1 // #define EIGEN_TAUCS_SUPPORT
2 // #define EIGEN_CHOLMOD_SUPPORT
3 #include <iostream>
4 #include <Eigen/Sparse>
5 
6 // g++ -DSIZE=10000 -DDENSITY=0.001  sparse_cholesky.cpp -I.. -DDENSEMATRI -O3 -g0 -DNDEBUG   -DNBTRIES=1 -I /home/gael/Coding/LinearAlgebra/taucs_full/src/ -I/home/gael/Coding/LinearAlgebra/taucs_full/build/linux/  -L/home/gael/Coding/LinearAlgebra/taucs_full/lib/linux/ -ltaucs /home/gael/Coding/LinearAlgebra/GotoBLAS/libgoto.a -lpthread -I /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Include/ $CHOLLIB -I /home/gael/Coding/LinearAlgebra/SuiteSparse/UFconfig/ /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a   /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Lib/libcholmod.a -lmetis /home/gael/Coding/LinearAlgebra/SuiteSparse/AMD/Lib/libamd.a  /home/gael/Coding/LinearAlgebra/SuiteSparse/CAMD/Lib/libcamd.a   /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a  /home/gael/Coding/LinearAlgebra/SuiteSparse/COLAMD/Lib/libcolamd.a -llapack && ./a.out
7 
8 #define NOGMM
9 #define NOMTL
10 
11 #ifndef SIZE
12 #define SIZE 10
13 #endif
14 
15 #ifndef DENSITY
16 #define DENSITY 0.01
17 #endif
18 
19 #ifndef REPEAT
20 #define REPEAT 1
21 #endif
22 
23 #include "BenchSparseUtil.h"
24 
25 #ifndef MINDENSITY
26 #define MINDENSITY 0.0004
27 #endif
28 
29 #ifndef NBTRIES
30 #define NBTRIES 10
31 #endif
32 
33 #define BENCH(X) \
34   timer.reset(); \
35   for (int _j=0; _j<NBTRIES; ++_j) { \
36     timer.start(); \
37     for (int _k=0; _k<REPEAT; ++_k) { \
38         X  \
39   } timer.stop(); }
40 
41 // typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;
42 typedef SparseMatrix<Scalar,SelfAdjoint|LowerTriangular> EigenSparseSelfAdjointMatrix;
43 
44 void fillSpdMatrix(float density, int rows, int cols,  EigenSparseSelfAdjointMatrix& dst)
45 {
46   dst.startFill(rows*cols*density);
47   for(int j = 0; j < cols; j++)
48   {
49     dst.fill(j,j) = internal::random<Scalar>(10,20);
50     for(int i = j+1; i < rows; i++)
51     {
52       Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;
53       if (v!=0)
54         dst.fill(i,j) = v;
55     }
56 
57   }
58   dst.endFill();
59 }
60 
61 #include <Eigen/Cholesky>
62 
63 template<int Backend>
64 void doEigen(const char* name, const EigenSparseSelfAdjointMatrix& sm1, int flags = 0)
65 {
66   std::cout << name << "..." << std::flush;
67   BenchTimer timer;
68   timer.start();
69   SparseLLT<EigenSparseSelfAdjointMatrix,Backend> chol(sm1, flags);
70   timer.stop();
71   std::cout << ":\t" << timer.value() << endl;
72 
73   std::cout << "  nnz: " << sm1.nonZeros() << " => " << chol.matrixL().nonZeros() << "\n";
74 //   std::cout << "sparse\n" << chol.matrixL() << "%\n";
75 }
76 
77 int main(int argc, char *argv[])
78 {
79   int rows = SIZE;
80   int cols = SIZE;
81   float density = DENSITY;
82   BenchTimer timer;
83 
84   VectorXf b = VectorXf::Random(cols);
85   VectorXf x = VectorXf::Random(cols);
86 
87   bool densedone = false;
88 
89   //for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
90 //   float density = 0.5;
91   {
92     EigenSparseSelfAdjointMatrix sm1(rows, cols);
93     std::cout << "Generate sparse matrix (might take a while)...\n";
94     fillSpdMatrix(density, rows, cols, sm1);
95     std::cout << "DONE\n\n";
96 
97     // dense matrices
98     #ifdef DENSEMATRIX
99     if (!densedone)
100     {
101       densedone = true;
102       std::cout << "Eigen Dense\t" << density*100 << "%\n";
103       DenseMatrix m1(rows,cols);
104       eiToDense(sm1, m1);
105       m1 = (m1 + m1.transpose()).eval();
106       m1.diagonal() *= 0.5;
107 
108 //       BENCH(LLT<DenseMatrix> chol(m1);)
109 //       std::cout << "dense:\t" << timer.value() << endl;
110 
111       BenchTimer timer;
112       timer.start();
113       LLT<DenseMatrix> chol(m1);
114       timer.stop();
115       std::cout << "dense:\t" << timer.value() << endl;
116       int count = 0;
117       for (int j=0; j<cols; ++j)
118         for (int i=j; i<rows; ++i)
119           if (!internal::isMuchSmallerThan(internal::abs(chol.matrixL()(i,j)), 0.1))
120             count++;
121       std::cout << "dense: " << "nnz = " << count << "\n";
122 //       std::cout << "dense:\n" << m1 << "\n\n" << chol.matrixL() << endl;
123     }
124     #endif
125 
126     // eigen sparse matrices
127     doEigen<Eigen::DefaultBackend>("Eigen/Sparse", sm1, Eigen::IncompleteFactorization);
128 
129     #ifdef EIGEN_CHOLMOD_SUPPORT
130     doEigen<Eigen::Cholmod>("Eigen/Cholmod", sm1, Eigen::IncompleteFactorization);
131     #endif
132 
133     #ifdef EIGEN_TAUCS_SUPPORT
134     doEigen<Eigen::Taucs>("Eigen/Taucs", sm1, Eigen::IncompleteFactorization);
135     #endif
136 
137     #if 0
138     // TAUCS
139     {
140       taucs_ccs_matrix A = sm1.asTaucsMatrix();
141 
142       //BENCH(taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);)
143 //       BENCH(taucs_supernodal_factor_to_ccs(taucs_ccs_factor_llt_ll(&A));)
144 //       std::cout << "taucs:\t" << timer.value() << endl;
145 
146       taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);
147 
148       for (int j=0; j<cols; ++j)
149       {
150         for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)
151           std::cout << chol->values.d[i] << " ";
152       }
153     }
154 
155     // CHOLMOD
156     #ifdef EIGEN_CHOLMOD_SUPPORT
157     {
158       cholmod_common c;
159       cholmod_start (&c);
160       cholmod_sparse A;
161       cholmod_factor *L;
162 
163       A = sm1.asCholmodMatrix();
164       BenchTimer timer;
165 //       timer.reset();
166       timer.start();
167       std::vector<int> perm(cols);
168 //       std::vector<int> set(ncols);
169       for (int i=0; i<cols; ++i)
170         perm[i] = i;
171 //       c.nmethods = 1;
172 //       c.method[0] = 1;
173 
174       c.nmethods = 1;
175       c.method [0].ordering = CHOLMOD_NATURAL;
176       c.postorder = 0;
177       c.final_ll = 1;
178 
179       L = cholmod_analyze_p(&A, &perm[0], &perm[0], cols, &c);
180       timer.stop();
181       std::cout << "cholmod/analyze:\t" << timer.value() << endl;
182       timer.reset();
183       timer.start();
184       cholmod_factorize(&A, L, &c);
185       timer.stop();
186       std::cout << "cholmod/factorize:\t" << timer.value() << endl;
187 
188       cholmod_sparse* cholmat = cholmod_factor_to_sparse(L, &c);
189 
190       cholmod_print_factor(L, "Factors", &c);
191 
192       cholmod_print_sparse(cholmat, "Chol", &c);
193       cholmod_write_sparse(stdout, cholmat, 0, 0, &c);
194 //
195 //       cholmod_print_sparse(&A, "A", &c);
196 //       cholmod_write_sparse(stdout, &A, 0, 0, &c);
197 
198 
199 //       for (int j=0; j<cols; ++j)
200 //       {
201 //           for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)
202 //             std::cout << chol->values.s[i] << " ";
203 //       }
204     }
205     #endif
206 
207     #endif
208 
209 
210 
211   }
212 
213 
214   return 0;
215 }
216 
217