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; }
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; }
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; }
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; }
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; }
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, <L, <R, &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( <L, /**/ <R, 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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }
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; }