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_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_Apply_G_rf(
int variant, int type, int n_repeats, int m, int k, int n, int b_alg,
FLA_Obj A, FLA_Obj A_ref, FLA_Obj G, FLA_Obj P,
double *dtime, double *diff, double *gflops )
{
int irep;
double
dtime_old = 1.0e9;
FLA_Obj
A_save, G_save, norm;
if ( FLA_Obj_is_real( A ) )
{
if (
//( variant == 1 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 1 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 1 && type == FLA_ALG_BLOCKED ) ||
//( variant == 2 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 2 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 2 && type == FLA_ALG_BLOCKED ) ||
//( variant == 3 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 3 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 3 && type == FLA_ALG_BLOCKED ) ||
//( variant == 6 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 6 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 6 && type == FLA_ALG_BLOCKED ) ||
//( variant == 9 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 9 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 9 && type == FLA_ALG_BLOCKED ) ||
( variant == 4 ) ||
( variant == 5 ) ||
( variant == 7 ) ||
( variant == 8 ) ||
FALSE
)
{
*gflops = 0.0;
*diff = 0.0;
return;
}
}
else if ( FLA_Obj_is_complex( A ) )
{
if (
//( variant == 1 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 1 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 1 && type == FLA_ALG_BLOCKED ) ||
//( variant == 2 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 2 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 2 && type == FLA_ALG_BLOCKED ) ||
//( variant == 3 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 3 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 3 && type == FLA_ALG_BLOCKED ) ||
//( variant == 6 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 6 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 6 && type == FLA_ALG_BLOCKED ) ||
//( variant == 9 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 9 && type == FLA_ALG_UNB_ASM ) ||
//( variant == 9 && type == FLA_ALG_BLOCKED ) ||
( variant == 4 ) ||
( variant == 5 ) ||
( variant == 7 ) ||
( variant == 8 ) ||
FALSE
)
{
*gflops = 0.0;
*diff = 0.0;
return;
}
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, G, &G_save );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
//dim_t b_flash_m = b_alg;
//dim_t b_flash_n = n;
//FLASH_Obj_create_hier_copy_of_flat_ext( A, 1, &b_flash_m, &b_flash_n, &AH );
//printf ( "flash dims: %d x %d\n", FLA_Obj_length( AH ), FLA_Obj_width( AH ) );
FLA_Copy_external( A, A_save );
FLA_Copy_external( G, G_save );
for ( irep = 0 ; irep < n_repeats; irep++ ){
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
//FLASH_Obj_hierarchify( A_save, AH );
*dtime = FLA_Clock();
switch( variant ){
case 0:
break;
// Time variant 1
case 1:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Apply_G_rf_opt_var1( G, A );
break;
case FLA_ALG_UNB_ASM:
FLA_Apply_G_rf_asm_var1( G, A );
break;
case FLA_ALG_BLOCKED:
FLA_Apply_G_rf_blk_var1( G, A, b_alg );
break;
}
break;
}
// Time variant 2
case 2:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Apply_G_rf_opt_var2( G, A );
break;
case FLA_ALG_UNB_ASM:
FLA_Apply_G_rf_asm_var2( G, A );
break;
case FLA_ALG_BLOCKED:
FLA_Apply_G_rf_blk_var2( G, A, b_alg );
break;
}
break;
}
// Time variant 3
case 3:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Apply_G_rf_opt_var3( G, A );
break;
case FLA_ALG_UNB_ASM:
FLA_Apply_G_rf_asm_var3( G, A );
break;
case FLA_ALG_BLOCKED:
FLA_Apply_G_rf_blk_var3( G, A, b_alg );
break;
}
break;
}
// Time variant 6
case 6:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Apply_G_rf_opt_var6( G, A );
break;
case FLA_ALG_UNB_ASM:
FLA_Apply_G_rf_asm_var6( G, A );
break;
case FLA_ALG_BLOCKED:
FLA_Apply_G_rf_blk_var6( G, A, b_alg );
break;
}
break;
}
// Time variant 9
case 9:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Apply_G_rf_opt_var9( G, A );
break;
case FLA_ALG_UNB_ASM:
FLA_Apply_G_rf_asm_var9( G, A );
break;
case FLA_ALG_BLOCKED:
FLA_Apply_G_rf_blk_var9( G, A, b_alg );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
if ( variant == 1 && type == FLA_ALG_UNB_OPT )
{
//FLA_Obj_show( "A_ref", A, "%9.2e + %9.2e ", "" );
//FLA_Obj_show( "A", A, "%9.2e ", "" );
FLA_Copy( A, A_ref );
*diff = 0.0;
}
else
{
//FLA_Obj_show( "A", A, "%9.2e + %9.2e ", "" );
//if ( variant == 7 && type == FLA_ALG_UNB_ASM )
//FLA_Obj_show( "A", A, "%9.2e", "" );
//if ( variant == 9 ) FLASH_Obj_flatten( AH, A );
FLA_Axpy( FLA_MINUS_ONE, A_ref, A );
FLA_Norm_frob( A, norm );
FLA_Obj_extract_real_scalar( norm, diff );
//*diff = FLA_Max_elemwise_diff( A_ref, A );
}
*gflops = 6.0 * k * m * ( n - 1 ) /
dtime_old / 1e9;
if ( FLA_Obj_is_complex( A ) )
*gflops *= 2.0;
*dtime = dtime_old;
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
//FLASH_Obj_free( &AH );
FLA_Obj_free( &A_save );
FLA_Obj_free( &G_save );
FLA_Obj_free( &norm );
}
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;
}
void time_Tevd_v(
int variant, int type, int n_repeats, int m, int k_accum, int b_alg, int n_iter_max,
FLA_Obj A_orig, FLA_Obj d, FLA_Obj e, FLA_Obj G, FLA_Obj R, FLA_Obj W, FLA_Obj A, FLA_Obj l,
double *dtime, double *diff1, double* diff2, double *gflops )
{
int irep;
double
k, dtime_old = 1.0e9;
FLA_Obj
A_save, G_save, d_save, e_save;
if (
//( variant == 0 ) ||
//( variant == 1 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 2 && type == FLA_ALG_UNB_OPT ) ||
FALSE
)
{
*dtime = 0.0;
*gflops = 0.0;
*diff1 = 0.0;
*diff2 = 0.0;
return;
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, G, &G_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, d, &d_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, e, &e_save );
FLA_Copy_external( A, A_save );
FLA_Copy_external( G, G_save );
FLA_Copy_external( d, d_save );
FLA_Copy_external( e, e_save );
for ( irep = 0 ; irep < n_repeats; irep++ ){
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
FLA_Copy_external( d_save, d );
FLA_Copy_external( e_save, e );
*dtime = FLA_Clock();
switch( variant ){
case 0:
REF_Tevd_v( d, e, A );
break;
// Time variant 1
case 1:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Tevd_v_opt_var1( n_iter_max, d, e, G, A, b_alg );
break;
}
break;
}
// Time variant 2
case 2:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Tevd_v_opt_var2( n_iter_max, d, e, G, R, W, A, b_alg );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
{
FLA_Obj V, A_rev_evd, norm, eye;
FLA_Copy( d, l );
//FLA_Obj_show( "A_save", A_save, "%9.2e + %9.2e ", "" );
//FLA_Obj_show( "A_evd", A, "%9.2e + %9.2e ", "" );
FLA_Sort_evd( FLA_FORWARD, l, A );
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &V );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_rev_evd );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &eye );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, l, A );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, A, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
/*
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A, D, FLA_ZERO, A_rev_evd );
FLA_Copy( A_rev_evd, D );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, D, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
*/
//FLA_Obj_show( "A_rev_evd", A_rev_evd, "%9.2e + %9.2e ", "" );
FLA_Axpy( FLA_MINUS_ONE, A_orig, A_rev_evd );
FLA_Norm_frob( A_rev_evd, norm );
FLA_Obj_extract_real_scalar( norm, diff1 );
//*diff = FLA_Max_elemwise_diff( A_orig, A_rev_evd );
FLA_Set_to_identity( eye );
FLA_Copy( V, A_rev_evd );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, V, A_rev_evd, FLA_MINUS_ONE, eye );
FLA_Norm_frob( eye, norm );
FLA_Obj_extract_real_scalar( norm, diff2 );
/*
FLA_Obj_free( &EL );
FLA_Obj_free( &EU );
FLA_Obj_free( &D );
FLA_Obj_free( &dc );
FLA_Obj_free( &ec );
*/
FLA_Obj_free( &V );
FLA_Obj_free( &A_rev_evd );
FLA_Obj_free( &eye );
FLA_Obj_free( &norm );
}
k = 2.00;
if ( FLA_Obj_is_complex( A ) )
{
*gflops = (
( 4.5 * k * m * m ) +
2.0 * ( 3.0 * k * m * m * m ) ) /
dtime_old / 1e9;
}
else
{
*gflops = (
( 4.5 * k * m * m ) +
1.0 * ( 3.0 * k * m * m * m ) ) /
dtime_old / 1e9;
}
*dtime = dtime_old;
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
FLA_Copy_external( d_save, d );
FLA_Copy_external( e_save, e );
FLA_Obj_free( &A_save );
FLA_Obj_free( &G_save );
FLA_Obj_free( &d_save );
FLA_Obj_free( &e_save );
}
void time_Lyap_h(
int variant, int type, int n_repeats, int m, int nb_alg,
FLA_Obj isgn, FLA_Obj A, FLA_Obj C, FLA_Obj C_ref, FLA_Obj scale,
double *dtime, double *diff, double *gflops )
{
int irep;
double dtime_old = 1.0e9;
FLA_Obj C_save, norm;
fla_blocksize_t* bp;
fla_lyap_t* cntl_lyap_unb;
fla_lyap_t* cntl_lyap_opt;
fla_lyap_t* cntl_lyap_blk;
if ( type == FLA_ALG_UNB_OPT && variant > 4 )
{
*gflops = 0.0;
*diff = 0.0;
return;
}
bp = FLA_Blocksize_create( nb_alg, nb_alg, nb_alg, nb_alg );
cntl_lyap_unb = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_UNB_VAR_OFFSET + variant,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL );
cntl_lyap_opt = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_OPT_VAR_OFFSET + variant,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL );
cntl_lyap_blk = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_BLK_VAR_OFFSET + variant,
bp,
fla_scal_cntl_blas,
fla_lyap_cntl_leaf,
fla_sylv_cntl,
fla_gemm_cntl_blas,
fla_gemm_cntl_blas,
fla_hemm_cntl_blas,
fla_her2k_cntl_blas );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &C_save );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( C ), 1, 1, 0, 0, &norm );
FLA_Copy_external( C, C_save );
for ( irep = 0 ; irep < n_repeats; irep++ )
{
FLA_Copy_external( C_save, C );
*dtime = FLA_Clock();
switch( variant )
{
case 0:
REF_Lyap_h( isgn, A, C, scale );
break;
case 1:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var1( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var1( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var1( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 2:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var2( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var2( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var2( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 3:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var3( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var3( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var3( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 4:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var4( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var4( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var4( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
FLA_Blocksize_free( bp );
FLA_Cntl_obj_free( cntl_lyap_unb );
FLA_Cntl_obj_free( cntl_lyap_opt );
FLA_Cntl_obj_free( cntl_lyap_blk );
/*
if ( variant == 0 )
{
FLA_Copy_external( C, C_ref );
*diff = 0.0;
}
else
{
FLA_Hermitianize( FLA_UPPER_TRIANGULAR, C );
*diff = FLA_Max_elemwise_diff( C, C_ref );
}
*/
{
FLA_Obj X, W;
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &X );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &W );
FLA_Copy( C, X );
FLA_Hermitianize( FLA_UPPER_TRIANGULAR, X );
FLA_Gemm( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, X, FLA_ZERO, W );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, X, A, FLA_ONE, W );
FLA_Scal( isgn, W );
/*
if ( variant == 3 && type == FLA_ALG_UNBLOCKED )
{
FLA_Obj_show( "W", W, "%10.3e + %10.3e ", "" );
FLA_Obj_show( "C_save", C_save, "%10.3e + %10.3e ", "" );
}
*/
FLA_Axpy( FLA_MINUS_ONE, C_save, W );
FLA_Norm1( W, norm );
FLA_Obj_extract_real_scalar( norm, diff );
FLA_Obj_free( &X );
FLA_Obj_free( &W );
}
*gflops = ( 2.0 / 3.0 ) * ( m * m * m ) /
dtime_old / 1e9;
if ( FLA_Obj_is_complex( C ) )
*gflops *= 4.0;
*dtime = dtime_old;
FLA_Copy_external( C_save, C );
FLA_Obj_free( &C_save );
FLA_Obj_free( &norm );
}
void time_Hevd_lv_components(
int variant, int type, int n_repeats, int m, int n_iter_max, int k_accum, int b_alg,
FLA_Obj A, FLA_Obj l,
double* dtime, double* diff1, double* diff2, double* gflops,
double* dtime_tred, double* gflops_tred,
double* dtime_tevd, double* gflops_tevd,
double* dtime_appq, double* gflops_appq, int* k_perf )
{
int i;
double k;
double dtime_save = 1.0e9;
double dtime_tred_save = 1.0e9;
double dtime_tevd_save = 1.0e9;
double dtime_appq_save = 1.0e9;
double flops_tred;
double flops_tevd;
double flops_appq;
double mult_tred;
double mult_tevd;
double mult_appq;
FLA_Obj A_save, Z;
if (
( variant == -3 ) ||
( variant == -4 ) ||
( variant == -5 ) ||
//( variant == 0 ) ||
//( variant == -1 ) ||
//( variant == -2 ) ||
//( variant == 1 ) ||
//( variant == 2 ) ||
//( variant == 3 ) ||
//( variant == 4 ) ||
FALSE
)
{
*gflops = 0.0;
*dtime = 0.0;
*diff1 = 0.0;
*diff2 = 0.0;
*dtime_tred = 0.0;
*dtime_tevd = 0.0;
*dtime_appq = 0.0;
*gflops_tred = 0.0;
*gflops_tevd = 0.0;
*gflops_appq = 0.0;
*k_perf = 0;
return;
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
FLA_Copy_external( A, A_save );
for ( i = 0 ; i < n_repeats; i++ ){
FLA_Copy_external( A_save, A );
*dtime = FLA_Clock();
switch( variant ){
case -3:
{
*k_perf = 0;
REF_Hevd_lv( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -4:
{
*k_perf = 0;
REF_Hevdd_lv( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -5:
{
*k_perf = 0;
REF_Hevdr_lv( A, l, Z,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case 0:
{
*k_perf = 0;
REF_Hevd_lv_components( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -1:
{
*k_perf = 0;
REF_Hevdd_lv_components( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -2:
{
*k_perf = 0;
REF_Hevdr_lv_components( A, l, Z,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
// Time variant 1
case 1:
{
*k_perf = FLA_Hevd_lv_var1_components( n_iter_max, A, l, k_accum, b_alg,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
// Time variant 2
case 2:
{
*k_perf = FLA_Hevd_lv_var2_components( n_iter_max, A, l, k_accum, b_alg,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
}
*dtime = FLA_Clock() - *dtime;
if ( *dtime < dtime_save )
{
dtime_save = *dtime;
dtime_tred_save = *dtime_tred;
dtime_tevd_save = *dtime_tevd;
dtime_appq_save = *dtime_appq;
}
}
*dtime = dtime_save;
*dtime_tred = dtime_tred_save;
*dtime_tevd = dtime_tevd_save;
*dtime_appq = dtime_appq_save;
//if ( variant == -3 || variant == 0 )
//printf( "\ndtime is %9.3e\n", *dtime );
{
FLA_Obj V, A_rev_evd, norm, eye;
if ( variant == -2 || variant == -5 ) FLA_Copy( Z, A );
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &V );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_rev_evd );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &eye );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, l, A );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, A, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
//FLA_Obj_show( "A_rev_evd", A_rev_evd, "%9.2e + %9.2e ", "" );
FLA_Axpy( FLA_MINUS_ONE, A_save, A_rev_evd );
FLA_Norm_frob( A_rev_evd, norm );
FLA_Obj_extract_real_scalar( norm, diff1 );
FLA_Set_to_identity( eye );
FLA_Copy( V, A_rev_evd );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, V, A_rev_evd, FLA_MINUS_ONE, eye );
FLA_Norm_frob( eye, norm );
FLA_Obj_extract_real_scalar( norm, diff2 );
FLA_Obj_free( &V );
FLA_Obj_free( &A_rev_evd );
FLA_Obj_free( &eye );
FLA_Obj_free( &norm );
}
k = 2.00;
flops_tred = ( ( 4.0 / 3.0 ) * m * m * m );
flops_tevd = ( 4.5 * k * m * m +
3.0 * k * m * m * m );
if ( variant == -1 || variant == -2 ||
variant == -4 || variant == -5 )
flops_appq = ( 2.0 * m * m * m );
else
flops_appq = ( 4.0 / 3.0 * m * m * m );
/*
if ( FLA_Obj_is_complex( A ) )
{
*gflops = ( 4.0 * flops_tred +
2.0 * flops_tevd +
4.0 * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( 4.0 * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( 2.0 * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( 4.0 * flops_appq ) / *dtime_appq / 1e9;
}
else
{
*gflops = ( 1.0 * flops_tred +
1.0 * flops_tevd +
1.0 * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( 1.0 * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( 1.0 * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( 1.0 * flops_appq ) / *dtime_appq / 1e9;
}
*/
if ( FLA_Obj_is_complex( A ) )
{
mult_tred = 4.0;
mult_tevd = 2.0;
mult_appq = 4.0;
}
else
{
mult_tred = 1.0;
mult_tevd = 1.0;
mult_appq = 1.0;
}
*gflops = ( mult_tred * flops_tred +
mult_tevd * flops_tevd +
mult_appq * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( mult_tred * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( mult_tevd * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( mult_appq * flops_appq ) / *dtime_appq / 1e9;
FLA_Copy_external( A_save, A );
FLA_Obj_free( &A_save );
FLA_Obj_free( &Z );
}