test_simeq_newton5.rb running test case 1, n=2, nlin=2 var1 0 0 0 1 var2 -1 -1 0 1 var3 -1 -1 -1 -1 vari1 -1 -1 -1 -1 vari2 -1 -1 -1 -1 a[0][0]=1.0 a[0][1]=1.0 a[0][2]=1.0 a[0][3]=0.0 a[1][0]=1.0 a[1][1]=1.0 a[1][2]=0.0 a[1][3]=1.0 build_y running x_soln[0]=1.0 x_soln[1]=2.0 x_soln[2]=1.0 x_soln[3]=4.0 y[0]=4.0 y[1]=7.0 print_eqn running solve system of equations a * x = y for x the equations are for i=0,1 a[i][0]*x0 + a[i][1]*x1 + * x0 * x0 + = y[i] * x1 * x1 = y[i] desired solution, may not be unique x_soln[0]=1.0 x_soln[1]=2.0 initial guess x[0]=0.5 x[1]=0.5 simeq_newton5 running n=2, nlin=2 a[0][0]=1.0 a[0][1]=1.0 a[0][2]=1.0 a[0][3]=0.0 y[0]=4.0 a[1][0]=1.0 a[1][1]=1.0 a[1][2]=0.0 a[1][3]=1.0 y[1]=7.0 initial guess at solution, can be bad x[0]=0.5 x[1]=0.5 x[2]=0.25 x[3]=0.25 residual x_resid[0]= -4.0 residual x_resid[1]= -6.75 simeq_newton5 itr 0, initial residual=10.75 ja computed ja[0][0]=2.0 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=2.0 ja inverted ja[0][0]=0.6666666666666666 ja[0][1]=-0.3333333333333333 ja[1][0]=-0.3333333333333333 ja[1][1]=0.6666666666666666 change x_tmp2[0]=-0.4166666666666665 change x_tmp2[1]=-3.166666666666667 x_next[0]=0.9166666666666665 x_next[1]=3.666666666666667 x_next[2]=0.8402777777777775 x_next[3]=13.444444444444446 residual x_resid[0]=-4.0 residual x_resid[1]=-6.75 simeq_newton5 itr 1, prev=10.75, residual=12.45138888888889 b reduced to 0.5 ja computed ja[0][0]=2.0 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=2.0 ja inverted ja[0][0]=0.6666666666666666 ja[0][1]=-0.3333333333333333 ja[1][0]=-0.3333333333333333 ja[1][1]=0.6666666666666666 change x_tmp2[0]=-0.4166666666666665 change x_tmp2[1]=-3.166666666666667 x_next[0]=0.7083333333333333 x_next[1]=2.0833333333333335 x_next[2]=0.501736111111111 x_next[3]=4.340277777777779 residual x_resid[0]=-4.0 residual x_resid[1]=-6.75 simeq_newton5 itr 2, prev=10.75, residual=0.8385416666666674 b increased to 0.70715 ja computed ja[0][0]=2.4166666666666665 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=5.166666666666667 ja inverted ja[0][0]=0.4498186215235792 ja[0][1]=-0.08706166868198308 ja[1][0]=-0.08706166868198308 ja[1][1]=0.21039903264812576 change x_tmp2[0]=-0.3293278919790406 change x_tmp2[1]=0.08927851672712636 x_next[0]=0.9412175521463118 x_next[1]=2.0202000302297463 x_next[2]=0.8858904804682951 x_next[3]=4.081208162140268 residual x_resid[0]=-0.7065972222222219 residual x_resid[1]=0.13194444444444553 simeq_newton5 itr 3, prev=0.8385416666666674, residual=0.19531768167197194 b increased to 1.0 ja computed ja[0][0]=2.8824351042926235 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=5.0404000604594925 ja inverted ja[0][0]=0.3725729451689183 ja[0][1]=-0.07391733606458092 ja[1][0]=-0.07391733606458092 ja[1][1]=0.2130619242883432 change x_tmp2[0]=-0.06003966621204288 change x_tmp2[1]=0.020368504383957348 x_next[0]=1.0012572183583546 x_next[1]=1.9998315258457888 x_next[2]=1.0025160173147096 x_next[3]=3.999326131766696 residual x_resid[0]=-0.15269193715564677 residual x_resid[1]=0.04262574451632517 simeq_newton5 itr 4, prev=0.19531768167197194, residual=0.004019637489692585 ja computed ja[0][0]=3.002514436716709 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=4.999663051691577 ja inverted ja[0][0]=0.3568241420898143 ja[0][1]=-0.0713696379937218 ja[1][0]=-0.0713696379937218 ja[1][1]=0.21428836841939508 change x_tmp2[0]=0.0012566563885518043 change x_tmp2[1]=-0.00016836742976649138 x_next[0]=1.0000005619698027 x_next[1]=1.9999998932755554 x_next[2]=1.0000011239399211 x_next[3]=3.999999573102233 residual x_resid[0]=0.003604761518852584 residual x_resid[1]=0.0004148759708400007 simeq_newton5 itr 5, prev=0.004019637489692585, residual=1.6075328694853397e-06 ja computed ja[0][0]=3.0000011239396054 ja[0][1]=1.0 ja[1][0]=1.0 ja[1][1]=4.999999786551111 ja inverted ja[0][0]=0.35714271487229526 ja[0][1]=-0.0714285460237278 ja[1][0]=-0.0714285460237278 ja[1][1]=0.21428571835255525 change x_tmp2[0]=5.619696904613762e-07 change x_tmp2[1]=-1.0672442446006121e-07 x_next[0]=1.0000000000001121 x_next[1]=1.9999999999999798 x_next[2]=1.0000000000002243 x_next[3]=3.999999999999919 residual x_resid[0]=1.5791852785440597e-06 residual x_resid[1]=2.8347590941280032e-08 simeq_newton5 itr 6, prev=1.6075328694853397e-06, residual=3.268496584496461e-13 converged last residual = 3.268496584496461e-13 Simeq_newton5.rb finished print_results running, Returned solution vs expected solution x[0]=1.0000000000001121 err=1.1213252548714081e-13 x[1]=1.9999999999999798 err=-2.020605904817785e-14 Returned solution in given equation, sum of errors=3.268496584496461e-13 test case 1 finished