taucs.cpp

/*
  Copyright ©2013 The Regents of the University of California
  (Regents). All Rights Reserved. Permission to use, copy, modify, and
  distribute this software and its documentation for educational,
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  LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
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*/

#include "taucs.hpp"
#include "timer.hpp"
#include "display.hpp"
#include "solvers.h"
#include <cstdlib>
#include <iostream>
using namespace std;
using namespace alglib;

vector<Node*>* debug_nodes = 0;

extern "C" {
#include "taucs.h"
int taucs_linsolve (taucs_ccs_matrix* A, // input matrix
                    void** factorization, // an approximate inverse
                    int nrhs, // number of right-hand sides
                    void* X, // unknowns
                    void* B, // right-hand sides
                    char* options[], // options (what to do and how)
                    void* arguments[]); // option arguments
}

ostream &operator<< (ostream &out, taucs_ccs_matrix *A) {
    out << "n: " << A->n << endl;
    out << "m: " << A->m << endl;
    out << "flags: " << A->flags << endl;
    out << "colptr: ";
    for (int i = 0; i <= A->n; i++)
        out << (i==0?"":", ") << A->colptr[i];
    out << endl;
    out << "rowind: ";
    for (int j = 0; j <= A->colptr[A->n]; j++)
        out << (j==0?"":", ") << A->rowind[j];
    out << endl;
    out << "values.d: ";
    for (int j = 0; j <= A->colptr[A->n]; j++)
        out << (j==0?"":", ") << A->values.d[j];
    out << endl;
    return out;
}

taucs_ccs_matrix *sparse_to_taucs (const SpMat<double> &As) {
    // assumption: A is square and symmetric
    int n = As.n;
    int nnz = 0;
    for (int i = 0; i < n; i++) {
        for (int k = 0; k < (int)As.rows[i].indices.size(); k++) {
            int j = As.rows[i].indices[k];
            if (j < i)
                continue;
            nnz++;
        }
    }
    taucs_ccs_matrix *At = taucs_ccs_create(n,n, nnz, TAUCS_DOUBLE | TAUCS_SYMMETRIC | TAUCS_LOWER);
    int pos = 0;
    for (int i = 0; i < n; i++) {
        At->colptr[i] = pos;
        for (int k = 0; k < (int)As.rows[i].indices.size(); k++) {
            int j = As.rows[i].indices[k];
            if (j < i)
                continue;
            At->rowind[pos] = j;
            At->values.d[pos] = As.rows[i].entries[k];
            pos++;
        }
    }
    At->colptr[n] = pos;
    return At;
}

template <int m> taucs_ccs_matrix *sparse_to_taucs (const SpMat< Mat<m,m> > &As) {
    // assumption: A is square and symmetric
    int n = As.n;
    int nnz = 0;
    for (int i = 0; i < n; i++) {
        for (int jj = 0; jj < (int)As.rows[i].indices.size(); jj++) {
            int j = As.rows[i].indices[jj];
            if (j < i)
                continue;
            nnz += (j==i) ? m*(m+1)/2 : m*m;
        }
    }
    taucs_ccs_matrix *At = taucs_ccs_create
        (n*m,n*m, nnz, TAUCS_DOUBLE | TAUCS_SYMMETRIC | TAUCS_LOWER);
    int pos = 0;
    for (int i = 0; i < n; i++) {
        for (int k = 0; k < m; k++) {
            At->colptr[i*m+k] = pos;
            for (int jj = 0; jj < (int)As.rows[i].indices.size(); jj++) {
                int j = As.rows[i].indices[jj];
                if (j < i)
                    continue;
                const Mat<m,m> &Aij = As.rows[i].entries[jj];
                for (int l = (i==j) ? k : 0; l < m; l++) {
                    At->rowind[pos] = j*m+l;
                    At->values.d[pos] = Aij(k,l);
                    pos++;
                }
            }
        }
    }
    At->colptr[n*m] = pos;
    return At;
}

vector<double> alglib_linear_solve(const SpMat<double>& A, const vector<double>& b) {
    const int n = b.size();
    real_2d_array M;
    real_1d_array x,c;
    M.setlength(n,n);
    x.setlength(n);
    c.setcontent(n,&b[0]);
    for (int i = 0; i < A.m; i++) {
        const SpVec<double> &row = A.rows[i];
        for (int j = 0; j < A.n; j++)
            M(i,j) = 0;
        for (size_t jj = 0; jj < row.indices.size(); jj++) {
            int j = row.indices[jj];
            M(i,j) = row.entries[jj];
        }
    }
    
    ae_int_t info;
    densesolverreport rep;    
    rmatrixsolve(M,n,c,info,rep,x);
    
    vector<double> ret(n);
    for (int i=0; i<n; i++)
        ret[i] = x[i];
    
    return ret;
}

template<int C>
vector<Vec<C> > alglib_linear_solve_vec(const SpMat<Mat<C,C> >& A, const vector<Vec<C> >& b) {
    const int n = b.size()*C;
    real_2d_array M;
    real_1d_array x,c;
    M.setlength(n,n);
    x.setlength(n);
    c.setlength(n);
    for (int i=0; i<n; i++)
        c[i] = b[i/C][i%C];
    for (int i = 0; i < A.m; i++) {
        const SpVec<Mat<C,C> > &row = A.rows[i];
        for (size_t jj = 0; jj < row.indices.size(); jj++) {
            int j = row.indices[jj];
            for (int si=0; si<C; si++)
                for (int sj=0; sj<C; sj++)
                    M(i*C+si,j*C+sj) = row.entries[jj](si,sj);
        }
    }

    ae_int_t info;
    densesolverreport rep;    
    rmatrixsolve(M,n,c,info,rep,x);
    
    vector<Vec<C> > ret(n);
    for (int i=0; i<n; i++)
        ret[i/C][i%C] = x[i];
    
    return ret;
}

vector<double> taucs_linear_solve (const SpMat<double> &A, const vector<double> &b) {
    if (b.size() < 20) 
        return alglib_linear_solve(A,b);
    
    // taucs_logfile("stdout");
    taucs_ccs_matrix *Ataucs = sparse_to_taucs(A);
    vector<double> x(b.size());
    char *options[] = {(char*)"taucs.factor.LLT=true", NULL};
    int retval = taucs_linsolve(Ataucs, NULL, 1, &x[0], (double*)&b[0], options, NULL);
    if (retval != TAUCS_SUCCESS) {
        cerr << "Error: TAUCS(scalar) failed with return value " << retval << endl;
        segfault();
        exit(EXIT_FAILURE);
    }
    taucs_ccs_free(Ataucs);
    return x;
}

template <int m> vector< Vec<m> > taucs_linear_solve
    (const SpMat< Mat<m,m> > &A, const vector< Vec<m> > &b) {
    if (b.size() < 6) 
        return alglib_linear_solve_vec(A,b);
    
    // taucs_logfile("stdout");
    taucs_ccs_matrix *Ataucs = sparse_to_taucs(A);
    vector< Vec<m> > x(b.size());
    char *options[] = {(char*)"taucs.factor.LLT=true", NULL};
    int retval = taucs_linsolve(Ataucs, NULL, 1, &x[0], (double*)&b[0], options, NULL);
    if (retval != TAUCS_SUCCESS) {
        cerr << "Error: TAUCS(vector) failed with return value " << retval << endl;
        segfault();
        exit(EXIT_FAILURE);
    }
    taucs_ccs_free(Ataucs);
    return x;
}

template vector<Vec3> taucs_linear_solve (const SpMat<Mat3x3> &A,
                                          const vector<Vec3> &b);