Building igl statically and moving to the dep scripts

Fixing dep build script on Windows and removing some warnings.

Use bundled igl by default.

Not building with the dependency scripts if not explicitly stated. This way, it will stay in
Fix the libigl patch to include C source files in header only mode.

src/libigl/igl/eigs.cpp

@@ -0,0 +1,176 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "eigs.h"
+
+#include "cotmatrix.h"
+#include "sort.h"
+#include "slice.h"
+#include "massmatrix.h"
+#include <iostream>
+
+template <
+  typename Atype,
+  typename Btype,
+  typename DerivedU,
+  typename DerivedS>
+IGL_INLINE bool igl::eigs(
+  const Eigen::SparseMatrix<Atype> & A,
+  const Eigen::SparseMatrix<Btype> & iB,
+  const size_t k,
+  const EigsType type,
+  Eigen::PlainObjectBase<DerivedU> & sU,
+  Eigen::PlainObjectBase<DerivedS> & sS)
+{
+  using namespace Eigen;
+  using namespace std;
+  const size_t n = A.rows();
+  assert(A.cols() == n && "A should be square.");
+  assert(iB.rows() == n && "B should be match A's dims.");
+  assert(iB.cols() == n && "B should be square.");
+  assert(type == EIGS_TYPE_SM && "Only low frequencies are supported");
+  DerivedU U(n,k);
+  DerivedS S(k,1);
+  typedef Atype Scalar;
+  typedef Eigen::Matrix<typename DerivedU::Scalar,DerivedU::RowsAtCompileTime,1> VectorXS;
+  // Rescale B for better numerics
+  const Scalar rescale = std::abs(iB.diagonal().maxCoeff());
+  const Eigen::SparseMatrix<Btype> B = iB/rescale;
+
+  Scalar tol = 1e-4;
+  Scalar conv = 1e-14;
+  int max_iter = 100;
+  int i = 0;
+  //std::cout<<"start"<<std::endl;
+  while(true)
+  {
+    //std::cout<<i<<std::endl;
+    // Random initial guess
+    VectorXS y = VectorXS::Random(n,1);
+    Scalar eff_sigma = 0;
+    if(i>0)
+    {
+      eff_sigma = 1e-8+std::abs(S(i-1));
+    }
+    // whether to use rayleigh quotient method
+    bool ray = false;
+    Scalar err = std::numeric_limits<Scalar>::infinity();
+    int iter;
+    Scalar sigma = std::numeric_limits<Scalar>::infinity();
+    VectorXS x;
+    for(iter = 0;iter<max_iter;iter++)
+    {
+      if(i>0 && !ray)
+      {
+        // project-out existing modes
+        for(int j = 0;j<i;j++)
+        {
+          const VectorXS u = U.col(j);
+          y = (y - u*u.dot(B*y)/u.dot(B * u)).eval();
+        }
+      }
+      // normalize
+      x = y/sqrt(y.dot(B*y));
+
+      // current guess at eigen value
+      sigma = x.dot(A*x)/x.dot(B*x);
+      //x *= sigma>0?1.:-1.;
+
+      Scalar err_prev = err;
+      err = (A*x-sigma*B*x).array().abs().maxCoeff();
+      if(err<conv)
+      {
+        break;
+      }
+      if(ray || err<tol)
+      {
+        eff_sigma = sigma;
+        ray = true;
+      }
+
+      Scalar tikhonov = std::abs(eff_sigma)<1e-12?1e-10:0;
+      switch(type)
+      {
+        default:
+          assert(false && "Not supported");
+          break;
+        case EIGS_TYPE_SM:
+        {
+          SimplicialLDLT<SparseMatrix<Scalar> > solver;
+          const SparseMatrix<Scalar> C = A-eff_sigma*B+tikhonov*B;
+          //mw.save(C,"C");
+          //mw.save(eff_sigma,"eff_sigma");
+          //mw.save(tikhonov,"tikhonov");
+          solver.compute(C);
+          switch(solver.info())
+          {
+            case Eigen::Success:
+              break;
+            case Eigen::NumericalIssue:
+              cerr<<"Error: Numerical issue."<<endl;
+              return false;
+            default:
+              cerr<<"Error: Other."<<endl;
+              return false;
+          }
+          const VectorXS rhs = B*x;
+          y = solver.solve(rhs);
+          //mw.save(rhs,"rhs");
+          //mw.save(y,"y");
+          //mw.save(x,"x");
+          //mw.write("eigs.mat");
+          //if(i == 1)
+          //return false;
+          break;
+        }
+      }
+    }
+    if(iter == max_iter)
+    {
+      cerr<<"Failed to converge."<<endl;
+      return false;
+    }
+    if(
+      i==0 || 
+      (S.head(i).array()-sigma).abs().maxCoeff()>1e-14 ||
+      ((U.leftCols(i).transpose()*B*x).array().abs()<=1e-7).all()
+      )
+    {
+      //cout<<"Found "<<i<<"th mode"<<endl;
+      U.col(i) = x;
+      S(i) = sigma;
+      i++;
+      if(i == k)
+      {
+        break;
+      }
+    }else
+    {
+      //std::cout<<"i: "<<i<<std::endl;
+      //std::cout<<"  "<<S.head(i).transpose()<<" << "<<sigma<<std::endl;
+      //std::cout<<"  "<<(S.head(i).array()-sigma).abs().maxCoeff()<<std::endl;
+      //std::cout<<"  "<<(U.leftCols(i).transpose()*B*x).array().abs().transpose()<<std::endl;
+      // restart with new random guess.
+      cout<<"igl::eigs RESTART"<<endl;
+    }
+  }
+  // finally sort
+  VectorXi I;
+  igl::sort(S,1,false,sS,I);
+  igl::slice(U,I,2,sU);
+  sS /= rescale;
+  sU /= sqrt(rescale);
+  return true;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::eigs<double, double, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(Eigen::SparseMatrix<double, 0, int> const&, Eigen::SparseMatrix<double, 0, int> const&, const size_t, igl::EigsType, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
+#ifdef WIN32
+template bool igl::eigs<double, double, Eigen::Matrix<double,-1,-1,0,-1,-1>, Eigen::Matrix<double,-1,1,0,-1,1> >(Eigen::SparseMatrix<double,0,int> const &,Eigen::SparseMatrix<double,0,int> const &, const size_t, igl::EigsType, Eigen::PlainObjectBase< Eigen::Matrix<double,-1,-1,0,-1,-1> > &, Eigen::PlainObjectBase<Eigen::Matrix<double,-1,1,0,-1,1> > &);
+#endif
+#endif