int Symm_ru_blk_var6( FLA_Obj A, FLA_Obj B, FLA_Obj C, int nb_alg )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj BL,    BR,       B0,  B1,  B2;

  FLA_Obj CL,    CR,       C0,  C1,  C2;

  int b;

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

  FLA_Part_1x2( B,    &BL,  &BR,      0, FLA_RIGHT );

  FLA_Part_1x2( C,    &CL,  &CR,      0, FLA_RIGHT );

  while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){

    b = min( FLA_Obj_length( ATL ), nb_alg );

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

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, &B1, /**/ &B2,
                           b, FLA_LEFT );

    FLA_Repart_1x2_to_1x3( CL,  /**/ CR,        &C0, &C1, /**/ &C2,
                           b, FLA_LEFT );

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

    /*C1 = B0 * A01 + B1 * A11 + B2 * A12' + C1;*/
    FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, B0, A01, FLA_ONE, C1);
    FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, B1, A11, FLA_ONE, C1);
    FLA_Gemm(FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, B2, A12, FLA_ONE, C1);

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

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

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, /**/ B1, B2,
                              FLA_RIGHT );

    FLA_Cont_with_1x3_to_1x2( &CL,  /**/ &CR,        C0, /**/ C1, C2,
                              FLA_RIGHT );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_find_zero_on_diagonal( FLA_Obj A )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_LU_find_zero_on_diagonal_check( A );

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

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

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

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

    if ( FLA_Obj_equals( alpha11, FLA_ZERO ) ) 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 FLA_SUCCESS;
}
int Symm_ru_unb_var4( FLA_Obj A, FLA_Obj B, FLA_Obj C )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj BL,    BR,       B0,  b1,  B2;

  FLA_Obj CL,    CR,       C0,  c1,  C2;

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

  FLA_Part_1x2( B,    &BL,  &BR,      0, FLA_LEFT );

  FLA_Part_1x2( C,    &CL,  &CR,      0, FLA_LEFT );

  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 );

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, /**/ &b1, &B2,
                           1, FLA_RIGHT );

    FLA_Repart_1x2_to_1x3( CL,  /**/ CR,        &C0, /**/ &c1, &C2,
                           1, FLA_RIGHT );

    /*------------------------------------------------------------*/
		//c1 = (b1 * alpha11) + c1;
    FLA_Axpy(alpha11, b1, c1);
    
    //c1 = (B2 * a12t') + c1;
    FLA_Gemv(FLA_NO_TRANSPOSE, FLA_ONE, B2, a12t, FLA_ONE, c1);
    
    //C2 = (b1 * a12t) + C2
    FLA_Ger(FLA_ONE, a12t, b1, C0);

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

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

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, b1, /**/ B2,
                              FLA_LEFT );

    FLA_Cont_with_1x3_to_1x2( &CL,  /**/ &CR,        C0, c1, /**/ C2,
                              FLA_LEFT );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Trmm_rlt_blk_var2( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_trmm_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj BL,    BR,       B0,  B1,  B2;

  dim_t b;

  FLA_Scal_internal( alpha, B,
                     FLA_Cntl_sub_scal( cntl ) );

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

  FLA_Part_1x2( B,    &BL,  &BR,      0, FLA_RIGHT );

  while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){

    b = FLA_Determine_blocksize( ATL, FLA_TL, 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_TL );

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, &B1, /**/ &B2,
                           b, FLA_LEFT );

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

    /* B2 = B2 + B1 * A21'; */
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_TRANSPOSE,
                       FLA_ONE, B1, A21, FLA_ONE, B2,
                       FLA_Cntl_sub_gemm( cntl ) );

    /* B1 = B1 * tril( A11 )'; */
    FLA_Trmm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_TRANSPOSE, diagA,
                       FLA_ONE, A11, B1,
                       FLA_Cntl_sub_trmm( cntl ) );

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

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

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, /**/ B1, B2,
                              FLA_RIGHT );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Sylv_nn_blk_var17( FLA_Obj isgn, FLA_Obj A, FLA_Obj B, FLA_Obj C, FLA_Obj scale, fla_sylv_t* cntl )
{
  FLA_Obj BTL,   BTR,      B00, B01, B02, 
          BBL,   BBR,      B10, B11, B12,
                           B20, B21, B22;

  FLA_Obj CL,    CR,       C0,  C1,  C2;

  dim_t b;

  FLA_Part_2x2( B,    &BTL, &BTR,
                      &BBL, &BBR,     0, 0, FLA_TL );

  FLA_Part_1x2( C,    &CL,  &CR,      0, FLA_LEFT );

  while ( FLA_Obj_length( BTL ) < FLA_Obj_length( B ) ){

    b = FLA_Determine_blocksize( CR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( BTL, /**/ BTR,       &B00, /**/ &B01, &B02,
                        /* ************* */   /* ******************** */
                                                &B10, /**/ &B11, &B12,
                           BBL, /**/ BBR,       &B20, /**/ &B21, &B22,
                           b, b, FLA_BR );

    FLA_Repart_1x2_to_1x3( CL,  /**/ CR,        &C0, /**/ &C1, &C2,
                           b, FLA_RIGHT );

    // Loop Invariant:
    // CL = 
    // CR = 

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

    // C1 = sylv( A, B11, C1 -/+ C0 * B01 );
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_NEGATE( isgn ), C0, B01, FLA_ONE, C1,
                       FLA_Cntl_sub_gemm1( cntl ) );

    FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                       isgn, A, B11, C1, scale,
                       FLA_Cntl_sub_sylv1( cntl ) );

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

    FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR,       B00, B01, /**/ B02,
                                                     B10, B11, /**/ B12,
                            /* ************** */  /* ****************** */
                              &BBL, /**/ &BBR,       B20, B21, /**/ B22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &CL,  /**/ &CR,        C0, C1, /**/ C2,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Trsm_luc_unb_var1( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj BT,              B0,
          BB,              b1t,
                           B2;

  FLA_Scal_external( alpha, B );

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

  FLA_Part_2x1( B,    &BT, 
                      &BB,            0, FLA_BOTTOM );

  while ( FLA_Obj_length( ABR ) < 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_TL );

    FLA_Repart_2x1_to_3x1( BT,                &B0, 
                                              &b1t, 
                        /* ** */            /* *** */
                           BB,                &B2,        1, FLA_TOP );

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

    /* b1t = b1t - a12t * B2; */
    FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, B2, a12t, FLA_ONE, b1t );

    /* b1t = b1t / alpha11; */
    if ( diagA != FLA_UNIT_DIAG )
      FLA_Inv_scalc_external( FLA_CONJUGATE, alpha11, b1t );

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

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

    FLA_Cont_with_3x1_to_2x1( &BT,                B0, 
                            /* ** */           /* *** */
                                                  b1t, 
                              &BB,                B2,     FLA_BOTTOM );

  }

  return FLA_SUCCESS;
}
Example #7
0
FLA_Error FLA_Trmm_lln_unb_var2( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj BT,              B0,
          BB,              b1t,
                           B2;

  FLA_Scal_external( alpha, B );

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

  FLA_Part_2x1( B,    &BT, 
                      &BB,            0, FLA_BOTTOM );

  while ( FLA_Obj_length( ABR ) < 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_TL );

    FLA_Repart_2x1_to_3x1( BT,                &B0, 
                                              &b1t, 
                        /* ** */            /* *** */
                           BB,                &B2,        1, FLA_TOP );

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

    /* B2  = B2 + a21 * b1t; */
    FLA_Ger_external( FLA_ONE, a21, b1t, B2 );

    /* b1t = alpha11 * b1t; */
    if ( diagA != FLA_UNIT_DIAG )
      FLA_Scal_external( alpha11, b1t );

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

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

    FLA_Cont_with_3x1_to_2x1( &BT,                B0, 
                            /* ** */           /* *** */
                                                  b1t, 
                              &BB,                B2,     FLA_BOTTOM );

  }

  return FLA_SUCCESS;
}
Example #8
0
FLA_Error LU_blk_var4( FLA_Obj A, int nb_alg )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

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

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

    b = min( FLA_Obj_length( ABR ), nb_alg );

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

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

    /* A11 = A11 - A10 * A01 ); */
    FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
              FLA_MINUS_ONE, A10, A01, FLA_ONE, A11 );

    /* A11 = LU( A11 ); */
    LU_unb_var4( A11 );

    /* A12 = A12 - A10 * A02; */
    FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
              FLA_MINUS_ONE, A10, A02, FLA_ONE, A12 );

    /* A12 = inv( trilu( A11 ) ) * A12; */
    FLA_Trsm( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
              FLA_ONE, A11, A12 );

    /* A21 = A21 - A20 * A01; */
    FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
              FLA_MINUS_ONE, A20, A01, FLA_ONE, A21 );

    /* A21 = A21 * inv( triu( A11 ) ); */
    FLA_Trsm( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
              FLA_ONE, A11, A21 );

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

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

  return FLA_SUCCESS;
}
Example #9
0
FLA_Error FLA_QR_UT_unb_var1( FLA_Obj A, FLA_Obj t )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj tLt,   tRt,      t0t,  tau1,  t2t;


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

  FLA_Part_1x2( t,    &tLt,  &tRt,      0, FLA_LEFT );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

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

    FLA_Repart_1x2_to_1x3( tLt,  /**/ tRt,      &t0t, /**/ &tau1, &t2t,
                           1, FLA_RIGHT );

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

    // Compute tau11 and u21 from alpha11 and a21 such that tau11 and u21
    // determine a Householder transform H such that applying H from the
    // left to the column vector consisting of alpha11 and a21 annihilates
    // the entries in a21 (and updates alpha11).
    FLA_Househ2_UT( FLA_LEFT,
                    alpha11,
                    a21, tau1 );

    // / a12t \ =  H / a12t \
    // \ A22  /      \ A22  /
    //
    // where H is formed from tau11 and u21.
    FLA_Apply_H2_UT( FLA_LEFT, tau1, a21, a12t,
                                          A22 );

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

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

    FLA_Cont_with_1x3_to_1x2( &tLt,  /**/ &tRt,      t0t, tau1, /**/ t2t,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}
Example #10
0
FLA_Error FLA_Syrk_ln_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C )
{
  FLA_Obj AT,              A0,
          AB,              a1t,
                           A2;

  FLA_Obj CTL,   CTR,      C00,  c01,     C02, 
          CBL,   CBR,      c10t, gamma11, c12t,
                           C20,  c21,     C22;

  FLA_Scalr_external( FLA_LOWER_TRIANGULAR, beta, C );

  FLA_Part_2x1( A,    &AT, 
                      &AB,            0, FLA_BOTTOM );

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_BR );

  while ( FLA_Obj_length( AB ) < FLA_Obj_length( A ) ){

    FLA_Repart_2x1_to_3x1( AT,                &A0, 
                                              &a1t, 
                        /* ** */            /* *** */
                           AB,                &A2,        1, FLA_TOP );

    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00,  &c01,     /**/ &C02,
                                                &c10t, &gamma11, /**/ &c12t,
                        /* ************* */   /* ************************** */
                           CBL, /**/ CBR,       &C20,  &c21,     /**/ &C22,
                           1, 1, FLA_TL );

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

    /* c10t    = c10t    + A0  * a1t' */
    FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, A0, a1t, FLA_ONE, c10t );

    /* gamma11 = gamma11 + a1t * a1t' */
    FLA_Dots_external( alpha, a1t, a1t, FLA_ONE, gamma11 );

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

    FLA_Cont_with_3x1_to_2x1( &AT,                A0, 
                            /* ** */           /* *** */
                                                  a1t, 
                              &AB,                A2,     FLA_BOTTOM );

    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00,  /**/ c01,     C02,
                            /* ************** */  /* ************************ */
                                                     c10t, /**/ gamma11, c12t,
                              &CBL, /**/ &CBR,       C20,  /**/ c21,     C22,
                              FLA_BR );

  }

  return FLA_SUCCESS;
}
Example #11
0
int Trsm_unb_var2( FLA_Obj L, FLA_Obj B )
{
  FLA_Obj LTL,   LTR,      L00,  l01,      L02, 
          LBL,   LBR,      l10t, lambda11, l12t,
                           L20,  l21,      L22;

  FLA_Obj BT,              B0,
          BB,              b1t,
                           B2;

  FLA_Part_2x2( L,    &LTL, &LTR,
                      &LBL, &LBR,     0, 0, FLA_TL );

  FLA_Part_2x1( B,    &BT, 
                      &BB,            0, FLA_TOP );

  while ( FLA_Obj_length( LTL ) < FLA_Obj_length( L ) ){

    FLA_Repart_2x2_to_3x3( LTL, /**/ LTR,       &L00,  /**/ &l01,      &L02,
                        /* ************* */   /* *************************** */
                                                &l10t, /**/ &lambda11, &l12t,
                           LBL, /**/ LBR,       &L20,  /**/ &l21,      &L22,
                           1, 1, FLA_BR );

    FLA_Repart_2x1_to_3x1( BT,                &B0, 
                        /* ** */            /* *** */
                                              &b1t, 
                           BB,                &B2,        1, FLA_BOTTOM );

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

    /* b1t = b1t / lambda11 */
    FLA_Inv_scal( lambda11, b1t );

    /* B2 = B2 - l21 * b1t */
    FLA_Ger( FLA_MINUS_ONE, l21, b1t, B2 );


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

    FLA_Cont_with_3x3_to_2x2( &LTL, /**/ &LTR,       L00,  l01,      /**/ L02,
                                                     l10t, lambda11, /**/ l12t,
                            /* ************** */  /* ************************* */
                              &LBL, /**/ &LBR,       L20,  l21,      /**/ L22,
                              FLA_TL );

    FLA_Cont_with_3x1_to_2x1( &BT,                B0, 
                                                  b1t, 
                            /* ** */           /* *** */
                              &BB,                B2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}
Example #12
0
FLA_Error FLA_Syrk_ut_blk_var1( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C, fla_syrk_t* cntl )
{
  FLA_Obj AL,    AR,       A0,  A1,  A2;

  FLA_Obj CTL,   CTR,      C00, C01, C02, 
          CBL,   CBR,      C10, C11, C12,
                           C20, C21, C22;

  dim_t b;

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_LEFT );

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_TL );

  while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){

    b = FLA_Determine_blocksize( AR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_1x2_to_1x3( AL,  /**/ AR,        &A0, /**/ &A1, &A2,
                           b, FLA_RIGHT );

    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00, /**/ &C01, &C02,
                        /* ************* */   /* ******************** */
                                                &C10, /**/ &C11, &C12,
                           CBL, /**/ CBR,       &C20, /**/ &C21, &C22,
                           b, b, FLA_BR );

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

    /* C12 = C12 + A1' * A2 */
    FLA_Gemm_internal( FLA_TRANSPOSE, FLA_NO_TRANSPOSE, 
                       alpha, A1, A2, beta, C12,
                       FLA_Cntl_sub_gemm( cntl ) );

    /* C11 = C11 + A1' * A1 */
    FLA_Syrk_internal( FLA_UPPER_TRIANGULAR, FLA_TRANSPOSE, 
                       alpha, A1, beta, C11,
                       FLA_Cntl_sub_syrk( cntl ) );

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

    FLA_Cont_with_1x3_to_1x2( &AL,  /**/ &AR,        A0, A1, /**/ A2,
                              FLA_LEFT );

    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00, C01, /**/ C02,
                                                     C10, C11, /**/ C12,
                            /* ************** */  /* ****************** */
                              &CBL, /**/ &CBR,       C20, C21, /**/ C22,
                              FLA_TL );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Trinv_uu_blk_var3( FLA_Obj A, fla_trinv_t* cntl )
{
    FLA_Obj ATL,   ATR,      A00, A01, A02,
            ABL,   ABR,      A10, A11, A12,
            A20, A21, A22;

    dim_t b;

    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 );

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

        // A12 = -triuu( A11 ) \ A12;
        FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                           FLA_MINUS_ONE, A11, A12,
                           FLA_Cntl_sub_trsm1( cntl ) );

        // A02 = A01 * A12 + A02;
        FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                           FLA_ONE, A01, A12, FLA_ONE, A02,
                           FLA_Cntl_sub_gemm( cntl ) );

        // A01 = A01 / triuu( A11 );
        FLA_Trsm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                           FLA_ONE, A11, A01,
                           FLA_Cntl_sub_trsm2( cntl ) );

        // A11 = inv( A11 );
        FLA_Trinv_internal( FLA_UPPER_TRIANGULAR, FLA_NONUNIT_DIAG, A11,
                            FLA_Cntl_sub_trinv( cntl ) );

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

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

    }

    return FLA_SUCCESS;
}
Example #14
0
FLA_Error FLA_Chol_u_blk_var1( FLA_Obj A, fla_chol_t* cntl )
{
  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;
}
Example #15
0
int LU_blk_var3( FLA_Obj A, int nb_alg )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  int b;

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

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

    b = min( FLA_Obj_length( ABR ), nb_alg );

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

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

    // A01 := inv(L00) * A01
    FLA_Trsm( FLA_LEFT, FLA_LOWER_TRIANGULAR,
	      FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
	      FLA_ONE, A00, A01 );

    // A11 := LU(A11 - A10 * A01)
    FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                FLA_MINUS_ONE, A10, A01, FLA_ONE, A11);
    LU_unb_var3(A11);

    // A21 := (A21 - A20 * A01) * inv(U11)
    FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
	      FLA_MINUS_ONE, A20, A01, FLA_ONE, A21);
    FLA_Trsm( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
	      FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
	      FLA_ONE, A11, A21);

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

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

  }

  return FLA_SUCCESS;
}
int SLAP_Syrk_ln_unb_var3( FLA_Obj A, FLA_Obj C )
{
  FLA_Obj AT,              A0,
          AB,              a1t,
                           A2;

  FLA_Obj CTL,   CTR,      C00,  c01,     C02, 
          CBL,   CBR,      c10t, gamma11, c12t,
                           C20,  c21,     C22;

  FLA_Part_2x1( A,    &AT, 
                      &AB,            0, FLA_BOTTOM );

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_BR );

  while ( FLA_Obj_length( AB ) < FLA_Obj_length( A ) ){

    FLA_Repart_2x1_to_3x1( AT,                &A0, 
                                              &a1t, 
                        /* ** */            /* *** */
                           AB,                &A2,        1, FLA_TOP );

    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00,  &c01,     /**/ &C02,
                                                &c10t, &gamma11, /**/ &c12t,
                        /* ************* */   /* ************************** */
                           CBL, /**/ CBR,       &C20,  &c21,     /**/ &C22,
                           1, 1, FLA_TL );

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

    	    FLA_Gemv(FLA_NO_TRANSPOSE, FLA_ONE, A2, a1t, FLA_ONE, c21);
	    FLA_Dots(FLA_ONE, a1t, a1t, FLA_ONE, gamma11);

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

    FLA_Cont_with_3x1_to_2x1( &AT,                A0, 
                            /* ** */           /* *** */
                                                  a1t, 
                              &AB,                A2,     FLA_BOTTOM );

    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00,  /**/ c01,     C02,
                            /* ************** */  /* ************************ */
                                                     c10t, /**/ gamma11, c12t,
                              &CBL, /**/ &CBR,       C20,  /**/ c21,     C22,
                              FLA_BR );

  }

  return FLA_SUCCESS;
}
Example #17
0
FLA_Error FLA_Herk_lh_unb_var1( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C )
{
  FLA_Obj AL,    AR,       A0,  a1,  A2;

  FLA_Obj CTL,   CTR,      C00,  c01,     C02, 
          CBL,   CBR,      c10t, gamma11, c12t,
                           C20,  c21,     C22;

  FLA_Scalr_external( FLA_LOWER_TRIANGULAR, beta, C );

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_LEFT );

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_TL );

  while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){

    FLA_Repart_1x2_to_1x3( AL,  /**/ AR,        &A0, /**/ &a1, &A2,
                           1, FLA_RIGHT );

    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00,  /**/ &c01,     &C02,
                        /* ************* */   /* ************************** */
                                                &c10t, /**/ &gamma11, &c12t,
                           CBL, /**/ CBR,       &C20,  /**/ &c21,     &C22,
                           1, 1, FLA_BR );

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

    /* C10 = C10 + A1' * A0 */
    /* c10t    = c10t    + A0' * a1 */
    FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, alpha, A0, a1, FLA_ONE, c10t );

    /* gamma11 = gamma11 + a1' * a1 */
    FLA_Dotcs_external( FLA_CONJUGATE, alpha, a1, a1, FLA_ONE, gamma11 );

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

    FLA_Cont_with_1x3_to_1x2( &AL,  /**/ &AR,        A0, a1, /**/ A2,
                              FLA_LEFT );

    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00,  c01,     /**/ C02,
                                                     c10t, gamma11, /**/ c12t,
                            /* ************** */  /* ************************ */
                              &CBL, /**/ &CBR,       C20,  c21,     /**/ C22,
                              FLA_TL );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_nopiv_unb_var3( FLA_Obj A )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

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

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

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

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

    // a01 = trilu( A00 ) \ a10
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );

    // alpha11 = alpha11 - a10t * a01
    FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    // a21 = a21 - A20 * a01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    // a21 = a21 / alpha11
    FLA_Inv_scal_external( alpha11, a21 );

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

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

  }

  if ( FLA_Obj_width( ATR ) > 0 )
    // ATR = trilu( ATL ) \ ATR
    FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, ATL, ATR );

  return FLA_SUCCESS;
}
Example #19
0
FLA_Error FLA_Trmm_run_unb_var2( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj BL,    BR,       B0,  b1,  B2;

  FLA_Scal_external( alpha, B );

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

  FLA_Part_1x2( B,    &BL,  &BR,      0, FLA_RIGHT );

  while ( FLA_Obj_length( ABR ) < 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_TL );

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, &b1, /**/ &B2,
                           1, FLA_LEFT );

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

    /* B2 = B2 + b1 * a12t; */
    FLA_Ger_external( FLA_ONE, b1, a12t, B2 );

    /* b1 = b1 * alpha11; */
    if ( diagA != FLA_UNIT_DIAG )
      FLA_Scal_external( alpha11, b1 );

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

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

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, /**/ b1, B2,
                              FLA_RIGHT );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Trsm_rlc_unb_var1( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj BL,    BR,       B0,  b1,  B2;

  FLA_Scal_external( alpha, B );

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

  FLA_Part_1x2( B,    &BL,  &BR,      0, FLA_RIGHT );

  while ( FLA_Obj_length( ABR ) < 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_TL );

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, &b1, /**/ &B2,
                           1, FLA_LEFT );

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

    /* b1 = b1 - B2 * a21; */
    FLA_Gemvc_external( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, B2, a21, FLA_ONE, b1 );

    /* b1 = b1 / alpha11; */
    if ( diagA != FLA_UNIT_DIAG )
      FLA_Inv_scalc_external( FLA_CONJUGATE, alpha11, b1 );

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

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

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, /**/ b1, B2,
                              FLA_RIGHT );

  }

  return FLA_SUCCESS;
}
Example #21
0
FLA_Error FLA_Syrk_ut_unb_var3( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C )
{
  FLA_Obj AL,    AR,       A0,  a1,  A2;

  FLA_Obj CTL,   CTR,      C00,  c01,     C02, 
          CBL,   CBR,      c10t, gamma11, c12t,
                           C20,  c21,     C22;

  FLA_Scalr_external( FLA_UPPER_TRIANGULAR, beta, C );

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_RIGHT );

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_BR );

  while ( FLA_Obj_width( AR ) < FLA_Obj_width( A ) ){

    FLA_Repart_1x2_to_1x3( AL,  /**/ AR,        &A0, &a1, /**/ &A2,
                           1, FLA_LEFT );

    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00,  &c01,     /**/ &C02,
                                                &c10t, &gamma11, /**/ &c12t,
                        /* ************* */   /* ************************** */
                           CBL, /**/ CBR,       &C20,  &c21,     /**/ &C22,
                           1, 1, FLA_TL );

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

    /* c12t    = c12t    + A2' * a1 */
    FLA_Gemv_external( FLA_TRANSPOSE, alpha, A2, a1, FLA_ONE, c12t );

    /* gamma11 = gamma11 + a1 * a1' */
    FLA_Dots_external( alpha, a1, a1, FLA_ONE, gamma11 );

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

    FLA_Cont_with_1x3_to_1x2( &AL,  /**/ &AR,        A0, /**/ a1, A2,
                              FLA_RIGHT );

    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00,  /**/ c01,     C02,
                            /* ************** */  /* ************************ */
                                                     c10t, /**/ gamma11, c12t,
                              &CBL, /**/ &CBR,       C20,  /**/ c21,     C22,
                              FLA_BR );

  }

  return FLA_SUCCESS;
}
Example #22
0
FLA_Error FLA_Ttmm_u_blk_var1( FLA_Obj A, fla_ttmm_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

  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 );

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

    // A00 = A00 + A01 * A01'
    FLA_Herk_internal( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
                       FLA_ONE, A01, FLA_ONE, A00,
                       FLA_Cntl_sub_herk( cntl ) );

    // A01 = A01 * triu( A11 )'
    FLA_Trmm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, A11, A01,
                       FLA_Cntl_sub_trmm( cntl ) );

    // A11 = triu( A11 ) * triu( A11 )'
    FLA_Ttmm_internal( FLA_UPPER_TRIANGULAR, A11,
                       FLA_Cntl_sub_ttmm( cntl ) );

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

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

  }

  return FLA_SUCCESS;
}
Example #23
0
FLA_Error FLA_Chol_u_unb_var2( FLA_Obj A )
{
  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;
}
Example #24
0
FLA_Error FLA_Chol_l_unb_var1( FLA_Obj A )
{
  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 );

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

    // a10t = a10t * inv( tril( A00 )' )
    // a10t' = inv( conj( tril( A00 ) ) ) * a10t'
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a10t );

    // alpha11 = alpha11 - a10t * a10t'
    FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a10t, a10t, 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;
}
Example #25
0
FLA_Error FLA_Chol_u_unb_var3( FLA_Obj A )
{
  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;
}
FLA_Error FLA_Trinv_ln_unb_var3( FLA_Obj A )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  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 );

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

    // a21 = -a21 / alpha11;
    FLA_Scal_external( FLA_MINUS_ONE, a21 );
    FLA_Inv_scal_external( alpha11, a21 );

    // A20 = a21 * a10t + A20;
    FLA_Ger_external( FLA_ONE, a21, a10t, A20 );

    // a10t = a10t / alpha11;
    FLA_Inv_scal_external( alpha11, a10t );

    // alpha11 = 1.0 / alpha11;
    FLA_Invert( FLA_NO_CONJUGATE, alpha11 );

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

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

  }

  return FLA_SUCCESS;
}
Example #27
0
FLA_Error FLA_Chol_l_unb_var3( FLA_Obj A )
{
  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 = sqrt( alpha11 )
    r_val = FLA_Sqrt( alpha11 );

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

    // a21 = a21 / alpha11
    FLA_Inv_scal_external( alpha11, a21 );

    // A22 = A22 - a21 * a21'
    FLA_Her_external( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, a21, A22 );

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

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

  return r_val;
}
Example #28
0
FLA_Error LU_unb_var4( FLA_Obj A )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  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 - a10t * a01; */
    FLA_Dots( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    /* a12t = a12t - a10t * A02; */
    FLA_Gemv( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );

    /* a21 = a21 - A20 * a01; */
    FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    /* a21 = a21 / alpha11; */
    FLA_Inv_scal( alpha11, a21 );

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

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

  return FLA_SUCCESS;
}
Example #29
0
FLA_Error FLA_Scalr_u_blk_var4( FLA_Obj alpha, FLA_Obj A, fla_scalr_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  dim_t b;

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

  while ( FLA_Obj_min_dim( ATL ) > 0 ){

    b = FLA_Determine_blocksize( ATL, FLA_TL, 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_TL );

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

    // A11 = alpha * triu( A11 );
    FLA_Scalr_internal( FLA_UPPER_TRIANGULAR, alpha, A11,
                        FLA_Cntl_sub_scalr( cntl ) );

    // A01 = alpha * A01;
    FLA_Scal_internal( alpha, A01,
                       FLA_Cntl_sub_scal( cntl ) );

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

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

  return FLA_SUCCESS;
}
FLA_Error FLA_Trinv_ln_unb_var2( FLA_Obj A )
{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  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 );

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

    // a21 = tril( A22 ) \ a21;
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, A22, a21 );

    // a21 = -a21 / alpha11;
    FLA_Scal_external( FLA_MINUS_ONE, a21 );
    FLA_Inv_scal_external( alpha11, a21 );

    // alpha11 = 1.0 / alpha11;
    FLA_Invert( FLA_NO_CONJUGATE, alpha11 );

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

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

  }

  return FLA_SUCCESS;
}