FLA_Error FLA_Her2k_lh_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C ) { FLA_Obj AL, AR, A0, a1, A2; FLA_Obj BL, BR, B0, b1, B2; 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_1x2( B, &BL, &BR, 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_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &b1, &B2, 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 ); /*------------------------------------------------------------*/ /* c21 = c21 + A2' * b1 */ FLA_Gemv_external( FLA_CONJ_TRANSPOSE, alpha, A2, b1, FLA_ONE, c21 ); /* c21 = c21 + B2' * a1 */ FLA_Gemv_external( FLA_CONJ_TRANSPOSE, alpha, B2, a1, FLA_ONE, c21 ); /* gamma11 = gamma11 + a1' * b1 + b1' * a1 */ FLA_Dot2cs_external( FLA_CONJUGATE, alpha, a1, b1, FLA_ONE, gamma11 ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, a1, /**/ A2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, b1, /**/ B2, 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_Trsv_un_blk_var2( FLA_Diag diagA, FLA_Obj A, FLA_Obj x, fla_trsv_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj xT, x0, xB, x1, x2; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x1( x, &xT, &xB, 0, FLA_BOTTOM ); 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_2x1_to_3x1( xT, &x0, &x1, /* ** */ /* ** */ xB, &x2, b, FLA_TOP ); /*------------------------------------------------------------*/ /* x1 = triu( A11 ) \ x1; */ FLA_Trsv_internal( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, diagA, A11, x1, FLA_Cntl_sub_trsv( cntl ) ); /* x0 = x0 - A01 * x1; */ FLA_Gemv_internal( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A01, x1, FLA_ONE, x0, FLA_Cntl_sub_gemv( 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_3x1_to_2x1( &xT, x0, /* ** */ /* ** */ x1, &xB, x2, FLA_BOTTOM ); } return FLA_SUCCESS; }
FLA_Error FLA_Symm_lu_blk_var7( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_symm_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_BR ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_BOTTOM ); FLA_Part_2x1( C, &CT, &CB, 0, FLA_BOTTOM ); 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_2x1_to_3x1( BT, &B0, &B1, /* ** */ /* ** */ BB, &B2, b, FLA_TOP ); FLA_Repart_2x1_to_3x1( CT, &C0, &C1, /* ** */ /* ** */ CB, &C2, b, FLA_TOP ); /*------------------------------------------------------------*/ /* C0 = C0 + A01 * B1 */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A01, B1, FLA_ONE, C0, FLA_Cntl_sub_gemm1( cntl ) ); /* C1 = C1 + A01' * B0 */ FLA_Gemm_internal( FLA_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A01, B0, FLA_ONE, C1, FLA_Cntl_sub_gemm2( cntl ) ); /* C1 = C1 + A11 * B1 */ FLA_Symm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, alpha, A11, B1, FLA_ONE, C1, FLA_Cntl_sub_symm( 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_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; }
FLA_Error FLA_Symm_rl_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C ) { FLA_Obj ATL, ATR, A00, a01, A02, ABL, ABR, a10t, alpha11, a12t, A20, a21, A22; FLA_Obj BL, BR, B0, b1t, B2; FLA_Obj CL, CR, C0, c1t, C2; FLA_Scal_external( beta, C ); 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, /**/ &b1t, &B2, 1, FLA_RIGHT ); FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, /**/ &c1t, &C2, 1, FLA_RIGHT ); /*------------------------------------------------------------*/ /* C0 = C0 + b1t * a10t */ FLA_Ger_external( alpha, b1t, a10t, C0 ); /* c1t = c1t + b1t * alpha11 */ FLA_Axpys_external( alpha, alpha11, b1t, FLA_ONE, c1t ); /* C2 = C2 + b1t * a21' */ FLA_Ger_external( alpha, b1t, a21, C2 ); /*------------------------------------------------------------*/ 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, b1t, /**/ B2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, c1t, /**/ C2, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_unb_var2( FLA_Obj A, FLA_Obj T ) { FLA_Obj ATL, ATR, A00, a01, A02, ABL, ABR, a10t, alpha11, a12t, A20, a21, A22; FLA_Obj TTL, TTR, T00, t01, T02, TBL, TBR, t10t, tau11, t12t, T20, t21, T22; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); 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_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02, /* ************* */ /* ************************ */ &t10t, /**/ &tau11, &t12t, TBL, /**/ TBR, &T20, /**/ &t21, &T22, 1, 1, FLA_BR ); /*------------------------------------------------------------*/ // 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, tau11 ); // / a12t \ = H / a12t \ // \ A22 / \ A22 / // // where H is formed from tau11 and u21. FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, a12t, A22 ); // t01 = a10t' + A20' * u21; FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 ); FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02, a10t, alpha11, /**/ a12t, /* ************** */ /* ************************ */ &ABL, /**/ &ABR, A20, a21, /**/ A22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02, t10t, tau11, /**/ t12t, /* ************** */ /* ********************** */ &TBL, /**/ &TBR, T20, t21, /**/ T22, FLA_TL ); } return FLA_SUCCESS; }
FLA_Error FLA_Syr2k_ln_unb_var3( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C ) { FLA_Obj AT, A0, AB, a1t, A2; FLA_Obj BT, B0, BB, b1t, B2; 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_TOP ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_TL ); while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){ FLA_Repart_2x1_to_3x1( AT, &A0, /* ** */ /* ** */ &a1t, AB, &A2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &b1t, BB, &B2, 1, FLA_BOTTOM ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, /**/ &c01, &C02, /* ************* */ /* ************************** */ &c10t, /**/ &gamma11, &c12t, CBL, /**/ CBR, &C20, /**/ &c21, &C22, 1, 1, FLA_BR ); /*------------------------------------------------------------*/ /* c10t = c10t + a1t * B0' */ FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, B0, a1t, FLA_ONE, c10t ); /* c21 = c21 + B2 * a1t' */ FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, B2, a1t, FLA_ONE, c21 ); /* gamma11 = gamma11 + a1t * b1t' + b1t * a1t' */ FLA_Dot2s_external( alpha, a1t, b1t, FLA_ONE, gamma11 ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, a1t, /* ** */ /* ** */ &AB, A2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &BT, B0, b1t, /* ** */ /* ** */ &BB, B2, FLA_TOP ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, c01, /**/ C02, c10t, gamma11, /**/ c12t, /* ************** */ /* ************************ */ &CBL, /**/ &CBR, C20, c21, /**/ C22, FLA_TL ); } return FLA_SUCCESS; }