root/library/bdm/itpp_ext.cpp @ 679

//
// 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);
        }
}

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;
}

//#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 = xa;
                for (k = 1; k < n; k++) {
                        s += 1.0 / k;
                }
                ps =  s - el;
        } else if ( (xa + 0.5) == ( (int) (xa + 0.5))) {
                n = 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 (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 = A * seed;
                        tmp = tmp % M;
                        seed = 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;
}

}