Lemma is an Electromagnetics API
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logbarriercg_newton.h 75KB

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  1. /* This file is part of Lemma, a geophysical modelling and inversion API */
  2. /* This Source Code Form is subject to the terms of the Mozilla Public
  3. * License, v. 2.0. If a copy of the MPL was not distributed with this
  4. * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
  5. /**
  6. @file
  7. @author Trevor Irons
  8. @date 10/11/2010
  9. @version $Id: logbarriercg.h 88 2013-09-06 17:24:44Z tirons $
  10. **/
  11. #ifndef LOGBARRIERCG_INC
  12. #define LOGBARRIERCG_INC
  13. #include <Eigen/IterativeLinearSolvers>
  14. #include <iostream>
  15. #include <iomanip>
  16. #include <fstream>
  17. #include <Eigen/Eigen>
  18. #include "cg.h"
  19. #include "bicgstab.h"
  20. #include "lemma.h"
  21. namespace Lemma {
  22. template < typename Scalar >
  23. Scalar PhiB (const Scalar& mux, const Scalar& muy, const Scalar& minVal,
  24. const Scalar& maxVal, const VectorXr x) {
  25. Scalar phib = std::abs((x.array() - minVal).log().sum()*mux);
  26. phib += std::abs((maxVal - x.array()).log().sum()*muy);
  27. return phib;
  28. }
  29. // PhiB for block log barrier
  30. template < typename Scalar >
  31. Scalar PhiB2 (const Scalar& mux, const Scalar& muy, const Scalar& minVal,
  32. const Scalar& maxVal, const VectorXr x, const int& block,
  33. const int &nblocks) {
  34. Scalar phib = std::abs((x.array() - minVal).log().sum()*mux);
  35. //phib += std::abs((maxVal - x.array()).log().sum()*muy);
  36. for (int ib=0; ib<nblocks; ++ib) {
  37. //HiSegments(ib) = x.segment(ib*block, block).sum();
  38. phib += Scalar(block)*std::log(maxVal - x.segment(ib*block, block).sum())*muy;
  39. }
  40. return phib;
  41. }
  42. template < typename Scalar >
  43. Scalar PhiB2 (const Scalar& minVal, const Scalar& maxVal, const VectorXr x,
  44. const int& block, const int &nblocks) {
  45. Scalar phib = std::abs((x.array() - minVal).log().sum());
  46. //phib += std::abs((maxVal - x.array()).log().sum()*muy);
  47. for (int ib=0; ib<nblocks; ++ib) {
  48. //HiSegments(ib) = x.segment(ib*block, block).sum();
  49. phib += Scalar(block)*std::log(maxVal - x.segment(ib*block, block).sum());
  50. }
  51. return phib;
  52. }
  53. template < typename Scalar >
  54. Scalar PhiB2_NN (const Scalar& mux, const Scalar& minVal, const VectorXr x) {
  55. Scalar phib = std::abs((x.array() - minVal).log().sum()*mux);
  56. return phib;
  57. }
  58. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  59. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  60. * (minVal, maxVal) \f$. Note that this method optimized the complete
  61. * solution, using the large matrix ATA. If you have a system with a huge
  62. * number of columns, see the implicit version of this routine. Solution of
  63. * the dual problem (interior-point) follows "Tikhonov Regularization with
  64. * Nonnegativity constraint, (Calavetti et. al. 2004)"
  65. * @param[in] A is a Real Matrix.
  66. * @param[in] b is a Real vector
  67. * @param[in] x0 is a reference model.
  68. * @param[in] Wd is a Sparse Real matrix, that specifies data objective
  69. * function.
  70. * @param[in] Wm is a Sparse Real matrix, that sepcifies the model
  71. * objective function.
  72. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  73. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  74. */
  75. template < typename Scalar >
  76. VectorXr LogBarrierCG(const MatrixXr &A, const VectorXr &b,
  77. const VectorXr &x0,
  78. const Eigen::SparseMatrix<Scalar>& WdTWd,
  79. const Eigen::SparseMatrix<Scalar>& WmTWm,
  80. const Scalar &minVal,
  81. const Scalar &maxVal) {
  82. // Check that everything is aligned OK
  83. if (A.rows() != b.size() ) {
  84. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  85. exit(1);
  86. }
  87. /////////////////////////////////////////////
  88. // Build all the large static matrices
  89. // NOTE, ATA can be large. For some problems an implicit algorithm may
  90. // be better suited.
  91. //Eigen::SparseMatrix<Scalar> WmTWm = Wm.transpose()*Wm;
  92. //Eigen::SparseMatrix<Scalar> WdTWd = Wd.transpose()*Wd;
  93. MatrixXr ATWdTWdA = A.transpose()*WdTWd*A;
  94. /////////////////////////
  95. // Jacobi Preconditioner
  96. Eigen::SparseMatrix<Scalar> MM (ATWdTWdA.rows(), ATWdTWdA.cols());
  97. for (int i=0; i<ATWdTWdA.rows(); ++i) {
  98. MM.insert(i,i) = 1. / ATWdTWdA(i,i);
  99. }
  100. MM.finalize();
  101. int N = A.cols(); // number of model
  102. int M = A.rows(); // number of data
  103. int MAXITER = 100; // M*N;
  104. Scalar SIGMA = 1e-2; // 1e-1;
  105. // Determine starting lambda_0, find lim_sup of the norm of impulse
  106. // responses and scale.
  107. /// @todo the starting lambda is not always a very good number.
  108. Scalar limsup = 1e10;
  109. for (int i=0; i<N; ++i) {
  110. VectorXr Spike = VectorXr::Zero(N);
  111. Spike(i) = (minVal + maxVal) / 2.;
  112. limsup = std::min(limsup, (ATWdTWdA*Spike).array().abs().maxCoeff());
  113. }
  114. Scalar lambda = limsup;
  115. Scalar mux0 = 1e-1*lambda;
  116. Scalar muy0 = 1e-1*lambda;
  117. Scalar epsilon = 1e-20; // Ratio between phib and phim+phid
  118. // initial guess, start with reference model
  119. VectorXr x=x0;
  120. // predicted b
  121. VectorXr b_pre = A*x;
  122. Scalar phid = (b - (b_pre)).norm();
  123. Scalar phim = x.norm();
  124. Scalar phib = PhiB(mux0, muy0, minVal, maxVal, x);
  125. Scalar mux = mux0;
  126. Scalar muy = muy0;
  127. Scalar tol = 1e-5*phid; // 1e-14;
  128. std::fstream phireport("phimphid.dat", std::ios::out);
  129. /// @todo add stopping criteria.
  130. //int iLambda = MAXITER - 1;
  131. for (int ii=0; ii<MAXITER; ++ii) {
  132. //lambda = Lambdas[iLambda];
  133. //iLambda -= 1;
  134. // Phi_m is just L2Norm right now. Maybe add s, alpha_T2, and
  135. // alpha_z terms
  136. VectorXr Xm1 = x;
  137. int iter = N*M;
  138. mux = mux0;
  139. muy = muy0;
  140. int iloop(0);
  141. do {
  142. ///////////////////////////////////////////////////////////
  143. // Log barrier terms
  144. VectorXr X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  145. VectorXr Y1 = VectorXr::Ones(N).array() / (maxVal-x.array()) ;
  146. VectorXr X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  147. VectorXr Y2 = VectorXr::Ones(N).array() / ((maxVal-x.array())*(maxVal-x.array()));
  148. /////////////////////////////////////////////////////////////
  149. // Solve system
  150. tol = 1e-5*phid;// 1e-14;
  151. iter = N*M;
  152. //////////////////////////
  153. // CG solution of complete system
  154. VectorXr b2 = (-A.transpose()*WdTWd*(b_pre-b)).array() -
  155. (lambda*WmTWm*(x0-x0)).array() +
  156. 2.*mux*X1.array() + 2.*muy*Y1.array();
  157. // Eigen requires these temporaries :(
  158. MatrixXr A2 = ATWdTWdA;
  159. A2 += lambda*WmTWm;
  160. A2.diagonal() += mux*X2 + muy*Y2;
  161. VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  162. // update x
  163. VectorXr h = ztilde; // - x;
  164. Scalar d = std::min(1., 0.995*(x.array()/h.array().abs()).minCoeff() );
  165. x += d*h;
  166. // Determine mu steps to take
  167. VectorXr s1 = mux * (X2.asDiagonal()*ztilde - 2.*X1);
  168. VectorXr s2 = muy * (Y2.asDiagonal()*ztilde - 2.*Y1);
  169. // determine mu for next step
  170. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  171. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  172. b_pre = A*x;
  173. phid = (WdTWd*(b-b_pre)).norm() ; //(b - (b_pre)).norm();
  174. phim = (WmTWm*(x-x0)).norm();
  175. phib = PhiB(mux, muy, minVal, maxVal, x);
  176. ++iloop;
  177. } while (std::abs(phib / (phid+lambda*phim)) > epsilon);
  178. // report
  179. phireport.precision(12);
  180. std::cout << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  181. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  182. << iter << "\t" << iloop << std::endl;
  183. phireport << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  184. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  185. << iter << "\t" << iloop << std::endl;
  186. std::fstream modfile;
  187. std::string fname = "iteration" + to_string(ii) + ".dat";
  188. modfile.open( fname.c_str(), std::ios::out);
  189. modfile << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  190. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t" << iter << "\n";
  191. modfile << x << "\n";
  192. modfile.close();
  193. // update lambda
  194. /// @todo smarter lambda change
  195. lambda *= .9;
  196. }
  197. phireport.close();
  198. // TODO, determine optimal solution
  199. return x;
  200. }
  201. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  202. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  203. * (minVal, maxVal) \f$. Note that this method optimized the complete
  204. * solution, using the large matrix ATA. If you have a system with a huge
  205. * number of columns, see the implicit version of this routine. Solution of
  206. * the dual problem (interior-point) follows "Tikhonov Regularization with
  207. * Nonnegativity constraint, (Calavetti et. al. 2004)"
  208. * @param[in] A is a Real Matrix.
  209. * @param[in] b is a Real vector
  210. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  211. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  212. */
  213. template < typename Scalar >
  214. VectorXr LogBarrierCG(const MatrixXr &A, const VectorXr &b, const Scalar &minVal,
  215. const Scalar &maxVal) {
  216. // Check that everything is aligned OK
  217. if (A.rows() != b.size() ) {
  218. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  219. exit(1);
  220. }
  221. // TODO make ATA implicit
  222. MatrixXr ATA = A.transpose()*A;
  223. int N = A.cols(); // number of model
  224. int M = A.rows(); // number of data
  225. int MAXITER = 100; // M*N;
  226. Scalar SIGMA = 1e-2; //1e-1;
  227. Scalar delta = 1e-4;
  228. // Cholesky preconditioner
  229. //Eigen::FullPivLU <MatrixXr> Pre;
  230. //Eigen::ColPivHouseholderQR <MatrixXr> Pre;
  231. //Pre.compute(ATA);
  232. // Determine starting lambda_0, find lim_sup of the norm of impulse responses and scale
  233. Scalar limsup = 1e10;
  234. for (int i=0; i<N; ++i) {
  235. VectorXr Spike = VectorXr::Zero(N);
  236. Spike(i) = (minVal + maxVal) / 2.;
  237. limsup = std::min(limsup, (ATA*Spike).array().abs().maxCoeff());
  238. }
  239. Scalar lambda = 1e3*limsup;//e-1;//limsup;
  240. Scalar mux0 = 1e-1*lambda;
  241. Scalar muy0 = 1e-1*lambda;
  242. Scalar epsilon = 1e-20; // Ratio between phib and phim+phid
  243. /////////////////////////////
  244. // logX spacing
  245. //Scalar MinLam = 1e-24;
  246. //Scalar MaxLam = 1e-4;
  247. //VectorXr Lambdas;
  248. //Scalar LS = 5000;
  249. //Scalar dl10 = std::log(LS*MaxLam+1.)/(Scalar)MAXITER;
  250. //Lambdas = 1./LS*(dl10*VectorXr::LinSpaced(MAXITER+1, 0, MAXITER)).array().exp()
  251. // + MinLam - 1./LS;
  252. // initial guess, just near zero for now
  253. VectorXr x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  254. // predicted b
  255. VectorXr b_pre = A*x;
  256. Scalar phid = (b - (b_pre)).norm();
  257. Scalar phim = x.norm();
  258. Scalar phib = PhiB(mux0, muy0, minVal, maxVal, x);
  259. Scalar mux = mux0;
  260. Scalar muy = muy0;
  261. Scalar tol = 1e-5*phid; // 1e-14;
  262. std::fstream phireport("phimphid.dat", std::ios::out);
  263. /// @todo add stopping criteria.
  264. //int iLambda = MAXITER - 1;
  265. for (int ii=0; ii<MAXITER; ++ii) {
  266. //lambda = Lambdas[iLambda];
  267. //iLambda -= 1;
  268. // Phi_m is just L2Norm right now. Maybe add s, alpha_T2, and
  269. // alpha_z terms
  270. VectorXr WmT_Wm = VectorXr::Ones(N).array()*lambda;
  271. VectorXr Xm1 = x;
  272. int iter = N*M;
  273. mux = mux0;
  274. muy = muy0;
  275. int iloop(0);
  276. do {
  277. VectorXr X1(x.size());
  278. VectorXr Y1(x.size());
  279. VectorXr X2(x.size());
  280. VectorXr Y2(x.size());
  281. VectorXr b2;
  282. //VectorXr HiSegments = VectorXr::Zero(nblocks);
  283. MatrixXr A2;
  284. ///////////////////////////////////
  285. // setup
  286. #ifdef LEMMAUSEOMP
  287. #pragma omp parallel sections
  288. {
  289. #endif
  290. ///////////////////////////////////////////////////////////
  291. // Log barrier terms
  292. #ifdef LEMMAUSEOMP
  293. #pragma omp section
  294. #endif
  295. {
  296. X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  297. }
  298. #ifdef LEMMAUSEOMP
  299. #pragma omp section
  300. #endif
  301. {
  302. Y1 = VectorXr::Ones(N).array() / (maxVal-x.array()) ;
  303. }
  304. #ifdef LEMMAUSEOMP
  305. #pragma omp section
  306. #endif
  307. {
  308. X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  309. }
  310. #ifdef LEMMAUSEOMP
  311. #pragma omp section
  312. #endif
  313. {
  314. Y2 = VectorXr::Ones(N).array() / ((maxVal-x.array())*(maxVal-x.array()));
  315. }
  316. #ifdef LEMMAUSEOMP
  317. } // parallel sections
  318. #endif
  319. #ifdef LEMMAUSEOMP
  320. #pragma omp parallel sections
  321. {
  322. #endif
  323. #ifdef LEMMAUSEOMP
  324. #pragma omp section
  325. #endif
  326. {
  327. b2 = -(A.transpose()*(b_pre-b)).array() -
  328. (WmT_Wm.array()*x.array()).array() +
  329. (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  330. }
  331. #ifdef LEMMAUSEOMP
  332. #pragma omp section
  333. #endif
  334. {
  335. A2 = ATA;
  336. A2.diagonal().array() += WmT_Wm.array() + mux*X2.array() +
  337. muy*Y2.array();
  338. }
  339. #ifdef LEMMAUSEOMP
  340. } // parallel sections
  341. #endif
  342. // // Jacobi Preconditioner
  343. // Eigen::SparseMatrix<Scalar> MM =
  344. // Eigen::SparseMatrix<Scalar>(A2.rows(), A2.cols());
  345. // for (int i=0; i<ATA.rows(); ++i) {
  346. // MM.insert(i,i) = 1./ATA(i,i);
  347. // }
  348. // MM.finalize();
  349. /////////////////////////////////////////////////////////////
  350. // Solve system,
  351. // CG solution of complete system
  352. // TODO add reference model
  353. tol = 1e-5*phid+mux+muy;// 1e-14;
  354. iter = N*M;
  355. //std::cout << "Call cg" << std::endl;
  356. // Decomposition preconditioner
  357. //Pre.setThreshold(1e1*tol);
  358. //Pre.compute(A2);
  359. // Jacobi Preconditioner
  360. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  361. // Decomposition preconditioner
  362. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, Pre, iter, tol);
  363. // No preconditioner
  364. VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, iter, tol);
  365. //std::cout << "out cg" << std::endl;
  366. /////////////////////////////////////////////////////////////
  367. // update x, mux, muy
  368. //VectorXr h = ztilde; // - x;
  369. VectorXr s1, s2;
  370. // update x
  371. //VectorXr h = ztilde; // - x;
  372. //Scalar d = std::min(1., 0.995*(x.array()/h.array().abs()).minCoeff() );
  373. //x += d*h;
  374. Scalar d = std::min(1.,0.995*(x.array()/ztilde.array().abs()).minCoeff());
  375. x += d*ztilde;
  376. // // Fix any overstepping
  377. // for (int ib=0; ib<nblocks; ++ib) {
  378. // while (x.segment(ib*block, block).sum() > maxVal) {
  379. // x.segment(ib*block, block).array() *= (.9);
  380. // }
  381. // }
  382. // for (int i=0; i<x.size(); ++i) {
  383. // if (x(i) < minVal) {
  384. // x(i) = minVal + delta;
  385. // }
  386. // }
  387. b_pre = A*x;
  388. #ifdef LEMMAUSEOMP
  389. #pragma omp parallel sections
  390. {
  391. #endif
  392. #ifdef LEMMAUSEOMP
  393. #pragma omp section
  394. #endif
  395. {
  396. phib = PhiB(mux, muy, minVal, maxVal, x);
  397. }
  398. #ifdef LEMMAUSEOMP
  399. #pragma omp section
  400. #endif
  401. {
  402. phid = (b - (b_pre)).norm();
  403. }
  404. #ifdef LEMMAUSEOMP
  405. #pragma omp section
  406. #endif
  407. {
  408. phim = x.norm();
  409. }
  410. #ifdef LEMMAUSEOMP
  411. }
  412. #endif
  413. // Determine mu steps to take
  414. #ifdef LEMMAUSEOMP
  415. #pragma omp parallel sections
  416. {
  417. #endif
  418. #ifdef LEMMAUSEOMP
  419. #pragma omp section
  420. #endif
  421. {
  422. s1 = mux * (X2.asDiagonal()*(x+ztilde) - 2.*X1);
  423. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  424. }
  425. #ifdef LEMMAUSEOMP
  426. #pragma omp section
  427. #endif
  428. {
  429. s2 = muy * (Y2.asDiagonal()*(x+ztilde) - 2.*Y1);
  430. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  431. }
  432. #ifdef LEMMAUSEOMP
  433. }
  434. #endif
  435. ++iloop;
  436. } while (std::abs(phib / (phid+lambda*phim)) > epsilon);
  437. // report
  438. phireport.precision(12);
  439. std::cout << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  440. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  441. << iter << "\t" << iloop << std::endl;
  442. phireport << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  443. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  444. << iter << "\t" << iloop << std::endl;
  445. // write model file
  446. std::fstream modfile;
  447. std::string fname = "iteration" + to_string(ii) + ".dat";
  448. modfile.open( fname.c_str(), std::ios::out);
  449. modfile << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  450. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t" << iter << "\n";
  451. modfile << x << "\n";
  452. modfile.close();
  453. // write predicted data file
  454. std::fstream predata;
  455. fname = "iteration" + to_string(ii) + "pre.dat";
  456. predata.open(fname.c_str(), std::ios::out);
  457. predata << b_pre << std::endl;
  458. predata.close();
  459. // update lambda
  460. // @todo smarter lambda change
  461. lambda *= .92;
  462. }
  463. phireport.close();
  464. // TODO, determine optimal solution
  465. return x;
  466. }
  467. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  468. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  469. * (minVal, maxVal) \f$. Note that this method optimized the complete
  470. * solution, using the large matrix ATA. If you have a system with a huge
  471. * number of columns, see the implicit version of this routine. Solution of
  472. * the dual problem (interior-point) follows "Tikhonov Regularization with
  473. * Nonnegativity constraint, (Calavetti et. al. 2004)"
  474. * @param[in] A is a Real Matrix.
  475. * @param[in] b is a Real vector
  476. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  477. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  478. * @param[in] block is the number of parameters to sum together for the
  479. * upper barrier term. So block block number parameters are kept under maxVal.
  480. * as such A.rows() / block must be evenly divisible.
  481. */
  482. template <typename Scalar>
  483. VectorXr LogBarrierCG(const MatrixXr &A, const VectorXr &b, const Scalar &minVal,
  484. const Scalar &maxVal, const int& block) {
  485. // Check that everything is aligned OK
  486. if (A.rows() != b.size() ) {
  487. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  488. exit(1);
  489. }
  490. // write predicted data file
  491. std::fstream obsdata;
  492. std::string fname = "obsdata.dat";
  493. obsdata.open(fname.c_str(), std::ios::out);
  494. obsdata << b << std::endl;
  495. obsdata.close();
  496. // #ifdef LEMMAUSEVTK
  497. // double blue[3] = {0.0,0.0,1.0};
  498. // double red[3] = {1.0,0.0,0.0};
  499. // VectorXr ind = VectorXr::LinSpaced(b.size(), 1, b.size());
  500. // #endif
  501. // TODO make ATA implicit
  502. MatrixXr ATA = A.transpose()*A;
  503. int N = A.cols(); // number of model
  504. int M = A.rows(); // number of data
  505. int MAXITER = 100; // M*N;
  506. Scalar SIGMA = 1e-2; //1e-1;
  507. Scalar delta = 1e-4;
  508. // Cholesky preconditioner
  509. //Eigen::FullPivLU <MatrixXr> Pre;
  510. //Eigen::ColPivHouseholderQR <MatrixXr> Pre;
  511. //Pre.compute(ATA);
  512. // Determine starting lambda_0, find lim_sup of the norm of impulse responses and scale
  513. Scalar limsup = 1e10;
  514. for (int i=0; i<N; ++i) {
  515. VectorXr Spike = VectorXr::Zero(N);
  516. Spike(i) = (minVal + maxVal) / 2.;
  517. limsup = std::min(limsup, (ATA*Spike).array().abs().maxCoeff());
  518. }
  519. Scalar lambda = 1e-6;//*limsup;//e-1;//limsup;
  520. Scalar mux0 = 1e-1*lambda;
  521. Scalar muy0 = 1e-1*lambda;
  522. Scalar epsilon = 1e-25; // Ratio between phib and phim+phid
  523. /////////////////////////////
  524. // logX spacing
  525. //Scalar MinLam = 1e-24;
  526. //Scalar MaxLam = 1e-4;
  527. //VectorXr Lambdas;
  528. //Scalar LS = 5000;
  529. //Scalar dl10 = std::log(LS*MaxLam+1.)/(Scalar)MAXITER;
  530. //Lambdas = 1./LS*(dl10*VectorXr::LinSpaced(MAXITER+1, 0, MAXITER)).array().exp()
  531. // + MinLam - 1./LS;
  532. // initial guess, just near zero for now
  533. VectorXr x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  534. // predicted b
  535. VectorXr b_pre = A*x;
  536. int nblocks = x.size()/block;
  537. Scalar phid = (b - (b_pre)).norm();
  538. Scalar phim = x.norm();
  539. Scalar phib = PhiB2(mux0, muy0, minVal, maxVal, x, block, nblocks);
  540. Scalar mux = mux0;
  541. Scalar muy = muy0;
  542. Scalar tol = 1e-5*phid; // 1e-14;
  543. std::fstream phireport("phimphid.dat", std::ios::out);
  544. /// @todo add stopping criteria.
  545. //int iLambda = MAXITER - 1;
  546. for (int ii=0; ii<MAXITER; ++ii) {
  547. //lambda = Lambdas[iLambda];
  548. //iLambda -= 1;
  549. // Phi_m is just L2Norm right now. Maybe add s, alpha_T2, and
  550. // alpha_z terms
  551. VectorXr WmT_Wm = VectorXr::Ones(N).array()*lambda;
  552. VectorXr Xm1 = x;
  553. int iter = N*M;
  554. mux = mux0;
  555. muy = muy0;
  556. int iloop(0);
  557. // #ifdef LEMMAUSEVTK
  558. // matplot::Plot2D_VTK p_2d("x(t)","y(t)",800,600);
  559. // p_2d.plot(ind, b, blue, "-");
  560. // p_2d.plot(ind, b_pre, red, "-");
  561. // p_2d.show();
  562. // #endif
  563. do {
  564. VectorXr X1(x.size());
  565. VectorXr Y1(x.size());
  566. VectorXr X2(x.size());
  567. VectorXr Y2(x.size());
  568. VectorXr b2;
  569. //VectorXr HiSegments = VectorXr::Zero(nblocks);
  570. MatrixXr A2;
  571. ///////////////////////////////////
  572. // setup
  573. #ifdef LEMMAUSEOMP
  574. #pragma omp parallel sections
  575. {
  576. #endif
  577. ///////////////////////////////////////////////////////////
  578. // Log barrier terms
  579. #ifdef LEMMAUSEOMP
  580. #pragma omp section
  581. #endif
  582. {
  583. X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  584. }
  585. #ifdef LEMMAUSEOMP
  586. #pragma omp section
  587. #endif
  588. {
  589. for (int ib=0; ib<nblocks; ++ib) {
  590. //HiSegments(ib) = x.segment(ib*block, block).sum();
  591. Y1.segment(ib*block, block) = VectorXr::Ones(block).array() /
  592. (maxVal - x.segment(ib*block, block).sum());
  593. }
  594. //for (int ix=0; ix<x.size(); ++ix) {
  595. // Y1(ix) = 1./( (maxVal-HiSegments(ib)) );
  596. //}
  597. //Y1 = VectorXr::Ones(N).array() / (maxVal-x.array()) ;
  598. }
  599. #ifdef LEMMAUSEOMP
  600. #pragma omp section
  601. #endif
  602. {
  603. X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  604. }
  605. #ifdef LEMMAUSEOMP
  606. #pragma omp section
  607. #endif
  608. {
  609. for (int ib=0; ib<nblocks; ++ib) {
  610. //HiSegments(ib) = x.segment( ib*block, block ).sum();
  611. Y2.segment(ib*block, block) = VectorXr::Ones(block).array() /
  612. ( (maxVal-x.segment(ib*block, block).sum()) *
  613. (maxVal-x.segment(ib*block, block).sum()) );
  614. }
  615. //Y2 = VectorXr::Ones(N).array() / ((maxVal-x.array())*(maxVal-x.array()));
  616. //std::cout << Y1.transpose() << std::endl << std::endl;
  617. //std::cout << Y2.transpose() << std::endl;
  618. }
  619. #ifdef LEMMAUSEOMP
  620. } // parallel sections
  621. #endif
  622. #ifdef LEMMAUSEOMP
  623. #pragma omp parallel sections
  624. {
  625. #endif
  626. #ifdef LEMMAUSEOMP
  627. #pragma omp section
  628. #endif
  629. {
  630. b2 = -(A.transpose()*(b_pre-b)).array() -
  631. (WmT_Wm.array()*x.array()).array() +
  632. (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  633. }
  634. #ifdef LEMMAUSEOMP
  635. #pragma omp section
  636. #endif
  637. {
  638. A2 = ATA;
  639. A2.diagonal().array() += WmT_Wm.array() + mux*X2.array() +
  640. muy*Y2.array();
  641. }
  642. #ifdef LEMMAUSEOMP
  643. } // parallel sections
  644. #endif
  645. // // Jacobi Preconditioner
  646. // Eigen::SparseMatrix<Scalar> MM =
  647. // Eigen::SparseMatrix<Scalar>(A2.rows(), A2.cols());
  648. // for (int i=0; i<ATA.rows(); ++i) {
  649. // MM.insert(i,i) = 1./ATA(i,i);
  650. // }
  651. // MM.finalize();
  652. /////////////////////////////////////////////////////////////
  653. // Solve system,
  654. // CG solution of complete system
  655. // TODO add reference model
  656. tol = 1e-5*phid+mux+muy;// 1e-14;
  657. iter = N*M;
  658. //std::cout << "Call cg" << std::endl;
  659. // Decomposition preconditioner
  660. //Pre.setThreshold(1e1*tol);
  661. //Pre.compute(A2);
  662. // Jacobi Preconditioner
  663. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  664. // Decomposition preconditioner
  665. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, Pre, iter, tol);
  666. // No preconditioner
  667. VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, iter, tol);
  668. //std::cout << "out cg" << std::endl;
  669. /////////////////////////////////////////////////////////////
  670. // update x, mux, muy
  671. //VectorXr h = ztilde; // - x;
  672. VectorXr s1, s2;
  673. // update x
  674. //VectorXr h = ztilde; // - x;
  675. //Scalar d = std::min(1., 0.995*(x.array()/h.array().abs()).minCoeff() );
  676. //x += d*h;
  677. Scalar d = std::min(1.,0.995*(x.array()/ztilde.array().abs()).minCoeff());
  678. x += d*ztilde;
  679. // // Fix any overstepping
  680. // for (int ib=0; ib<nblocks; ++ib) {
  681. // while (x.segment(ib*block, block).sum() > maxVal) {
  682. // x.segment(ib*block, block).array() *= (.9);
  683. // }
  684. // }
  685. // for (int i=0; i<x.size(); ++i) {
  686. // if (x(i) < minVal) {
  687. // x(i) = minVal + delta;
  688. // }
  689. // }
  690. b_pre = A*x;
  691. #ifdef LEMMAUSEOMP
  692. #pragma omp parallel sections
  693. {
  694. #endif
  695. #ifdef LEMMAUSEOMP
  696. #pragma omp section
  697. #endif
  698. {
  699. phib = PhiB2(mux, muy, minVal, maxVal, x, block, nblocks);
  700. }
  701. #ifdef LEMMAUSEOMP
  702. #pragma omp section
  703. #endif
  704. {
  705. phid = (b - (b_pre)).norm();
  706. }
  707. #ifdef LEMMAUSEOMP
  708. #pragma omp section
  709. #endif
  710. {
  711. phim = x.norm();
  712. }
  713. #ifdef LEMMAUSEOMP
  714. }
  715. #endif
  716. // Determine mu steps to take
  717. #ifdef LEMMAUSEOMP
  718. #pragma omp parallel sections
  719. {
  720. #endif
  721. #ifdef LEMMAUSEOMP
  722. #pragma omp section
  723. #endif
  724. {
  725. s1 = mux * (X2.asDiagonal()*(x+ztilde) - 2.*X1);
  726. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  727. }
  728. #ifdef LEMMAUSEOMP
  729. #pragma omp section
  730. #endif
  731. {
  732. s2 = muy * (Y2.asDiagonal()*(x+ztilde) - 2.*Y1);
  733. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  734. }
  735. #ifdef LEMMAUSEOMP
  736. }
  737. #endif
  738. ++iloop;
  739. } while (std::abs(phib / (phid+lambda*phim)) > epsilon);
  740. // report
  741. phireport.precision(12);
  742. std::cout << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  743. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  744. << iter << "\t" << iloop << std::endl;
  745. phireport << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  746. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  747. << iter << "\t" << iloop << std::endl;
  748. std::fstream modfile;
  749. std::string fname = "iteration" + to_string(ii) + ".dat";
  750. modfile.open( fname.c_str(), std::ios::out);
  751. modfile << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  752. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t" << iter << "\n";
  753. modfile << x << "\n";
  754. modfile.close();
  755. // write predicted data file
  756. std::fstream predata;
  757. fname = "iteration" + to_string(ii) + "pre.dat";
  758. predata.open(fname.c_str(), std::ios::out);
  759. predata << b_pre << std::endl;
  760. predata.close();
  761. // update lambda
  762. // @todo smarter lambda change
  763. lambda *= .85;
  764. }
  765. phireport.close();
  766. // TODO, determine optimal solution
  767. return x;
  768. }
  769. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  770. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  771. * (minVal, maxVal) \f$. Note that this method optimized the complete
  772. * solution, using the large matrix ATA. If you have a system with a huge
  773. * number of columns, see the implicit version of this routine. Solution of
  774. * the dual problem (interior-point) follows "Tikhonov Regularization with
  775. * Nonnegativity constraint, (Calavetti et. al. 2004)"
  776. * @param[in] A is a Real Matrix.
  777. * @param[in] xref is a reference model
  778. * @param[in] b is a Real vector
  779. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  780. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  781. * @param[in] block is the number of parameters to sum together for the
  782. * upper barrier term. So block block number parameters are kept under maxVal.
  783. * as such A.rows() / block must be evenly divisible.
  784. * @param[in] WdTWd is the data objective function
  785. * @param[in] WmTWm is the model objective function
  786. */
  787. template <typename Scalar>
  788. VectorXr LogBarrierCG(const MatrixXr &A, const VectorXr &xr,
  789. const VectorXr &b, const Scalar &minVal,
  790. const Scalar &maxVal, const int& block,
  791. const Eigen::SparseMatrix<Scalar>& WdTWd,
  792. const Eigen::SparseMatrix<Scalar>& WmTWm, Real lambda0=1e1) {
  793. // Check that everything is aligned OK
  794. if (A.rows() != b.size() ) {
  795. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  796. std::cerr << "A.rows() " << A.rows() << "\n";
  797. std::cerr << "A.cols() " << A.cols() << "\n";
  798. std::cerr << "b.size() " << b.size() << "\n";
  799. exit(1);
  800. }
  801. // write predicted data file
  802. std::fstream obsdata;
  803. std::string fname = "obsdata.dat";
  804. obsdata.open(fname.c_str(), std::ios::out);
  805. obsdata << b << std::endl;
  806. obsdata.close();
  807. // TODO make ATA implicit
  808. MatrixXr ATWdTWdA = A.transpose()*WdTWd*A;
  809. int N = A.cols(); // number of model
  810. int M = A.rows(); // number of data
  811. int MAXITER = 175; // M*N;
  812. Scalar SIGMA = .25;//5.85; //1e-2; // .25; //1e-2; // 1e-1;
  813. Scalar delta = 1e-4;
  814. // // Determine starting lambda_0, find lim_sup of the norm of impulse responses and scale
  815. // Scalar limsup = 1e10;
  816. // for (int i=0; i<N; ++i) {
  817. // VectorXr Spike = VectorXr::Zero(N);
  818. // Spike(i) = (minVal + maxVal) / 2.;
  819. // limsup = std::min(limsup, (ATWdTWdA*Spike).array().abs().maxCoeff());
  820. // }
  821. Scalar lambda = lambda0; //*limsup;//e-1;//limsup;
  822. Scalar epsilon = 1e-15; // Ratio between phib and phim+phid
  823. // initial guess, just near zero for now
  824. VectorXr x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  825. // predicted b
  826. VectorXr b_pre = A*x;
  827. int nblocks = x.size()/block;
  828. Scalar phid = (WdTWd*(b - b_pre)).norm();
  829. Scalar phim = (WmTWm*(x - xr)).norm();
  830. Scalar phib = PhiB2(minVal, maxVal, x, block, nblocks);
  831. Scalar mux = (phid + lambda*phim) / phib;
  832. Scalar muy = mux;
  833. //Scalar tol;// = 1e-5*phid; // 1e-14;
  834. std::fstream phireport("phimphid.dat", std::ios::out);
  835. Eigen::ConjugateGradient< MatrixXr > cg;
  836. /// @todo add stopping criteria.
  837. for (int ii=0; ii<MAXITER; ++ii) {
  838. int iter = N*M;
  839. mux = (phid + lambda*phim) / phib;
  840. muy = mux;
  841. int iloop(0);
  842. int itertot(0);
  843. VectorXr h;
  844. bool cont(true);
  845. do {
  846. //restart:
  847. VectorXr X1(x.size());
  848. VectorXr Y1(x.size());
  849. VectorXr X2(x.size());
  850. VectorXr Y2(x.size());
  851. VectorXr b2;
  852. MatrixXr A2;
  853. ///////////////////////////////////
  854. // setup
  855. ///////////////////////////////////////////////////////////
  856. // Log barrier terms
  857. X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  858. for (int ib=0; ib<nblocks; ++ib) {
  859. Y1.segment(ib*block, block) = VectorXr::Ones(block).array() /
  860. (maxVal - x.segment(ib*block, block).sum());
  861. }
  862. X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  863. for (int ib=0; ib<nblocks; ++ib) {
  864. Y2.segment(ib*block, block) = VectorXr::Ones(block).array() /
  865. ( (maxVal-x.segment(ib*block, block).sum()) *
  866. (maxVal-x.segment(ib*block, block).sum()) );
  867. }
  868. // Newton step
  869. //b2 = - (A.transpose()*WdTWd*(b_pre-b)).array()
  870. // - lambda*(WmTWm*(x-xr)).array()
  871. // + (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  872. // Full
  873. b2 = (A.transpose()*WdTWd*(b)).array()
  874. //- lambda*(WmTWm*(x-xr)).array()
  875. + (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  876. A2 = ATWdTWdA;
  877. A2 += lambda*WmTWm;
  878. A2.diagonal().array() += mux*X2.array() + muy*Y2.array();
  879. // // Jacobi Preconditioner
  880. // Eigen::SparseMatrix<Scalar> MM =
  881. // Eigen::SparseMatrix<Scalar>(A2.rows(), A2.cols());
  882. // for (int i=0; i<ATWdTWdA.rows(); ++i) {
  883. // MM.insert(i,i) = 1./ATWdTWdA(i,i);
  884. // }
  885. // MM.finalize();
  886. /////////////////////////////////////////////////////////////
  887. // Solve system,
  888. // CG solution of complete system
  889. // TODO add reference model
  890. //tol = 1e-5*phid+mux+muy;// 1e-14;
  891. iter = N*M;
  892. //std::cout << "Call cg" << std::endl;
  893. // Decomposition preconditioner
  894. //Pre.setThreshold(1e1*tol);
  895. //Pre.compute(A2);
  896. // Jacobi Preconditioner
  897. //VectorXr ztilde = CGJ(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  898. // Decomposition preconditioner
  899. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, Pre, iter, tol);
  900. // No preconditioner
  901. // Newton Setp
  902. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, iter, tol);
  903. // Full soln
  904. //VectorXr ztilde = CG(A2, x, b2, iter, tol);
  905. //std::cout << "out cg" << std::endl;
  906. cg.compute(A2);
  907. VectorXr ztilde = cg.solveWithGuess(b2, x);
  908. iter = cg.iterations();
  909. //tol = cg.error();
  910. ++iloop;
  911. itertot += iter;
  912. /////////////////////////////////////////////////////////////
  913. // update x, mux, muy
  914. //VectorXr h = ztilde; // - x;
  915. // update x
  916. h = ztilde - x;
  917. // determing steplength
  918. //Scalar d = std::min(1., 0.925*(x.array()/h.array().abs()).minCoeff() );
  919. Scalar d(1.);
  920. for (int ix=0; ix<x.size(); ++ix) {
  921. if (h[ix] < 0.) {
  922. d = std::min(d, (Scalar).925*(x[ix]/std::abs(h[ix])));
  923. }
  924. }
  925. // if (d < 1e-5) {
  926. // std::cout << "not going anywhere d=" << d << " |h| = " << h.norm() << "\n";
  927. // //break;
  928. // mux = (phid + lambda*phim) / phib;
  929. // muy = mux;
  930. // x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  931. // //goto restart; // Gasp!
  932. // continue;
  933. // }
  934. // Newton
  935. //Scalar d = std::min(1., 0.9*((x.array()/ztilde.array()).abs()).minCoeff());
  936. // Make step
  937. x += d*h; // whole soln
  938. //x += d*ztilde; // Newton
  939. // Fix any overstepping
  940. for (int ib=0; ib<nblocks; ++ib) {
  941. while (x.segment(ib*block, block).sum() >= maxVal) {
  942. x.segment(ib*block, block).array() *= .99;
  943. }
  944. }
  945. for (int i=0; i<x.size(); ++i) {
  946. if (x(i) < minVal) {
  947. x(i) = minVal + delta;
  948. }
  949. }
  950. b_pre = A*x;
  951. phib = PhiB2(mux, muy, minVal, maxVal, x, block, nblocks);
  952. phid = (WdTWd*(b-b_pre)).norm();
  953. phim = (WmTWm*(x-xr)).norm();
  954. // Determine mu steps to take
  955. VectorXr s1 = mux * (X2.asDiagonal()*(ztilde) - 2.*X1);
  956. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  957. VectorXr s2 = muy * (Y2.asDiagonal()*(ztilde) - 2.*Y1);
  958. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  959. if ( (std::abs(phib / (phid+lambda*phim)) < epsilon)) {
  960. //if ( (std::abs(phib / (phid+lambda*phim)) < epsilon) && h.norm() < 1e-5) {
  961. cont = false;
  962. }
  963. } while ( cont );
  964. // report
  965. //std::cout << std::ios::left;
  966. //std::cout.precision(8);
  967. std::cout << std::setw(6) << ii << std::scientific << std::setw(18) << phim << std::setw(18) << phid
  968. << std::setw(18) << lambda << std::setw(18) << mux << std::setw(18) << muy
  969. << std::setw(12) << itertot << std::setw(12) << iloop << std::setw(18) << h.norm() << std::endl;
  970. phireport.precision(12);
  971. phireport << ii << "\t" << phim << "\t" << phid
  972. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  973. << itertot << "\t" << iloop << "\t" << h.norm() << std::endl;
  974. std::fstream modfile;
  975. std::string fname = "iteration" + to_string(ii) + ".dat";
  976. modfile.open( fname.c_str(), std::ios::out);
  977. modfile << ii << "\t" << phim << "\t" << phid
  978. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t" << iter << "\n";
  979. modfile << x << "\n";
  980. modfile.close();
  981. // write predicted data file
  982. std::fstream predata;
  983. fname = "iteration" + to_string(ii) + "pre.dat";
  984. predata.open(fname.c_str(), std::ios::out);
  985. predata << b_pre << std::endl;
  986. predata.close();
  987. // update lambda
  988. // @todo smarter lambda change
  989. lambda *= .9;
  990. }
  991. phireport.close();
  992. // TODO, determine optimal solution
  993. return x;
  994. }
  995. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  996. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  997. * (minVal, maxVal) \f$. Note that this method optimized the complete
  998. * solution, using the large matrix ATA. If you have a system with a huge
  999. * number of columns, see the implicit version of this routine. Solution of
  1000. * the dual problem (interior-point) follows "Tikhonov Regularization with
  1001. * Nonnegativity constraint, (Calavetti et. al. 2004)". This routine only imposes non-negativity. No upper bound
  1002. * @param[in] A is a Real Matrix.
  1003. * @param[in] xref is a reference model
  1004. * @param[in] b is a Real vector
  1005. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  1006. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  1007. * @param[in] block is the number of parameters to sum together for the
  1008. * upper barrier term. So block block number parameters are kept under maxVal.
  1009. * as such A.rows() / block must be evenly divisible.
  1010. * @param[in] WdTWd is the data objective function
  1011. * @param[in] WmTWm is the model objective function
  1012. */
  1013. template <typename Scalar>
  1014. VectorXr LogBarrierCG_NN(const MatrixXr &A, const VectorXr &xr,
  1015. const VectorXr &b, const Scalar &minVal,
  1016. const Eigen::SparseMatrix<Scalar>& WdTWd,
  1017. const Eigen::SparseMatrix<Scalar>& WmTWm, Real lambda0=1e1) {
  1018. // Check that everything is aligned OK
  1019. if (A.rows() != b.size() ) {
  1020. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  1021. std::cerr << "A.rows() " << A.rows() << "\n";
  1022. std::cerr << "A.cols() " << A.cols() << "\n";
  1023. std::cerr << "b.size() " << b.size() << "\n";
  1024. exit(1);
  1025. }
  1026. // write predicted data file
  1027. std::fstream obsdata;
  1028. std::string fname = "obsdata.dat";
  1029. obsdata.open(fname.c_str(), std::ios::out);
  1030. obsdata << b << std::endl;
  1031. obsdata.close();
  1032. // TODO make ATA implicit, or at least only compute half
  1033. MatrixXr ATWdTWdA = A.transpose()*WdTWd*A;
  1034. int N = A.cols(); // number of model
  1035. int M = A.rows(); // number of data
  1036. int MAXITER = 175; // M*N;
  1037. Scalar SIGMA = .25;//5.85; //1e-2; // .25; //1e-2; // 1e-1;
  1038. Scalar delta = 1e-12;
  1039. // // Determine starting lambda_0, find lim_sup of the norm of impulse responses and scale
  1040. // Scalar limsup = 1e10;
  1041. // for (int i=0; i<N; ++i) {
  1042. // VectorXr Spike = VectorXr::Zero(N);
  1043. // Spike(i) = (minVal + maxVal) / 2.;
  1044. // limsup = std::min(limsup, (ATWdTWdA*Spike).array().abs().maxCoeff());
  1045. // }
  1046. Scalar lambda = lambda0; //*limsup;//e-1;//limsup;
  1047. Scalar epsilon = 1e-16; // Ratio between phib and phim+phid
  1048. // initial guess, just near zero for now
  1049. VectorXr x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  1050. // predicted b
  1051. VectorXr b_pre = A*x;
  1052. //Eigen::ConjugateGradient< MatrixXr > cg;
  1053. // Use ILUT preconditioner
  1054. Eigen::ConjugateGradient< MatrixXr, Eigen::Upper, Eigen::DiagonalPreconditioner<Real> > cg;
  1055. //Eigen::ConjugateGradient< MatrixXr, Eigen::Upper, Eigen::IncompleteLUT<Real> > cg;
  1056. Scalar phid = (WdTWd*(b - b_pre)).norm();
  1057. Scalar phim = (WmTWm*(x - xr)).norm();
  1058. Scalar phib = PhiB2_NN(1., minVal, x);
  1059. Scalar mux = (phid + lambda*phim) / phib;
  1060. //Scalar tol; // = 1e-5*phid; // 1e-14;
  1061. std::fstream phireport("phimphid.dat", std::ios::out);
  1062. mux = (phid + lambda*phim) / phib;
  1063. /// @todo add stopping criteria.
  1064. for (int ii=0; ii<MAXITER; ++ii) {
  1065. int iter = N*M;
  1066. int iloop(0);
  1067. int itertot(0);
  1068. //VectorXr h;
  1069. VectorXr ztilde;
  1070. bool cont(true);
  1071. do {
  1072. //restart:
  1073. VectorXr X1(x.size());
  1074. VectorXr X2(x.size());
  1075. VectorXr b2;
  1076. MatrixXr A2;
  1077. ///////////////////////////////////
  1078. // setup
  1079. ///////////////////////////////////////////////////////////
  1080. // Log barrier terms
  1081. X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  1082. X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  1083. // Full
  1084. b2 = (A.transpose()*WdTWd*(b-b_pre)).array()
  1085. - lambda*(WmTWm*(x-xr)).array()
  1086. + (2.*mux)*X1.array(); // + (2.*muy)*Y1.array();
  1087. // The first two terms could be moved out of the loop, don't know if its worth it
  1088. A2 = ATWdTWdA;
  1089. A2 += lambda*WmTWm;
  1090. A2.diagonal().array() += mux*X2.array();
  1091. /////////////////////////////////////////////////////////////
  1092. // Solve system,
  1093. // CG solution of complete system
  1094. // TODO add reference model
  1095. //tol = 1e-5*phid+mux;// 1e-14;
  1096. iter = N*M;
  1097. // Full soln
  1098. //VectorXr ztilde = CG(A2, x, b2, iter, tol);
  1099. cg.compute(A2);
  1100. //ztilde = cg.solveWithGuess(b2, x);
  1101. ztilde = cg.solve(b2); // Newton step, don't guess!
  1102. //std::cout << "out cg" << std::endl;
  1103. iter = cg.iterations();
  1104. //tol = cg.error();
  1105. ++iloop;
  1106. itertot += iter;
  1107. /////////////////////////////////////////////////////////////
  1108. // update x, mux, muy
  1109. //h = ztilde - x;
  1110. // determing steplength
  1111. Scalar d(1.);
  1112. for (int ix=0; ix<x.size(); ++ix) {
  1113. if (ztilde[ix] < 0.) {
  1114. d = std::min(d, (Scalar).925*(x[ix]/std::abs(ztilde[ix])));
  1115. }
  1116. }
  1117. // if (d < 1e-5) {
  1118. // std::cout << "not going anywhere d=" << d << " |h| = " << h.norm() << "\n";
  1119. // //break;
  1120. // mux = (phid + lambda*phim) / phib;
  1121. // muy = mux;
  1122. // x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  1123. // //goto restart; // Gasp!
  1124. // continue;
  1125. // }
  1126. // Newton
  1127. //Scalar d = std::min(1., 0.9*((x.array()/ztilde.array()).abs()).minCoeff());
  1128. // Make step
  1129. x += d*ztilde; // whole soln
  1130. // Fix any overstepping
  1131. for (int i=0; i<x.size(); ++i) {
  1132. if (x(i) < minVal) {
  1133. x(i) = minVal + delta;
  1134. }
  1135. }
  1136. b_pre = A*x;
  1137. phib = PhiB2_NN(mux, minVal, x);
  1138. phid = (WdTWd*(b-b_pre)).norm();
  1139. phim = (WmTWm*(x-xr)).norm();
  1140. // Determine mu steps to take
  1141. VectorXr s1 = mux * (X2.asDiagonal()*(ztilde) - 2.*X1);
  1142. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  1143. if ( (std::abs(phib / (phid+lambda*phim)) < epsilon)) {
  1144. //if ( (std::abs(phib / (phid+lambda*phim)) < epsilon) && h.norm() < 1e-5) {
  1145. cont = false;
  1146. }
  1147. } while ( cont );
  1148. // report
  1149. //std::cout << std::ios::left;
  1150. //std::cout.precision(8);
  1151. std::cout << std::setw(6) << ii << std::scientific << std::setw(18) << phim << std::setw(18) << phid
  1152. << std::setw(18) << lambda << std::setw(18) << mux
  1153. << std::setw(12) << itertot << std::setw(12) << iloop << std::setw(18) << ztilde.norm() << std::endl;
  1154. phireport.precision(12);
  1155. phireport << ii << "\t" << phim << "\t" << phid
  1156. << "\t" << lambda << "\t" << mux << "\t"
  1157. << itertot << "\t" << iloop << "\t" << ztilde.norm() << std::endl;
  1158. std::fstream modfile;
  1159. std::string fname = "iteration" + to_string(ii) + ".dat";
  1160. modfile.open( fname.c_str(), std::ios::out);
  1161. modfile << ii << "\t" << phim << "\t" << phid
  1162. << "\t" << lambda << "\t" << mux << "\t" << iter << "\n";
  1163. modfile << x << "\n";
  1164. modfile.close();
  1165. // write predicted data file
  1166. std::fstream predata;
  1167. fname = "iteration" + to_string(ii) + "pre.dat";
  1168. predata.open(fname.c_str(), std::ios::out);
  1169. predata << b_pre << std::endl;
  1170. predata.close();
  1171. // update lambda
  1172. // @todo smarter lambda change
  1173. lambda *= .9;
  1174. }
  1175. phireport.close();
  1176. // TODO, determine optimal solution
  1177. return x;
  1178. }
  1179. // Specialized Function that incorporates a buried modulus function.
  1180. // solves the usual problem Ax = b, where A \in C but x and b are real.
  1181. // b = mod(Ax).
  1182. template <typename Scalar>
  1183. VectorXr Tikhonov_CG(const MatrixXr &A, const VectorXr &xr,
  1184. const VectorXr &b,
  1185. const Eigen::SparseMatrix<Scalar>& WdTWd,
  1186. const Eigen::SparseMatrix<Scalar>& WmTWm, Real lambda0=1e1) {
  1187. // Check that everything is aligned OK
  1188. if (A.rows() != b.size() ) {
  1189. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  1190. std::cerr << "A.rows() " << A.rows() << "\n";
  1191. std::cerr << "A.cols() " << A.cols() << "\n";
  1192. std::cerr << "b.size() " << b.size() << "\n";
  1193. exit(1);
  1194. }
  1195. // write predicted data file
  1196. std::fstream obsdata;
  1197. std::string fname = "obsdata.dat";
  1198. obsdata.open(fname.c_str(), std::ios::out);
  1199. obsdata << b.array() << std::endl;
  1200. obsdata.close();
  1201. // TODO make ATA implicit
  1202. MatrixXr ATWdTWdA = A.transpose()*WdTWd*A;
  1203. int N = A.cols(); // number of model
  1204. int M = A.rows(); // number of dat
  1205. int MAXITER = 175; // M*N;
  1206. //Scalar SIGMA = .25;//5.85; //1e-2; // .25; //1e-2; // 1e-1;
  1207. Scalar delta = 1e-4;
  1208. Scalar lambda = lambda0; // * limsup;//e-1;//limsup;
  1209. Scalar epsilon = 1e-15; // Ratio between phib and phim+phid
  1210. // initial guess, just near zero for now
  1211. VectorXr x = VectorXr::Zero(N).array() + delta;// ((minVal + maxVal) / 2.);
  1212. // predicted b
  1213. VectorXr b_pre = A*x;
  1214. Scalar phid = (WdTWd*(b - b_pre)).norm();
  1215. Scalar phim = (WmTWm*(x - xr)).norm();
  1216. Scalar tol = 1e-5*phid; // 1e-14;
  1217. std::fstream phireport("phimphid.dat", std::ios::out);
  1218. //ConjugateGradient<SparseMatrix<double> > cg;
  1219. // can't use Eigen, b/c we have mixed types of Re and complex
  1220. Eigen::ConjugateGradient< MatrixXr > cg;
  1221. //Eigen::BiCGSTAB< MatrixXcr > solver;
  1222. /// @todo add stopping criteria.
  1223. for (int ii=0; ii<MAXITER; ++ii) {
  1224. int iter = N*M;
  1225. int iloop(0);
  1226. int itertot(0);
  1227. VectorXr h;
  1228. bool cont(true);
  1229. do {
  1230. //restart:
  1231. //VectorXr b2;
  1232. //MatrixXr A2;
  1233. ///////////////////////////////////
  1234. // setup
  1235. // Newton step
  1236. //b2 = - (A.transpose()*WdTWd*(b_pre-b)).array()
  1237. // - lambda*(WmTWm*(x-xr)).array();
  1238. // + (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  1239. // Full
  1240. VectorXr b2 = A.transpose()*WdTWd*b;
  1241. MatrixXr A2 = ATWdTWdA;
  1242. A2 += lambda*WmTWm;
  1243. // // Jacobi Preconditioner
  1244. // Eigen::SparseMatrix<Scalar> MM =
  1245. // Eigen::SparseMatrix<Scalar>(A2.rows(), A2.cols());
  1246. // for (int i=0; i<ATWdTWdA.rows(); ++i) {
  1247. // MM.insert(i,i) = 1./ATWdTWdA(i,i);
  1248. // }
  1249. // MM.finalize();
  1250. /////////////////////////////////////////////////////////////
  1251. // Solve system,
  1252. // CG solution of complete system
  1253. // TODO add reference model
  1254. tol = 1e-5*phid;// 1e-14;
  1255. iter = N*M;
  1256. //std::cout << "Call cg" << std::endl;
  1257. // Decomposition preconditioner
  1258. //Pre.setThreshold(1e1*tol);
  1259. //Pre.compute(A2);
  1260. // Jacobi Preconditioner
  1261. //VectorXr ztilde = CGJ(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  1262. // Decomposition preconditioner
  1263. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, Pre, iter, tol);
  1264. // No preconditioner
  1265. // Newton Setp
  1266. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, iter, tol);
  1267. // Full soln
  1268. //cg.compute(A2);
  1269. //cg.setTolerance(tol);
  1270. //VectorXr ztilde = (cg.solveWithGuess(b2,x.cast<Complex>())).real();
  1271. //iter = cg.iterations();
  1272. //VectorXr ztilde = CG(A2, x, b2, iter, tol);
  1273. //cg.setTolerance();
  1274. cg.compute(A2);
  1275. x = cg.solveWithGuess(b2, x);
  1276. b_pre = A*x;
  1277. phid = (WdTWd*(b - b_pre)).norm();
  1278. phim = (WmTWm*(x - xr)).norm();
  1279. //std::cout << "out cg" << std::endl;
  1280. ++iloop;
  1281. itertot += iter;
  1282. /////////////////////////////////////////////////////////////
  1283. // update x, mux, muy
  1284. //VectorXr h = ztilde; // - x;
  1285. // update x
  1286. //h = ztilde - x;
  1287. // determing steplength
  1288. //Scalar d = std::min(1., 0.925*(x.array()/h.array().abs()).minCoeff() );
  1289. // Scalar d(1.);
  1290. // for (int ix=0; ix<x.size(); ++ix) {
  1291. // if (h[ix] < 0.) {
  1292. // d = std::min(d, (Scalar).925*(x[ix]/std::abs(h[ix])));
  1293. // }
  1294. // }
  1295. // if (d < 1e-5) {
  1296. // std::cout << "not going anywhere d=" << d << " |h| = " << h.norm() << "\n";
  1297. // //break;
  1298. // mux = (phid + lambda*phim) / phib;
  1299. // muy = mux;
  1300. // x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  1301. // //goto restart; // Gasp!
  1302. // continue;
  1303. // }
  1304. // Newton
  1305. //Scalar d = std::min(1., 0.9*((x.array()/ztilde.array()).abs()).minCoeff());
  1306. // Make step
  1307. //x += d*h; // whole soln
  1308. //x += d*ztilde; // Newton
  1309. // // TODO readd
  1310. // // Fix any overstepping
  1311. // for (int ib=0; ib<nblocks; ++ib) {
  1312. // while (x.segment(ib*block, block).sum() >= maxVal) {
  1313. // x.segment(ib*block, block).array() *= .99;
  1314. // }
  1315. // }
  1316. /*
  1317. for (int i=0; i<x.size(); ++i) {
  1318. if (x(i) < minVal) {
  1319. x(i) = minVal + delta;
  1320. }
  1321. }
  1322. b_pre = (A*x).array().abs();
  1323. phib = PhiB2(mux, muy, minVal, maxVal, x, block, nblocks);
  1324. phid = (WdTWd*(b-b_pre)).norm();
  1325. phim = (WmTWm*(x-xr)).norm();
  1326. // Determine mu steps to take
  1327. VectorXr s1 = mux * (X2.asDiagonal()*(ztilde) - 2.*X1);
  1328. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  1329. VectorXr s2 = muy * (Y2.asDiagonal()*(ztilde) - 2.*Y1);
  1330. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  1331. if ( (std::abs(phib / (phid+lambda*phim)) < epsilon)) {
  1332. //if ( (std::abs(phib / (phid+lambda*phim)) < epsilon) && h.norm() < 1e-5) {
  1333. cont = false;
  1334. }
  1335. */
  1336. cont = false;
  1337. } while ( cont );
  1338. // report
  1339. std::cout << std::ios::left;
  1340. std::cout.precision(8);
  1341. std::cout << std::setw(6) << ii << std::scientific << std::setw(18) << phim << std::setw(18) << phid
  1342. << std::setw(18) << lambda << std::setw(18) << cg.error()
  1343. << std::setw(12) << cg.iterations() << std::endl;
  1344. phireport.precision(12);
  1345. phireport << ii << "\t" << phim << "\t" << phid
  1346. << "\t" << lambda << "\t" << 0.0 << "\t" << 0.0 << "\t"
  1347. << cg.iterations() << "\t" << 0.0 << "\t" << 0.0 << std::endl;
  1348. std::fstream modfile;
  1349. std::string fname = "iteration" + to_string(ii) + ".dat";
  1350. modfile.open( fname.c_str(), std::ios::out);
  1351. modfile << ii << "\t" << phim << "\t" << phid
  1352. << "\t" << lambda << "\t" << 0 << "\t" << 0 << "\t" << cg.iterations() << "\n";
  1353. modfile << x << "\n";
  1354. modfile.close();
  1355. // write predicted data file
  1356. std::fstream predata;
  1357. fname = "iteration" + to_string(ii) + "pre.dat";
  1358. predata.open(fname.c_str(), std::ios::out);
  1359. predata << b_pre << std::endl;
  1360. predata.close();
  1361. // update lambda
  1362. // @todo smarter lambda change
  1363. lambda *= .9;
  1364. }
  1365. phireport.close();
  1366. // TODO, determine optimal solution
  1367. return x;
  1368. }
  1369. /** Impliments a logarithmic barrier CG solution of a Real linear system of
  1370. * the form \f[ \mathbf{A} \mathbf{x} = \mathbf{b} \f] s.t. \f$ x \in
  1371. * (minVal, maxVal) \f$. Note that this method optimized the complete
  1372. * solution, using the large matrix ATA. If you have a system with a huge
  1373. * number of columns, see the implicit version of this routine. Solution of
  1374. * the dual problem (interior-point) follows "Tikhonov Regularization with
  1375. * Nonnegativity constraint, (Calavetti et. al. 2004)"
  1376. * Seeks the overdetermined least squares solution
  1377. * @param[in] A is a Real Matrix.
  1378. * @param[in] b is a Real vector
  1379. * @param[in] minVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  1380. * @param[in] maxVal is the minimum allowed value \f$ x \in (minVal, maxVal) \f$
  1381. * @param[in] block is the number of parameters to sum together for the
  1382. * upper barrier term. So block block number parameters are kept under maxVal.
  1383. * as such A.rows() / block must be evenly divisible.
  1384. */
  1385. template <typename Scalar>
  1386. VectorXr LogBarrierCGLS(const MatrixXr &A, const VectorXr &b, const Scalar &minVal,
  1387. const Scalar &maxVal, const int& block) {
  1388. // Check that everything is aligned OK
  1389. if (A.rows() != b.size() ) {
  1390. std::cerr << "Matrix A is not aligned with Vector b" << "\n";
  1391. exit(1);
  1392. }
  1393. // write predicted data file
  1394. std::fstream obsdata;
  1395. std::string fname = "obsdata.dat";
  1396. obsdata.open(fname.c_str(), std::ios::out);
  1397. obsdata << b << std::endl;
  1398. obsdata.close();
  1399. // #ifdef LEMMAUSEVTK
  1400. // double blue[3] = {0.0,0.0,1.0};
  1401. // double red[3] = {1.0,0.0,0.0};
  1402. // VectorXr ind = VectorXr::LinSpaced(b.size(), 1, b.size());
  1403. // #endif
  1404. // TODO make ATA implicit
  1405. MatrixXr ATA = A.transpose()*A;
  1406. int N = A.cols(); // number of model
  1407. int M = A.rows(); // number of data
  1408. int MAXITER = 100; // M*N;
  1409. Scalar SIGMA = .25; // 1e-2; //1e-1;
  1410. Scalar delta = 1e-8;
  1411. // Cholesky preconditioner
  1412. //Eigen::FullPivLU <MatrixXr> Pre;
  1413. //Eigen::ColPivHouseholderQR <MatrixXr> Pre;
  1414. //Pre.compute(ATA);
  1415. // Determine starting lambda_0, find lim_sup of the norm of impulse responses and scale
  1416. Scalar limsup = 1e10;
  1417. for (int i=0; i<N; ++i) {
  1418. VectorXr Spike = VectorXr::Zero(N);
  1419. Spike(i) = (minVal + maxVal) / 2.;
  1420. limsup = std::min(limsup, (ATA*Spike).array().abs().maxCoeff());
  1421. }
  1422. Scalar lambda = 1e-6;//*limsup;//e-1;//limsup;
  1423. Scalar mux0 = 1e-1*lambda;
  1424. Scalar muy0 = 1e-1*lambda;
  1425. Scalar epsilon = 1e-5; // Ratio between phib and phim+phid
  1426. /////////////////////////////
  1427. // logX spacing
  1428. //Scalar MinLam = 1e-24;
  1429. //Scalar MaxLam = 1e-4;
  1430. //VectorXr Lambdas;
  1431. //Scalar LS = 5000;
  1432. //Scalar dl10 = std::log(LS*MaxLam+1.)/(Scalar)MAXITER;
  1433. //Lambdas = 1./LS*(dl10*VectorXr::LinSpaced(MAXITER+1, 0, MAXITER)).array().exp()
  1434. // + MinLam - 1./LS;
  1435. // initial guess, just near zero for now
  1436. VectorXr x = VectorXr::Zero(N).array() + minVal+delta;// ((minVal + maxVal) / 2.);
  1437. // predicted b
  1438. VectorXr b_pre = A*x;
  1439. int nblocks = x.size()/block;
  1440. Scalar phid = (b - (b_pre)).norm();
  1441. Scalar phim = x.norm();
  1442. Scalar phib = PhiB2(mux0, muy0, minVal, maxVal, x, block, nblocks);
  1443. Scalar mux = mux0;
  1444. Scalar muy = muy0;
  1445. Scalar tol = 1e-5*phid; // 1e-14;
  1446. std::fstream phireport("phimphid.dat", std::ios::out);
  1447. /// @todo add stopping criteria.
  1448. //int iLambda = MAXITER - 1;
  1449. for (int ii=0; ii<MAXITER; ++ii) {
  1450. //lambda = Lambdas[iLambda];
  1451. //iLambda -= 1;
  1452. // Phi_m is just L2Norm right now. Maybe add s, alpha_T2, and
  1453. // alpha_z terms
  1454. VectorXr WmT_Wm = VectorXr::Ones(N).array()*lambda;
  1455. VectorXr Xm1 = x;
  1456. int iter = N*M;
  1457. int iloop(0);
  1458. do {
  1459. VectorXr X1(x.size());
  1460. VectorXr Y1(x.size());
  1461. VectorXr X2(x.size());
  1462. VectorXr Y2(x.size());
  1463. VectorXr b2;
  1464. //VectorXr HiSegments = VectorXr::Zero(nblocks);
  1465. MatrixXr A2;
  1466. ///////////////////////////////////
  1467. // setup
  1468. #ifdef LEMMAUSEOMP
  1469. #pragma omp parallel sections
  1470. {
  1471. #endif
  1472. ///////////////////////////////////////////////////////////
  1473. // Log barrier terms
  1474. #ifdef LEMMAUSEOMP
  1475. #pragma omp section
  1476. #endif
  1477. {
  1478. X1 = VectorXr::Ones(N).array() / (x.array()-minVal) ;
  1479. }
  1480. #ifdef LEMMAUSEOMP
  1481. #pragma omp section
  1482. #endif
  1483. {
  1484. for (int ib=0; ib<nblocks; ++ib) {
  1485. //HiSegments(ib) = x.segment(ib*block, block).sum();
  1486. Y1.segment(ib*block, block) = VectorXr::Ones(block).array() /
  1487. (maxVal - x.segment(ib*block, block).sum());
  1488. }
  1489. //for (int ix=0; ix<x.size(); ++ix) {
  1490. // Y1(ix) = 1./( (maxVal-HiSegments(ib)) );
  1491. //}
  1492. //Y1 = VectorXr::Ones(N).array() / (maxVal-x.array()) ;
  1493. }
  1494. #ifdef LEMMAUSEOMP
  1495. #pragma omp section
  1496. #endif
  1497. {
  1498. X2 = VectorXr::Ones(N).array() / ((x.array()-minVal)*(x.array()-minVal));
  1499. }
  1500. #ifdef LEMMAUSEOMP
  1501. #pragma omp section
  1502. #endif
  1503. {
  1504. for (int ib=0; ib<nblocks; ++ib) {
  1505. //HiSegments(ib) = x.segment( ib*block, block ).sum();
  1506. Y2.segment(ib*block, block) = VectorXr::Ones(block).array() /
  1507. ( (maxVal-x.segment(ib*block, block).sum()) *
  1508. (maxVal-x.segment(ib*block, block).sum()) );
  1509. }
  1510. //Y2 = VectorXr::Ones(N).array() / ((maxVal-x.array())*(maxVal-x.array()));
  1511. //std::cout << Y1.transpose() << std::endl << std::endl;
  1512. //std::cout << Y2.transpose() << std::endl;
  1513. }
  1514. #ifdef LEMMAUSEOMP
  1515. } // parallel sections
  1516. #endif
  1517. #ifdef LEMMAUSEOMP
  1518. #pragma omp parallel sections
  1519. {
  1520. #endif
  1521. #ifdef LEMMAUSEOMP
  1522. #pragma omp section
  1523. #endif
  1524. {
  1525. b2 = -(A.transpose()*(b_pre-b)).array() -
  1526. (WmT_Wm.array()*x.array()).array() +
  1527. (2.*mux)*X1.array() + (2.*muy)*Y1.array();
  1528. }
  1529. #ifdef LEMMAUSEOMP
  1530. #pragma omp section
  1531. #endif
  1532. {
  1533. A2 = ATA;
  1534. A2.diagonal().array() += WmT_Wm.array() + mux*X2.array() +
  1535. muy*Y2.array();
  1536. }
  1537. #ifdef LEMMAUSEOMP
  1538. } // parallel sections
  1539. #endif
  1540. // // Jacobi Preconditioner
  1541. // Eigen::SparseMatrix<Scalar> MM =
  1542. // Eigen::SparseMatrix<Scalar>(A2.rows(), A2.cols());
  1543. // for (int i=0; i<ATA.rows(); ++i) {
  1544. // MM.insert(i,i) = 1./ATA(i,i);
  1545. // }
  1546. // MM.finalize();
  1547. /////////////////////////////////////////////////////////////
  1548. // Solve system,
  1549. // CG solution of complete system
  1550. // TODO add reference model
  1551. tol = 1e-5*phid+mux+muy;// 1e-14;
  1552. iter = N*M;
  1553. //std::cout << "Call cg" << std::endl;
  1554. // Decomposition preconditioner
  1555. //Pre.setThreshold(1e1*tol);
  1556. //Pre.compute(A2);
  1557. // Jacobi Preconditioner
  1558. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, MM, iter, tol);
  1559. // Decomposition preconditioner
  1560. //VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, Pre, iter, tol);
  1561. // No preconditioner
  1562. VectorXr ztilde = CG(A2, VectorXr::Zero(N), b2, iter, tol);
  1563. //std::cout << "out cg" << std::endl;
  1564. /////////////////////////////////////////////////////////////
  1565. // update x, mux, muy
  1566. //VectorXr h = ztilde; // - x;
  1567. VectorXr s1, s2;
  1568. // update x
  1569. //VectorXr h = ztilde; // - x;
  1570. //Scalar d = std::min(1., 0.995*(x.array()/h.array().abs()).minCoeff() );
  1571. //x += d*h;
  1572. Scalar d = std::min(1.,0.995*(x.array()/ztilde.array().abs()).minCoeff());
  1573. x += d*ztilde;
  1574. // // Fix any overstepping
  1575. // for (int ib=0; ib<nblocks; ++ib) {
  1576. // while (x.segment(ib*block, block).sum() > maxVal) {
  1577. // x.segment(ib*block, block).array() *= (.9);
  1578. // }
  1579. // }
  1580. // for (int i=0; i<x.size(); ++i) {
  1581. // if (x(i) < minVal) {
  1582. // x(i) = minVal + delta;
  1583. // }
  1584. // }
  1585. b_pre = A*x;
  1586. #ifdef LEMMAUSEOMP
  1587. #pragma omp parallel sections
  1588. {
  1589. #endif
  1590. #ifdef LEMMAUSEOMP
  1591. #pragma omp section
  1592. #endif
  1593. {
  1594. phib = PhiB2(mux, muy, minVal, maxVal, x, block, nblocks);
  1595. }
  1596. #ifdef LEMMAUSEOMP
  1597. #pragma omp section
  1598. #endif
  1599. {
  1600. phid = (b - (b_pre)).norm();
  1601. }
  1602. #ifdef LEMMAUSEOMP
  1603. #pragma omp section
  1604. #endif
  1605. {
  1606. phim = x.norm();
  1607. }
  1608. #ifdef LEMMAUSEOMP
  1609. }
  1610. #endif
  1611. // Determine mu steps to take
  1612. #ifdef LEMMAUSEOMP
  1613. #pragma omp parallel sections
  1614. {
  1615. #endif
  1616. #ifdef LEMMAUSEOMP
  1617. #pragma omp section
  1618. #endif
  1619. {
  1620. s1 = mux * (X2.asDiagonal()*(x+ztilde) - 2.*X1);
  1621. mux = SIGMA/((Scalar)(N)) * std::abs( s1.dot(x) ) ;
  1622. }
  1623. #ifdef LEMMAUSEOMP
  1624. #pragma omp section
  1625. #endif
  1626. {
  1627. s2 = muy * (Y2.asDiagonal()*(x+ztilde) - 2.*Y1);
  1628. muy = SIGMA/((Scalar)(N)) * std::abs( s2.dot(x) ) ;
  1629. }
  1630. #ifdef LEMMAUSEOMP
  1631. }
  1632. #endif
  1633. ++iloop;
  1634. } while (std::abs(phib / (phid+lambda*phim)) > epsilon);
  1635. // report
  1636. phireport.precision(12);
  1637. std::cout << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  1638. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  1639. << iter << "\t" << iloop << std::endl;
  1640. phireport << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  1641. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t"
  1642. << iter << "\t" << iloop << std::endl;
  1643. std::fstream modfile;
  1644. std::string fname = "iteration" + to_string(ii) + ".dat";
  1645. modfile.open( fname.c_str(), std::ios::out);
  1646. modfile << ii << "\t" << x.norm() << "\t" << (b-(A*x)).norm()
  1647. << "\t" << lambda << "\t" << mux << "\t" << muy << "\t" << iter << "\n";
  1648. modfile << x << "\n";
  1649. modfile.close();
  1650. // write predicted data file
  1651. std::fstream predata;
  1652. fname = "iteration" + to_string(ii) + "pre.dat";
  1653. predata.open(fname.c_str(), std::ios::out);
  1654. predata << b_pre << std::endl;
  1655. predata.close();
  1656. // update lambda
  1657. // @todo smarter lambda change
  1658. lambda *= .85;
  1659. }
  1660. phireport.close();
  1661. // TODO, determine optimal solution
  1662. return x;
  1663. }
  1664. }
  1665. #endif // ----- #ifndef LOGBARRIERCG_INC -----