int Gemm_unb_var2( FLA_Obj A, FLA_Obj B, FLA_Obj C ) { FLA_Obj BL, BR, B0, b1, B2; FLA_Obj CL, CR, C0, c1, C2; 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 ) ){ 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 ); /*------------------------------------------------------------*/ FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A, b1, FLA_ONE, c1 ); /*------------------------------------------------------------*/ 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; }
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 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; }
int Trsm_unb_var1( 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 - l10t * B0 */ FLA_Gemv( FLA_TRANSPOSE, FLA_MINUS_ONE, B0, l10t, FLA_ONE, b1t ); /* b1t = b1t / lambda11 */ FLA_Inv_scal( lambda11, b1t ); /*------------------------------------------------------------*/ 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; }
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; }
int Gemm_unb_var3( FLA_Obj A, FLA_Obj B, FLA_Obj C ) { FLA_Obj AT, A0, AB, a1t, A2; FLA_Obj CT, C0, CB, c1t, C2; FLA_Part_2x1( A, &AT, &AB, 0, FLA_TOP ); FLA_Part_2x1( C, &CT, &CB, 0, FLA_TOP ); 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( CT, &C0, /* ** */ /* *** */ &c1t, CB, &C2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ FLA_Gemv( FLA_TRANSPOSE, FLA_ONE, B, a1t, FLA_ONE, c1t ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, a1t, /* ** */ /* *** */ &AB, A2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &CT, C0, c1t, /* ** */ /* *** */ &CB, C2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Hess_UT_step_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_Obj yT, y0, yB, psi1, y2; FLA_Obj zT, z0, zB, zeta1, z2; FLA_Obj y, z; FLA_Obj inv_tau11; FLA_Obj minus_inv_tau11; FLA_Obj first_elem; FLA_Obj beta; FLA_Obj conj_beta; FLA_Obj dot_product; FLA_Obj a21_t, a21_b; FLA_Datatype datatype_A; dim_t m_A; dim_t b_alg; b_alg = FLA_Obj_length( T ); datatype_A = FLA_Obj_datatype( A ); m_A = FLA_Obj_length( A ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &conj_beta ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &dot_product ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z ); FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); FLA_Part_2x1( y, &yT, &yB, 0, FLA_TOP ); FLA_Part_2x1( z, &zT, &zB, 0, FLA_TOP ); while ( FLA_Obj_length( ATL ) < b_alg ) { 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 ); FLA_Repart_2x1_to_3x1( yT, &y0, /* ** */ /* **** */ &psi1, yB, &y2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( zT, &z0, /* ** */ /* ***** */ &zeta1, zB, &z2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ if ( FLA_Obj_length( A22 ) > 0 ) { FLA_Part_2x1( a21, &a21_t, &a21_b, 1, FLA_TOP ); // [ u21, tau11, a21 ] = House( a21 ); FLA_Househ2_UT( FLA_LEFT, a21_t, a21_b, tau11 ); // inv_tau11 = 1 / tau11; // minus_inv_tau11 = -1 / tau11; FLA_Set( FLA_ONE, inv_tau11 ); FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 ); FLA_Copy( inv_tau11, minus_inv_tau11 ); FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 ); // Save first element of a21_t and set it to one so we can use a21 as // u21 in subsequent computations. We will restore a21_t later on. FLA_Copy( a21_t, first_elem ); FLA_Set( FLA_ONE, a21_t ); // y21 = A22' * u21; FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 ); // z21 = A22 * u21; FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 ); // beta = u21' * z21 / 2; // conj_beta = conj(beta); FLA_Dotc( FLA_CONJUGATE, a21, z2, beta ); FLA_Inv_scal( FLA_TWO, beta ); FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta ); // y21' = ( y21' - beta / tau * u21' ) / tau; // y21 = ( y21 - conj(beta) / tau * u21 ) / tau; FLA_Scal( minus_inv_tau11, conj_beta ); FLA_Axpy( conj_beta, a21, y2 ); FLA_Scal( inv_tau11, y2 ); // z21 = ( z21 - beta / tau * u21 ) / tau; FLA_Scal( minus_inv_tau11, beta ); FLA_Axpy( beta, a21, z2 ); FLA_Scal( inv_tau11, z2 ); // a12t = a12t * ( I - u21 * u21' / tau ); // = a12t - ( a12t * u21 ) * u21' / tau; FLA_Dot( a12t, a21, dot_product ); FLA_Scal( minus_inv_tau11, dot_product ); FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t ); // A02 = A02 * ( I - u21 * u21' / tau ); // = A02 - ( A02 * u21 ) * u21' / tau; FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 ); FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 ); // A22 = A22 - u21 * y21' - z21 * u21'; FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 ); FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 ); // t01 = U20' * u21; FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 ); // Restore first element of a21. FLA_Copy( first_elem, a21_t ); } /*------------------------------------------------------------*/ 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 ); FLA_Cont_with_3x1_to_2x1( &yT, y0, psi1, /* ** */ /* **** */ &yB, y2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &zT, z0, zeta1, /* ** */ /* ***** */ &zB, z2, FLA_TOP ); } FLA_Obj_free( &inv_tau11 ); FLA_Obj_free( &minus_inv_tau11 ); FLA_Obj_free( &first_elem ); FLA_Obj_free( &beta ); FLA_Obj_free( &conj_beta ); FLA_Obj_free( &dot_product ); FLA_Obj_free( &y ); FLA_Obj_free( &z ); return FLA_SUCCESS; }
int Symm_ru_unb_var6( 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_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 ) ){ 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 ); FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, &c1, /**/ &C2, 1, FLA_LEFT ); /*------------------------------------------------------------*/ /*c1 = B0 * a01 + c1; c1 = SLAP_Gemv_n(1,B0,a01,c1);*/ FLA_Gemv(FLA_NO_TRANSPOSE, FLA_ONE, B0, a01, FLA_ONE, c1); /*c1 = alpha11 * b1 + c1; c1 = SLAP_Axpy(alpha11,b1,c1);*/ FLA_Axpy(alpha11,b1,c1); /*c1 = B2 * a21 + c1; c1 = SLAP_Gemv_n(1,B2,a12,c1);*/ FLA_Gemv(FLA_NO_TRANSPOSE, FLA_ONE, B2, a12t, FLA_ONE, c1); /*------------------------------------------------------------*/ 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 ); FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, /**/ c1, C2, FLA_RIGHT ); } return FLA_SUCCESS; }
int Symm_unb_var6( 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 BT, B0, BB, b1t, B2; FLA_Obj CT, C0, CB, c1t, C2; 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 ) ){ FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02, /* ************* */ /* ************************** */ &a10t, /**/ &alpha11, &a12t, ABL, /**/ ABR, &A20, /**/ &a21, &A22, 1, 1, FLA_BR ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* *** */ &b1t, BB, &B2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( CT, &C0, /* ** */ /* *** */ &c1t, CB, &C2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ // c1t = c1t + a10t*B0 + alpha11*b1t + a21t*B2; FLA_Gemv(FLA_TRANSPOSE, FLA_ONE, B0, a10t, FLA_ONE, c1t); FLA_Gemv(FLA_TRANSPOSE, FLA_ONE, B2, a21, FLA_ONE, c1t); FLA_Axpy(alpha11, b1t, c1t); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02, a10t, alpha11, /**/ a12t, /* ************** */ /* ************************ */ &ABL, /**/ &ABR, A20, a21, /**/ A22, FLA_TL ); FLA_Cont_with_3x1_to_2x1( &BT, B0, b1t, /* ** */ /* *** */ &BB, B2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &CT, C0, c1t, /* ** */ /* *** */ &CB, C2, FLA_TOP ); } return FLA_SUCCESS; }