FLA_Bsvd_v_opt_var1.c File Reference

(r)

Functions
FLA_Error	FLA_Bsvd_v_opt_var1 (dim_t n_iter_max, FLA_Obj d, FLA_Obj e, FLA_Obj G, FLA_Obj H, FLA_Obj U, FLA_Obj V, dim_t b_alg)
FLA_Error	FLA_Bsvd_v_ops_var1 (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_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_var1 (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_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_var1 (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, 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_var1 (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, 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_var1()

FLA_Error FLA_Bsvd_v_opc_var1	(	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,
		scomplex *	buff_U,
		int	rs_U,
		int	cs_U,
		scomplex *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg )

{
    scomplex  one        = bl1_c1();
    float     rzero      = bl1_s0();
 
    int       maxitr     = 6;
 
    float     eps;
    float     tolmul;
    float     tol;
    float     thresh;
 
    scomplex* G;
    scomplex* H;
    float*    d1;
    float*    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_ops( FLA_MACH_EPS );
    tolmul = max( 10.0F, min( 100.0F, powf( eps, -0.125F ) ) );
    FLA_Bsvd_compute_tol_thresh_ops( 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;
 
    // Iterate until the matrix has completely deflated.
    for ( total_deflations = 0; done != TRUE; )
    {
 
        // Initialize G and H to contain only identity rotations.
        bl1_csetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_G, rs_G, cs_G );
        bl1_csetm( 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;  )
        {
            // 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_ops( 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 )
                {
                    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;
 
            // 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 a split occurs. Iteration continues 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_ops_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 were observed.
            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 );
 
            // 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;
 
            // Make sure we haven't exceeded our maximum iteration count.
            if ( n_iter_prev >= n_iter_max * min_m_n )
            {
                FLA_Abort();
                //return FLA_FAILURE;
            }
        }
 
        // 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;
 
        // 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_blc_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_blc_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var6( n_iter_perf_sweep_max,
                                 m_U,
                                 n_UV_apply,
                                 buff_G, rs_G, cs_G,
                                 buff_U, rs_U, cs_U,
                                 b_alg );
        //FLA_Apply_G_rf_blc_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_blc_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var6( n_iter_perf_sweep_max,
                                 m_V,
                                 n_UV_apply,
                                 buff_H, rs_H, cs_H,
                                 buff_V, rs_V, cs_V,
                                 b_alg );
 
        // Increment the total number of iterations previously performed.
        n_iter_prev += n_iter_perf_sweep_max;
    }
 
    // Make all the singular values positive.
    {
        int    i;
        float  minus_one = bl1_sm1();
 
        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_csscalv( BLIS1_NO_CONJUGATE,
                             m_V,
                             &minus_one,
                             buff_V + (i  )*cs_V, rs_V );
            }
        }
    }
 
    return FLA_SUCCESS;
}

References bl1_c1(), bl1_csetm(), bl1_csscalv(), bl1_s0(), bl1_sm1(), BLIS1_NO_CONJUGATE, FLA_Abort(), FLA_Apply_G_rf_blc_var3(), FLA_Bsvd_compute_tol_thresh_ops(), FLA_Bsvd_find_submatrix_ops(), FLA_Bsvd_iteracc_v_ops_var1(), FLA_Mach_params_ops(), and i.

Referenced by FLA_Bsvd_v_opt_var1().

FLA_Bsvd_v_opd_var1()

FLA_Error FLA_Bsvd_v_opd_var1	(	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_U,
		int	rs_U,
		int	cs_U,
		double *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg )

{
    dcomplex  one        = bl1_z1();
    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 );
#ifdef PRINTF
    printf( "FLA_Bsvd_v_opd_var1: tolmul = %12.6e\n", tolmul );
    printf( "FLA_Bsvd_v_opd_var1: tol    = %12.6e\n", tol );
    printf( "FLA_Bsvd_v_opd_var1: thresh = %12.6e\n", thresh );
#endif
 
    // 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;
 
    // 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_var1: 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_var1: superdiagonal is completely zero.\n" );
                    printf( "FLA_Bsvd_v_opd_var1: 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_var1: ij_begin = %d\n", ij_begin );
            printf( "FLA_Bsvd_v_opd_var1: ijTL     = %d\n", ijTL );
            printf( "FLA_Bsvd_v_opd_var1: ijBR     = %d\n", ijBR );
            printf( "FLA_Bsvd_v_opd_var1: 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 a split occurs. Iteration continues 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 were observed.
            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_var1: deflations observed       = %d\n", n_deflations );
            printf( "FLA_Bsvd_v_opd_var1: total deflations observed = %d\n", total_deflations );
            printf( "FLA_Bsvd_v_opd_var1: 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;
 
            // Make sure we haven't exceeded our maximum iteration count.
            if ( n_iter_prev >= n_iter_max * min_m_n )
            {
#ifdef PRINTF
                printf( "FLA_Bsvd_v_opd_var1: reached maximum total number of iterations: %d\n", n_iter_prev );
#endif
                FLA_Abort();
                //return FLA_FAILURE;
            }
        }
 
        // 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_var1: applying %d sets of Givens rotations\n", n_iter_perf_sweep_max );
        printf( "FLA_Bsvd_v_opd_var1: m_U = %d\n", m_U );
        printf( "FLA_Bsvd_v_opd_var1: m_V = %d\n", m_V );
        printf( "FLA_Bsvd_v_opd_var1: 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_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var6( n_iter_perf_sweep_max,
                                 m_U,
                                 n_UV_apply,
                                 buff_G, rs_G, cs_G,
                                 buff_U, rs_U, cs_U,
                                 b_alg );
        //FLA_Apply_G_rf_bld_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bld_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var6( n_iter_perf_sweep_max,
                                 m_V,
                                 n_UV_apply,
                                 buff_H, rs_H, cs_H,
                                 buff_V, rs_V, cs_V,
                                 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_var1: total number of iterations performed: %d\n", n_iter_prev );
#endif
    }
 
    // 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_dm1(), bl1_dscalv(), bl1_z1(), bl1_zsetm(), BLIS1_NO_CONJUGATE, FLA_Abort(), FLA_Apply_G_rf_bld_var3(), 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_var1().

FLA_Bsvd_v_ops_var1()

FLA_Error FLA_Bsvd_v_ops_var1	(	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_U,
		int	rs_U,
		int	cs_U,
		float *	buff_V,
		int	rs_V,
		int	cs_V,
		int	b_alg )

{
    scomplex  one        = bl1_c1();
    float     rzero      = bl1_s0();
 
    int       maxitr     = 6;
 
    float     eps;
    float     tolmul;
    float     tol;
    float     thresh;
 
    scomplex* G;
    scomplex* H;
    float*    d1;
    float*    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_ops( FLA_MACH_EPS );
    tolmul = max( 10.0F, min( 100.0F, powf( eps, -0.125F ) ) );
    FLA_Bsvd_compute_tol_thresh_ops( 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;
 
    // Iterate until the matrix has completely deflated.
    for ( total_deflations = 0; done != TRUE; )
    {
 
        // Initialize G and H to contain only identity rotations.
        bl1_csetm( m_GH_sweep_max,
                   n_GH,
                   &one,
                   buff_G, rs_G, cs_G );
        bl1_csetm( 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;  )
        {
 
            // 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_ops( 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 )
                {
                    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;
 
            // 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 a split occurs. Iteration continues 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_ops_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 were observed.
            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 );
 
            // 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;
 
            // Make sure we haven't exceeded our maximum iteration count.
            if ( n_iter_prev >= n_iter_max * min_m_n )
            {
                FLA_Abort();
                //return FLA_FAILURE;
            }
        }
 
        // 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;
 
        // 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_bls_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bls_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var6( n_iter_perf_sweep_max,
                                 m_U,
                                 n_UV_apply,
                                 buff_G, rs_G, cs_G,
                                 buff_U, rs_U, cs_U,
                                 b_alg );
        //FLA_Apply_G_rf_blc_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_bls_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_bld_var6( n_iter_perf_sweep_max,
                                 m_V,
                                 n_UV_apply,
                                 buff_H, rs_H, cs_H,
                                 buff_V, rs_V, cs_V,
                                 b_alg );
 
        // Increment the total number of iterations previously performed.
        n_iter_prev += n_iter_perf_sweep_max;
 
    }
 
    // Make all the singular values positive.
    {
        int    i;
        float  minus_one = bl1_sm1();
 
        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_sscalv( BLIS1_NO_CONJUGATE,
                            m_V,
                            &minus_one,
                            buff_V + (i  )*cs_V, rs_V );
            }
        }
    }
 
    return n_iter_prev;
}

References bl1_c1(), bl1_csetm(), bl1_s0(), bl1_sm1(), bl1_sscalv(), BLIS1_NO_CONJUGATE, FLA_Abort(), FLA_Apply_G_rf_bls_var3(), FLA_Bsvd_compute_tol_thresh_ops(), FLA_Bsvd_find_submatrix_ops(), FLA_Bsvd_iteracc_v_ops_var1(), FLA_Mach_params_ops(), and i.

Referenced by FLA_Bsvd_v_opt_var1().

FLA_Bsvd_v_opt_var1()

FLA_Error FLA_Bsvd_v_opt_var1	(	dim_t	n_iter_max,
		FLA_Obj	d,
		FLA_Obj	e,
		FLA_Obj	G,
		FLA_Obj	H,
		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_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_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_U = FLA_FLOAT_PTR( U );
        float*    buff_V = FLA_FLOAT_PTR( V );
 
        r_val = FLA_Bsvd_v_ops_var1( 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_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_U = FLA_DOUBLE_PTR( U );
        double*   buff_V = FLA_DOUBLE_PTR( V );
 
        r_val = FLA_Bsvd_v_opd_var1( 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_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 );
        scomplex* buff_U = FLA_COMPLEX_PTR( U );
        scomplex* buff_V = FLA_COMPLEX_PTR( V );
 
        r_val = FLA_Bsvd_v_opc_var1( 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_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 );
        dcomplex* buff_U = FLA_DOUBLE_COMPLEX_PTR( U );
        dcomplex* buff_V = FLA_DOUBLE_COMPLEX_PTR( V );
 
        r_val = FLA_Bsvd_v_opz_var1( 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_U, rs_U, cs_U,
                                     buff_V, rs_V, cs_V,
                                     b_alg );
 
        break;
    }
    }
 
    return r_val;
}

References FLA_Bsvd_v_opc_var1(), FLA_Bsvd_v_opd_var1(), FLA_Bsvd_v_ops_var1(), FLA_Bsvd_v_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), and FLA_Obj_width().

Referenced by FLA_Svd_uv_unb_var1().

FLA_Bsvd_v_opz_var1()

FLA_Error FLA_Bsvd_v_opz_var1	(	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,
		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    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 );
#ifdef PRINTF
    printf( "FLA_Bsvd_v_opz_var1: tolmul = %12.6e\n", tolmul );
    printf( "FLA_Bsvd_v_opz_var1: tol    = %12.6e\n", tol );
    printf( "FLA_Bsvd_v_opz_var1: thresh = %12.6e\n", thresh );
#endif
 
    // 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;
 
    // 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_var1: 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_var1: superdiagonal is completely zero.\n" );
                    printf( "FLA_Bsvd_v_opz_var1: 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_var1: ij_begin = %d\n", ij_begin );
            printf( "FLA_Bsvd_v_opz_var1: ijTL     = %d\n", ijTL );
            printf( "FLA_Bsvd_v_opz_var1: ijBR     = %d\n", ijBR );
            printf( "FLA_Bsvd_v_opz_var1: 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 a split occurs. Iteration continues 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 were observed.
            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_var1: deflations observed       = %d\n", n_deflations );
            printf( "FLA_Bsvd_v_opz_var1: total deflations observed = %d\n", total_deflations );
            printf( "FLA_Bsvd_v_opz_var1: 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;
 
            // Make sure we haven't exceeded our maximum iteration count.
            if ( n_iter_prev >= n_iter_max * min_m_n )
            {
#ifdef PRINTF
                printf( "FLA_Bsvd_v_opz_var1: reached maximum total number of iterations: %d\n", n_iter_prev );
#endif
                FLA_Abort();
                //return FLA_FAILURE;
            }
        }
 
        // 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_var1: applying %d sets of Givens rotations\n", n_iter_perf_sweep_max );
        printf( "FLA_Bsvd_v_opz_var1: m_U = %d\n", m_U );
        printf( "FLA_Bsvd_v_opz_var1: m_V = %d\n", m_V );
        printf( "FLA_Bsvd_v_opz_var1: 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_blz_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_blz_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var6( n_iter_perf_sweep_max,
                                 m_U,
                                 n_UV_apply,
                                 buff_G, rs_G, cs_G,
                                 buff_U, rs_U, cs_U,
                                 b_alg );
        //FLA_Apply_G_rf_blz_var5( n_iter_perf_sweep_max,
        FLA_Apply_G_rf_blz_var3( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var9( n_iter_perf_sweep_max,
                                 //FLA_Apply_G_rf_blz_var6( n_iter_perf_sweep_max,
                                 m_V,
                                 n_UV_apply,
                                 buff_H, rs_H, cs_H,
                                 buff_V, rs_V, cs_V,
                                 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_var1: total number of iterations performed: %d\n", n_iter_prev );
#endif
    }
 
    // 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_dm1(), bl1_z1(), bl1_zdscalv(), bl1_zsetm(), BLIS1_NO_CONJUGATE, FLA_Abort(), FLA_Apply_G_rf_blz_var3(), 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_var1().