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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(), 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(), 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(), 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; }
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; }
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(), 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; }
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; }
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; }