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Functions
FLA_Chol_u.h File Reference

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Functions

FLA_Error FLA_Chol_u_blk_var1 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_u_blk_var2 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_u_blk_var3 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_u_unb_var1 (FLA_Obj A)
FLA_Error FLA_Chol_u_unb_var2 (FLA_Obj A)
FLA_Error FLA_Chol_u_unb_var3 (FLA_Obj A)
FLA_Error FLA_Chol_u_opt_var1 (FLA_Obj A)
FLA_Error FLA_Chol_u_ops_var1 (int mn_A, float *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opd_var1 (int mn_A, double *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opc_var1 (int mn_A, scomplex *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opz_var1 (int mn_A, dcomplex *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opt_var2 (FLA_Obj A)
FLA_Error FLA_Chol_u_ops_var2 (int mn_A, float *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opd_var2 (int mn_A, double *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opc_var2 (int mn_A, scomplex *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opz_var2 (int mn_A, dcomplex *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opt_var3 (FLA_Obj A)
FLA_Error FLA_Chol_u_ops_var3 (int mn_A, float *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opd_var3 (int mn_A, double *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opc_var3 (int mn_A, scomplex *A, int rs_A, int cs_A)
FLA_Error FLA_Chol_u_opz_var3 (int mn_A, dcomplex *A, int rs_A, int cs_A)

Function Documentation

References FLA_Chol_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Herk_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trsm_internal().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02,
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

  int r_val = FLA_SUCCESS;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    /*------------------------------------------------------------*/

    // A01 = inv( triu( A00 )' ) * A01
    FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
                       FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, A00, A01,
                       FLA_Cntl_sub_trsm( cntl ) );

    // A11 = A11 - A01' * A01
    FLA_Herk_internal( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, A01, FLA_ONE, A11,
                       FLA_Cntl_sub_herk( cntl ) );

    // A11 = chol( A11 )
    r_val = FLA_Chol_internal( FLA_UPPER_TRIANGULAR, A11,
                               FLA_Cntl_sub_chol( cntl ) );

    if ( r_val != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) + r_val );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
  }

  return r_val;
}

References FLA_Chol_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Gemm_internal(), FLA_Herk_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trsm_internal().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02,
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

  int r_val = FLA_SUCCESS;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    /*------------------------------------------------------------*/

    // A11 = A11 - A01' * A01
    FLA_Herk_internal( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, A01, FLA_ONE, A11,
                       FLA_Cntl_sub_herk( cntl ) );

    // A12 = A12 - A02' * A01
    FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A01, A02, FLA_ONE, A12,
                       FLA_Cntl_sub_gemm( cntl ) );

    // A11 = chol( A11 )
    r_val = FLA_Chol_internal( FLA_UPPER_TRIANGULAR, A11,
                               FLA_Cntl_sub_chol( cntl ) );

    if ( r_val != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) + r_val );

    // A12 = inv( triu( A11 )' ) * A12
    FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
                       FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, A11, A12,
                       FLA_Cntl_sub_trsm( cntl ) );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
  }

  return r_val;
}

References FLA_Chol_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Herk_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trsm_internal().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02,
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

  int r_val = FLA_SUCCESS;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    /*------------------------------------------------------------*/

    // A11 = chol( A11 )
    r_val = FLA_Chol_internal( FLA_UPPER_TRIANGULAR, A11,
                               FLA_Cntl_sub_chol( cntl ) );

    if ( r_val != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) + r_val );

    // A12 = inv( triu( A11 )' ) * A12
    FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
                       FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, A11, A12,
                       FLA_Cntl_sub_trsm( cntl ) );

    // A22 = A22 - A12' * A12
    FLA_Herk_internal( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, A12, FLA_ONE, A22,
                       FLA_Cntl_sub_herk( cntl ) );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
  }

  return r_val;
}
FLA_Error FLA_Chol_u_opc_var1 ( int  mn_A,
scomplex A,
int  rs_A,
int  cs_A 
)

References bl1_cdots(), bl1_ctrsv(), BLIS1_CONJ_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var1().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    scomplex* a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;

    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Trsv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a01 );
    bl1_ctrsv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_cdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_csqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opc_var2 ( int  mn_A,
scomplex A,
int  rs_A,
int  cs_A 
)

References bl1_cdots(), bl1_cgemv(), bl1_cinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_TRANSPOSE, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var2().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* A02       = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_cdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, a01, FLA_ONE, a12t );
    bl1_cgemv( BLIS1_TRANSPOSE,
               BLIS1_CONJUGATE,
               mn_behind,
               mn_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a12t, cs_A );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_csqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opc_var3 ( int  mn_A,
scomplex A,
int  rs_A,
int  cs_A 
)

References bl1_cher(), bl1_cinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_UPPER_TRIANGULAR, and FLA_MINUS_ONE.

Referenced by FLA_Chol_u_opt_var3().

{
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_csqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    // FLA_Herc_external( FLA_UPPER_TRIANGULAR, FLA_MINUS_ONE, a12t, A22 );
    bl1_cher( BLIS1_UPPER_TRIANGULAR,
              BLIS1_CONJUGATE,
              mn_ahead,
              buff_m1,
              a12t, cs_A,
              A22, rs_A, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opd_var1 ( int  mn_A,
double *  A,
int  rs_A,
int  cs_A 
)

References bl1_ddots(), bl1_dtrsv(), BLIS1_CONJ_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var1().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    double*   A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    double*   a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    double*   alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;

    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Trsv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a01 );
    bl1_dtrsv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_ddots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_dsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opd_var2 ( int  mn_A,
double *  A,
int  rs_A,
int  cs_A 
)

References bl1_ddots(), bl1_dgemv(), bl1_dinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_TRANSPOSE, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var2().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    double*   a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    double*   alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   A02       = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_ddots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, a01, FLA_ONE, a12t );
    bl1_dgemv( BLIS1_TRANSPOSE,
               BLIS1_CONJUGATE,
               mn_behind,
               mn_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a12t, cs_A );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_dsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_dinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opd_var3 ( int  mn_A,
double *  A,
int  rs_A,
int  cs_A 
)

References bl1_dinvscalv(), bl1_dsyr(), BLIS1_NO_CONJUGATE, BLIS1_UPPER_TRIANGULAR, and FLA_MINUS_ONE.

Referenced by FLA_Chol_u_opt_var3().

{
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    double*   alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_dsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_dinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    // FLA_Herc_external( FLA_UPPER_TRIANGULAR, FLA_MINUS_ONE, a12t, A22 );
    bl1_dsyr( BLIS1_UPPER_TRIANGULAR,
              mn_ahead,
              buff_m1,
              a12t, cs_A,
              A22, rs_A, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_ops_var1 ( int  mn_A,
float *  A,
int  rs_A,
int  cs_A 
)

References bl1_sdots(), bl1_strsv(), BLIS1_CONJ_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var1().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    float*    A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    float*    a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    float*    alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;

    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Trsv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a01 );
    bl1_strsv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_sdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_ssqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_ops_var2 ( int  mn_A,
float *  A,
int  rs_A,
int  cs_A 
)

References bl1_sdots(), bl1_sgemv(), bl1_sinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_TRANSPOSE, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var2().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    float*    a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    float*    alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    A02       = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_sdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, a01, FLA_ONE, a12t );
    bl1_sgemv( BLIS1_TRANSPOSE,
               BLIS1_CONJUGATE,
               mn_behind,
               mn_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a12t, cs_A );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_ssqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_sinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_ops_var3 ( int  mn_A,
float *  A,
int  rs_A,
int  cs_A 
)

References bl1_sinvscalv(), bl1_ssyr(), BLIS1_NO_CONJUGATE, BLIS1_UPPER_TRIANGULAR, and FLA_MINUS_ONE.

Referenced by FLA_Chol_u_opt_var3().

{
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    float*    alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_ssqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_sinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    // FLA_Herc_external( FLA_UPPER_TRIANGULAR, FLA_MINUS_ONE, a12t, A22 );
    bl1_ssyr( BLIS1_UPPER_TRIANGULAR,
              mn_ahead,
              buff_m1,
              a12t, cs_A,
              A22, rs_A, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}

References FLA_Chol_u_opc_var1(), FLA_Chol_u_opd_var1(), FLA_Chol_u_ops_var1(), FLA_Chol_u_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Chol_u().

{
  FLA_Error    r_val = FLA_SUCCESS;
  FLA_Datatype datatype;
  int          mn_A;
  int          rs_A, cs_A;

  datatype = FLA_Obj_datatype( A );

  mn_A     = FLA_Obj_length( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );

      r_val = FLA_Chol_u_ops_var1( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );

      r_val = FLA_Chol_u_opd_var1( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opc_var1( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opz_var1( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }
  }

  return r_val;
}

References FLA_Chol_u_opc_var2(), FLA_Chol_u_opd_var2(), FLA_Chol_u_ops_var2(), FLA_Chol_u_opz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Chol_u().

{
  FLA_Error    r_val = FLA_SUCCESS;
  FLA_Datatype datatype;
  int          mn_A;
  int          rs_A, cs_A;

  datatype = FLA_Obj_datatype( A );

  mn_A     = FLA_Obj_length( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );

      r_val = FLA_Chol_u_ops_var2( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );

      r_val = FLA_Chol_u_opd_var2( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opc_var2( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opz_var2( mn_A,
                                   buff_A, rs_A, cs_A );
      
      break;
    }
  }

  return r_val;
}

References FLA_Chol_u_opc_var3(), FLA_Chol_u_opd_var3(), FLA_Chol_u_ops_var3(), FLA_Chol_u_opz_var3(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Chol_u().

{
  FLA_Error    r_val = FLA_SUCCESS;
  FLA_Datatype datatype;
  int          mn_A;
  int          rs_A, cs_A;

  datatype = FLA_Obj_datatype( A );

  mn_A     = FLA_Obj_length( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );

      r_val = FLA_Chol_u_ops_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );

      r_val = FLA_Chol_u_opd_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opc_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opz_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }
  }

  return r_val;
}
FLA_Error FLA_Chol_u_opz_var1 ( int  mn_A,
dcomplex A,
int  rs_A,
int  cs_A 
)

References bl1_zdots(), bl1_ztrsv(), BLIS1_CONJ_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var1().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    dcomplex* A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    dcomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;

    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Trsv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a01 );
    bl1_ztrsv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_zdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_zsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opz_var2 ( int  mn_A,
dcomplex A,
int  rs_A,
int  cs_A 
)

References bl1_zdots(), bl1_zgemv(), bl1_zinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_TRANSPOSE, FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_Chol_u_opt_var2().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    dcomplex* a01       = buff_A + (i  )*cs_A + (0  )*rs_A;
    dcomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* A02       = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );
    bl1_zdots( BLIS1_CONJUGATE,
               mn_behind,
               buff_m1,
               a01, rs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, a01, FLA_ONE, a12t );
    bl1_zgemv( BLIS1_TRANSPOSE,
               BLIS1_CONJUGATE,
               mn_behind,
               mn_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a12t, cs_A );

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_zsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_zinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Chol_u_opz_var3 ( int  mn_A,
dcomplex A,
int  rs_A,
int  cs_A 
)

References bl1_zher(), bl1_zinvscalv(), BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, BLIS1_UPPER_TRIANGULAR, and FLA_MINUS_ONE.

Referenced by FLA_Chol_u_opt_var3().

{
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       i;
  FLA_Error e_val;

  for ( i = 0; i < mn_A; ++i )
  {
    dcomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

    /*------------------------------------------------------------*/

    // r_val = FLA_Sqrt( alpha11 );
    // if ( r_val != FLA_SUCCESS )
    //   return ( FLA_Obj_length( A00 ) + 1 );
    bl1_zsqrte( alpha11, &e_val );
    if ( e_val != FLA_SUCCESS ) return mn_behind;

    // FLA_Inv_scal_external( alpha11, a12t );
    bl1_zinvscalv( BLIS1_NO_CONJUGATE,
                   mn_ahead,
                   alpha11,
                   a12t, cs_A );

    // FLA_Herc_external( FLA_UPPER_TRIANGULAR, FLA_MINUS_ONE, a12t, A22 );
    bl1_zher( BLIS1_UPPER_TRIANGULAR,
              BLIS1_CONJUGATE,
              mn_ahead,
              buff_m1,
              a12t, cs_A,
              A22, rs_A, cs_A );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}

References FLA_Cont_with_3x3_to_2x2(), FLA_Dotcs_external(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), FLA_Sqrt(), and FLA_Trsv_external().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02,
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  int r_val = FLA_SUCCESS;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    /*------------------------------------------------------------*/

    // a01 = inv( tril( A00 )' ) * a01
    FLA_Trsv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a01 );

    // alpha11 = alpha11 - a01' * a01
    FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );

    // alpha11 = sqrt( alpha11 )
    r_val = FLA_Sqrt( alpha11 );

    if ( r_val != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
  }

  return r_val;
}

References FLA_Cont_with_3x3_to_2x2(), FLA_Dotcs_external(), FLA_Gemvc_external(), FLA_Inv_scal_external(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Sqrt().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02,
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  int r_val = FLA_SUCCESS;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    /*------------------------------------------------------------*/

    // alpha11 = alpha11 - a01' * a01
    FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a01, a01, FLA_ONE, alpha11 );

    // a12t = a12t - a01' * A02
    // a12t' = a12t' - A02' * conj(a01)
    FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, a01, FLA_ONE, a12t );

    // alpha11 = sqrt( alpha11 )
    r_val = FLA_Sqrt( alpha11 );

    if ( r_val != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) );

    // a12t = a12t / alpha11
    FLA_Inv_scal_external( alpha11, a12t );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
  }

  return r_val;
}

References FLA_Cont_with_3x3_to_2x2(), FLA_Herc_external(), FLA_Inv_scal_external(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Sqrt().

Referenced by FLA_Chol_u().

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02,
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  int value = 0;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    /*------------------------------------------------------------*/

    // alpha11 = sqrt( alpha11 )
    value = FLA_Sqrt( alpha11 );

    if ( value != FLA_SUCCESS )
      return ( FLA_Obj_length( A00 ) );

    // a12t = a12t / alpha11
    FLA_Inv_scal_external( alpha11, a12t );

    // A22 = A22 - a12t' * a12t
    FLA_Herc_external( FLA_UPPER_TRIANGULAR, FLA_CONJUGATE, FLA_MINUS_ONE, a12t, A22 );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
  }

  return value;
}