source: cpp/frams/model/similarity/SVD/lapack.cpp @ 377

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/*
 * AutoBuffer from https://github.com/Itseez/opencv/blob/master/modules/core/include/opencv2/core/utility.hpp
 * VBLAS, JacobiSVDImpl_ from https://github.com/Itseez/opencv/blob/master/modules/core/src/lapack.cpp
 * changes:
 * - "RNG rng(0x12345678)" replaced with "srand(time(NULL))"
 * - "rng.next()" replaced with "rand()"
 * MK, 04.2015:
 * - commented out "srand(time(NULL))" - this line would affect everything else that uses the standard global r.n.g., and would introduce uncontrolled indeterminism
 */
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <limits>
#include <cfloat>
#include <assert.h>
#include "lapack.h"
#include <stdlib.h> //rand(), embarcadero
#include <math.h> //hypot(), embarcadero

typedef unsigned char uchar;

#if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700
#pragma float_control(precise, on)
#endif

template<typename _Tp, size_t fixed_size = 1024 / sizeof (_Tp) + 8 > class AutoBuffer
{
public:
    typedef _Tp value_type;

    //! the default constructor
    AutoBuffer();
    //! constructor taking the real buffer size
    AutoBuffer(size_t _size);

    //! the copy constructor
    AutoBuffer(const AutoBuffer<_Tp, fixed_size>& buf);
    //! the assignment operator
    AutoBuffer<_Tp, fixed_size>& operator=(const AutoBuffer<_Tp, fixed_size>& buf);

    //! destructor. calls deallocate()
    ~AutoBuffer();

    //! allocates the new buffer of size _size. if the _size is small enough, stack-allocated buffer is used
    void allocate(size_t _size);
    //! deallocates the buffer if it was dynamically allocated
    void deallocate();
    //! resizes the buffer and preserves the content
    void resize(size_t _size);
    //! returns the current buffer size
    size_t size() const;
    //! returns pointer to the real buffer, stack-allocated or head-allocated
    operator _Tp* ();
    //! returns read-only pointer to the real buffer, stack-allocated or head-allocated
    operator const _Tp* () const;

protected:
    //! pointer to the real buffer, can point to buf if the buffer is small enough
    _Tp* ptr;
    //! size of the real buffer
    size_t sz;
    //! pre-allocated buffer. At least 1 element to confirm C++ standard reqirements
    _Tp buf[(fixed_size > 0) ? fixed_size : 1];
};

/////////////////////////////// AutoBuffer implementation ////////////////////////////////////////

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::AutoBuffer()
{
    ptr = buf;
    sz = fixed_size;
}

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::AutoBuffer(size_t _size)
{
    ptr = buf;
    sz = fixed_size;
    allocate(_size);
}

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::AutoBuffer(const AutoBuffer<_Tp, fixed_size>& abuf)
{
    ptr = buf;
    sz = fixed_size;
    allocate(abuf.size());
    for (size_t i = 0; i < sz; i++)
        ptr[i] = abuf.ptr[i];
}

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>&
AutoBuffer<_Tp, fixed_size>::operator=(const AutoBuffer<_Tp, fixed_size>& abuf)
{
    if (this != &abuf)
    {
        deallocate();
        allocate(abuf.size());
        for (size_t i = 0; i < sz; i++)
            ptr[i] = abuf.ptr[i];
    }
    return *this;
}

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::~AutoBuffer()
{
    deallocate();
}

template<typename _Tp, size_t fixed_size> inline void
AutoBuffer<_Tp, fixed_size>::allocate(size_t _size)
{
    if (_size <= sz)
    {
        sz = _size;
        return;
    }
    deallocate();
    if (_size > fixed_size)
    {
        ptr = new _Tp[_size];
        sz = _size;
    }
}

template<typename _Tp, size_t fixed_size> inline void
AutoBuffer<_Tp, fixed_size>::deallocate()
{
    if (ptr != buf)
    {
        delete[] ptr;
        ptr = buf;
        sz = fixed_size;
    }
}

template<typename _Tp, size_t fixed_size> inline void
AutoBuffer<_Tp, fixed_size>::resize(size_t _size)
{
    if (_size <= sz)
    {
        sz = _size;
        return;
    }
    //size_t i, prevsize = sz, minsize = MIN(prevsize, _size);
    size_t i, prevsize = sz, minsize = prevsize < _size ? prevsize : _size;
    _Tp* prevptr = ptr;

    ptr = _size > fixed_size ? new _Tp[_size] : buf;
    sz = _size;

    if (ptr != prevptr)
        for (i = 0; i < minsize; i++)
            ptr[i] = prevptr[i];
    for (i = prevsize; i < _size; i++)
        ptr[i] = _Tp();

    if (prevptr != buf)
        delete[] prevptr;
}

template<typename _Tp, size_t fixed_size> inline size_t
AutoBuffer<_Tp, fixed_size>::size() const
{
    return sz;
}

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::operator _Tp* ()
{
    return ptr;
}

template<typename _Tp, size_t fixed_size> inline
AutoBuffer<_Tp, fixed_size>::operator const _Tp* () const
{
    return ptr;
}

template<typename T> struct VBLAS
{

    int dot(const T*, const T*, int, T*) const
    {
        return 0;
    }

    int givens(T*, T*, int, T, T) const
    {
        return 0;
    }

    int givensx(T*, T*, int, T, T, T*, T*) const
    {
        return 0;
    }
};

template<typename _Tp> void
JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep,
               int m, int n, int n1, double minval, _Tp eps)
{
    VBLAS<_Tp> vblas;
    AutoBuffer<double> Wbuf(n);
    double* W = Wbuf;
    int i, j, k, iter, max_iter = std::max(m, 30);
    _Tp c, s;
    double sd;
    astep /= sizeof (At[0]);
    vstep /= sizeof (Vt[0]);

    for (i = 0; i < n; i++)
    {
        for (k = 0, sd = 0; k < m; k++)
        {
            _Tp t = At[i * astep + k];
            sd += (double) t*t;
        }
        W[i] = sd;

        if (Vt)
        {
            for (k = 0; k < n; k++)
                Vt[i * vstep + k] = 0;
            Vt[i * vstep + i] = 1;
        }
    }

    for (iter = 0; iter < max_iter; iter++)
    {
        bool changed = false;

        for (i = 0; i < n - 1; i++)
            for (j = i + 1; j < n; j++)
            {
                _Tp *Ai = At + i*astep, *Aj = At + j*astep;
                double a = W[i], p = 0, b = W[j];

                for (k = 0; k < m; k++)
                    p += (double) Ai[k] * Aj[k];

                if (std::abs(p) <= eps * std::sqrt((double) a * b))
                    continue;

                p *= 2;
                double beta = a - b, gamma = hypot((double) p, beta);
                if (beta < 0)
                {
                    double delta = (gamma - beta)*0.5;
                    s = (_Tp) std::sqrt(delta / gamma);
                    c = (_Tp) (p / (gamma * s * 2));
                }
                else
                {
                    c = (_Tp) std::sqrt((gamma + beta) / (gamma * 2));
                    s = (_Tp) (p / (gamma * c * 2));
                }

                a = b = 0;
                for (k = 0; k < m; k++)
                {
                    _Tp t0 = c * Ai[k] + s * Aj[k];
                    _Tp t1 = -s * Ai[k] + c * Aj[k];
                    Ai[k] = t0;
                    Aj[k] = t1;

                    a += (double) t0*t0;
                    b += (double) t1*t1;
                }
                W[i] = a;
                W[j] = b;

                changed = true;

                if (Vt)
                {
                    _Tp *Vi = Vt + i*vstep, *Vj = Vt + j*vstep;
                    k = vblas.givens(Vi, Vj, n, c, s);

                    for (; k < n; k++)
                    {
                        _Tp t0 = c * Vi[k] + s * Vj[k];
                        _Tp t1 = -s * Vi[k] + c * Vj[k];
                        Vi[k] = t0;
                        Vj[k] = t1;
                    }
                }
            }
        if (!changed)
            break;
    }

    for (i = 0; i < n; i++)
    {
        for (k = 0, sd = 0; k < m; k++)
        {
            _Tp t = At[i * astep + k];
            sd += (double) t*t;
        }
        W[i] = std::sqrt(sd);
    }

    for (i = 0; i < n - 1; i++)
    {
        j = i;
        for (k = i + 1; k < n; k++)
        {
            if (W[j] < W[k])
                j = k;
        }
        if (i != j)
        {
            std::swap(W[i], W[j]);
            if (Vt)
            {
                for (k = 0; k < m; k++)
                    std::swap(At[i * astep + k], At[j * astep + k]);

                for (k = 0; k < n; k++)
                    std::swap(Vt[i * vstep + k], Vt[j * vstep + k]);
            }
        }
    }

    for (i = 0; i < n; i++)
        _W[i] = (_Tp) W[i];

    if (!Vt)
        return;

    //srand(time(NULL));
    for (i = 0; i < n1; i++)
    {
        sd = i < n ? W[i] : 0;

        while (sd <= minval)
        {
            // if we got a zero singular value, then in order to get the corresponding left singular vector
            // we generate a random vector, project it to the previously computed left singular vectors,
            // subtract the projection and normalize the difference.
            const _Tp val0 = (_Tp) (1. / m);
            for (k = 0; k < m; k++)
            {
                _Tp val = (rand() & 256) != 0 ? val0 : -val0;
                At[i * astep + k] = val;
            }
            for (iter = 0; iter < 2; iter++)
            {
                for (j = 0; j < i; j++)
                {
                    sd = 0;
                    for (k = 0; k < m; k++)
                        sd += At[i * astep + k] * At[j * astep + k];
                    _Tp asum = 0;
                    for (k = 0; k < m; k++)
                    {
                        _Tp t = (_Tp) (At[i * astep + k] - sd * At[j * astep + k]);
                        At[i * astep + k] = t;
                        asum += std::abs(t);
                    }
                    asum = asum ? 1 / asum : 0;
                    for (k = 0; k < m; k++)
                        At[i * astep + k] *= asum;
                }
            }
            sd = 0;
            for (k = 0; k < m; k++)
            {
                _Tp t = At[i * astep + k];
                sd += (double) t*t;
            }
            sd = std::sqrt(sd);
        }

        s = (_Tp) (1 / sd);
        for (k = 0; k < m; k++)
            At[i * astep + k] *= s;
    }
}

void Lapack::JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1 = -1)
{
    JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, DBL_MIN, DBL_EPSILON * 10);
}