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; }
void time_Axpyt( int param_combo, int type, int nrepeats, int m, int n, FLA_Obj A, FLA_Obj C, FLA_Obj C_ref, double *dtime, double *diff, double *gflops ) { int irep; double dtime_old = 1.0e9; FLA_Obj C_old; FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &C_old ); FLA_Copy_external( C, C_old ); for ( irep = 0 ; irep < nrepeats; irep++ ){ FLA_Copy_external( C_old, C ); *dtime = FLA_Clock(); switch( param_combo ){ // Time parameter combination 0 case 0:{ switch( type ){ case FLA_ALG_REFERENCE: REF_Axpyt( FLA_NO_TRANSPOSE, FLA_ONE, A, C ); break; case FLA_ALG_FRONT: FLA_Axpyt( FLA_NO_TRANSPOSE, FLA_ONE, A, C ); break; default: printf("trouble\n"); } break; } case 1:{ switch( type ){ case FLA_ALG_REFERENCE: REF_Axpyt( FLA_TRANSPOSE, FLA_ONE, A, C ); break; case FLA_ALG_FRONT: FLA_Axpyt( FLA_TRANSPOSE, FLA_ONE, A, C ); break; default: printf("trouble\n"); } break; } case 2:{ switch( type ){ case FLA_ALG_REFERENCE: REF_Axpyt( FLA_CONJ_NO_TRANSPOSE, FLA_ONE, A, C ); break; case FLA_ALG_FRONT: FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, FLA_ONE, A, C ); break; default: printf("trouble\n"); } break; } case 3:{ switch( type ){ case FLA_ALG_REFERENCE: REF_Axpyt( FLA_CONJ_TRANSPOSE, FLA_ONE, A, C ); break; case FLA_ALG_FRONT: FLA_Axpyt( FLA_CONJ_TRANSPOSE, FLA_ONE, A, C ); break; default: printf("trouble\n"); } break; } } *dtime = FLA_Clock() - *dtime; dtime_old = min( *dtime, dtime_old ); } if ( type == FLA_ALG_REFERENCE ) { FLA_Copy_external( C, C_ref ); *diff = 0.0; } else { *diff = FLA_Max_elemwise_diff( C, C_ref ); } *gflops = 2.0 * m * n / dtime_old / 1.0e9; if ( FLA_Obj_is_complex( A ) ) *gflops *= 4.0; *dtime = dtime_old; FLA_Copy_external( C_old, C ); FLA_Obj_free( &C_old ); }