 0.300000 0.286601 -0.877641 -0.877631 1.146151e-05 2 0.400000 0.368424 -1.147261 -1.147277 1.362885e-05 2 0.500000 0.438791 -1.397642 -1.397646 2.525510e-06 2 0.600000 0.495201 -1.624486 -1.624478 4.916080e-06 2 0.700000 0.535390 -1.823825 -1.823819 3.307265e-06 2 0.800000 0.557365 -1.992078 -1.992101 1.173618e-05 2 0.900000 0.559449 -2.126103 -2.126077 1.208716e-05 2 x f3 f_ana'' f_num'' r'' 3 0.100000 0.095310 -0.826446 -0.826495 5.909803e-05 3 0.200000 0.182322 -0.694444 -0.694445 8.274037e-08 3 0.300000 0.262364 -0.591716 -0.591749 5.559389e-05 3 0.400000 0.336472 -0.510204 -0.510175 5.653863e-05 3 0.500000 0.405465 -0.444444 -0.444422 4.987730e-05 3 0.600000 0.470004 -0.390625 -0.390701 1.954820e-04 3 0.700000 0.530628 -0.346021 -0.346029 2.311987e-05 3 0.800000 0.587787 -0.308642 -0.308642 8.274037e-08 3 0.900000 0.641854 -0.277008 -0.276917 3.282657e-04 2 x f4 f_ana'' f_num'' r'' 4 0.100000 0.104881 0.931793 0.931782 1.132865e-05 4 0.200000 0.219089 0.874835 0.874842 8.258883e-06 4 0.300000 0.342053 0.826459 0.826450 1.028323e-05 4 0.400000 0.473286 0.784786 0.784789 3.576587e-06 4 0.500000 0.612372 0.748455 0.748512 7.637601e-05 4 0.600000 0.758947 0.716454 0.716455 1.592545e-06 4 0.700000 0.912688 0.688013 0.688005 1.090419e-05 4 0.800000 1.073313 0.662539 0.662581 6.405829e-05 4 0.900000 1.240564 0.639565 0.639655 1.413567e-04Output from: /usr/bin/python N02.py - N03.py:
Python Listing: N03.py.
from math import * from Integration import * print "Question a" def f0(x): return x*e**x def f1(x): return x*sin(x) def f2(x): return x*cos(x) def f3(x): return log(1.0+x) def f4(x): return x*sqrt(1.0+x) def F0(x): return (x-1)*e**x def F1(x): return sin(x)-x*cos(x) def F2(x): return x*sin(x)+cos(x) def F3(x): u=1.0+x return u*log(u)-u def F4(x): u=sqrt(1.0+x) return 2.0/5.0*u**5-2.0/3.0*u**3 a=1.0 b=2.0 fs=[f0,f1,f2,f3,f4] Fs=[F0,F1,F2,F3,F4] print "Question b" for n in range( len(fs) ): f=fs[n] F=Fs[n] text=[ "n", "i", "a", "\tb", "\tAna", "\tTrapez", "\tr", ] print "\t".join(text) ana=F(b)-F(a) for i in range(1,11): num=Trapezoids_R(f,a,b,5*i) text=[ "%d" % n, "%d" % i, "%.6f" % a, "%.6f" % b, "%.6f" % ana, "%.6f" % num, "%.6e" % abs( (ana-num)/ana ), ] print "\t".join(text) print "Question c" for n in range( len(fs) ): f=fs[n] F=Fs[n] text=[ "n", "i", "a", "\tb", "\tAna", "\tSimpson", "\tr", ] print "\t".join(text) ana=F(b)-F(a) for i in range(1,11): num=Simpsons_R(f,a,b,5*i) text=[ "%d" % n, "%d" % i, "%.6f" % a, "%.6f" % b, "%.6f" % ana, "%.6f" % num, "%.6e" % abs( (ana-num)/ana ), ] print "\t".join(text) def BC(): for n in range( len(fs) ): f=fs[n] F=Fs[n] text=[ "$n$", "$i$", "$a$", "$b$", "Ana", "Trapez", "$r$", ] print "\\begin{tabular}{"+"c"*7+"}" print " & ".join(text)+"\\\\" print "\\hline" ana=F(b)-F(a) for i in range(1,11): num=Trapezoids_R(f,a,b,5*i) text=[ "%d" % n, "%d" % (5*i), "%.6f" % a, "%.6f" % b, "%.6f" % ana, "%.6f" % num, "%.6e" % abs( (ana-num)/ana ), ] print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" text=[ "$n$", "$i$", "$a$", "$b$", "Ana", "Simpson", "$r$", ] print "\\begin{tabular}{"+"c"*7+"}" print " & ".join(text)+"\\\\" print "\\hline" ana=F(b)-F(a) for i in range(1,11): num=Simpsons_R(f,a,b,5*i) text=[ "%d" % n, "%d" % (5*i), "%.6f" % a, "%.6f" % b, "%.6f" % ana, "%.6f" % num, "%.6e" % abs( (ana-num)/ana ), ] print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" #BC()Question a Question b n i a b Ana Trapez r 0 1 1.000000 2.000000 7.389056 7.444767 7.539639e-03 0 2 1.000000 2.000000 7.389056 7.402995 1.886378e-03 0 3 1.000000 2.000000 7.389056 7.395252 8.385110e-04 0 4 1.000000 2.000000 7.389056 7.392541 4.716863e-04 0 5 1.000000 2.000000 7.389056 7.391287 3.018863e-04 0 6 1.000000 2.000000 7.389056 7.390605 2.096459e-04 0 7 1.000000 2.000000 7.389056 7.390194 1.540267e-04 0 8 1.000000 2.000000 7.389056 7.389927 1.179273e-04 0 9 1.000000 2.000000 7.389056 7.389745 9.317745e-05 0 10 1.000000 2.000000 7.389056 7.389614 7.547392e-05 n i a b Ana Trapez r 1 1 1.000000 2.000000 1.440422 1.436071 3.021219e-03 1 2 1.000000 2.000000 1.440422 1.439335 7.549663e-04 1 3 1.000000 2.000000 1.440422 1.439939 3.355127e-04 1 4 1.000000 2.000000 1.440422 1.440151 1.887204e-04 1 5 1.000000 2.000000 1.440422 1.440248 1.207795e-04 1 6 1.000000 2.000000 1.440422 1.440302 8.387401e-05 1 7 1.000000 2.000000 1.440422 1.440334 6.162145e-05 1 8 1.000000 2.000000 1.440422 1.440354 4.717879e-05 1 9 1.000000 2.000000 1.440422 1.440369 3.727699e-05 1 10 1.000000 2.000000 1.440422 1.440379 3.019432e-05 n i a b Ana Trapez r 2 1 1.000000 2.000000 0.020675 0.014221 3.121591e-01 2 2 1.000000 2.000000 0.020675 0.019063 7.796211e-02 2 3 1.000000 2.000000 0.020675 0.019958 3.464344e-02 2 4 1.000000 2.000000 0.020675 0.020272 1.948568e-02 2 5 1.000000 2.000000 0.020675 0.020417 1.247046e-02 2 6 1.000000 2.000000 0.020675 0.020496 8.659903e-03 2 7 1.000000 2.000000 0.020675 0.020543 6.362316e-03 2 8 1.000000 2.000000 0.020675 0.020574 4.871117e-03 2 9 1.000000 2.000000 0.020675 0.020595 3.848767e-03 2 10 1.000000 2.000000 0.020675 0.020610 3.117492e-03 n i a b Ana Trapez r 3 1 1.000000 2.000000 0.909543 0.908987 6.103794e-04 3 2 1.000000 2.000000 0.909543 0.909404 1.526751e-04 3 3 1.000000 2.000000 0.909543 0.909481 6.786222e-05 3 4 1.000000 2.000000 0.909543 0.909508 3.817380e-05 3 5 1.000000 2.000000 0.909543 0.909520 2.443162e-05 3 6 1.000000 2.000000 0.909543 0.909527 1.696655e-05 3 7 1.000000 2.000000 0.909543 0.909531 1.246528e-05 3 8 1.000000 2.000000 0.909543 0.909534 9.543765e-06 3 9 1.000000 2.000000 0.909543 0.909536 7.540770e-06 3 10 1.000000 2.000000 0.909543 0.909537 6.108034e-06 n i a b Ana Trapez r 4 1 1.000000 2.000000 2.394158 2.395963 7.540102e-04 4 2 1.000000 2.000000 2.394158 2.394609 1.885204e-04 4 3 1.000000 2.000000 2.394158 2.394358 8.378831e-05 4 4 1.000000 2.000000 2.394158 2.394271 4.713121e-05 4 5 1.000000 2.000000 2.394158 2.394230 3.016406e-05 4 6 1.000000 2.000000 2.394158 2.394208 2.094730e-05 4 7 1.000000 2.000000 2.394158 2.394195 1.538987e-05 4 8 1.000000 2.000000 2.394158 2.394186 1.178287e-05 4 9 1.000000 2.000000 2.394158 2.394180 9.309928e-06 4 10 1.000000 2.000000 2.394158 2.394176 7.541044e-06 Question c n i a b Ana Simpson r 0 1 1.000000 2.000000 7.389056 7.389071 1.957102e-06 0 2 1.000000 2.000000 7.389056 7.389057 1.224672e-07 0 3 1.000000 2.000000 7.389056 7.389056 2.419649e-08 0 4 1.000000 2.000000 7.389056 7.389056 7.656524e-09 0 5 1.000000 2.000000 7.389056 7.389056 3.136227e-09 0 6 1.000000 2.000000 7.389056 7.389056 1.512487e-09 0 7 1.000000 2.000000 7.389056 7.389056 8.164075e-10 0 8 1.000000 2.000000 7.389056 7.389056 4.785653e-10 0 9 1.000000 2.000000 7.389056 7.389056 2.987663e-10 0 10 1.000000 2.000000 7.389056 7.389056 1.960247e-10 n i a b Ana Simpson r 1 1 1.000000 2.000000 1.440422 1.440423 4.513908e-07 1 2 1.000000 2.000000 1.440422 1.440422 2.818965e-08 1 3 1.000000 2.000000 1.440422 1.440422 5.567513e-09 1 4 1.000000 2.000000 1.440422 1.440422 1.761506e-09 1 5 1.000000 2.000000 1.440422 1.440422 7.214959e-10 1 6 1.000000 2.000000 1.440422 1.440422 3.479402e-10 1 7 1.000000 2.000000 1.440422 1.440422 1.878064e-10 1 8 1.000000 2.000000 1.440422 1.440422 1.100876e-10 1 9 1.000000 2.000000 1.440422 1.440422 6.872670e-11 1 10 1.000000 2.000000 1.440422 1.440422 4.509236e-11 n i a b Ana Simpson r 2 1 1.000000 2.000000 0.020675 0.020677 1.035440e-04 2 2 1.000000 2.000000 0.020675 0.020675 6.462846e-06 2 3 1.000000 2.000000 0.020675 0.020675 1.276295e-06 2 4 1.000000 2.000000 0.020675 0.020675 4.037928e-07 2 5 1.000000 2.000000 0.020675 0.020675 1.653869e-07 2 6 1.000000 2.000000 0.020675 0.020675 7.975650e-08 2 7 1.000000 2.000000 0.020675 0.020675 4.305021e-08 2 8 1.000000 2.000000 0.020675 0.020675 2.523509e-08 2 9 1.000000 2.000000 0.020675 0.020675 1.575410e-08 2 10 1.000000 2.000000 0.020675 0.020675 1.033609e-08 n i a b Ana Simpson r 3 1 1.000000 2.000000 0.909543 0.909542 1.069873e-07 3 2 1.000000 2.000000 0.909543 0.909542 6.708674e-09 3 3 1.000000 2.000000 0.909543 0.909543 1.325980e-09 3 4 1.000000 2.000000 0.909543 0.909543 4.196379e-10 3 5 1.000000 2.000000 0.909543 0.909543 1.719010e-10 3 6 1.000000 2.000000 0.909543 0.909543 8.290372e-11 3 7 1.000000 2.000000 0.909543 0.909543 4.475216e-11 3 8 1.000000 2.000000 0.909543 0.909543 2.623336e-11 3 9 1.000000 2.000000 0.909543 0.909543 1.637829e-11 3 10 1.000000 2.000000 0.909543 0.909543 1.074516e-11 n i a b Ana Simpson r 4 1 1.000000 2.000000 2.394158 2.394158 2.376000e-08 4 2 1.000000 2.000000 2.394158 2.394158 1.487775e-09 4 3 1.000000 2.000000 2.394158 2.394158 2.939840e-10 4 4 1.000000 2.000000 2.394158 2.394158 9.303056e-11 4 5 1.000000 2.000000 2.394158 2.394158 3.810828e-11 4 6 1.000000 2.000000 2.394158 2.394158 1.837970e-11 4 7 1.000000 2.000000 2.394158 2.394158 9.919194e-12 4 8 1.000000 2.000000 2.394158 2.394158 5.814329e-12 4 9 1.000000 2.000000 2.394158 2.394158 3.629458e-12 4 10 1.000000 2.000000 2.394158 2.394158 2.382417e-12Output from: /usr/bin/python N03.py - N04.py:
Python Listing: N04.py.
from math import * from Lagrange import * print "Question bc" xs=[ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] ys=[ [ 5.0, 1.0,-2.0, 3.0, 0.0, -2.0, 1.0], [ 1.0,-2.0, 0.0, 3.0,-2.0, 1.0, 5.0], ] text=[ "i" ] for j in range( len(xs) ): text.append( "%.6f" % xs[j] ) print "\t".join(text) for i in range( len(xs) ): Hi=Lagrange_H_P(i,xs) text=["%d" % i ] for j in range( len(xs) ): value=Polynomia_Calc(Hi,xs[j]) text.append( "%.6f" % value ) print "\t".join(text) print "Question bc" text=[ "n" ] for j in range( len(xs) ): text.append( "%.6f" % xs[j] ) print "\t".join(text) for n in range( len(ys) ): P=Lagrange_P(xs,ys[n]) text=["%d" % n ] for j in range( len(xs) ): value=Polynomia_Calc(P,xs[j]) text.append( "%.6f" % value ) print "\t".join(text) def Run(): print "\\begin{tabular}{c"+"c"*len(xs)+"}" text=[ "i" ] for j in range( len(xs) ): text.append( "%.6f" % xs[j] ) print " & ".join(text)+"\\\\" print "\\hline" for i in range( len(xs) ): Hi=Lagrange_H_P(i,xs) text=["%d" % i ] for j in range( len(xs) ): value=Polynomia_Calc(Hi,xs[j]) text.append( "%.6f" % value ) print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" print "\\begin{tabular}{c"+"c"*len(xs)+"}" text=[ "n" ] for j in range( len(xs) ): text.append( "%.6f" % xs[j] ) print " & ".join(text)+"\\\\" print "\\hline" for n in range( len(ys) ): P=Lagrange_P(xs,ys[n]) text=["%d" % n ] for j in range( len(xs) ): value=Polynomia_Calc(P,xs[j]) text.append( "%.6f" % value ) print " & ".join(text)+"\\\\" print "\\hline" print "\\end{tabular}" #Run()Question bc i 0.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 0 1.000000 -0.000000 -0.000000 -0.000000 -0.000000 -0.000000 -0.000000 1 0.000000 1.000000 0.000000 0.000000 -0.000000 -0.000000 -0.000000 2 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 -0.000000 3 0.000000 -0.000000 -0.000000 1.000000 0.000000 0.000000 0.000000 4 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 5 0.000000 -0.000000 -0.000000 -0.000000 0.000000 1.000000 0.000000 6 0.000000 0.000000 0.000000 0.000000 0.000000 -0.000000 1.000000 Question bc n 0.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 0 5.000000 1.000000 -2.000000 3.000000 -0.000000 -2.000000 1.000000 1 1.000000 -2.000000 0.000000 3.000000 -2.000000 1.000000 5.000000Output from: /usr/bin/python N04.py
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