Mosek.cpp

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/*
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * Written (W) 2012 Fernando José Iglesias García
 * Copyright (C) 2012 Fernando José Iglesias García
 */

#ifdef USE_MOSEK

//#define DEBUG_MOSEK
//#define DEBUG_SOLUTION

#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/Mosek.h>
#include <shogun/lib/SGVector.h>

using namespace shogun;

CMosek::CMosek()
: CSGObject()
{
}

CMosek::CMosek(int32_t num_con, int32_t num_var)
: CSGObject()
{
    // Create MOSEK environment
    m_rescode = MSK_makeenv(&m_env, NULL, NULL, NULL, NULL);

#ifdef DEBUG_MOSEK
    // Direct the environment's log stream to SG_PRINT
    if ( m_rescode == MSK_RES_OK )
    {
        m_rescode = MSK_linkfunctoenvstream(m_env, MSK_STREAM_LOG,
                NULL, CMosek::print);
    }
#endif

    // Initialize the environment
    if ( m_rescode == MSK_RES_OK )
    {
        m_rescode = MSK_initenv(m_env);
    }

    // Create an optimization task
    if ( m_rescode == MSK_RES_OK )
    {
        m_rescode = MSK_maketask(m_env, num_con, num_var, &m_task);
    }

#ifdef DEBUG_MOSEK
    // Direct the task's log stream to SG_PRINT
    if ( m_rescode == MSK_RES_OK )
    {
        m_rescode = MSK_linkfunctotaskstream(m_task, MSK_STREAM_LOG,
                NULL, CMosek::print);
    }
#endif
}

CMosek::~CMosek()
{
    delete_problem();
}

void MSKAPI CMosek::print(void* handle, char str[])
{
    SG_SPRINT("%s", str);
}

MSKrescodee CMosek::init_sosvm(int32_t M, int32_t N,
        int32_t num_aux, int32_t num_aux_con,
        SGMatrix< float64_t > C, SGVector< float64_t > lb,
        SGVector< float64_t > ub, SGMatrix< float64_t > A,
        SGVector< float64_t > b)
{
    // Give an estimate of the size of the input data to increase the
    // speed of inputting
    int32_t num_var = M+N+num_aux;
    int32_t num_con = N*N+num_aux_con;
    // NOTE: However, to input this step is completely optional and MOSEK
    // will automatically allocate more resources if necessary
    m_rescode = MSK_putmaxnumvar(m_task, num_var);
    // Neither the number of constraints nor the number of non-zero elements
    // is known a priori, rough estimates are given here
    m_rescode = MSK_putmaxnumcon(m_task, num_con);
    // A = [-dPsi(y) | -I_N ] with M+N columns => max. M+1 nnz per row
    m_rescode = MSK_putmaxnumanz(m_task, (M+1)*N*N);

    // Append optimization variables initialized to zero
    m_rescode = MSK_append(m_task, MSK_ACC_VAR, num_var);
    // Append empty constraints initialized with no bounds
    m_rescode = MSK_append(m_task, MSK_ACC_CON, num_con);
    // Set the constant term in the objective equal to zero
    m_rescode = MSK_putcfix(m_task, 0.0);

    for ( int32_t j = 0 ; j < num_var && m_rescode == MSK_RES_OK ; ++j )
    {
        // Set the linear term c_j in the objective
        if ( j < M+num_aux )
            m_rescode = MSK_putcj(m_task, j, 0.0);
        else
            m_rescode = MSK_putcj(m_task, j, 1.0);

        // Set the bounds on x_j: blx[j] <= x_j <= bux[j]
        // TODO set bounds lb and ub given by init_opt for w
        if ( j < M )
        {
            m_rescode = MSK_putbound(m_task, MSK_ACC_VAR, j,
                    MSK_BK_FR, -MSK_INFINITY, +MSK_INFINITY);
        }

        // The slack and the auxiliary variables are required to be positive
        if ( j >= M )
        {
            m_rescode = MSK_putbound(m_task, MSK_ACC_VAR, j,
                    MSK_BK_LO, 0.0, +MSK_INFINITY);
        }
    }

    // Input the matrix Q^0 for the objective
    //
    // NOTE: In MOSEK we minimize x'*Q^0*x. C != Q0 but Q0 is
    // just an extended version of C with zeros that make no
    // difference in MOSEK's sparse representation
    m_rescode = wrapper_putqobj(C);

    // Input the matrix A and the vector b for the contraints A*x <= b
    m_rescode = wrapper_putaveclist(m_task, A);
    m_rescode = wrapper_putboundlist(m_task, b);

    REQUIRE(m_rescode == MSK_RES_OK, "MOSEK Error in CMosek::init_sosvm(). "
            "Enable DEBUG_MOSEK for details.\n");

    return m_rescode;
}

MSKrescodee CMosek::add_constraint_sosvm(
        SGVector< float64_t > dPsi,
        index_t con_idx,
        index_t train_idx,
        int32_t num_aux,
        float64_t bi)
{
    // Count the number of non-zero element in dPsi
    int32_t nnz = CMath::get_num_nonzero(dPsi.vector, dPsi.vlen);
    // Indices of the non-zero elements in the row of A to add
    SGVector< index_t > asub(nnz+1); // +1 because of the -1 element
    // Values of the non-zero elements
    SGVector< float64_t > aval(nnz+1);
    // Next element to add in asub and aval
    index_t idx = 0;

    for ( int32_t i = 0 ; i < dPsi.vlen ; ++i )
    {
        if ( dPsi[i] != 0 )
        {
            asub[idx] = i;
            aval[idx] = dPsi[i];
            ++idx;
        }
    }

    ASSERT(idx == nnz);

    asub[idx] = dPsi.vlen + num_aux + train_idx;
    aval[idx] = -1;

    m_rescode = MSK_putavec(m_task, MSK_ACC_CON, con_idx, nnz+1,
            asub.vector, aval.vector);

    if ( m_rescode == MSK_RES_OK )
    {
        m_rescode = MSK_putbound(m_task, MSK_ACC_CON, con_idx, 
                MSK_BK_UP, -MSK_INFINITY, bi);
    }

    return m_rescode;
}

MSKrescodee CMosek::wrapper_putaveclist(
        MSKtask_t & task, 
        SGMatrix< float64_t > A)
{
    // Indices to the rows of A to replace, all the rows
    SGVector< index_t > sub(A.num_rows);
    for ( index_t i = 0 ; i < A.num_rows ; ++i )
        sub[i] = i;

    // Non-zero elements of A
    int32_t nnza = CMath::get_num_nonzero(A.matrix, A.num_rows*A.num_cols);
    SGVector< float64_t > aval(nnza);
    // For each of the rows, indices to non-zero elements
    SGVector< index_t > asub(nnza);
    // For each row, pointer to the first non-zero element
    // in aval
    SGVector< int32_t > ptrb(A.num_rows);
    // Next position to write in aval and asub
    index_t idx = 0;
    // Switch if the first non-zero element in each row 
    // has been found
    bool first_nnz_found = false;

    for ( index_t i = 0 ; i < A.num_rows ; ++i )
    {
        first_nnz_found = false;

        for ( index_t j = 0 ; j < A.num_cols ; ++j )
        {
            if ( A(i,j) )
            {
                aval[idx] = A(i,j);
                asub[idx] = j;

                if ( !first_nnz_found )
                {
                    ptrb[i] = idx;
                    first_nnz_found = true;
                }

                ++idx;
            }
        }

        // Handle rows whose elements are all zero
        // TODO does it make sense that a row in A has all its elements
        // equal to zero?
        if ( !first_nnz_found )
            ptrb[i] = ( i ? ptrb[i-1] : 0 );
    }

    // For each row, pointer to the last+1 non-zero element 
    // in aval
    SGVector< int32_t > ptre(A.num_rows);
    for ( index_t i = 0 ; i < A.num_rows-1 ; ++i )
        ptre[i] = ptrb[i+1];

    if ( A.num_rows > 0 )
        ptre[A.num_rows-1] = nnza;

    MSKrescodee ret = MSK_putaveclist(task, MSK_ACC_CON, A.num_rows, sub.vector,
            ptrb.vector, ptre.vector,
            asub.vector, aval.vector);

    REQUIRE(ret == MSK_RES_OK, "MOSEK Error in CMosek::wrapper_putaveclist(). "
            "Enable DEBUG_MOSEK for details.\n");

    return ret;
}

MSKrescodee CMosek::wrapper_putboundlist(MSKtask_t & task, SGVector< float64_t > b)
{
    // Indices to the bounds that should be replaced, b.vlen bounds starting
    // from zero
    SGVector< index_t > sub(b.vlen);
    for ( index_t i = 0 ; i < b.vlen ; ++i )
        sub[i] = i;

    // Type of the bounds and lower bound values
    MSKboundkeye* bk = SG_MALLOC(MSKboundkeye, b.vlen);
    SGVector< float64_t > bl(b.vlen);
    for ( index_t i = 0 ; i < b.vlen ; ++i )
    {
        bk[i] =  MSK_BK_UP;
        bl[i] = -MSK_INFINITY;
    }

    MSKrescodee ret =  MSK_putboundlist(task, MSK_ACC_CON, b.vlen, sub.vector,
            bk, bl.vector, b.vector);

    SG_FREE(bk);

    REQUIRE(ret == MSK_RES_OK, "MOSEK Error in CMosek::wrapper_putboundlist(). "
            "Enable DEBUG_MOSEK for details.\n");

    return ret;
}

MSKrescodee CMosek::wrapper_putqobj(SGMatrix< float64_t > Q0) const
{
    // Shorthands for the dimensions of the matrix
    index_t N = Q0.num_rows;
    index_t M = Q0.num_cols;

    // Count the number of non-zero elements in the lower 
    // triangular part of the matrix
    int32_t nnz = 0;
    for ( index_t i = 0 ; i < N ; ++i )
        for ( index_t j = i ; j < M ; ++j )
            nnz += ( Q0[j + i*M] ? 1 : 0 );

    // i subscript for non-zero elements of Q0
    SGVector< index_t > qosubi(nnz);
    // j subscript for non-zero elements of Q0
    SGVector< index_t > qosubj(nnz);
    // Values of non-zero elements of Q0
    SGVector< float64_t > qoval(nnz);
    // Next position to write in the vectors
    index_t idx = 0;

    for ( index_t i = 0 ; i < N ; ++i )
        for ( index_t j = i ; j < M ; ++j )
        {
            if ( Q0[j + i*M] )
            {
                qosubi[idx] = i;
                qosubj[idx] = j;
                 qoval[idx] = Q0[j + i*M]; 

                ++idx;
            }
        }

    return MSK_putqobj(m_task, nnz, qosubi.vector,
            qosubj.vector, qoval.vector);
}

MSKrescodee CMosek::optimize(SGVector< float64_t > sol)
{
    m_rescode = MSK_optimize(m_task);

#ifdef DEBUG_MOSEK
    // Print a summary containing information about the solution
    MSK_solutionsummary(m_task, MSK_STREAM_LOG);
#endif

    // Read the solution
    if ( m_rescode == MSK_RES_OK )
    {
        // Solution status
        MSKsolstae solsta;
        // FIXME posible solutions are:
        // MSK_SOL_ITR: the interior solution
        // MSK_SOL_BAS: the basic solution
        // MSK_SOL_ITG: the integer solution
        MSK_getsolutionstatus(m_task, MSK_SOL_ITR, NULL, &solsta);

        switch (solsta)
        {
        case MSK_SOL_STA_OPTIMAL:
        case MSK_SOL_STA_NEAR_OPTIMAL:
            MSK_getsolutionslice(m_task,
                    // Request the interior solution
                    MSK_SOL_ITR,
                    // of the optimization vector
                    MSK_SOL_ITEM_XX,
                    0,
                    sol.vlen,
                    sol.vector);
#ifdef DEBUG_SOLUTION
            sol.display_vector("Solution");
#endif
            break;
        case MSK_SOL_STA_DUAL_INFEAS_CER:
        case MSK_SOL_STA_PRIM_INFEAS_CER:
        case MSK_SOL_STA_NEAR_DUAL_INFEAS_CER:
        case MSK_SOL_STA_NEAR_PRIM_INFEAS_CER:
#ifdef DEBUG_MOSEK
            SG_PRINT("Primal or dual infeasibility "
                 "certificate found\n");
#endif
            break;
        case MSK_SOL_STA_UNKNOWN:
#ifdef DEBUG_MOSEK
            SG_PRINT("Undetermined solution status\n");
#endif
            break;
        default:
#ifdef DEBUG_MOSEK
            SG_PRINT("Other solution status\n");
#endif
            break;  // to avoid compile error when DEBUG_MOSEK
                // is not defined
        }
    }

    // In case any error occurred, print the appropriate error message
    if ( m_rescode != MSK_RES_OK )
    {
        char symname[MSK_MAX_STR_LEN];
        char desc[MSK_MAX_STR_LEN];

        MSK_getcodedesc(m_rescode, symname, desc);

        SG_PRINT("An error occurred optimizing with MOSEK\n");
        SG_PRINT("ERROR %s - '%s'\n", symname, desc);
    }

    return m_rescode;
}

void CMosek::delete_problem()
{
    MSK_deletetask(&m_task);
    MSK_deleteenv(&m_env);
}

void CMosek::display_problem()
{
    int32_t num_var, num_con;
    m_rescode = MSK_getnumvar(m_task, &num_var);
    m_rescode = MSK_getnumcon(m_task, &num_con);

    SG_PRINT("\nMatrix Q^0:\n");
    for ( int32_t i = 0 ; i < num_var ; ++i )
    {
        for ( int32_t j = 0 ; j < num_var ; ++j )
        {
            float64_t qij;
            m_rescode = MSK_getqobjij(m_task, i, j, &qij);
            if ( qij != 0.0 )
                SG_PRINT("(%d,%d)\t%.2f\n", i, j, qij);
        }
    }
    SG_PRINT("\n");

    SG_PRINT("\nVector c:\n");
    SGVector< float64_t > c(num_var);
    m_rescode = MSK_getc(m_task, c.vector);
    c.display_vector();

    SG_PRINT("\n\nMatrix A:\n");
    for ( int32_t i = 0 ; i < num_con ; ++i )
    {
        for ( int32_t j = 0 ; j < num_var ; ++j )
        {
            float64_t aij;
            m_rescode = MSK_getaij(m_task, i, j, &aij);
            if ( aij != 0.0 )
                SG_PRINT("(%d,%d)\t%.2f\n", i, j, aij);
        }
    }
    SG_PRINT("\n");

    SG_PRINT("\nConstraint Bounds, vector b:\n");
    for ( int32_t i = 0 ; i < num_con ; ++i )
    {
        MSKboundkeye bk;
        float64_t bl, bu;
        m_rescode = MSK_getbound(m_task, MSK_ACC_CON, i, &bk, &bl, &bu);

        SG_PRINT("%6.2f %6.2f\n", bl, bu);
    }

    SG_PRINT("\nVariable Bounds, vectors lb and ub:\n");
    for ( int32_t i = 0 ; i < num_var ; ++i )
    {
        MSKboundkeye bk;
        float64_t bl, bu;
        m_rescode = MSK_getbound(m_task, MSK_ACC_VAR, i, &bk, &bl, &bu);

        SG_PRINT("%6.2f %6.2f\n", bl, bu);
    }
    SG_PRINT("\n");
}


#endif /* USE_MOSEK */