FLA_Error FLA_Hemm_ru_blk_var10( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl )
{
  FLA_Obj BT,              B0,
          BB,              B1,
                           B2;

  FLA_Obj CT,              C0,
          CB,              C1,
                           C2;

  dim_t b;

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

  FLA_Part_2x1( C,    &CT, 
                      &CB,            0, FLA_BOTTOM );

  while ( FLA_Obj_length( BB ) < FLA_Obj_length( B ) ){

    b = FLA_Determine_blocksize( BT, FLA_TOP, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x1_to_3x1( BT,                &B0, 
                                              &B1, 
                        /* ** */            /* ** */
                           BB,                &B2,        b, FLA_TOP );

    FLA_Repart_2x1_to_3x1( CT,                &C0, 
                                              &C1, 
                        /* ** */            /* ** */
                           CB,                &C2,        b, FLA_TOP );

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

    /* C1 = C1 + B1 * A */
    FLA_Hemm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                       alpha, A, B1, beta, C1,
                       FLA_Cntl_sub_hemm( cntl ) );

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

    FLA_Cont_with_3x1_to_2x1( &BT,                B0, 
                            /* ** */           /* ** */
                                                  B1, 
                              &BB,                B2,     FLA_BOTTOM );

    FLA_Cont_with_3x1_to_2x1( &CT,                C0, 
                            /* ** */           /* ** */
                                                  C1, 
                              &CB,                C2,     FLA_BOTTOM );

  }

  return FLA_SUCCESS;
}
Beispiel #2
0
FLA_Error FLA_Hemm_lu_blk_var9( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl )
{
  FLA_Obj BL,    BR,       B0,  B1,  B2;

  FLA_Obj CL,    CR,       C0,  C1,  C2;

  dim_t b;

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

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

  while ( FLA_Obj_width( BL ) < FLA_Obj_width( B ) ){

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

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

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

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

    /* C1 = C1 + A * B1 */
    FLA_Hemm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                       alpha, A, B1, beta, C1,
                       FLA_Cntl_sub_hemm( cntl ) );

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

    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_Eig_gest_nl_blk_var1( FLA_Obj A, FLA_Obj Y, FLA_Obj B, fla_eig_gest_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02,
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj BTL,   BTR,      B00, B01, B02,
          BBL,   BBR,      B10, B11, B12,
                           B20, B21, B22;

  FLA_Obj YT,              Y01,
          YB,              Y11,
                           Y21;

  FLA_Obj Y21_l, Y21_r;

  dim_t b;

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

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

  FLA_Part_2x1( Y,    &YT, 
                      &YB,            0, FLA_TOP );

  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 );

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

    FLA_Repart_2x1_to_3x1( YT,                  &Y01,
                        /* ** */              /* *** */
                                                &Y11,
                           YB,                  &Y21,        b, FLA_BOTTOM );

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

    FLA_Part_1x2( Y21,    &Y21_l, &Y21_r,     b, FLA_LEFT );

    // Y21 = A22 * B21;
    FLA_Hemm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
                       FLA_ONE, A22, B21, FLA_ZERO, Y21_l,
                       FLA_Cntl_sub_hemm( cntl ) );

    // A21 = A21 * tril( B11 );
    FLA_Trmm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
                       FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, B11, A21,
                       FLA_Cntl_sub_trmm1( cntl ) );

    // A21 = A21 + 1/2 * Y21;
    FLA_Axpy_internal( FLA_ONE_HALF, Y21_l, A21,
                       FLA_Cntl_sub_axpy1( cntl ) );

    // A11 = tril( B11 )' * A11 * tril( B11 );
    FLA_Eig_gest_internal( FLA_NO_INVERSE, FLA_LOWER_TRIANGULAR,
                           A11, Y11, B11,
                           FLA_Cntl_sub_eig_gest( cntl ) );

    // A11 = A11 + A21' * B21 + B21' * A21;
    FLA_Her2k_internal( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE,
                        FLA_ONE, A21, B21, FLA_ONE, A11,
                        FLA_Cntl_sub_her2k( cntl ) );

    // A21 = A21 + 1/2 * Y21;
    FLA_Axpy_internal( FLA_ONE_HALF, Y21_l, A21,
                       FLA_Cntl_sub_axpy2( cntl ) );

    // A21 = tril( B22 )' * A21;
    FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
                       FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, B22, A21,
                       FLA_Cntl_sub_trmm2( cntl ) );

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

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

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

    FLA_Cont_with_3x1_to_2x1( &YT,                   Y01,
                                                     Y11,
                            /* ** */              /* *** */
                              &YB,                   Y21,     FLA_TOP );
  }

  return FLA_SUCCESS;
}
Beispiel #4
0
FLA_Error FLA_Hemm_lu_blk_var3( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj BT,              B0,
          BB,              B1,
                           B2;

  FLA_Obj CT,              C0,
          CB,              C1,
                           C2;

  dim_t b;

  FLA_Scal_internal( beta, C,
                     FLA_Cntl_sub_scal( cntl ) );

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

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

  FLA_Part_2x1( C,    &CT, 
                      &CB,            0, FLA_TOP );

  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 );

    FLA_Repart_2x1_to_3x1( BT,                &B0, 
                        /* ** */            /* ** */
                                              &B1, 
                           BB,                &B2,        b, FLA_BOTTOM );

    FLA_Repart_2x1_to_3x1( CT,                &C0, 
                        /* ** */            /* ** */
                                              &C1, 
                           CB,                &C2,        b, FLA_BOTTOM );

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

    /* C1 = C1 + A11 * B1 */
    FLA_Hemm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                       alpha, A11, B1, FLA_ONE, C1,
                       FLA_Cntl_sub_hemm( cntl ) );

    /* C1 = C1 + A12 * B2 */
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                       alpha, A12, B2, FLA_ONE, C1,
                       FLA_Cntl_sub_gemm1( cntl ) );

    /* C2 = C2 + A12' * B1 */
    FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, 
                       alpha, A12, B1, FLA_ONE, C2,
                       FLA_Cntl_sub_gemm2( cntl ) );

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

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

    FLA_Cont_with_3x1_to_2x1( &BT,                B0, 
                                                  B1, 
                            /* ** */           /* ** */
                              &BB,                B2,     FLA_TOP );

    FLA_Cont_with_3x1_to_2x1( &CT,                C0, 
                                                  C1, 
                            /* ** */           /* ** */
                              &CB,                C2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Lyap_n_blk_var1( FLA_Obj isgn, FLA_Obj A, FLA_Obj C, FLA_Obj scale, fla_lyap_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;
  FLA_Obj CTL,   CTR,      C00, C01, C02, 
          CBL,   CBR,      C10, C11, C12,
                           C20, C21, C22;
  dim_t   b;

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

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

  while ( FLA_Obj_length( CTL ) > 0 ){

    b = FLA_Determine_blocksize( CTL, 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_2x2_to_3x3( CTL, /**/ CTR,       &C00, &C01, /**/ &C02,
                                                &C10, &C11, /**/ &C12,
                        /* ************* */   /* ******************** */
                           CBL, /**/ CBR,       &C20, &C21, /**/ &C22,
                           b, b, FLA_TL );

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

    // C12 = isgn * C12 - A12 * C22;
    // C12 = sylv( A11, A22', C12 );
    FLA_Hemm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
                       FLA_MINUS_ONE, C22, A12, isgn, C12,
                       FLA_Cntl_sub_hemm( cntl ) );
    FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                       FLA_ONE, A11, A22, C12, scale,
                       FLA_Cntl_sub_sylv( cntl ) );

    // C11 = isgn * C11 - A12 * C12' - C12 * A12';
    FLA_Her2k_internal( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
                        FLA_MINUS_ONE, A12, C12, isgn, C11,
                        FLA_Cntl_sub_her2k( cntl ) );

    // C11 = lyap_n( A11, C11 );
    FLA_Lyap_internal( FLA_NO_TRANSPOSE, FLA_ONE, A11, C11, scale,
                       FLA_Cntl_sub_lyap( 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_3x3_to_2x2( &CTL, /**/ &CTR,       C00, /**/ C01, C02,
                            /* ************** */  /* ****************** */
                                                     C10, /**/ C11, C12,
                              &CBL, /**/ &CBR,       C20, /**/ C21, C22,
                              FLA_BR );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Eig_gest_il_blk_var2( FLA_Obj A, FLA_Obj Y, FLA_Obj B, fla_eig_gest_t* cntl )
{
  FLA_Obj ATL,   ATR,      A00, A01, A02,
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj BTL,   BTR,      B00, B01, B02,
          BBL,   BBR,      B10, B11, B12,
                           B20, B21, B22;

  FLA_Obj YL,    YR,       Y10, Y11, Y12;

  FLA_Obj Y10_t,
          Y10_b;

  dim_t b;

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

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

  FLA_Part_1x2( Y,    &YL,  &YR,      0, FLA_LEFT );

  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 );

    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( YL,  /**/ YR,        &Y10, /**/ &Y11, &Y12,
                           b, FLA_RIGHT );

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

    FLA_Part_2x1( Y10,   &Y10_t, 
                         &Y10_b,    b, FLA_TOP );

    // Y10 = 1/2 * B10 * A00;
    FLA_Hemm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
                       FLA_ONE_HALF, A00, B10, FLA_ZERO, Y10_t,
                       FLA_Cntl_sub_hemm( cntl ) );

    // A10 = A10 - Y10;
    FLA_Axpy_internal( FLA_MINUS_ONE, Y10_t, A10,
                       FLA_Cntl_sub_axpy1( cntl ) );

    // A11 = A11 - A10 * B10' - B10 * A10';
    FLA_Her2k_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
                        FLA_MINUS_ONE, A10, B10, FLA_ONE, A11,
                        FLA_Cntl_sub_her2k( cntl ) );

    // A11 = inv( tril( B11 ) ) * A11 * inv( tril( B11 )' );
    FLA_Eig_gest_internal( FLA_INVERSE, FLA_LOWER_TRIANGULAR,
                           A11, Y11, B11,
                           FLA_Cntl_sub_eig_gest( cntl ) );

    // A21 = A21 - A20 * B10';
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, A20, B10, FLA_ONE, A21,
                       FLA_Cntl_sub_gemm1( cntl ) );

    // A21 = A21 * inv( tril( B11 )' );
    FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
                       FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, B11, A21,
                       FLA_Cntl_sub_trsm1( cntl ) );

    // A10 = A10 - Y10;
    FLA_Axpy_internal( FLA_MINUS_ONE, Y10_t, A10,
                       FLA_Cntl_sub_axpy2( cntl ) );

    // A10 = inv( tril( B11 ) ) * A10;
    FLA_Trsm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, B11, A10,
                       FLA_Cntl_sub_trsm2( cntl ) );

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

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

    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( &YL,  /**/ &YR,        Y10, Y11, /**/ Y12,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}
Beispiel #7
0
FLA_Error FLA_Hemm_rl_blk_var6( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl )
{
  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;

  dim_t b;

  FLA_Scal_internal( beta, C,
                     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 );

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

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

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

    /* C1 = C1 + B0 * A10' */
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, 
                       alpha, B0, A10, FLA_ONE, C1,
                       FLA_Cntl_sub_gemm1( cntl ) );

    /* C1 = C1 + B1 * A11 */
    FLA_Hemm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR, 
                       alpha, A11, B1, FLA_ONE, C1,
                       FLA_Cntl_sub_hemm( cntl ) );

    /* C1 = C1 + B2 * A21 */
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                       alpha, B2, A21, FLA_ONE, C1,
                       FLA_Cntl_sub_gemm2( 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 );

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

  }

  return FLA_SUCCESS;
}