FLA_Bsvd_v_opt_var2.c File Reference

(r)

Functions
FLA_Error	FLA_Bsvd_v_opt_var2 (dim_t n_iter_max, FLA_Obj d, FLA_Obj e, FLA_Obj G, FLA_Obj H, FLA_Obj RG, FLA_Obj RH, FLA_Obj W, FLA_Obj U, FLA_Obj V, dim_t b_alg)
FLA_Error	FLA_Bsvd_v_ops_var2 (int min_m_n, int m_U, int m_V, int n_GH, int n_iter_max, float *buff_d, int inc_d, float *buff_e, int inc_e, scomplex *buff_G, int rs_G, int cs_G, scomplex *buff_H, int rs_H, int cs_H, float *buff_RG, int rs_RG, int cs_RG, float *buff_RH, int rs_RH, int cs_RH, float *buff_W, int rs_W, int cs_W, float *buff_U, int rs_U, int cs_U, float *buff_V, int rs_V, int cs_V, int b_alg)
FLA_Error	FLA_Bsvd_v_opd_var2 (int min_m_n, int m_U, int m_V, int n_GH, int n_iter_max, double *buff_d, int inc_d, double *buff_e, int inc_e, dcomplex *buff_G, int rs_G, int cs_G, dcomplex *buff_H, int rs_H, int cs_H, double *buff_RG, int rs_RG, int cs_RG, double *buff_RH, int rs_RH, int cs_RH, double *buff_W, int rs_W, int cs_W, double *buff_U, int rs_U, int cs_U, double *buff_V, int rs_V, int cs_V, int b_alg)
FLA_Error	FLA_Bsvd_v_opc_var2 (int min_m_n, int m_U, int m_V, int n_GH, int n_iter_max, float *buff_d, int inc_d, float *buff_e, int inc_e, scomplex *buff_G, int rs_G, int cs_G, scomplex *buff_H, int rs_H, int cs_H, float *buff_RG, int rs_RG, int cs_RG, float *buff_RH, int rs_RH, int cs_RH, scomplex *buff_W, int rs_W, int cs_W, scomplex *buff_U, int rs_U, int cs_U, scomplex *buff_V, int rs_V, int cs_V, int b_alg)
FLA_Error	FLA_Bsvd_v_opz_var2 (int min_m_n, int m_U, int m_V, int n_GH, int n_iter_max, double *buff_d, int inc_d, double *buff_e, int inc_e, dcomplex *buff_G, int rs_G, int cs_G, dcomplex *buff_H, int rs_H, int cs_H, double *buff_RG, int rs_RG, int cs_RG, double *buff_RH, int rs_RH, int cs_RH, dcomplex *buff_W, int rs_W, int cs_W, dcomplex *buff_U, int rs_U, int cs_U, dcomplex *buff_V, int rs_V, int cs_V, int b_alg)

Function Documentation

FLA_Bsvd_v_opc_var2()

FLA_Error FLA_Bsvd_v_opc_var2	(	int	min_m_n,
		int	m_U,
		int	m_V,
		int	n_GH,
		int	n_iter_max,
		float *	buff_d,
		int	inc_d,
		float *	buff_e,
		int	inc_e,
		scomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		scomplex *	buff_H,
		int	rs_H,
		int	cs_H,
		float *	buff_RG,
		int	rs_RG,
		int	cs_RG,
		float *	buff_RH,
		int	rs_RH,
		int	cs_RH,
		scomplex *	buff_W,
		int	rs_W,
		int	cs_W,
		scomplex *	buff_U,
		int	rs_U,
		int	cs_U,
		scomplex *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg
	)

{
    FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
 
    return FLA_SUCCESS;
}

References i.

Referenced by FLA_Bsvd_v_opt_var2().

FLA_Bsvd_v_opd_var2()

FLA_Error FLA_Bsvd_v_opd_var2	(	int	min_m_n,
		int	m_U,
		int	m_V,
		int	n_GH,
		int	n_iter_max,
		double *	buff_d,
		int	inc_d,
		double *	buff_e,
		int	inc_e,
		dcomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		dcomplex *	buff_H,
		int	rs_H,
		int	cs_H,
		double *	buff_RG,
		int	rs_RG,
		int	cs_RG,
		double *	buff_RH,
		int	rs_RH,
		int	cs_RH,
		double *	buff_W,
		int	rs_W,
		int	cs_W,
		double *	buff_U,
		int	rs_U,
		int	cs_U,
		double *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg
	)

{
    dcomplex  one        = bl1_z1();
    double    rone       = bl1_d1();
    double    rzero      = bl1_d0();
 
    int       maxitr     = 6;
 
    double    eps;
    double    tolmul;
    double    tol;
    double    thresh;
 
    dcomplex* G;
    dcomplex* H;
    double*   d1;
    double*   e1;
    int       r_val;
    int       done;
    int       m_GH_sweep_max;
    int       ij_begin;
    int       ijTL, ijBR;
    int       m_A11;
    int       n_iter_perf;
    int       n_UV_apply;
    int       total_deflations;
    int       n_deflations;
    int       n_iter_prev;
    int       n_iter_perf_sweep_max;
 
    // Compute some convergence constants.
    eps    = FLA_Mach_params_opd( FLA_MACH_EPS );
    tolmul = max( 10.0, min( 100.0, pow( eps, -0.125 ) ) );
    FLA_Bsvd_compute_tol_thresh_opd( min_m_n,
                                     tolmul,
                                     maxitr,
                                     buff_d, inc_d,
                                     buff_e, inc_e,
                                     &tol,
                                     &thresh );
 
    // Initialize our completion flag.
    done = FALSE;
 
    // Initialize a counter that holds the maximum number of rows of G
    // and H that we would need to initialize for the next sweep.
    m_GH_sweep_max = min_m_n - 1;
 
    // Initialize a counter for the total number of iterations performed.
    n_iter_prev = 0;
 
    // Initialize RG and RH to identity.
    bl1_dident( min_m_n,
                buff_RG, rs_RG, cs_RG );
    bl1_dident( min_m_n,
                buff_RH, rs_RH, cs_RH );
 
    // Iterate until the matrix has completely deflated.
    for ( total_deflations = 0; done != TRUE; )
    {
 
        // Initialize G and H to contain only identity rotations.
        bl1_zsetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_G, rs_G, cs_G );
        bl1_zsetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_H, rs_H, cs_H );
 
        // Keep track of the maximum number of iterations performed in the
        // current sweep. This is used when applying the sweep's Givens
        // rotations.
        n_iter_perf_sweep_max = 0;
 
        // Perform a sweep: Move through the matrix and perform a bidiagonal
        // SVD on each non-zero submatrix that is encountered. During the
        // first time through, ijTL will be 0 and ijBR will be min_m_n - 1.
        for ( ij_begin = 0; ij_begin < min_m_n;  )
        {
 
#ifdef PRINTF
if ( ij_begin == 0 )
printf( "FLA_Bsvd_v_opd_var2: beginning new sweep (ij_begin = %d)\n", ij_begin );
#endif
 
            // Search for the first submatrix along the diagonal that is
            // bounded by zeroes (or endpoints of the matrix). If no
            // submatrix is found (ie: if the entire superdiagonal is zero
            // then FLA_FAILURE is returned. This function also inspects
            // superdiagonal elements for proximity to zero. If a given
            // element is close enough to zero, then it is deemed
            // converged and manually set to zero.
            r_val = FLA_Bsvd_find_submatrix_opd( min_m_n,
                                                 ij_begin,
                                                 buff_d, inc_d,
                                                 buff_e, inc_e,
                                                 &ijTL,
                                                 &ijBR );
 
            // Verify that a submatrix was found. If one was not found,
            // then we are done with the current sweep. Furthermore, if
            // a submatrix was not found AND we began our search at the
            // beginning of the matrix (ie: ij_begin == 0), then the
            // matrix has completely deflated and so we are done with
            // Francis step iteration.
            if ( r_val == FLA_FAILURE )
            {
                if ( ij_begin == 0 )
                {
#ifdef PRINTF
printf( "FLA_Bsvd_v_opd_var2: superdiagonal is completely zero.\n" );
printf( "FLA_Bsvd_v_opd_var2: Francis iteration is done!\n" );
#endif
                    done = TRUE;
                }
 
                // Break out of the current sweep so we can apply the last
                // remaining Givens rotations.
                break;
            }
 
            // If we got this far, then:
            //   (a) ijTL refers to the index of the first non-zero
            //       superdiagonal along the diagonal, and
            //   (b) ijBR refers to either:
            //       - the first zero element that occurs after ijTL, or
            //       - the the last diagonal element.
            // Note that ijTL and ijBR also correspond to the first and
            // last diagonal elements of the submatrix of interest. Thus,
            // we may compute the dimension of this submatrix as:
            m_A11 = ijBR - ijTL + 1;
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opd_var2: ij_begin = %d\n", ij_begin );
printf( "FLA_Bsvd_v_opd_var2: ijTL     = %d\n", ijTL );
printf( "FLA_Bsvd_v_opd_var2: ijBR     = %d\n", ijBR );
printf( "FLA_Bsvd_v_opd_var2: m_A11    = %d\n", m_A11 );
#endif
 
            // Adjust ij_begin, which gets us ready for the next submatrix
            // search in the current sweep.
            ij_begin = ijBR + 1;
 
            // Index to the submatrices upon which we will operate.
            d1 = buff_d + ijTL * inc_d;
            e1 = buff_e + ijTL * inc_e;
            G  = buff_G + ijTL * rs_G;
            H  = buff_H + ijTL * rs_H;
 
            // Search for a batch of singular values, recursing on deflated
            // subproblems whenever possible. A new singular value search is
            // performed as long as
            //   (a) there is still matrix left to operate on, and
            //   (b) the number of iterations performed in this batch is
            //       less than n_G.
            // If/when either of the two above conditions fails to hold,
            // the function returns.
            n_deflations = FLA_Bsvd_iteracc_v_opd_var1( m_A11,
                                                        n_GH,
                                                        ijTL,
                                                        tol,
                                                        thresh,
                                                        d1, inc_d,
                                                        e1, inc_e,
                                                        G,  rs_G, cs_G,
                                                        H,  rs_H, cs_H,
                                                        &n_iter_perf );
 
            // Record the number of deflations that occurred.
            total_deflations += n_deflations;
 
            // Update the maximum number of iterations performed in the
            // current sweep.
            n_iter_perf_sweep_max = max( n_iter_perf_sweep_max, n_iter_perf );
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opd_var2: deflations observed       = %d\n", n_deflations );
printf( "FLA_Bsvd_v_opd_var2: total deflations observed = %d\n", total_deflations );
printf( "FLA_Bsvd_v_opd_var2: num iterations performed  = %d\n", n_iter_perf );
#endif
 
            // Store the most recent value of ijBR in m_G_sweep_max.
            // When the sweep is done, this value will contain the minimum
            // number of rows of G and H we can apply and safely include all
            // non-identity rotations that were computed during the
            // singular value searches.
            m_GH_sweep_max = ijBR;
 
        }
 
        // The sweep is complete. Now we must apply the Givens rotations
        // that were accumulated during the sweep.
 
        // Recall that the number of columns of U and V to which we apply
        // rotations is one more than the number of rotations.
        n_UV_apply = m_GH_sweep_max + 1;
 
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opd_var2: applying %d sets of Givens rotations\n", n_iter_perf_sweep_max );
printf( "FLA_Bsvd_v_opd_var2: m_U = %d\n", m_U );
printf( "FLA_Bsvd_v_opd_var2: m_V = %d\n", m_V );
printf( "FLA_Bsvd_v_opd_var2: napp= %d\n", n_UV_apply );
#endif
 
        // Apply the Givens rotations. Note that we only apply k sets of
        // rotations, where k = n_iter_perf_sweep_max. Also note that we only
        // apply to n_UV_apply columns of U and V since this is the most we
        // need to touch given the most recent value stored to m_GH_sweep_max.
        //FLA_Apply_G_rf_bld_var5b( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var9b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var6b( n_iter_perf_sweep_max,
                                  min_m_n,
                                  n_UV_apply,
                                  n_iter_prev,
                                  buff_G,  rs_G,  cs_G,
                                  buff_RG, rs_RG, cs_RG,
                                  b_alg );
        //FLA_Apply_G_rf_bld_var5b( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var9b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var6b( n_iter_perf_sweep_max,
                                  min_m_n,
                                  n_UV_apply,
                                  n_iter_prev,
                                  buff_H,  rs_H,  cs_H,
                                  buff_RH, rs_RH, cs_RH,
                                  b_alg );
 
        // Increment the total number of iterations previously performed.
        n_iter_prev += n_iter_perf_sweep_max;
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opd_var2: total number of iterations performed: %d\n", n_iter_prev );
#endif
    }
 
    // Copy the contents of Q to temporary storage.
    bl1_dcopymt( BLIS1_NO_TRANSPOSE,
                 m_U,
                 m_V,
                 buff_U, rs_U, cs_U,
                 buff_W, rs_W, cs_W );
// W needs to be max_m_n-by-min_m_n!!!!!!!!!!!!!!!
 
    // Multiply U by R, overwriting U.
    bl1_dgemm( BLIS1_NO_TRANSPOSE,
               BLIS1_NO_TRANSPOSE,
               m_U,
               m_V,
               m_V,
               &rone,
               ( double* )buff_W,  rs_W,  cs_W,
                          buff_RG, rs_RG, cs_RG,
               &rzero,
               ( double* )buff_U,  rs_U,  cs_U );
 
    bl1_dcopymt( BLIS1_NO_TRANSPOSE,
                 m_V,
                 m_V,
                 buff_V, rs_V, cs_V,
                 buff_W, rs_W, cs_W );
 
    // Multiply V by R, overwriting V.
    bl1_dgemm( BLIS1_NO_TRANSPOSE,
               BLIS1_NO_TRANSPOSE,
               m_V,
               m_V,
               m_V,
               &rone,
               ( double* )buff_W,  rs_W,  cs_W,
                          buff_RH, rs_RH, cs_RH,
               &rzero,
               ( double* )buff_V,  rs_V,  cs_V );
 
    // Make all the singular values positive.
    {
        int    i;
        double minus_one = bl1_dm1();
 
        for ( i = 0; i < min_m_n; ++i )
        {
            if ( buff_d[ (i  )*inc_d ] < rzero )
            {
                buff_d[ (i  )*inc_d ] = -buff_d[ (i  )*inc_d ];
                
                // Scale the right singular vectors.
                bl1_dscalv( BLIS1_NO_CONJUGATE,
                            m_V,
                            &minus_one,
                            buff_V + (i  )*cs_V, rs_V );
            }
        }
    }
 
    return n_iter_prev;
}

References bl1_d0(), bl1_d1(), bl1_dcopymt(), bl1_dgemm(), bl1_dident(), bl1_dm1(), bl1_dscalv(), bl1_z1(), bl1_zsetm(), BLIS1_NO_CONJUGATE, BLIS1_NO_TRANSPOSE, FLA_Apply_G_rf_bld_var3b(), FLA_Bsvd_compute_tol_thresh_opd(), FLA_Bsvd_find_submatrix_opd(), FLA_Bsvd_iteracc_v_opd_var1(), FLA_Mach_params_opd(), and i.

Referenced by FLA_Bsvd_v_opt_var2().

FLA_Bsvd_v_ops_var2()

FLA_Error FLA_Bsvd_v_ops_var2	(	int	min_m_n,
		int	m_U,
		int	m_V,
		int	n_GH,
		int	n_iter_max,
		float *	buff_d,
		int	inc_d,
		float *	buff_e,
		int	inc_e,
		scomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		scomplex *	buff_H,
		int	rs_H,
		int	cs_H,
		float *	buff_RG,
		int	rs_RG,
		int	cs_RG,
		float *	buff_RH,
		int	rs_RH,
		int	cs_RH,
		float *	buff_W,
		int	rs_W,
		int	cs_W,
		float *	buff_U,
		int	rs_U,
		int	cs_U,
		float *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg
	)

{
    FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
 
    return FLA_SUCCESS;
}

References i.

Referenced by FLA_Bsvd_v_opt_var2().

FLA_Bsvd_v_opt_var2()

FLA_Error FLA_Bsvd_v_opt_var2	(	dim_t	n_iter_max,
		FLA_Obj	d,
		FLA_Obj	e,
		FLA_Obj	G,
		FLA_Obj	H,
		FLA_Obj	RG,
		FLA_Obj	RH,
		FLA_Obj	W,
		FLA_Obj	U,
		FLA_Obj	V,
		dim_t	b_alg
	)

{
    FLA_Error    r_val = FLA_SUCCESS;
    FLA_Datatype datatype;
    int          m_U, m_V, n_GH;
    int          inc_d;
    int          inc_e;
    int          rs_G, cs_G;
    int          rs_H, cs_H;
    int          rs_RG, cs_RG;
    int          rs_RH, cs_RH;
    int          rs_W, cs_W;
    int          rs_U, cs_U;
    int          rs_V, cs_V;
 
    datatype = FLA_Obj_datatype( U );
 
    m_U        = FLA_Obj_length( U );
    m_V        = FLA_Obj_length( V );
    n_GH       = FLA_Obj_width( G );
 
    inc_d      = FLA_Obj_vector_inc( d );
    inc_e      = FLA_Obj_vector_inc( e );
    
    rs_G       = FLA_Obj_row_stride( G );
    cs_G       = FLA_Obj_col_stride( G );
 
    rs_H       = FLA_Obj_row_stride( H );
    cs_H       = FLA_Obj_col_stride( H );
 
    rs_RG      = FLA_Obj_row_stride( RG );
    cs_RG      = FLA_Obj_col_stride( RG );
 
    rs_RH      = FLA_Obj_row_stride( RH );
    cs_RH      = FLA_Obj_col_stride( RH );
 
    rs_W       = FLA_Obj_row_stride( W );
    cs_W       = FLA_Obj_col_stride( W );
 
    rs_U       = FLA_Obj_row_stride( U );
    cs_U       = FLA_Obj_col_stride( U );
 
    rs_V       = FLA_Obj_row_stride( V );
    cs_V       = FLA_Obj_col_stride( V );
 
 
    switch ( datatype )
    {
        case FLA_FLOAT:
        {
            float*    buff_d = FLA_FLOAT_PTR( d );
            float*    buff_e = FLA_FLOAT_PTR( e );
            scomplex* buff_G = FLA_COMPLEX_PTR( G );
            scomplex* buff_H = FLA_COMPLEX_PTR( H );
            float*    buff_RG = FLA_FLOAT_PTR( RG );
            float*    buff_RH = FLA_FLOAT_PTR( RH );
            float*    buff_W = FLA_FLOAT_PTR( W );
            float*    buff_U = FLA_FLOAT_PTR( U );
            float*    buff_V = FLA_FLOAT_PTR( V );
 
            r_val = FLA_Bsvd_v_ops_var2( min( m_U, m_V ),
                                                     m_U,
                                         m_V,
                                         n_GH,
                                         n_iter_max,
                                         buff_d, inc_d,
                                         buff_e, inc_e,
                                         buff_G, rs_G, cs_G,
                                         buff_H, rs_H, cs_H,
                                         buff_RG, rs_RG, cs_RG,
                                         buff_RH, rs_RH, cs_RH,
                                         buff_W, rs_W, cs_W,
                                         buff_U, rs_U, cs_U,
                                         buff_V, rs_V, cs_V,
                                         b_alg );
 
            break;
        }
 
        case FLA_DOUBLE:
        {
            double*   buff_d = FLA_DOUBLE_PTR( d );
            double*   buff_e = FLA_DOUBLE_PTR( e );
            dcomplex* buff_G = FLA_DOUBLE_COMPLEX_PTR( G );
            dcomplex* buff_H = FLA_DOUBLE_COMPLEX_PTR( H );
            double*   buff_RG = FLA_DOUBLE_PTR( RG );
            double*   buff_RH = FLA_DOUBLE_PTR( RH );
            double*   buff_W = FLA_DOUBLE_PTR( W );
            double*   buff_U = FLA_DOUBLE_PTR( U );
            double*   buff_V = FLA_DOUBLE_PTR( V );
 
            r_val = FLA_Bsvd_v_opd_var2( min( m_U, m_V ),
                                                     m_U,
                                         m_V,
                                         n_GH,
                                         n_iter_max,
                                         buff_d, inc_d,
                                         buff_e, inc_e,
                                         buff_G, rs_G, cs_G,
                                         buff_H, rs_H, cs_H,
                                         buff_RG, rs_RG, cs_RG,
                                         buff_RH, rs_RH, cs_RH,
                                         buff_W, rs_W, cs_W,
                                         buff_U, rs_U, cs_U,
                                         buff_V, rs_V, cs_V,
                                         b_alg );
 
            break;
        }
 
        case FLA_COMPLEX:
        {
            float*    buff_d = FLA_FLOAT_PTR( d );
            float*    buff_e = FLA_FLOAT_PTR( e );
            scomplex* buff_G = FLA_COMPLEX_PTR( G );
            scomplex* buff_H = FLA_COMPLEX_PTR( H );
            float*    buff_RG = FLA_FLOAT_PTR( RG );
            float*    buff_RH = FLA_FLOAT_PTR( RH );
            scomplex* buff_W = FLA_COMPLEX_PTR( W );
            scomplex* buff_U = FLA_COMPLEX_PTR( U );
            scomplex* buff_V = FLA_COMPLEX_PTR( V );
 
            r_val = FLA_Bsvd_v_opc_var2( min( m_U, m_V ),
                                                     m_U,
                                         m_V,
                                         n_GH,
                                         n_iter_max,
                                         buff_d, inc_d,
                                         buff_e, inc_e,
                                         buff_G, rs_G, cs_G,
                                         buff_H, rs_H, cs_H,
                                         buff_RG, rs_RG, cs_RG,
                                         buff_RH, rs_RH, cs_RH,
                                         buff_W, rs_W, cs_W,
                                         buff_U, rs_U, cs_U,
                                         buff_V, rs_V, cs_V,
                                         b_alg );
 
            break;
        }
 
        case FLA_DOUBLE_COMPLEX:
        {
            double*   buff_d = FLA_DOUBLE_PTR( d );
            double*   buff_e = FLA_DOUBLE_PTR( e );
            dcomplex* buff_G = FLA_DOUBLE_COMPLEX_PTR( G );
            dcomplex* buff_H = FLA_DOUBLE_COMPLEX_PTR( H );
            double*   buff_RG = FLA_DOUBLE_PTR( RG );
            double*   buff_RH = FLA_DOUBLE_PTR( RH );
            dcomplex* buff_W = FLA_DOUBLE_COMPLEX_PTR( W );
            dcomplex* buff_U = FLA_DOUBLE_COMPLEX_PTR( U );
            dcomplex* buff_V = FLA_DOUBLE_COMPLEX_PTR( V );
 
            r_val = FLA_Bsvd_v_opz_var2( min( m_U, m_V ),
                                                     m_U,
                                         m_V,
                                         n_GH,
                                         n_iter_max,
                                         buff_d, inc_d,
                                         buff_e, inc_e,
                                         buff_G, rs_G, cs_G,
                                         buff_H, rs_H, cs_H,
                                         buff_RG, rs_RG, cs_RG,
                                         buff_RH, rs_RH, cs_RH,
                                         buff_W, rs_W, cs_W,
                                         buff_U, rs_U, cs_U,
                                         buff_V, rs_V, cs_V,
                                         b_alg );
 
            break;
        }
    }
 
    return r_val;
}

References FLA_Bsvd_v_opc_var2(), FLA_Bsvd_v_opd_var2(), FLA_Bsvd_v_ops_var2(), FLA_Bsvd_v_opz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), FLA_Obj_width(), and i.

Referenced by FLA_Svd_uv_unb_var2().

FLA_Bsvd_v_opz_var2()

FLA_Error FLA_Bsvd_v_opz_var2	(	int	min_m_n,
		int	m_U,
		int	m_V,
		int	n_GH,
		int	n_iter_max,
		double *	buff_d,
		int	inc_d,
		double *	buff_e,
		int	inc_e,
		dcomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		dcomplex *	buff_H,
		int	rs_H,
		int	cs_H,
		double *	buff_RG,
		int	rs_RG,
		int	cs_RG,
		double *	buff_RH,
		int	rs_RH,
		int	cs_RH,
		dcomplex *	buff_W,
		int	rs_W,
		int	cs_W,
		dcomplex *	buff_U,
		int	rs_U,
		int	cs_U,
		dcomplex *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg
	)

{
    dcomplex  one        = bl1_z1();
    double    rone       = bl1_d1();
    double    rzero      = bl1_d0();
 
    int       maxitr     = 6;
 
    double    eps;
    double    tolmul;
    double    tol;
    double    thresh;
 
    dcomplex* G;
    dcomplex* H;
    double*   d1;
    double*   e1;
    int       r_val;
    int       done;
    int       m_GH_sweep_max;
    int       ij_begin;
    int       ijTL, ijBR;
    int       m_A11;
    int       n_iter_perf;
    int       n_UV_apply;
    int       total_deflations;
    int       n_deflations;
    int       n_iter_prev;
    int       n_iter_perf_sweep_max;
 
    // Compute some convergence constants.
    eps    = FLA_Mach_params_opd( FLA_MACH_EPS );
    tolmul = max( 10.0, min( 100.0, pow( eps, -0.125 ) ) );
    FLA_Bsvd_compute_tol_thresh_opd( min_m_n,
                                     tolmul,
                                     maxitr,
                                     buff_d, inc_d,
                                     buff_e, inc_e,
                                     &tol,
                                     &thresh );
 
    // Initialize our completion flag.
    done = FALSE;
 
    // Initialize a counter that holds the maximum number of rows of G
    // and H that we would need to initialize for the next sweep.
    m_GH_sweep_max = min_m_n - 1;
 
    // Initialize a counter for the total number of iterations performed.
    n_iter_prev = 0;
 
    // Initialize RG and RH to identity.
    bl1_dident( min_m_n,
                buff_RG, rs_RG, cs_RG );
    bl1_dident( min_m_n,
                buff_RH, rs_RH, cs_RH );
 
    // Iterate until the matrix has completely deflated.
    for ( total_deflations = 0; done != TRUE; )
    {
 
        // Initialize G and H to contain only identity rotations.
        bl1_zsetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_G, rs_G, cs_G );
        bl1_zsetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_H, rs_H, cs_H );
 
        // Keep track of the maximum number of iterations performed in the
        // current sweep. This is used when applying the sweep's Givens
        // rotations.
        n_iter_perf_sweep_max = 0;
 
        // Perform a sweep: Move through the matrix and perform a bidiagonal
        // SVD on each non-zero submatrix that is encountered. During the
        // first time through, ijTL will be 0 and ijBR will be min_m_n - 1.
        for ( ij_begin = 0; ij_begin < min_m_n;  )
        {
 
#ifdef PRINTF
if ( ij_begin == 0 )
printf( "FLA_Bsvd_v_opz_var2: beginning new sweep (ij_begin = %d)\n", ij_begin );
#endif
 
            // Search for the first submatrix along the diagonal that is
            // bounded by zeroes (or endpoints of the matrix). If no
            // submatrix is found (ie: if the entire superdiagonal is zero
            // then FLA_FAILURE is returned. This function also inspects
            // superdiagonal elements for proximity to zero. If a given
            // element is close enough to zero, then it is deemed
            // converged and manually set to zero.
            r_val = FLA_Bsvd_find_submatrix_opd( min_m_n,
                                                 ij_begin,
                                                 buff_d, inc_d,
                                                 buff_e, inc_e,
                                                 &ijTL,
                                                 &ijBR );
 
            // Verify that a submatrix was found. If one was not found,
            // then we are done with the current sweep. Furthermore, if
            // a submatrix was not found AND we began our search at the
            // beginning of the matrix (ie: ij_begin == 0), then the
            // matrix has completely deflated and so we are done with
            // Francis step iteration.
            if ( r_val == FLA_FAILURE )
            {
                if ( ij_begin == 0 )
                {
#ifdef PRINTF
printf( "FLA_Bsvd_v_opz_var2: superdiagonal is completely zero.\n" );
printf( "FLA_Bsvd_v_opz_var2: Francis iteration is done!\n" );
#endif
                    done = TRUE;
                }
 
                // Break out of the current sweep so we can apply the last
                // remaining Givens rotations.
                break;
            }
 
            // If we got this far, then:
            //   (a) ijTL refers to the index of the first non-zero
            //       superdiagonal along the diagonal, and
            //   (b) ijBR refers to either:
            //       - the first zero element that occurs after ijTL, or
            //       - the the last diagonal element.
            // Note that ijTL and ijBR also correspond to the first and
            // last diagonal elements of the submatrix of interest. Thus,
            // we may compute the dimension of this submatrix as:
            m_A11 = ijBR - ijTL + 1;
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opz_var2: ij_begin = %d\n", ij_begin );
printf( "FLA_Bsvd_v_opz_var2: ijTL     = %d\n", ijTL );
printf( "FLA_Bsvd_v_opz_var2: ijBR     = %d\n", ijBR );
printf( "FLA_Bsvd_v_opz_var2: m_A11    = %d\n", m_A11 );
#endif
 
            // Adjust ij_begin, which gets us ready for the next submatrix
            // search in the current sweep.
            ij_begin = ijBR + 1;
 
            // Index to the submatrices upon which we will operate.
            d1 = buff_d + ijTL * inc_d;
            e1 = buff_e + ijTL * inc_e;
            G  = buff_G + ijTL * rs_G;
            H  = buff_H + ijTL * rs_H;
 
            // Search for a batch of singular values, recursing on deflated
            // subproblems whenever possible. A new singular value search is
            // performed as long as
            //   (a) there is still matrix left to operate on, and
            //   (b) the number of iterations performed in this batch is
            //       less than n_G.
            // If/when either of the two above conditions fails to hold,
            // the function returns.
            n_deflations = FLA_Bsvd_iteracc_v_opd_var1( m_A11,
                                                        n_GH,
                                                        ijTL,
                                                        tol,
                                                        thresh,
                                                        d1, inc_d,
                                                        e1, inc_e,
                                                        G,  rs_G, cs_G,
                                                        H,  rs_H, cs_H,
                                                        &n_iter_perf );
 
            // Record the number of deflations that occurred.
            total_deflations += n_deflations;
 
            // Update the maximum number of iterations performed in the
            // current sweep.
            n_iter_perf_sweep_max = max( n_iter_perf_sweep_max, n_iter_perf );
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opz_var2: deflations observed       = %d\n", n_deflations );
printf( "FLA_Bsvd_v_opz_var2: total deflations observed = %d\n", total_deflations );
printf( "FLA_Bsvd_v_opz_var2: num iterations performed  = %d\n", n_iter_perf );
#endif
 
            // Store the most recent value of ijBR in m_G_sweep_max.
            // When the sweep is done, this value will contain the minimum
            // number of rows of G and H we can apply and safely include all
            // non-identity rotations that were computed during the
            // singular value searches.
            m_GH_sweep_max = ijBR;
 
        }
 
        // The sweep is complete. Now we must apply the Givens rotations
        // that were accumulated during the sweep.
 
        // Recall that the number of columns of U and V to which we apply
        // rotations is one more than the number of rotations.
        n_UV_apply = m_GH_sweep_max + 1;
 
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opz_var2: applying %d sets of Givens rotations\n", n_iter_perf_sweep_max );
printf( "FLA_Bsvd_v_opz_var2: m_U = %d\n", m_U );
printf( "FLA_Bsvd_v_opz_var2: m_V = %d\n", m_V );
printf( "FLA_Bsvd_v_opz_var2: napp= %d\n", n_UV_apply );
#endif
 
        // Apply the Givens rotations. Note that we only apply k sets of
        // rotations, where k = n_iter_perf_sweep_max. Also note that we only
        // apply to n_UV_apply columns of U and V since this is the most we
        // need to touch given the most recent value stored to m_GH_sweep_max.
        //FLA_Apply_G_rf_bld_var5b( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var9b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var6b( n_iter_perf_sweep_max,
                                  min_m_n,
                                  n_UV_apply,
                                  n_iter_prev,
                                  buff_G,  rs_G,  cs_G,
                                  buff_RG, rs_RG, cs_RG,
                                  b_alg );
        //FLA_Apply_G_rf_bld_var5b( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var9b( n_iter_perf_sweep_max,
        //FLA_Apply_G_rf_bld_var6b( n_iter_perf_sweep_max,
                                  min_m_n,
                                  n_UV_apply,
                                  n_iter_prev,
                                  buff_H,  rs_H,  cs_H,
                                  buff_RH, rs_RH, cs_RH,
                                  b_alg );
 
        // Increment the total number of iterations previously performed.
        n_iter_prev += n_iter_perf_sweep_max;
 
#ifdef PRINTF
printf( "FLA_Bsvd_v_opz_var2: total number of iterations performed: %d\n", n_iter_prev );
#endif
    }
 
    // Copy the contents of Q to temporary storage.
    bl1_zcopymt( BLIS1_NO_TRANSPOSE,
                 m_U,
                 m_V,
                 buff_U, rs_U, cs_U,
                 buff_W, rs_W, cs_W );
// W needs to be max_m_n-by-min_m_n!!!!!!!!!!!!!!!
 
    // Multiply U by R, overwriting U.
    bl1_dgemm( BLIS1_NO_TRANSPOSE,
               BLIS1_NO_TRANSPOSE,
               2*m_U,
               m_V,
               m_V,
               &rone,
               ( double* )buff_W,  rs_W,  2*cs_W,
                          buff_RG, rs_RG,   cs_RG,
               &rzero,
               ( double* )buff_U,  rs_U,  2*cs_U );
 
    bl1_zcopymt( BLIS1_NO_TRANSPOSE,
                 m_V,
                 m_V,
                 buff_V, rs_V, cs_V,
                 buff_W, rs_W, cs_W );
 
    // Multiply V by R, overwriting V.
    bl1_dgemm( BLIS1_NO_TRANSPOSE,
               BLIS1_NO_TRANSPOSE,
               2*m_V,
               m_V,
               m_V,
               &rone,
               ( double* )buff_W,  rs_W,  2*cs_W,
                          buff_RH, rs_RH,   cs_RH,
               &rzero,
               ( double* )buff_V,  rs_V,  2*cs_V );
 
    // Make all the singular values positive.
    {
        int    i;
        double minus_one = bl1_dm1();
 
        for ( i = 0; i < min_m_n; ++i )
        {
            if ( buff_d[ (i  )*inc_d ] < rzero )
            {
                buff_d[ (i  )*inc_d ] = -buff_d[ (i  )*inc_d ];
                
                // Scale the right singular vectors.
                bl1_zdscalv( BLIS1_NO_CONJUGATE,
                             m_V,
                             &minus_one,
                             buff_V + (i  )*cs_V, rs_V );
            }
        }
    }
 
    return n_iter_prev;
}

References bl1_d0(), bl1_d1(), bl1_dgemm(), bl1_dident(), bl1_dm1(), bl1_z1(), bl1_zcopymt(), bl1_zdscalv(), bl1_zsetm(), BLIS1_NO_CONJUGATE, BLIS1_NO_TRANSPOSE, FLA_Apply_G_rf_bld_var3b(), FLA_Bsvd_compute_tol_thresh_opd(), FLA_Bsvd_find_submatrix_opd(), FLA_Bsvd_iteracc_v_opd_var1(), FLA_Mach_params_opd(), and i.

Referenced by FLA_Bsvd_v_opt_var2().