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Functions | |
| FLA_Error | FLA_QR_UT_unb_var1 (FLA_Obj A, FLA_Obj t) |
| FLA_Error | FLA_QR_UT_blk_var1 (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl) |
| FLA_Error | FLA_QR_UT_opt_var1 (FLA_Obj A, FLA_Obj t) |
| FLA_Error | FLA_QR_UT_ops_var1 (int m_A, int n_A, float *A, int rs_A, int cs_A, float *t, int inc_t) |
| FLA_Error | FLA_QR_UT_opd_var1 (int m_A, int n_A, double *A, int rs_A, int cs_A, double *t, int inc_t) |
| FLA_Error | FLA_QR_UT_opc_var1 (int m_A, int n_A, scomplex *A, int rs_A, int cs_A, scomplex *t, int inc_t) |
| FLA_Error | FLA_QR_UT_opz_var1 (int m_A, int n_A, dcomplex *A, int rs_A, int cs_A, dcomplex *t, int inc_t) |
| FLA_Error | FLA_QR_UT_unb_var2 (FLA_Obj A, FLA_Obj T) |
| FLA_Error | FLA_QR_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl) |
| FLA_Error | FLA_QR_UT_opt_var2 (FLA_Obj A, FLA_Obj T) |
| FLA_Error | FLA_QR_UT_ops_var2 (int m_A, int n_A, float *A, int rs_A, int cs_A, float *T, int rs_T, int cs_T) |
| FLA_Error | FLA_QR_UT_opd_var2 (int m_A, int n_A, double *A, int rs_A, int cs_A, double *T, int rs_T, int cs_T) |
| FLA_Error | FLA_QR_UT_opc_var2 (int m_A, int n_A, scomplex *A, int rs_A, int cs_A, scomplex *T, int rs_T, int cs_T) |
| FLA_Error | FLA_QR_UT_opz_var2 (int m_A, int n_A, dcomplex *A, int rs_A, int cs_A, dcomplex *T, int rs_T, int cs_T) |
| FLA_Error | FLA_QR_UT_blk_var3 (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl) |
| FLA_Error FLA_QR_UT_blk_var1 | ( | FLA_Obj | A, |
| FLA_Obj | T, | ||
| fla_qrut_t * | cntl | ||
| ) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Merge_2x1(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_internal(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_internal().
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj TL, TR, T0, T1, W12;
FLA_Obj T1T, T2B;
FLA_Obj AB1, AB2;
dim_t b_alg, b;
// Query the algorithmic blocksize by inspecting the length of T.
b_alg = FLA_Obj_length( T );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_1x2( T, &TL, &TR, 0, FLA_LEFT );
while ( FLA_Obj_min_dim( ABR ) > 0 ){
b = min( b_alg, FLA_Obj_min_dim( ABR ) );
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
/* ************* */ /* ******************** */
&A10, /**/ &A11, &A12,
ABL, /**/ ABR, &A20, /**/ &A21, &A22,
b, b, FLA_BR );
FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, /**/ &T1, &W12,
b, FLA_RIGHT );
/*------------------------------------------------------------*/
FLA_Part_2x1( T1, &T1T,
&T2B, b, FLA_TOP );
FLA_Merge_2x1( A11,
A21, &AB1 );
// Perform a QR factorization via the UT transform on AB1:
//
// / A11 \ -> QB1 R11
// \ A21 /
//
// where:
// - QB1 is formed from UB1 (which is stored column-wise below the
// diagonal of AB1) and T11 (which is stored to the upper triangle
// of T11).
// - R11 is stored to the upper triangle of AB1.
FLA_QR_UT_internal( AB1, T1T,
FLA_Cntl_sub_qrut( cntl ) );
if ( FLA_Obj_width( A12 ) > 0 )
{
FLA_Merge_2x1( A12,
A22, &AB2 );
// Apply the Householder transforms associated with UB1 and T11 to
// AB2:
//
// / A12 \ := QB1' / A12 \
// \ A22 / \ A22 /
//
// where QB1 is formed from UB1 and T11.
FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
AB1, T1T, W12, AB2,
FLA_Cntl_sub_apqut( cntl ) );
}
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ W12,
FLA_LEFT );
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_blk_var2 | ( | FLA_Obj | A, |
| FLA_Obj | T, | ||
| fla_qrut_t * | cntl | ||
| ) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_Merge_2x1(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x2(), FLA_QR_UT_internal(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().
Referenced by FLA_QR_UT_internal().
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj TTL, TTR, T00, T01, T02,
TBL, TBR, T10, T11, W12,
T20, T21, T22;
FLA_Obj AB1, AB2;
dim_t b;
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 ){
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 );
FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &T01, &T02,
/* ************* */ /* ******************** */
&T10, /**/ &T11, &W12,
TBL, /**/ TBR, &T20, /**/ &T21, &T22,
b, b, FLA_BR );
/*------------------------------------------------------------*/
FLA_Merge_2x1( A11,
A21, &AB1 );
// Perform a QR factorization via the UT transform on AB1:
//
// / A11 \ -> QB1 R11
// \ A21 /
//
// where:
// - QB1 is formed from UB1 (which is stored column-wise below the
// diagonal of AB1) and T11 (which is stored to the upper triangle
// of T11).
// - R11 is stored to the upper triangle of AB1.
FLA_QR_UT_internal( AB1, T11,
FLA_Cntl_sub_qrut( cntl ) );
if ( FLA_Obj_width( A12 ) > 0 )
{
FLA_Merge_2x1( A12,
A22, &AB2 );
// Apply the Householder transforms associated with UB1 and T11 to
// AB2:
//
// / A12 \ := QB1' / A12 \
// \ A22 / \ A22 /
//
// where QB1 is formed from UB1 and T11.
FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
AB1, T11, W12, AB2,
FLA_Cntl_sub_apqut( cntl ) );
}
// Update T
//
// T01 = A10' * U11 + A20' * U21;
//
// Recall: U11 = trilu( A11 );
// U21 = A21;
FLA_Copyt_external( FLA_CONJ_TRANSPOSE, A10, T01 );
FLA_Trmm_external( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, A11, T01 );
FLA_Gemm_external( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A20, A21, FLA_ONE, T01 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, T01, /**/ T02,
T10, T11, /**/ W12,
/* ************** */ /* ****************** */
&TBL, /**/ &TBR, T20, T21, /**/ T22,
FLA_TL );
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_blk_var3 | ( | FLA_Obj | A, |
| FLA_Obj | T, | ||
| fla_qrut_t * | cntl | ||
| ) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Merge_2x1(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_2x2(), FLA_QR_UT_internal(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_internal().
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj TWTL, TWTR, TW00, TW01, TW02,
TWBL, TWBR, TW10, T11, W12,
TW20, TW21, TW22;
FLA_Obj AB1, AB2;
dim_t b;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_2x2( TW, &TWTL, &TWTR,
&TWBL, &TWBR, 0, 0, FLA_TL );
while ( FLA_Obj_min_dim( ABR ) > 0 ){
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 );
FLA_Repart_2x2_to_3x3( TWTL, /**/ TWTR, &TW00, /**/ &TW01, &TW02,
/* ************* */ /* ******************** */
&TW10, /**/ &T11, &W12,
TWBL, /**/ TWBR, &TW20, /**/ &TW21, &TW22,
b, b, FLA_BR );
/*------------------------------------------------------------*/
FLA_Merge_2x1( A11,
A21, &AB1 );
// Perform a QR factorization via the UT transform on AB1:
//
// / A11 \ -> QB1 R11
// \ A21 /
//
// where:
// - QB1 is formed from UB1 (which is stored column-wise below the
// diagonal of AB1) and T11 (which is stored to the upper triangle
// of T11).
// - R11 is stored to the upper triangle of AB1.
FLA_QR_UT_internal( AB1, T11,
FLA_Cntl_sub_qrut( cntl ) );
if ( FLA_Obj_width( A12 ) > 0 )
{
FLA_Merge_2x1( A12,
A22, &AB2 );
// Apply the Householder transforms associated with UB1 and T11 to
// AB2:
//
// / A12 \ := QB1' / A12 \
// \ A22 / \ A22 /
//
// where QB1 is formed from UB1 and T11.
FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
AB1, T11, W12, AB2,
FLA_Cntl_sub_apqut( cntl ) );
}
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x3_to_2x2( &TWTL, /**/ &TWTR, TW00, TW01, /**/ TW02,
TW10, T11, /**/ W12,
/* ************** */ /* ****************** */
&TWBL, /**/ &TWBR, TW20, TW21, /**/ TW22,
FLA_TL );
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opc_var1 | ( | int | m_A, |
| int | n_A, | ||
| scomplex * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| scomplex * | t, | ||
| int | inc_t | ||
| ) |
References FLA_Apply_H2_UT_l_opc_var1(), and FLA_Househ2_UT_l_opc().
Referenced by FLA_QR_UT_opt_var1().
{
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
scomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
scomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
scomplex* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
scomplex* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
scomplex* tau1 = buff_t + (i )*inc_t;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau1 );
FLA_Househ2_UT_l_opc( m_ahead,
alpha11,
a21, rs_A,
tau1 );
// FLA_Apply_H2_UT( FLA_LEFT, tau1, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opc_var1( m_ahead,
n_ahead,
tau1,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opc_var2 | ( | int | m_A, |
| int | n_A, | ||
| scomplex * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| scomplex * | T, | ||
| int | rs_T, | ||
| int | cs_T | ||
| ) |
References bli_ccopyv(), bli_cgemv(), BLIS_CONJ_TRANSPOSE, BLIS_CONJUGATE, BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opc_var1(), FLA_Househ2_UT_l_opc(), and FLA_ONE.
Referenced by FLA_QR_UT_opt_var2().
{
scomplex* buff_1 = FLA_COMPLEX_PTR( FLA_ONE );
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
scomplex* a10t = buff_A + (0 )*cs_A + (i )*rs_A;
scomplex* A20 = buff_A + (0 )*cs_A + (i+1)*rs_A;
scomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
scomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
scomplex* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
scomplex* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
scomplex* tau11 = buff_T + (i )*cs_T + (i )*rs_T;
scomplex* t01 = buff_T + (i )*cs_T + (0 )*rs_T;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
int n_behind = i;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau11 );
FLA_Househ2_UT_l_opc( m_ahead,
alpha11,
a21, rs_A,
tau11 );
// FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opc_var1( m_ahead,
n_ahead,
tau11,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
// FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
bli_ccopyv( BLIS_CONJUGATE,
n_behind,
a10t, cs_A,
t01, rs_T );
// FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
bli_cgemv( BLIS_CONJ_TRANSPOSE,
BLIS_NO_CONJUGATE,
m_ahead,
n_behind,
buff_1,
A20, rs_A, cs_A,
a21, rs_A,
buff_1,
t01, rs_T );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opd_var1 | ( | int | m_A, |
| int | n_A, | ||
| double * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| double * | t, | ||
| int | inc_t | ||
| ) |
References FLA_Apply_H2_UT_l_opd_var1(), and FLA_Househ2_UT_l_opd().
Referenced by FLA_QR_UT_opt_var1().
{
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
double* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
double* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
double* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
double* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
double* tau1 = buff_t + (i )*inc_t;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau1 );
FLA_Househ2_UT_l_opd( m_ahead,
alpha11,
a21, rs_A,
tau1 );
// FLA_Apply_H2_UT( FLA_LEFT, tau1, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opd_var1( m_ahead,
n_ahead,
tau1,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opd_var2 | ( | int | m_A, |
| int | n_A, | ||
| double * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| double * | T, | ||
| int | rs_T, | ||
| int | cs_T | ||
| ) |
References bli_dcopyv(), bli_dgemv(), BLIS_CONJ_TRANSPOSE, BLIS_CONJUGATE, BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opd_var1(), FLA_Househ2_UT_l_opd(), and FLA_ONE.
Referenced by FLA_QR_UT_opt_var2().
{
double* buff_1 = FLA_DOUBLE_PTR( FLA_ONE );
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
double* a10t = buff_A + (0 )*cs_A + (i )*rs_A;
double* A20 = buff_A + (0 )*cs_A + (i+1)*rs_A;
double* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
double* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
double* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
double* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
double* tau11 = buff_T + (i )*cs_T + (i )*rs_T;
double* t01 = buff_T + (i )*cs_T + (0 )*rs_T;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
int n_behind = i;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau11 );
FLA_Househ2_UT_l_opd( m_ahead,
alpha11,
a21, rs_A,
tau11 );
// FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opd_var1( m_ahead,
n_ahead,
tau11,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
// FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
bli_dcopyv( BLIS_CONJUGATE,
n_behind,
a10t, cs_A,
t01, rs_T );
// FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
bli_dgemv( BLIS_CONJ_TRANSPOSE,
BLIS_NO_CONJUGATE,
m_ahead,
n_behind,
buff_1,
A20, rs_A, cs_A,
a21, rs_A,
buff_1,
t01, rs_T );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_ops_var1 | ( | int | m_A, |
| int | n_A, | ||
| float * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| float * | t, | ||
| int | inc_t | ||
| ) |
References FLA_Apply_H2_UT_l_ops_var1(), and FLA_Househ2_UT_l_ops().
Referenced by FLA_QR_UT_opt_var1().
{
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
float* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
float* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
float* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
float* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
float* tau1 = buff_t + (i )*inc_t;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau1 );
FLA_Househ2_UT_l_ops( m_ahead,
alpha11,
a21, rs_A,
tau1 );
// FLA_Apply_H2_UT( FLA_LEFT, tau1, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_ops_var1( m_ahead,
n_ahead,
tau1,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_ops_var2 | ( | int | m_A, |
| int | n_A, | ||
| float * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| float * | T, | ||
| int | rs_T, | ||
| int | cs_T | ||
| ) |
References bli_scopyv(), bli_sgemv(), BLIS_CONJ_TRANSPOSE, BLIS_CONJUGATE, BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_ops_var1(), FLA_Househ2_UT_l_ops(), and FLA_ONE.
Referenced by FLA_QR_UT_opt_var2().
{
float* buff_1 = FLA_FLOAT_PTR( FLA_ONE );
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
float* a10t = buff_A + (0 )*cs_A + (i )*rs_A;
float* A20 = buff_A + (0 )*cs_A + (i+1)*rs_A;
float* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
float* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
float* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
float* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
float* tau11 = buff_T + (i )*cs_T + (i )*rs_T;
float* t01 = buff_T + (i )*cs_T + (0 )*rs_T;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
int n_behind = i;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau11 );
FLA_Househ2_UT_l_ops( m_ahead,
alpha11,
a21, rs_A,
tau11 );
// FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_ops_var1( m_ahead,
n_ahead,
tau11,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
// FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
bli_scopyv( BLIS_CONJUGATE,
n_behind,
a10t, cs_A,
t01, rs_T );
// FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
bli_sgemv( BLIS_CONJ_TRANSPOSE,
BLIS_NO_CONJUGATE,
m_ahead,
n_behind,
buff_1,
A20, rs_A, cs_A,
a21, rs_A,
buff_1,
t01, rs_T );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opt_var1 | ( | FLA_Obj | A, |
| FLA_Obj | t | ||
| ) |
References FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), FLA_Obj_width(), FLA_QR_UT_opc_var1(), FLA_QR_UT_opd_var1(), FLA_QR_UT_ops_var1(), and FLA_QR_UT_opz_var1().
Referenced by FLA_QR_UT_internal().
{
FLA_Datatype datatype;
int m_A, n_A;
int rs_A, cs_A;
int inc_t;
datatype = FLA_Obj_datatype( A );
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
rs_A = FLA_Obj_row_stride( A );
cs_A = FLA_Obj_col_stride( A );
inc_t = FLA_Obj_vector_inc( t );
switch ( datatype )
{
case FLA_FLOAT:
{
float* buff_A = FLA_FLOAT_PTR( A );
float* buff_t = FLA_FLOAT_PTR( t );
FLA_QR_UT_ops_var1( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_t, inc_t );
break;
}
case FLA_DOUBLE:
{
double* buff_A = FLA_DOUBLE_PTR( A );
double* buff_t = FLA_DOUBLE_PTR( t );
FLA_QR_UT_opd_var1( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_t, inc_t );
break;
}
case FLA_COMPLEX:
{
scomplex* buff_A = FLA_COMPLEX_PTR( A );
scomplex* buff_t = FLA_COMPLEX_PTR( t );
FLA_QR_UT_opc_var1( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_t, inc_t );
break;
}
case FLA_DOUBLE_COMPLEX:
{
dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
dcomplex* buff_t = FLA_DOUBLE_COMPLEX_PTR( t );
FLA_QR_UT_opz_var1( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_t, inc_t );
break;
}
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opt_var2 | ( | FLA_Obj | A, |
| FLA_Obj | T | ||
| ) |
References FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_width(), FLA_QR_UT_opc_var2(), FLA_QR_UT_opd_var2(), FLA_QR_UT_ops_var2(), and FLA_QR_UT_opz_var2().
Referenced by FLA_QR_UT_internal().
{
FLA_Datatype datatype;
int m_A, n_A;
int rs_A, cs_A;
int rs_T, cs_T;
datatype = FLA_Obj_datatype( A );
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
rs_A = FLA_Obj_row_stride( A );
cs_A = FLA_Obj_col_stride( A );
rs_T = FLA_Obj_row_stride( T );
cs_T = FLA_Obj_col_stride( T );
switch ( datatype )
{
case FLA_FLOAT:
{
float* buff_A = FLA_FLOAT_PTR( A );
float* buff_T = FLA_FLOAT_PTR( T );
FLA_QR_UT_ops_var2( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_T, rs_T, cs_T );
break;
}
case FLA_DOUBLE:
{
double* buff_A = FLA_DOUBLE_PTR( A );
double* buff_T = FLA_DOUBLE_PTR( T );
FLA_QR_UT_opd_var2( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_T, rs_T, cs_T );
break;
}
case FLA_COMPLEX:
{
scomplex* buff_A = FLA_COMPLEX_PTR( A );
scomplex* buff_T = FLA_COMPLEX_PTR( T );
FLA_QR_UT_opc_var2( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_T, rs_T, cs_T );
break;
}
case FLA_DOUBLE_COMPLEX:
{
dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );
FLA_QR_UT_opz_var2( m_A,
n_A,
buff_A, rs_A, cs_A,
buff_T, rs_T, cs_T );
break;
}
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opz_var1 | ( | int | m_A, |
| int | n_A, | ||
| dcomplex * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| dcomplex * | t, | ||
| int | inc_t | ||
| ) |
References FLA_Apply_H2_UT_l_opz_var1(), and FLA_Househ2_UT_l_opz().
Referenced by FLA_QR_UT_opt_var1().
{
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
dcomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
dcomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
dcomplex* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
dcomplex* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
dcomplex* tau1 = buff_t + (i )*inc_t;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau1 );
FLA_Househ2_UT_l_opz( m_ahead,
alpha11,
a21, rs_A,
tau1 );
// FLA_Apply_H2_UT( FLA_LEFT, tau1, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opz_var1( m_ahead,
n_ahead,
tau1,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_opz_var2 | ( | int | m_A, |
| int | n_A, | ||
| dcomplex * | A, | ||
| int | rs_A, | ||
| int | cs_A, | ||
| dcomplex * | T, | ||
| int | rs_T, | ||
| int | cs_T | ||
| ) |
References bli_zcopyv(), bli_zgemv(), BLIS_CONJ_TRANSPOSE, BLIS_CONJUGATE, BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opz_var1(), FLA_Househ2_UT_l_opz(), and FLA_ONE.
Referenced by FLA_QR_UT_opt_var2().
{
dcomplex* buff_1 = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
int min_m_n = min( m_A, n_A );
int i;
for ( i = 0; i < min_m_n; ++i )
{
dcomplex* a10t = buff_A + (0 )*cs_A + (i )*rs_A;
dcomplex* A20 = buff_A + (0 )*cs_A + (i+1)*rs_A;
dcomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A;
dcomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A;
dcomplex* a12t = buff_A + (i+1)*cs_A + (i )*rs_A;
dcomplex* A22 = buff_A + (i+1)*cs_A + (i+1)*rs_A;
dcomplex* tau11 = buff_T + (i )*cs_T + (i )*rs_T;
dcomplex* t01 = buff_T + (i )*cs_T + (0 )*rs_T;
int m_ahead = m_A - i - 1;
int n_ahead = n_A - i - 1;
int n_behind = i;
/*------------------------------------------------------------*/
// FLA_Househ2_UT( FLA_LEFT,
// alpha11,
// a21, tau11 );
FLA_Househ2_UT_l_opz( m_ahead,
alpha11,
a21, rs_A,
tau11 );
// FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, a12t,
// A22 );
FLA_Apply_H2_UT_l_opz_var1( m_ahead,
n_ahead,
tau11,
a21, rs_A,
a12t, cs_A,
A22, rs_A, cs_A );
// FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
bli_zcopyv( BLIS_CONJUGATE,
n_behind,
a10t, cs_A,
t01, rs_T );
// FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
bli_zgemv( BLIS_CONJ_TRANSPOSE,
BLIS_NO_CONJUGATE,
m_ahead,
n_behind,
buff_1,
A20, rs_A, cs_A,
a21, rs_A,
buff_1,
t01, rs_T );
/*------------------------------------------------------------*/
}
return FLA_SUCCESS;
}
| FLA_Error FLA_QR_UT_unb_var1 | ( | FLA_Obj | A, |
| FLA_Obj | t | ||
| ) |
References FLA_Apply_H2_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_internal().
{
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_QR_UT_unb_var2 | ( | FLA_Obj | A, |
| FLA_Obj | T | ||
| ) |
References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_internal().
{
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;
}
1.7.6.1