function [A,b,x,t,L] = helio()
%HELIO Test matrix from helioseismology.
%
% [A,b,x,t,L] = helio()
%
% Generates a 212-by-100 test problem from inverse helioseismology.
% The solution x is a model solution with some typical features of
% real solutions to this problem.  The matrix L approximates the
% second derivative operator.
%
% The mesh is not uniform, and the solution x should be displayed
% as a function of t; i.e., plot(t,x).

% Per Christian Hansen, IMM, 08/03/94.

% The data was kindly provided by the authors of the following paper,
% where more information can be found:
%   J. Christensen-Dalsgaard, J. Schou & M. J. Thompson, "A comparison of
%   methods for inverting helioseismic data", Mon. Not. R. astr. Soc. 242
%   (1990), 353-369.

% The solution.
x = [...
   1.4664e+00
   1.6250e+00
   1.7557e+00
   1.8585e+00
   1.9334e+00
   1.9804e+00
   1.9995e+00
   1.9908e+00
   1.9541e+00
   1.8896e+00
   1.7972e+00
   1.6768e+00
   1.5286e+00
   1.3450e+00
   1.1796e+00
   1.0358e+00
   9.1087e-01
   8.0263e-01
   7.0907e-01
   6.2848e-01
   5.5938e-01
   5.0050e-01
   4.5078e-01
   4.0930e-01
   3.7531e-01
   3.4817e-01
   3.2741e-01
   3.1263e-01
   3.0357e-01
   3.0005e-01
   3.0006e-01
   3.0030e-01
   3.0071e-01
   3.0130e-01
   3.0208e-01
   3.0327e-01
   3.0583e-01
   3.1185e-01
   3.2144e-01
   3.2841e-01
   3.2677e-01
   3.2056e-01
   3.1705e-01
   3.1750e-01
   3.1993e-01
   3.2319e-01
   3.2718e-01
   3.3211e-01
   3.3818e-01
   3.4550e-01
   3.5390e-01
   3.6290e-01
   3.7170e-01
   3.7940e-01
   3.8526e-01
   3.8897e-01
   3.9075e-01
   3.9130e-01
   3.9150e-01
   3.9219e-01
   3.9392e-01
   3.9693e-01
   4.0116e-01
   4.0640e-01
   4.1241e-01
   4.1899e-01
   4.2599e-01
   4.3332e-01
   4.4094e-01
   4.4884e-01
   4.5699e-01
   4.6542e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01
   4.6590e-01 ];

% The abscissas.
t = [...
   9.5509e-03
   1.5367e-02
   2.1263e-02
   2.7263e-02
   3.3403e-02
   3.9719e-02
   4.6249e-02
   5.3033e-02
   6.0117e-02
   6.7555e-02
   7.5407e-02
   8.3740e-02
   9.2652e-02
   1.0232e-01
   1.1274e-01
   1.2395e-01
   1.3592e-01
   1.4856e-01
   1.6171e-01
   1.7534e-01
   1.8931e-01
   2.0346e-01
   2.1772e-01
   2.3201e-01
   2.4626e-01
   2.6041e-01
   2.7444e-01
   2.8831e-01
   3.0201e-01
   3.1555e-01
   3.2891e-01
   3.4210e-01
   3.5512e-01
   3.6798e-01
   3.8067e-01
   3.9321e-01
   4.0560e-01
   4.1783e-01
   4.2991e-01
   4.4186e-01
   4.5365e-01
   4.6531e-01
   4.7683e-01
   4.8822e-01
   4.9946e-01
   5.1057e-01
   5.2155e-01
   5.3240e-01
   5.4311e-01
   5.5370e-01
   5.6416e-01
   5.7450e-01
   5.8472e-01
   5.9482e-01
   6.0480e-01
   6.1466e-01
   6.2441e-01
   6.3405e-01
   6.4358e-01
   6.5299e-01
   6.6228e-01
   6.7146e-01
   6.8052e-01
   6.8945e-01
   6.9825e-01
   7.0692e-01
   7.1543e-01
   7.2377e-01
   7.3194e-01
   7.3994e-01
   7.4777e-01
   7.5544e-01
   7.6295e-01
   7.7030e-01
   7.7748e-01
   7.8452e-01
   7.9140e-01
   7.9814e-01
   8.0472e-01
   8.1117e-01
   8.1748e-01
   8.2365e-01
   8.2968e-01
   8.3558e-01
   8.4134e-01
   8.4698e-01
   8.5248e-01
   8.5785e-01
   8.6309e-01
   8.6821e-01
   8.7319e-01
   8.7806e-01
   8.8280e-01
   8.8742e-01
   8.9192e-01
   8.9630e-01
   9.0057e-01
   9.0472e-01
   9.0875e-01
   9.1267e-01
   9.1647e-01
   9.2016e-01
   9.2374e-01
   9.2721e-01
   9.3056e-01
   9.3381e-01
   9.3695e-01
   9.3999e-01
   9.4291e-01
   9.4574e-01
   9.4846e-01
   9.5107e-01
   9.5358e-01
   9.5600e-01
   9.5831e-01
   9.6053e-01
   9.6265e-01
   9.6468e-01
   9.6661e-01
   9.6845e-01
   9.7020e-01
   9.7186e-01
   9.7344e-01
   9.7494e-01
   9.7637e-01
   9.7773e-01
   9.7901e-01
   9.8024e-01
   9.8140e-01
   9.8250e-01
   9.8353e-01
   9.8451e-01
   9.8542e-01
   9.8627e-01
   9.8706e-01
   9.8780e-01
   9.8848e-01
   9.8911e-01
   9.8971e-01
   9.9026e-01
   9.9078e-01
   9.9126e-01
   9.9172e-01
   9.9215e-01
   9.9255e-01
   9.9293e-01
   9.9329e-01
   9.9363e-01
   9.9395e-01
   9.9426e-01
   9.9455e-01
   9.9482e-01
   9.9508e-01
   9.9533e-01
   9.9556e-01
   9.9579e-01
   9.9600e-01
   9.9620e-01
   9.9640e-01
   9.9658e-01
   9.9676e-01
   9.9693e-01
   9.9710e-01
   9.9725e-01
   9.9740e-01
   9.9755e-01
   9.9768e-01
   9.9782e-01
   9.9794e-01
   9.9806e-01
   9.9818e-01
   9.9829e-01
   9.9840e-01
   9.9850e-01
   9.9860e-01
   9.9869e-01
   9.9878e-01
   9.9886e-01
   9.9894e-01
   9.9902e-01
   9.9909e-01
   9.9915e-01
   9.9922e-01
   9.9928e-01
   9.9933e-01
   9.9938e-01
   9.9943e-01
   9.9948e-01
   9.9953e-01
   9.9958e-01
   9.9962e-01
   9.9966e-01
   9.9971e-01
   9.9975e-01
   9.9979e-01
   9.9983e-01
   9.9987e-01
   9.9992e-01
   9.9996e-01
   1.0000e+00 ];
% Take every second element.
t = t(2:2:200);

% The matrix.
 A = zeros(  212,  100);
 A(:,    1) = [ ...
  0.278413271292516E-07;
  0.350294569991313E-07;
  0.437619460386832E-07;
  0.542758243467459E-07;
  0.104834310650602E-05;
  0.123193977592786E-05;
  0.143221644432464E-05;
  0.167280998138199E-05;
  0.724193494304067E-08;
  0.913955247946047E-08;
  0.114053632958313E-07;
  0.141764659922578E-07;
  0.254739137045289E-10;
  0.340750713060661E-10;
  0.455161857579285E-10;
  0.299788355198977E-13;
  0.433227042650013E-13;
  0.615905978699231E-13;
  0.874385124884957E-13;
  0.537739508246423E-16;
  0.818032802369539E-16;
  0.122940258541592E-15;
  0.182864725072071E-15;
  0.807929914259777E-19;
  0.128563081059179E-18;
  0.203711658755664E-18;
  0.616724643244358E-22;
  0.104939419599650E-21;
  0.174878479633601E-21;
  0.290185169981972E-21;
  0.672720527617141E-25;
  0.120304074739951E-24;
  0.210646304274067E-24;
  0.364704335393590E-24;
  0.661920734707866E-28;
  0.123815341128625E-27;
  0.228098109260620E-27;
  0.297096363320044E-31;
  0.593639842266826E-31;
  0.115984922746828E-30;
  0.224251319400523E-30;
  0.232001506160961E-34;
  0.488898829364634E-34;
  0.100029100730379E-33;
  0.202173801478637E-33;
  0.921121408798246E-38;
  0.204215782614820E-37;
  0.439211658657918E-37;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
];
 A(:,    2) = [ ...
  0.177145540705829E-05;
  0.222294075118246E-05;
  0.276915736447363E-05;
  0.342393612286798E-05;
  0.190185555777150E-04;
  0.222520768506693E-04;
  0.257518769536865E-04;
  0.299350748107328E-04;
  0.467655042086534E-06;
  0.588320961909514E-06;
  0.731713990102927E-06;
  0.906279055860469E-06;
  0.566240855973929E-08;
  0.755602247888440E-08;
  0.100669449448472E-07;
  0.228336445746073E-10;
  0.329570257384357E-10;
  0.467860307330528E-10;
  0.663098201405227E-10;
  0.139741682374570E-12;
  0.212410661084748E-12;
  0.318894635168232E-12;
  0.473732606032952E-12;
  0.718187422877247E-15;
  0.114230458522301E-14;
  0.180873356739523E-14;
  0.188082372335557E-17;
  0.320074771727217E-17;
  0.533308077261885E-17;
  0.884571692367914E-17;
  0.705958904041586E-20;
  0.126297599445390E-19;
  0.221159988533239E-19;
  0.382839493310420E-19;
  0.239744103516362E-22;
  0.448731698366172E-22;
  0.826928897732050E-22;
  0.371995918091206E-25;
  0.744193653162013E-25;
  0.145520316755542E-24;
  0.281498623730977E-24;
  0.100797152234561E-27;
  0.212707277450341E-27;
  0.435640198887394E-27;
  0.881095625831973E-27;
  0.253581186033057E-30;
  0.563025000201026E-30;
  0.121222219898559E-29;
  0.596809659618253E-33;
  0.138915927480167E-32;
  0.314936481147271E-32;
  0.505603698648634E-36;
  0.127090695921738E-35;
  0.320843685524691E-35;
  0.764750451592900E-35;
  0.000000000000000E+00;
  0.139989943652245E-38;
  0.357513256855567E-38;
  0.893428019825253E-38;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
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  0.000000000000000E+00;
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  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.169362124012196E-03;
  0.204063562570411E-03;
  0.240325559602184E-03;
  0.277406391802515E-03;
  0.180384993363703E-03;
  0.216578719502536E-03;
  0.252699524281752E-03;
  0.157531762233987E-03;
  0.191478880253726E-03;
  0.228593126806231E-03;
  0.265187317936011E-03;
  0.167917087104286E-03;
  0.202877595583573E-03;
  0.240105646767574E-03;
  0.277610991091137E-03;
  0.178212123337573E-03;
  0.214479806373902E-03;
  0.251456154146013E-03;
  0.154085101350177E-03;
  0.188523978842170E-03;
  0.225972060022173E-03;
  0.262974753596268E-03;
  0.163921938835188E-03;
  0.199069371973337E-03;
  0.237129552886017E-03;
  0.274701245999154E-03;
  0.173882979169093E-03;
  0.209956017172885E-03;
  0.248012671093534E-03;
  0.183866312013947E-03;
  0.221074305763125E-03;
  0.258878512511274E-03;
  0.158360382108924E-03;
  0.193919834188705E-03;
  0.232180474483812E-03;
  0.269969814098658E-03;
  0.167917598510314E-03;
  0.204175721556510E-03;
  0.243090721852468E-03;
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  0.225506747923987E-03;
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  0.207305784172718E-03;
  0.247180829006766E-03;
  0.286234823789755E-03;
  0.178915461631846E-03;
  0.217384548498956E-03;
  0.257805265775346E-03;
  0.188419134325102E-03;
  0.227638557404930E-03;
  0.268276736008488E-03;
  0.198036917147704E-03;
  0.238046673132430E-03;
  0.278699142157279E-03;
  0.168830175560686E-03;
  0.207731735592631E-03;
  0.248532769532517E-03;
  0.289198874455110E-03;
  0.177585202408181E-03;
  0.217499705087221E-03;
  0.259012247681767E-03;
  0.299860727906776E-03;
  0.186561257798701E-03;
  0.227357105316628E-03;
  0.269424572351795E-03;
  0.195736746775310E-03;
  0.237321534427792E-03;
  0.279766265151693E-03;
  0.205086764502482E-03;
  0.247389720442470E-03;
  0.290069540014315E-03;
  0.173930620753993E-03;
  0.214589281632982E-03;
  0.257545607922793E-03;
  0.300406482438120E-03;
  0.182592144327032E-03;
  0.224237689849360E-03;
  0.267763315932257E-03;
  0.310834151292738E-03;
  0.200576471719671E-03;
  0.243981900993617E-03;
  0.288292646061450E-03;
  0.219225509887622E-03;
  0.264320567694654E-03;
  0.309028140719647E-03;
  0.191493347401206E-03;
  0.238187226031528E-03;
  0.285089698891738E-03;
  0.207498898376457E-03;
  0.257144603935444E-03;
  0.305968478883756E-03;
  0.223638042726293E-03;
  0.275902474569989E-03;
  0.326640852307492E-03;
  0.239881156602451E-03;
  0.294380042276998E-03;
  0.346937508140854E-03;
  0.201383148407785E-03;
  0.256199499034437E-03;
  0.312565879966087E-03;
  0.215331199179047E-03;
  0.272566919534256E-03;
  0.330498861899287E-03;
  0.229592156614444E-03;
  0.288955863524620E-03;
  0.348227515615918E-03;
  0.244158659583604E-03;
  0.305349134166022E-03;
  0.365821835970337E-03;
  0.259009342798322E-03;
  0.321739778314623E-03;
  0.274121198316379E-03;
  0.338129381916019E-03;
  0.226026524202894E-03;
  0.289462593499934E-03;
  0.354535836876835E-03;
  0.239649659022234E-03;
  0.370986376140081E-03;
  0.253613283078380E-03;
  0.320713911420967E-03;
  0.387542947066777E-03;
  0.267877332163380E-03;
  0.336563112540489E-03;
  0.282397122717271E-03;
  0.352528856367940E-03;
  0.297130833047277E-03;
  0.368589105661954E-03;
  0.239666527804161E-03;
  0.312032621224034E-03;
  0.384742366364321E-03;
  0.252353905040081E-03;
  0.327063881954359E-03;
  0.400968469165264E-03;
  0.265312595530531E-03;
  0.342195217058361E-03;
  0.417283018876446E-03;
  0.278531904484680E-03;
  0.357400807729391E-03;
  0.291997281294698E-03;
  0.372665209795287E-03;
  0.305687785655095E-03;
  0.387981907465473E-03;
  0.319583385206101E-03;
  0.403338476985482E-03;
  0.267704491008658E-03;
  0.355077725245678E-03;
  0.441985630487807E-03;
  0.298361921906576E-03;
  0.391387097494089E-03;
  0.330385909208530E-03;
  0.428260705334083E-03;
  0.363558903302419E-03;
  0.465566638013115E-03;
  0.397632166155404E-03;
  0.503284913577318E-03;
  0.318073067219871E-03;
  0.432377242333359E-03;
  0.347279355267460E-03;
  0.467613124243371E-03;
  0.377585316329032E-03;
  0.503232963183109E-03;
  0.408865946752712E-03;
  0.539195727867536E-03;
  0.440962964475489E-03;
  0.575521367721876E-03;
  0.506966926565156E-03;
  0.381331969776966E-03;
  0.540597679588473E-03;
  0.408310297061121E-03;
  0.574522951353629E-03;
  0.436199253741165E-03;
  0.608687073594183E-03;
  0.464971934292180E-03;
  0.643081529574374E-03;
  0.494565075001674E-03;
  0.677725093908066E-03;
  0.524906339649078E-03;
  0.555900122378716E-03;
  0.587445117048446E-03;
  0.619447444648813E-03;
  0.651798197310427E-03;
  0.684410883337705E-03;
  0.473513430478079E-03;
  0.717208610893749E-03;
];

% The right-hand side.
b = A*x;

% The regularization matrix.
if (nargout==5)
 L = zeros(   98,  100);
 L(:,    1) = [ ...
  0.647838128914922E+03;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
];
 L(:,    2) = [ ...
 -0.137472496710285E+04;
  0.738403176096186E+03;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
];
 L(:,    3) = [ ...
  0.726886838187924E+03;
 -0.143742075696657E+04;
  0.676537944255063E+03;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
];
 L(:,    4) = [ ...
  0.000000000000000E+00;
  0.699017580870382E+03;
 -0.130402196903147E+04;
  0.601023970746364E+03;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
];
 L(:,    5) = [ ...
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.627484024776405E+03;
 -0.114694082518367E+04;
  0.516928308330631E+03;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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  0.000000000000000E+00;
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  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
  0.000000000000000E+00;
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];
 L(:,   95) = [ ...
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];
 L(:,   96) = [ ...
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];
 L(:,   97) = [ ...
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];
 L(:,   98) = [ ...
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];
 L(:,   99) = [ ...
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 -0.244948930367874E+07;
];
 L(:,  100) = [ ...
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  0.117882716318827E+07;
];
L = sparse(L);
end
