FLA_LQ_UT_vars.h File Reference

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Functions

FLA_Error FLA_LQ_UT_Accum_T_blk_var1 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)
FLA_Error FLA_LQ_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)


Function Documentation

FLA_Error FLA_LQ_UT_Accum_T_blk_var1 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)

References FLA_Axpyt_external(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_MINUS_ONE, FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_external(), and FLA_Trsm_external().

Referenced by FLA_LQ_UT_internal().

00036 {
00037   FLA_Obj ATL,   ATR,      A00, A01, A02, 
00038           ABL,   ABR,      A10, A11, A12,
00039                            A20, A21, A22;
00040 
00041   FLA_Obj TTL,   TTR,      T00, T01, T02, 
00042           TBL,   TBR,      T10, T11, W12,
00043                            T20, T21, T22;
00044 
00045   FLA_Obj AB1;
00046 
00047   dim_t b;
00048 
00049   FLA_Part_2x2( A,    &ATL, &ATR,
00050                       &ABL, &ABR,     0, 0, FLA_TL );
00051 
00052   FLA_Part_2x2( T,    &TTL, &TTR,
00053                       &TBL, &TBR,     0, 0, FLA_TL );
00054 
00055   while ( FLA_Obj_min_dim( ABR ) > 0 ){
00056 
00057     b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
00058 
00059     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
00060                         /* ************* */   /* ******************** */
00061                                                 &A10, /**/ &A11, &A12,
00062                            ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
00063                            b, b, FLA_BR );
00064 
00065     FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00, /**/ &T01, &T02,
00066                         /* ************* */   /* ******************** */
00067                                                 &T10, /**/ &T11, &W12,
00068                            TBL, /**/ TBR,       &T20, /**/ &T21, &T22,
00069                            b, b, FLA_BR );
00070 
00071     /*------------------------------------------------------------*/
00072 
00073     /*
00074       [ U1, T11 ] = FLA_LQ_UT_internal( [ A11 A12 ], T11 );
00075     */
00076 
00077     FLA_Merge_1x2( A11, A12,   &AB1 );
00078 
00079     FLA_LQ_UT_internal( AB1, T11,
00080                         FLA_Cntl_sub_lqut( cntl ) );
00081 
00082     /*
00083       U11 = triuu( A11 )';
00084       U21 = A12';
00085     
00086       W12 = triu( inv(T11) )' * ( U11' * A21' + U21' * A22' );
00087     */
00088 
00089     FLA_Copyt_external( FLA_CONJ_TRANSPOSE, A21, W12 );
00090     FLA_Trmm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
00091                        FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
00092                        FLA_ONE, A11, W12 );
00093     FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
00094                        FLA_ONE, A12, A22, FLA_ONE, W12 );
00095     FLA_Trsm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
00096                        FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, 
00097                        FLA_ONE, T11, W12 );
00098 
00099     /*
00100       A22 = A22 - W12' * U21';
00101       A21 = A21 - W12' * U11';
00102     */
00103 
00104     FLA_Gemm_external( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, 
00105                        FLA_MINUS_ONE, W12, A12, FLA_ONE, A22 );
00106     FLA_Trmm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
00107                        FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
00108                        FLA_MINUS_ONE, A11, W12 );
00109     FLA_Axpyt_external( FLA_CONJ_TRANSPOSE, FLA_ONE, W12, A21 );
00110 
00111     /*
00112       Update T
00113     
00114       T01 = A01 * U11 + A02 * U21;
00115 
00116       Recall: U11 = triuu( A11 )';
00117               U21 = A12';
00118     */
00119 
00120     FLA_Copy_external( A01, T01 );
00121     FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
00122                        FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
00123                        FLA_ONE, A11, T01 );
00124     FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, 
00125                        FLA_ONE, A02, A12, FLA_ONE, T01 );
00126 
00127     /*------------------------------------------------------------*/
00128 
00129     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
00130                                                      A10, A11, /**/ A12,
00131                             /* ************** */  /* ****************** */
00132                               &ABL, /**/ &ABR,       A20, A21, /**/ A22,
00133                               FLA_TL );
00134 
00135     FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00, T01, /**/ T02,
00136                                                      T10, T11, /**/ W12,
00137                             /* ************** */  /* ****************** */
00138                               &TBL, /**/ &TBR,       T20, T21, /**/ T22,
00139                               FLA_TL );
00140 
00141   }
00142 
00143   return FLA_SUCCESS;
00144 }

FLA_Error FLA_LQ_UT_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)

References FLA_Axpy_external(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_external(), and FLA_Trsm_external().

Referenced by FLA_LQ_UT_internal().

00036 {
00037   FLA_Obj ATL,   ATR,      A00, A01, A02, 
00038           ABL,   ABR,      A10, A11, A12,
00039                            A20, A21, A22;
00040 
00041   FLA_Obj TT,              T0,
00042           TB,              T1,
00043                            W21;
00044 
00045   FLA_Obj W21TL,   W21TR,
00046           W21BL,   W21BR;
00047 
00048   FLA_Obj T1L,   T2R,      AB1;
00049 
00050   dim_t b;
00051 
00052   FLA_Part_2x2( A,    &ATL, &ATR,
00053                       &ABL, &ABR,     0, 0, FLA_TL );
00054 
00055   FLA_Part_2x1( T,    &TT,
00056                       &TB,            0, FLA_TOP );
00057 
00058   while ( FLA_Obj_min_dim( ABR ) > 0 ){
00059 
00060     b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
00061 
00062     FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
00063                         /* ************* */   /* ******************** */
00064                                                 &A10, /**/ &A11, &A12,
00065                            ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
00066                            b, b, FLA_BR );
00067 
00068     FLA_Repart_2x1_to_3x1( TT,                &T0,
00069                         /* ** */            /* ** */
00070                                               &T1,
00071                            TB,                &W21,        b, FLA_BOTTOM );
00072 
00073     /*------------------------------------------------------------*/
00074 
00075     /*
00076       T1L = FLA_Left_part( T1, b );
00077     */
00078 
00079     FLA_Part_1x2( T1,    &T1L,  &T2R,      b, FLA_LEFT );
00080 
00081     /*
00082       [ U1, T1L ] = FLA_LQ_UT_internal( [ A11 A12 ], T1L );
00083     */
00084 
00085     FLA_Merge_1x2( A11, A12,   &AB1 );
00086 
00087     FLA_LQ_UT_internal( AB1, T1L, 
00088                         FLA_Cntl_sub_lqut( cntl ));
00089 
00090 
00091     if ( FLA_Obj_length( A21 ) > 0 )
00092     {
00093       /*
00094         W21L  = FLA_Left_part( W21, b );
00095         W21TL = FLA_Top_part( W21L, FLA_Obj_length( A21 ) );
00096       */
00097 
00098       FLA_Part_2x2( W21,    &W21TL, &W21TR,
00099                             &W21BL, &W21BR,    FLA_Obj_length( A21 ), b, FLA_TL );
00100 
00101       /*
00102         U11 = triuu( A11 );
00103         U12 = A12;
00104       
00105         W21TL = ( A21 * U11' + A22 * U12' ) * triu( inv(T1L) );
00106       */
00107 
00108       FLA_Copy_external( A21, W21TL );
00109       FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
00110                          FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
00111                          FLA_ONE, A11, W21TL );
00112       FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
00113                          FLA_ONE, A22, A12, FLA_ONE, W21TL );
00114       FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
00115                          FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, 
00116                          FLA_ONE, T1L, W21TL );
00117 
00118       /*
00119         A22 = A22 - W21TL * U12;
00120         A21 = A21 - W21TL * U11;
00121       */
00122 
00123       FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
00124                          FLA_MINUS_ONE, W21TL, A12, FLA_ONE, A22 );
00125       FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
00126                          FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
00127                          FLA_MINUS_ONE, A11, W21TL );
00128       FLA_Axpy_external( FLA_ONE, W21TL, A21 );
00129     }
00130 
00131     /*------------------------------------------------------------*/
00132 
00133     FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
00134                                                      A10, A11, /**/ A12,
00135                             /* ************** */  /* ****************** */
00136                               &ABL, /**/ &ABR,       A20, A21, /**/ A22,
00137                               FLA_TL );
00138 
00139     FLA_Cont_with_3x1_to_2x1( &TT,                T0,
00140                                                   T1,
00141                             /* ** */           /* ** */
00142                               &TB,                W21,     FLA_TOP );
00143 
00144   }
00145 
00146   return FLA_SUCCESS;
00147 }


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