root/library/bdm/itpp_ext.cpp @ 996

//
// C++ Implementation: itpp_ext
//
// Description:
//
//
// Author: smidl <smidl@utia.cas.cz>, (C) 2008
//
// Copyright: See COPYING file that comes with this distribution
//
//

#include "itpp_ext.h"

#ifndef M_PI
#define M_PI        3.14159265358979323846
#endif
// from  algebra/lapack.h

extern "C" {  /* QR factorization of a general matrix A  */
        void dgeqrf_ ( int *m, int *n, double *a, int *lda, double *tau, double *work,
        int *lwork, int *info );
};

namespace itpp {
vec empty_vec = vec ( 0 );

Array<int> to_Arr ( const ivec &indices ) {
        Array<int> a ( indices.size() );
        for ( int i = 0; i < a.size(); i++ ) {
                a ( i ) = indices ( i );
        }
        return a;
}

ivec linspace ( int from, int to ) {
        int n = to - from + 1;
        int i;
        it_assert_debug ( n > 0, "wrong linspace" );
        ivec iv ( n );
        for ( i = 0; i < n; i++ ) iv ( i ) = from + i;
        return iv;
};

void set_subvector ( vec &ov, const ivec &iv, const vec &v ) {
        it_assert_debug ( ( iv.length() <= v.length() ),
                          "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out "
                          "of range of v" );
        for ( int i = 0; i < iv.length(); i++ ) {
                it_assert_debug ( iv ( i ) < ov.length(),
                                  "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out "
                                  "of range of v" );
                ov ( iv ( i ) ) = v ( i );
        }
}

//! return vector of elements at positions given by indexlist
vec get_vec ( const vec &v, const ivec &indexlist ) {
        int size = indexlist.size();
        vec temp ( size );
        for ( int i = 0; i < size; ++i ) {
                temp ( i ) = v._data() [indexlist ( i ) ];
        }
        return temp;
}

// Gamma
#define log std::log
#define exp std::exp
#define sqrt std::sqrt
#define R_FINITE std::isfinite

bvec operator> ( const vec &t1, const vec &t2 ) {
        it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" );
        bvec temp ( t1.length() );
        for ( int i = 0; i < t1.length(); i++ )
                temp ( i ) = ( t1[i] > t2[i] );
        return temp;
}

bvec operator< ( const vec &t1, const vec &t2 ) {
        it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" );
        bvec temp ( t1.length() );
        for ( int i = 0; i < t1.length(); i++ )
                temp ( i ) = ( t1[i] < t2[i] );
        return temp;
}


bvec operator& ( const bvec &a, const bvec &b ) {
        it_assert_debug ( b.size() == a.size(), "operator&(): Vectors of different lengths" );

        bvec temp ( a.size() );
        for ( int i = 0; i < a.size(); i++ ) {
                temp ( i ) = a ( i ) & b ( i );
        }
        return temp;
}

bvec operator| ( const bvec &a, const bvec &b ) {
        it_assert_debug ( b.size() == a.size(), "operator|(): Vectors of different lengths" );

        bvec temp ( a.size() );
        for ( int i = 0; i < a.size(); i++ ) {
                temp ( i ) = a ( i ) | b ( i );
        }
        return temp;
}

//! poor man's operator vec(bvec) - copied for svn version of itpp
ivec get_from_bvec ( const ivec &v, const bvec &binlist ) {
        int size = binlist.size();
        it_assert_debug ( v.size() == size, "Vec<>::operator()(bvec &): "
                          "Wrong size of binlist vector" );
        ivec temp ( size );
        int j = 0;
        for ( int i = 0; i < size; ++i )
                if ( binlist ( i ) == bin ( 1 ) )
                        temp ( j++ ) = v ( i );
        temp.set_size ( j, true );
        return temp;
}


//#if 0
Gamma_RNG::Gamma_RNG ( double a, double b ) {
        setup ( a, b );
}
double  Gamma_RNG::sample() {
        //A copy of rgamma code from the R package!!
        //

        /* Constants : */
        const static double sqrt32 = 5.656854;
        const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */

        /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k))
         * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k)
         * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k)
         */
        const static double q1 = 0.04166669;
        const static double q2 = 0.02083148;
        const static double q3 = 0.00801191;
        const static double q4 = 0.00144121;
        const static double q5 = -7.388e-5;
        const static double q6 = 2.4511e-4;
        const static double q7 = 2.424e-4;

        const static double a1 = 0.3333333;
        const static double a2 = -0.250003;
        const static double a3 = 0.2000062;
        const static double a4 = -0.1662921;
        const static double a5 = 0.1423657;
        const static double a6 = -0.1367177;
        const static double a7 = 0.1233795;

        /* State variables [FIXME for threading!] :*/
        static double aa = 0.;
        static double aaa = 0.;
        static double s, s2, d;    /* no. 1 (step 1) */
        static double q0, b, si, c;/* no. 2 (step 4) */

        double e, p, q, r, t, u, v, w, x, ret_val;
        double a = alpha;
        double scale = 1.0 / beta;

        if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) {
                it_error ( "Gamma_RNG wrong parameters" );
        }

        if ( a < 1. ) { /* GS algorithm for parameters a < 1 */
                if ( a == 0 )
                        return 0.;
                e = 1.0 + exp_m1 * a;
                for ( ;; ) {  //VS repeat
                        p = e * unif_rand();
                        if ( p >= 1.0 ) {
                                x = -log ( ( e - p ) / a );
                                if ( exp_rand() >= ( 1.0 - a ) * log ( x ) )
                                        break;
                        } else {
                                x = exp ( log ( p ) / a );
                                if ( exp_rand() >= x )
                                        break;
                        }
                }
                return scale * x;
        }

        /* --- a >= 1 : GD algorithm --- */

        /* Step 1: Recalculations of s2, s, d if a has changed */
        if ( a != aa ) {
                aa = a;
                s2 = a - 0.5;
                s = sqrt ( s2 );
                d = sqrt32 - s * 12.0;
        }
        /* Step 2: t = standard normal deviate,
                   x = (s,1/2) -normal deviate. */

        /* immediate acceptance (i) */
        t = norm_rand();
        x = s + 0.5 * t;
        ret_val = x * x;
        if ( t >= 0.0 )
                return scale * ret_val;

        /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */
        u = unif_rand();
        if ( ( d * u ) <= ( t * t * t ) )
                return scale * ret_val;

        /* Step 4: recalculations of q0, b, si, c if necessary */

        if ( a != aaa ) {
                aaa = a;
                r = 1.0 / a;
                q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r
                         + q2 ) * r + q1 ) * r;

                /* Approximation depending on size of parameter a */
                /* The constants in the expressions for b, si and c */
                /* were established by numerical experiments */

                if ( a <= 3.686 ) {
                        b = 0.463 + s + 0.178 * s2;
                        si = 1.235;
                        c = 0.195 / s - 0.079 + 0.16 * s;
                } else if ( a <= 13.022 ) {
                        b = 1.654 + 0.0076 * s2;
                        si = 1.68 / s + 0.275;
                        c = 0.062 / s + 0.024;
                } else {
                        b = 1.77;
                        si = 0.75;
                        c = 0.1515 / s;
                }
        }
        /* Step 5: no quotient test if x not positive */

        if ( x > 0.0 ) {
                /* Step 6: calculation of v and quotient q */
                v = t / ( s + s );
                if ( fabs ( v ) <= 0.25 )
                        q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v
                                                     + a3 ) * v + a2 ) * v + a1 ) * v;
                else
                        q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v );


                /* Step 7: quotient acceptance (q) */
                if ( log ( 1.0 - u ) <= q )
                        return scale * ret_val;
        }

        for ( ;; ) { //VS repeat
                /* Step 8: e = standard exponential deviate
                 *      u =  0,1 -uniform deviate
                 *      t = (b,si)-double exponential (laplace) sample */
                e = exp_rand();
                u = unif_rand();
                u = u + u - 1.0;
                if ( u < 0.0 )
                        t = b - si * e;
                else
                        t = b + si * e;
                /* Step  9:  rejection if t < tau(1) = -0.71874483771719 */
                if ( t >= -0.71874483771719 ) {
                        /* Step 10:      calculation of v and quotient q */
                        v = t / ( s + s );
                        if ( fabs ( v ) <= 0.25 )
                                q = q0 + 0.5 * t * t *
                                    ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v
                                        + a2 ) * v + a1 ) * v;
                        else
                                q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v );
                        /* Step 11:      hat acceptance (h) */
                        /* (if q not positive go to step 8) */
                        if ( q > 0.0 ) {
                                // TODO: w = expm1(q);
                                w = exp ( q ) - 1;
                                /*  ^^^^^ original code had approximation with rel.err < 2e-7 */
                                /* if t is rejected sample again at step 8 */
                                if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) )
                                        break;
                        }
                }
        } /* repeat .. until  `t' is accepted */
        x = s + 0.5 * t;
        return scale * x * x;
}


bool qr ( const mat &A, mat &R ) {
        int info;
        int m = A.rows();
        int n = A.cols();
        int lwork = n;
        int k = std::min ( m, n );
        vec tau ( k );
        vec work ( lwork );

        R = A;

        // perform workspace query for optimum lwork value
        int lwork_tmp = -1;
        dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp,
                  &info );
        if ( info == 0 ) {
                lwork = static_cast<int> ( work ( 0 ) );
                work.set_size ( lwork, false );
        }
        dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info );

        // construct R
        for ( int i = 0; i < m; i++ )
                for ( int j = 0; j < std::min ( i, n ); j++ )
                        R ( i, j ) = 0;

        return ( info == 0 );
}

//#endif
std::string num2str ( double d ) {
        char tmp[20];//that should do
        sprintf ( tmp, "%f", d );
        return std::string ( tmp );
};
std::string num2str ( int i ) {
        char tmp[10];//that should do
        sprintf ( tmp, "%d", i );
        return std::string ( tmp );
};

// digamma
// copied from C. Bonds' source
#include <math.h>
#define el 0.5772156649015329

double psi ( double x ) {
        double s, ps, xa, x2;
        int n, k;
        static double a[] = {
                -0.8333333333333e-01,
                0.83333333333333333e-02,
                -0.39682539682539683e-02,
                0.41666666666666667e-02,
                -0.75757575757575758e-02,
                0.21092796092796093e-01,
                -0.83333333333333333e-01,
                0.4432598039215686
        };

        xa = fabs ( x );
        s = 0.0;
        if ( ( x == ( int ) x ) && ( x <= 0.0 ) ) {
                ps = 1e308;
                return ps;
        }
        if ( xa == ( int ) xa ) {
                n = (int) xa;
                for ( k = 1; k < n; k++ ) {
                        s += 1.0 / k;
                }
                ps =  s - el;
        } else if ( ( xa + 0.5 ) == ( ( int ) ( xa + 0.5 ) ) ) {
                n = (int) (xa - 0.5);
                for ( k = 1; k <= n; k++ ) {
                        s += 1.0 / ( 2.0 * k - 1.0 );
                }
                ps = 2.0 * s - el - 1.386294361119891;
        } else {
                if ( xa < 10.0 ) {
                        n = 10 - ( int ) xa;
                        for ( k = 0; k < n; k++ ) {
                                s += 1.0 / ( xa + k );
                        }
                        xa += n;
                }
                x2 = 1.0 / ( xa * xa );
                ps = log ( xa ) - 0.5 / xa + x2 * ( ( ( ( ( ( ( a[7] * x2 + a[6] ) * x2 + a[5] ) * x2 +
                                                        a[4] ) * x2 + a[3] ) * x2 + a[2] ) * x2 + a[1] ) * x2 + a[0] );
                ps -= s;
        }
        if ( x < 0.0 )
                ps = ps - M_PI * std::cos ( M_PI * x ) / std::sin ( M_PI * x ) - 1.0 / x;
        return ps;
}

void triu ( mat &A ) {
        for ( int i = 1; i < A.rows(); i++ ) { // row cycle
                for ( int j = 0; (j < i) && (j<A.cols()); j++ ) {
                        A ( i, j ) = 0;
                }
        }
}

//! Storage of randun() internals
class RandunStorage {
        const int A;
        const int M;
        static double seed;
        static int counter;
public:
        RandunStorage() : A ( 16807 ), M ( 2147483647 ) {};
        //!set seed of the randun() generator
        void set_seed ( double seed0 ) {
                seed = seed0;
        }
        //! generate randun() sample
        double get() {
                long long tmp = (long long) (A * seed);
                tmp = tmp % M;
                seed = (double) tmp;
                counter++;
                return seed / M;
        }
};
static RandunStorage randun_global_storage;
double RandunStorage::seed = 1111111;
int RandunStorage::counter = 0;
double randun() {
        return randun_global_storage.get();
};
vec randun ( int n ) {
        vec res ( n );
        for ( int i = 0; i < n; i++ ) {
                res ( i ) = randun();
        };
        return res;
};
mat randun ( int n, int m ) {
        mat res ( n, m );
        for ( int i = 0; i < n*m; i++ ) {
                res ( i ) = randun();
        };
        return res;
};

ivec unique ( const ivec &in ) {
        ivec uniq ( 0 );
        int j = 0;
        bool found = false;
        for ( int i = 0; i < in.length(); i++ ) {
                found = false;
                j = 0;
                while ( ( !found ) && ( j < uniq.length() ) ) {
                        if ( in ( i ) == uniq ( j ) ) found = true;
                        j++;
                }
                if ( !found ) uniq = concat ( uniq, in ( i ) );
        }
        return uniq;
}

ivec unique_complement ( const ivec &in, const ivec &base ) {
        // almost a copy of unique
        ivec uniq ( 0 );
        int j = 0;
        bool found = false;
        for ( int i = 0; i < in.length(); i++ ) {
                found = false;
                j = 0;
                while ( ( !found ) && ( j < uniq.length() ) ) {
                        if ( in ( i ) == uniq ( j ) ) found = true;
                        j++;
                }
                j = 0;
                while ( ( !found ) && ( j < base.length() ) ) {
                        if ( in ( i ) == base ( j ) ) found = true;
                        j++;
                }
                if ( !found ) uniq = concat ( uniq, in ( i ) );
        }
        return uniq;
}

}