libflame  12600
Functions
FLA_Svv_2x2.c File Reference

(r12600)

Functions

FLA_Error FLA_Svv_2x2 (FLA_Obj alpha11, FLA_Obj alpha12, FLA_Obj alpha22, FLA_Obj sigma1, FLA_Obj sigma2, FLA_Obj gammaL, FLA_Obj sigmaL, FLA_Obj gammaR, FLA_Obj sigmaR)
FLA_Error FLA_Svv_2x2_ops (float *alpha11, float *alpha12, float *alpha22, float *sigma1, float *sigma2, float *gammaL, float *sigmaL, float *gammaR, float *sigmaR)
FLA_Error FLA_Svv_2x2_opd (double *alpha11, double *alpha12, double *alpha22, double *sigma1, double *sigma2, double *gammaL, double *sigmaL, double *gammaR, double *sigmaR)

Function Documentation

FLA_Error FLA_Svv_2x2 ( FLA_Obj  alpha11,
FLA_Obj  alpha12,
FLA_Obj  alpha22,
FLA_Obj  sigma1,
FLA_Obj  sigma2,
FLA_Obj  gammaL,
FLA_Obj  sigmaL,
FLA_Obj  gammaR,
FLA_Obj  sigmaR 
)

References FLA_Obj_datatype(), FLA_Svv_2x2_opd(), and FLA_Svv_2x2_ops().

{
    FLA_Datatype datatype;

    datatype = FLA_Obj_datatype( alpha11 );

    switch ( datatype )
    {
    case FLA_FLOAT:
    {
        float*  buff_alpha11 = FLA_FLOAT_PTR( alpha11 );
        float*  buff_alpha12 = FLA_FLOAT_PTR( alpha12 );
        float*  buff_alpha22 = FLA_FLOAT_PTR( alpha22 );
        float*  buff_sigma1  = FLA_FLOAT_PTR( sigma1 );
        float*  buff_sigma2  = FLA_FLOAT_PTR( sigma2 );
        float*  buff_gammaL  = FLA_FLOAT_PTR( gammaL );
        float*  buff_sigmaL  = FLA_FLOAT_PTR( sigmaL );
        float*  buff_gammaR  = FLA_FLOAT_PTR( gammaR );
        float*  buff_sigmaR  = FLA_FLOAT_PTR( sigmaR );

        FLA_Svv_2x2_ops( buff_alpha11,
                         buff_alpha12,
                         buff_alpha22,
                         buff_sigma1,
                         buff_sigma2,
                         buff_gammaL,
                         buff_sigmaL,
                         buff_gammaR,
                         buff_sigmaR );

        break;
    }

    case FLA_DOUBLE:
    {
        double* buff_alpha11 = FLA_DOUBLE_PTR( alpha11 );
        double* buff_alpha12 = FLA_DOUBLE_PTR( alpha12 );
        double* buff_alpha22 = FLA_DOUBLE_PTR( alpha22 );
        double* buff_sigma1  = FLA_DOUBLE_PTR( sigma1 );
        double* buff_sigma2  = FLA_DOUBLE_PTR( sigma2 );
        double* buff_gammaL  = FLA_DOUBLE_PTR( gammaL );
        double* buff_sigmaL  = FLA_DOUBLE_PTR( sigmaL );
        double* buff_gammaR  = FLA_DOUBLE_PTR( gammaR );
        double* buff_sigmaR  = FLA_DOUBLE_PTR( sigmaR );

        FLA_Svv_2x2_opd( buff_alpha11,
                         buff_alpha12,
                         buff_alpha22,
                         buff_sigma1,
                         buff_sigma2,
                         buff_gammaL,
                         buff_sigmaL,
                         buff_gammaR,
                         buff_sigmaR );

        break;
    }
    }

    return FLA_SUCCESS;
}
FLA_Error FLA_Svv_2x2_opd ( double *  alpha11,
double *  alpha12,
double *  alpha22,
double *  sigma1,
double *  sigma2,
double *  gammaL,
double *  sigmaL,
double *  gammaR,
double *  sigmaR 
)

References FLA_Mach_params_opd().

Referenced by FLA_Bsvd_iteracc_v_opd_var1(), and FLA_Svv_2x2().

{
    double zero = 0.0;
    double half = 0.5;
    double one  = 1.0;
    double two  = 2.0;
    double four = 4.0;

    double eps;

    double f, g, h;
    double clt, crt, slt, srt;
    double a, d, fa, ft, ga, gt, ha, ht, l;
    double m, mm, r, s, t, temp, tsign, tt;
    double ssmin, ssmax;
    double csl, snl;
    double csr, snr;

    int    gasmal, swap;
    int    pmax;

    f = *alpha11;
    g = *alpha12;
    h = *alpha22;

    eps = FLA_Mach_params_opd( FLA_MACH_EPS );

    ft = f;
    fa = fabs( f );
    ht = h;
    ha = fabs( h );

    // pmax points to the maximum absolute element of matrix.
    //   pmax = 1 if f largest in absolute values.
    //   pmax = 2 if g largest in absolute values.
    //   pmax = 3 if h largest in absolute values.

    pmax = 1;

    swap = ( ha > fa );
    if ( swap )
    {
        pmax = 3;

        temp = ft;
        ft = ht;
        ht = temp;

        temp = fa;
        fa = ha;
        ha = temp;
    }

    gt = g;
    ga = fabs( g );

    if ( ga == zero )
    {
        // Diagonal matrix case.

        ssmin = ha;
        ssmax = fa;
        clt   = one;
        slt   = zero;
        crt   = one;
        srt   = zero;
    }
    else
    {
        gasmal = TRUE;

        if ( ga > fa )
        {
            pmax = 2;

            if ( ( fa / ga ) < eps )
            {
                // Case of very large ga.

                gasmal = FALSE;

                ssmax  = ga;

                if ( ha > one ) ssmin = fa / ( ga / ha );
                else            ssmin = ( fa / ga ) * ha;

                clt = one;
                slt = ht / gt;
                crt = ft / gt;
                srt = one;
            }
        }

        if ( gasmal )
        {
            // Normal case.

            d = fa - ha;

            if ( d == fa ) l = one;
            else           l = d / fa;

            m = gt / ft;

            t = two - l;

            mm = m * m;
            tt = t * t;
            s = sqrt( tt + mm );

            if ( l == zero ) r = fabs( m );
            else             r = sqrt( l * l + mm );

            a = half * ( s + r );

            ssmin = ha / a;
            ssmax = fa * a;

            if ( mm == zero )
            {
                // Here, m is tiny.

                if ( l == zero ) t = signof( two, ft ) * signof( one, gt );
                else             t = gt / signof( d, ft ) + m / t;
            }
            else
            {
                t = ( m / ( s + t ) + m / ( r + l ) ) * ( one + a );
            }

            l = sqrt( t*t + four );
            crt = two / l;
            srt = t / l;
            clt = ( crt + srt * m ) / a;
            slt = ( ht / ft ) * srt / a;
        }
    }

    if ( swap )
    {
        csl = srt;
        snl = crt;
        csr = slt;
        snr = clt;
    }
    else
    {
        csl = clt;
        snl = slt;
        csr = crt;
        snr = srt;
    }


    // Correct the signs of ssmax and ssmin.

    if      ( pmax == 1 )
        tsign = signof( one, csr ) * signof( one, csl ) * signof( one, f );
    else if ( pmax == 2 )
        tsign = signof( one, snr ) * signof( one, csl ) * signof( one, g );
    else // if ( pmax == 3 )
        tsign = signof( one, snr ) * signof( one, snl ) * signof( one, h );

    ssmax = signof( ssmax, tsign );
    ssmin = signof( ssmin, tsign * signof( one, f ) * signof( one, h ) );

    // Save the output values.

    *sigma1 = ssmin;
    *sigma2 = ssmax;
    *gammaL = csl;
    *sigmaL = snl;
    *gammaR = csr;
    *sigmaR = snr;

    return FLA_SUCCESS;
}
FLA_Error FLA_Svv_2x2_ops ( float *  alpha11,
float *  alpha12,
float *  alpha22,
float *  sigma1,
float *  sigma2,
float *  gammaL,
float *  sigmaL,
float *  gammaR,
float *  sigmaR 
)

References FLA_Mach_params_ops().

Referenced by FLA_Bsvd_iteracc_v_ops_var1(), and FLA_Svv_2x2().

{
    float  zero = 0.0F;
    float  half = 0.5F;
    float  one  = 1.0F;
    float  two  = 2.0F;
    float  four = 4.0F;

    float  eps;

    float  f, g, h;
    float  clt, crt, slt, srt;
    float  a, d, fa, ft, ga, gt, ha, ht, l;
    float  m, mm, r, s, t, temp, tsign, tt;
    float  ssmin, ssmax;
    float  csl, snl;
    float  csr, snr;

    int    gasmal, swap;
    int    pmax;

    f = *alpha11;
    g = *alpha12;
    h = *alpha22;

    eps = FLA_Mach_params_ops( FLA_MACH_EPS );

    ft = f;
    fa = fabsf( f );
    ht = h;
    ha = fabsf( h );

    // pmax points to the maximum absolute element of matrix.
    //   pmax = 1 if f largest in absolute values.
    //   pmax = 2 if g largest in absolute values.
    //   pmax = 3 if h largest in absolute values.

    pmax = 1;

    swap = ( ha > fa );
    if ( swap )
    {
        pmax = 3;

        temp = ft;
        ft = ht;
        ht = temp;

        temp = fa;
        fa = ha;
        ha = temp;
    }

    gt = g;
    ga = fabsf( g );

    if ( ga == zero )
    {
        // Diagonal matrix case.

        ssmin = ha;
        ssmax = fa;
        clt   = one;
        slt   = zero;
        crt   = one;
        srt   = zero;
    }
    else
    {
        gasmal = TRUE;

        if ( ga > fa )
        {
            pmax = 2;

            if ( ( fa / ga ) < eps )
            {
                // Case of very large ga.

                gasmal = FALSE;

                ssmax  = ga;

                if ( ha > one ) ssmin = fa / ( ga / ha );
                else            ssmin = ( fa / ga ) * ha;

                clt = one;
                slt = ht / gt;
                crt = ft / gt;
                srt = one;
            }
        }

        if ( gasmal )
        {
            // Normal case.

            d = fa - ha;

            if ( d == fa ) l = one;
            else           l = d / fa;

            m = gt / ft;

            t = two - l;

            mm = m * m;
            tt = t * t;
            s = sqrtf( tt + mm );

            if ( l == zero ) r = fabsf( m );
            else             r = sqrtf( l * l + mm );

            a = half * ( s + r );

            ssmin = ha / a;
            ssmax = fa * a;

            if ( mm == zero )
            {
                // Here, m is tiny.

                if ( l == zero ) t = signof( two, ft ) * signof( one, gt );
                else             t = gt / signof( d, ft ) + m / t;
            }
            else
            {
                t = ( m / ( s + t ) + m / ( r + l ) ) * ( one + a );
            }

            l = sqrtf( t*t + four );
            crt = two / l;
            srt = t / l;
            clt = ( crt + srt * m ) / a;
            slt = ( ht / ft ) * srt / a;
        }
    }

    if ( swap )
    {
        csl = srt;
        snl = crt;
        csr = slt;
        snr = clt;
    }
    else
    {
        csl = clt;
        snl = slt;
        csr = crt;
        snr = srt;
    }


    // Correct the signs of ssmax and ssmin.

    if      ( pmax == 1 )
        tsign = signof( one, csr ) * signof( one, csl ) * signof( one, f );
    else if ( pmax == 2 )
        tsign = signof( one, snr ) * signof( one, csl ) * signof( one, g );
    else // if ( pmax == 3 )
        tsign = signof( one, snr ) * signof( one, snl ) * signof( one, h );

    ssmax = signof( ssmax, tsign );
    ssmin = signof( ssmin, tsign * signof( one, f ) * signof( one, h ) );

    // Save the output values.

    *sigma1 = ssmin;
    *sigma2 = ssmax;
    *gammaL = csl;
    *sigmaL = snl;
    *gammaR = csr;
    *sigmaR = snr;

    return FLA_SUCCESS;
}