FLA_Chol_l.h File Reference

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Functions

FLA_Error FLA_Chol_l_blk_var1 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_l_blk_var2 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_l_blk_var3 (FLA_Obj A, fla_chol_t *cntl)
FLA_Error FLA_Chol_l_unb_var1 (FLA_Obj A)
FLA_Error FLA_Chol_l_unb_var2 (FLA_Obj A)
FLA_Error FLA_Chol_l_unb_var3 (FLA_Obj A)


Function Documentation

FLA_Error FLA_Chol_l_blk_var1 ( FLA_Obj  A,
fla_chol_t cntl 
)

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

Referenced by FLA_Chol_l().

00038 {
00039   FLA_Obj ATL,   ATR,      A00, A01, A02,
00040           ABL,   ABR,      A10, A11, A12,
00041                            A20, A21, A22;
00042 
00043   dim_t b;
00044 
00045   int value = 0;
00046 
00047   FLA_Part_2x2( A,    &ATL, &ATR,
00048                       &ABL, &ABR,     0, 0, FLA_TL );
00049 
00050   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00051 
00052     b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
00053 
00054     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
00055                         /* ************* */   /* ******************** */
00056                                                 &A10, /**/ &A11, &A12,
00057                            ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
00058                            b, b, FLA_BR );
00059 
00060     /*------------------------------------------------------------*/
00061 
00062     if ( FLA_Obj_is_real( A ) )
00063     {
00064       /* A10 = A10 * inv( tril( A00 )' ); */
00065       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00066                          FLA_TRANSPOSE, FLA_NONUNIT_DIAG,
00067                          FLA_ONE, A00, A10,
00068                          FLA_Cntl_sub_trsm( cntl ) );
00069 
00070       /* A11 = A11 - A10 * A10'; */
00071       FLA_Syrk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00072                          FLA_MINUS_ONE, A10, FLA_ONE, A11,
00073                          FLA_Cntl_sub_syrk( cntl ) );
00074 
00075       /* A11 = chol( A11 ); */
00076       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00077                                  FLA_Cntl_sub_chol( cntl ) );
00078 
00079       if ( value != FLA_SUCCESS )
00080         return ( FLA_Obj_length( A00 ) + value );
00081     }
00082     else
00083     {
00084       /* A10 = A10 * inv( tril( A00 )' ); */
00085       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00086                          FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
00087                          FLA_ONE, A00, A10,
00088                          FLA_Cntl_sub_trsm( cntl ) );
00089 
00090       /* A11 = A11 - A10 * A10'; */
00091       FLA_Herk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00092                          FLA_MINUS_ONE, A10, FLA_ONE, A11,
00093                          FLA_Cntl_sub_herk( cntl ) );
00094 
00095       /* A11 = chol( A11 ); */
00096       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00097                                  FLA_Cntl_sub_chol( cntl ) );
00098 
00099       if ( value != FLA_SUCCESS )
00100         return ( FLA_Obj_length( A00 ) + value );
00101     }
00102 
00103     /*------------------------------------------------------------*/
00104 
00105     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
00106                                                      A10, A11, /**/ A12,
00107                             /* ************** */  /* ****************** */
00108                               &ABL, /**/ &ABR,       A20, A21, /**/ A22,
00109                               FLA_TL );
00110   }
00111 
00112   return value;
00113 }

FLA_Error FLA_Chol_l_blk_var2 ( FLA_Obj  A,
fla_chol_t cntl 
)

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

Referenced by FLA_Chol_l().

00038 {
00039   FLA_Obj ATL,   ATR,      A00, A01, A02,
00040           ABL,   ABR,      A10, A11, A12,
00041                            A20, A21, A22;
00042 
00043   dim_t b;
00044 
00045   int value = 0;
00046 
00047   FLA_Part_2x2( A,    &ATL, &ATR,
00048                       &ABL, &ABR,     0, 0, FLA_TL );
00049 
00050   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00051 
00052     b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
00053 
00054     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
00055                         /* ************* */   /* ******************** */
00056                                                 &A10, /**/ &A11, &A12,
00057                            ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
00058                            b, b, FLA_BR );
00059 
00060     /*------------------------------------------------------------*/
00061 
00062     if ( FLA_Obj_is_real( A ) )
00063     {
00064       /* A11 = A11 - A10 * A10'; */
00065       FLA_Syrk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00066                          FLA_MINUS_ONE, A10, FLA_ONE, A11,
00067                          FLA_Cntl_sub_syrk( cntl ) );
00068 
00069       /* A21 = A21 - A20 * A10'; */
00070       FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_TRANSPOSE,
00071                          FLA_MINUS_ONE, A20, A10, FLA_ONE, A21,
00072                          FLA_Cntl_sub_gemm( cntl ) );
00073 
00074       /* A11 = chol( A11 ); */
00075       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00076                                  FLA_Cntl_sub_chol( cntl ) );
00077 
00078       if ( value != FLA_SUCCESS )
00079         return ( FLA_Obj_length( A00 ) + value );
00080 
00081       /* A21 = A21 * inv( tril( A11 )' ); */
00082       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00083                          FLA_TRANSPOSE, FLA_NONUNIT_DIAG,
00084                          FLA_ONE, A11, A21,
00085                          FLA_Cntl_sub_trsm( cntl ) );
00086     }
00087     else
00088     {
00089       /* A11 = A11 - A10 * A10'; */
00090       FLA_Herk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00091                          FLA_MINUS_ONE, A10, FLA_ONE, A11,
00092                          FLA_Cntl_sub_herk( cntl ) );
00093 
00094       /* A21 = A21 - A20 * A10'; */
00095       FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
00096                          FLA_MINUS_ONE, A20, A10, FLA_ONE, A21,
00097                          FLA_Cntl_sub_gemm( cntl ) );
00098 
00099       /* A11 = chol( A11 ); */
00100       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00101                                  FLA_Cntl_sub_chol( cntl ) );
00102 
00103       if ( value != FLA_SUCCESS )
00104         return ( FLA_Obj_length( A00 ) + value );
00105 
00106       /* A21 = A21 * inv( tril( A11 )' ); */
00107       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00108                          FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
00109                          FLA_ONE, A11, A21,
00110                          FLA_Cntl_sub_trsm( cntl ) );
00111     }
00112 
00113     /*------------------------------------------------------------*/
00114 
00115     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
00116                                                      A10, A11, /**/ A12,
00117                             /* ************** */  /* ****************** */
00118                               &ABL, /**/ &ABR,       A20, A21, /**/ A22,
00119                               FLA_TL );
00120   }
00121 
00122   return value;
00123 }

FLA_Error FLA_Chol_l_blk_var3 ( FLA_Obj  A,
fla_chol_t cntl 
)

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

Referenced by FLA_Chol_l().

00036 {
00037   FLA_Obj ATL,   ATR,      A00, A01, A02,
00038           ABL,   ABR,      A10, A11, A12,
00039                            A20, A21, A22;
00040 
00041   dim_t b;
00042 
00043   int value = 0;
00044 
00045   FLA_Part_2x2( A,    &ATL, &ATR,
00046                       &ABL, &ABR,     0, 0, FLA_TL );
00047 
00048   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00049 
00050     b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
00051 
00052     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
00053                         /* ************* */   /* ******************** */
00054                                                 &A10, /**/ &A11, &A12,
00055                            ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
00056                            b, b, FLA_BR );
00057 
00058     /*------------------------------------------------------------*/
00059 
00060     if ( FLA_Obj_is_real( A ) )
00061     {
00062       /* A11 = chol( A11 ); */
00063       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00064                                  FLA_Cntl_sub_chol( cntl ) );
00065 
00066       if ( value != FLA_SUCCESS )
00067         return ( FLA_Obj_length( A00 ) + value );
00068 
00069       /* A21 = A21 * inv( tril( A11 )' ); */
00070       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00071                          FLA_TRANSPOSE, FLA_NONUNIT_DIAG,
00072                          FLA_ONE, A11, A21,
00073                          FLA_Cntl_sub_trsm( cntl ) );
00074 
00075       /* A22 = A22 - A21 * A21'; */
00076       FLA_Syrk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00077                          FLA_MINUS_ONE, A21, FLA_ONE, A22,
00078                          FLA_Cntl_sub_syrk( cntl ) );
00079     }
00080     else
00081     {
00082       /* A11 = chol( A11 ); */
00083       value = FLA_Chol_internal( FLA_LOWER_TRIANGULAR, A11,
00084                                  FLA_Cntl_sub_chol( cntl ) );
00085 
00086       if ( value != FLA_SUCCESS )
00087         return ( FLA_Obj_length( A00 ) + value );
00088 
00089       /* A21 = A21 * inv( tril( A11 )' ); */
00090       FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
00091                          FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
00092                          FLA_ONE, A11, A21,
00093                          FLA_Cntl_sub_trsm( cntl ) );
00094 
00095       /* A22 = A22 - A21 * A21'; */
00096       FLA_Herk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE,
00097                          FLA_MINUS_ONE, A21, FLA_ONE, A22,
00098                          FLA_Cntl_sub_herk( cntl ) );
00099     }
00100 
00101     /*------------------------------------------------------------*/
00102 
00103     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
00104                                                      A10, A11, /**/ A12,
00105                             /* ************** */  /* ****************** */
00106                               &ABL, /**/ &ABR,       A20, A21, /**/ A22,
00107                               FLA_TL );
00108   }
00109 
00110   return value;
00111 }

FLA_Error FLA_Chol_l_unb_var1 ( FLA_Obj  A  ) 

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

00038 {
00039   FLA_Obj ATL,   ATR,      A00,  a01,     A02,
00040           ABL,   ABR,      a10t, alpha11, a12t,
00041                            A20,  a21,     A22;
00042 
00043   int value = 0;
00044 
00045   FLA_Part_2x2( A,    &ATL, &ATR,
00046                       &ABL, &ABR,     0, 0, FLA_TL );
00047 
00048   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00049 
00050     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
00051                         /* ************* */   /* ************************** */
00052                                                 &a10t, /**/ &alpha11, &a12t,
00053                            ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
00054                            1, 1, FLA_BR );
00055 
00056     /*------------------------------------------------------------*/
00057 
00058     if ( FLA_Obj_is_real( A ) )
00059     {
00060       /* a10t = a10t * inv( tril( A00 )' ); */
00061       /* a10t' = inv( tril( A00 ) ) * a10t'; */
00062       FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a10t );
00063 
00064       /* alpha11 = alpha11 - a10t * a10t'; */
00065       FLA_Dots_external( FLA_MINUS_ONE, a10t, a10t, FLA_ONE, alpha11 );
00066 
00067       /* alpha11 = sqrt( alpha11 ); */
00068       value = FLA_Sqrt( alpha11 );
00069 
00070       if ( value != FLA_SUCCESS )
00071         return ( FLA_Obj_length( A00 ) + 1 );
00072     }
00073     else
00074     {
00075       /* a10t = a10t * inv( tril( A00 )' ); */
00076       /* a10t' = inv( conj( tril( A00 ) ) ) * a10t'; */
00077       FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG, A00, a10t );
00078 
00079       /* alpha11 = alpha11 - a10t * a10t'; */
00080       FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a10t, a10t, FLA_ONE, alpha11 );
00081 
00082       /* alpha11 = sqrt( alpha11 ); */
00083       value = FLA_Sqrt( alpha11 );
00084 
00085       if ( value != FLA_SUCCESS )
00086         return ( FLA_Obj_length( A00 ) + 1 );
00087     }
00088 
00089     /*------------------------------------------------------------*/
00090 
00091     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
00092                                                      a10t, alpha11, /**/ a12t,
00093                             /* ************** */  /* ************************ */
00094                               &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
00095                               FLA_TL );
00096   }
00097 
00098   return value;
00099 }

FLA_Error FLA_Chol_l_unb_var2 ( FLA_Obj  A  ) 

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

00038 {
00039   FLA_Obj ATL,   ATR,      A00,  a01,     A02,
00040           ABL,   ABR,      a10t, alpha11, a12t,
00041                            A20,  a21,     A22;
00042 
00043   int value = 0;
00044 
00045   FLA_Part_2x2( A,    &ATL, &ATR,
00046                       &ABL, &ABR,     0, 0, FLA_TL );
00047 
00048   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00049 
00050     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
00051                         /* ************* */   /* ************************** */
00052                                                 &a10t, /**/ &alpha11, &a12t,
00053                            ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
00054                            1, 1, FLA_BR );
00055 
00056     /*------------------------------------------------------------*/
00057 
00058     if ( FLA_Obj_is_real( A ) )
00059     {
00060       /* alpha11 = alpha11 - a10t * a10t'; */
00061       FLA_Dots_external( FLA_MINUS_ONE, a10t, a10t, FLA_ONE, alpha11 );
00062 
00063       /* a21 = a21 - A20 * a10t'; */
00064       FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a10t, FLA_ONE, a21 );
00065 
00066       /* alpha11 = sqrt( alpha11 ); */
00067       value = FLA_Sqrt( alpha11 );
00068 
00069       if ( value != FLA_SUCCESS )
00070         return ( FLA_Obj_length( A00 ) + 1 );
00071 
00072       /* a21 = a21 / alpha11; */
00073       FLA_Inv_scal_external( alpha11, a21 );
00074     }
00075     else
00076     {
00077       /* alpha11 = alpha11 - a10t * a10t'; */
00078       FLA_Dotcs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a10t, a10t, FLA_ONE, alpha11 );
00079 
00080       /* a21 = a21 - A20 * a10t'; */
00081       FLA_Gemvc_external( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A20, a10t, FLA_ONE, a21 );
00082 
00083       /* alpha11 = sqrt( alpha11 ); */
00084       value = FLA_Sqrt( alpha11 );
00085 
00086       if ( value != FLA_SUCCESS )
00087         return ( FLA_Obj_length( A00 ) + 1 );
00088 
00089       /* a21 = a21 / alpha11; */
00090       FLA_Inv_scal_external( alpha11, a21 );
00091     }
00092 
00093     /*------------------------------------------------------------*/
00094 
00095     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
00096                                                      a10t, alpha11, /**/ a12t,
00097                             /* ************** */  /* ************************ */
00098                               &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
00099                               FLA_TL );
00100   }
00101 
00102   return value;
00103 }

FLA_Error FLA_Chol_l_unb_var3 ( FLA_Obj  A  ) 

References FLA_Cont_with_3x3_to_2x2(), FLA_Her_external(), FLA_Inv_scal_external(), FLA_MINUS_ONE, FLA_Obj_is_real(), FLA_Obj_length(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), FLA_Sqrt(), and FLA_Syr_external().

00038 {
00039   FLA_Obj ATL,   ATR,      A00,  a01,     A02,
00040           ABL,   ABR,      a10t, alpha11, a12t,
00041                            A20,  a21,     A22;
00042 
00043   int value = 0;
00044 
00045   FLA_Part_2x2( A,    &ATL, &ATR,
00046                       &ABL, &ABR,     0, 0, FLA_TL );
00047 
00048   while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
00049 
00050     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
00051                         /* ************* */   /* ************************** */
00052                                                 &a10t, /**/ &alpha11, &a12t,
00053                            ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
00054                            1, 1, FLA_BR );
00055 
00056     /*------------------------------------------------------------*/
00057 
00058     if ( FLA_Obj_is_real( A ) )
00059     {
00060       /* alpha11 = sqrt( alpha11 ); */
00061       value = FLA_Sqrt( alpha11 );
00062 
00063       if ( value != FLA_SUCCESS )
00064         return ( FLA_Obj_length( A00 ) + 1 );
00065 
00066       /* a21 = a21 / alpha11; */
00067       FLA_Inv_scal_external( alpha11, a21 );
00068 
00069       /* A22 = A22 - a21 * a21'; */
00070       FLA_Syr_external( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, a21, A22 );
00071     }
00072     else
00073     {
00074       /* alpha11 = sqrt( alpha11 ); */
00075       value = FLA_Sqrt( alpha11 );
00076 
00077       if ( value != FLA_SUCCESS )
00078         return ( FLA_Obj_length( A00 ) + 1 );
00079 
00080       /* a21 = a21 / alpha11; */
00081       FLA_Inv_scal_external( alpha11, a21 );
00082 
00083       /* A22 = A22 - a21 * a21'; */
00084       FLA_Her_external( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, a21, A22 );
00085     }
00086 
00087     /*------------------------------------------------------------*/
00088 
00089     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
00090                                                      a10t, alpha11, /**/ a12t,
00091                             /* ************** */  /* ************************ */
00092                               &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
00093                               FLA_TL );
00094   }
00095 
00096   return value;
00097 }


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