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Functions | |
FLA_Error | FLA_LQ_UT_unb_var1 (FLA_Obj A, FLA_Obj t) |
FLA_Error | FLA_LQ_UT_blk_var1 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl) |
FLA_Error | FLA_LQ_UT_opt_var1 (FLA_Obj A, FLA_Obj t) |
FLA_Error | FLA_LQ_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_LQ_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_LQ_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_LQ_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_LQ_UT_unb_var2 (FLA_Obj A, FLA_Obj T) |
FLA_Error | FLA_LQ_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl) |
FLA_Error | FLA_LQ_UT_opt_var2 (FLA_Obj A, FLA_Obj T) |
FLA_Error | FLA_LQ_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_LQ_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_LQ_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_LQ_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_LQ_UT_blk_var3 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl) |
FLA_Error FLA_LQ_UT_blk_var1 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
fla_lqut_t * | cntl | ||
) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_LQ_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 AR1, AR2; 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_1x2( A11, A12, &AR1 ); // Perform an LQ factorization via the UT transform on AR1: // // ( A11 A12 ) -> L11 QR1 // // where: // - QR1 is formed from UR1 (which is stored row-wise above the // diagonal of AR1) and T11 (which is stored to the upper triangle // of T11). // - L11 is stored to the lower triangle of AR1. FLA_LQ_UT_internal( AR1, T1T, FLA_Cntl_sub_lqut( cntl )); if ( FLA_Obj_length( A21 ) > 0 ) { FLA_Merge_1x2( A21, A22, &AR2 ); // Apply the Householder transforms associated with UR1 and T11 to // AR2: // // ( A21 A22 ) := ( A21 A22 ) Q1 // // where QR1 is formed from UR1 and T11. FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE, AR1, T1T, W12, AR2, 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_LQ_UT_blk_var2 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
fla_lqut_t * | cntl | ||
) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().
Referenced by FLA_LQ_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 AR1, AR2; 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_1x2( A11, A12, &AR1 ); // Perform an LQ factorization via the UT transform on AR1: // // ( A11 A12 ) -> L11 QR1 // // where: // - QR1 is formed from UR1 (which is stored row-wise above the // diagonal of AR1) and T11 (which is stored to the upper triangle // of T11). // - L11 is stored to the lower triangle of AR1. FLA_LQ_UT_internal( AR1, T11, FLA_Cntl_sub_lqut( cntl ) ); if ( FLA_Obj_length( A21 ) > 0 ) { FLA_Merge_1x2( A21, A22, &AR2 ); // Apply the Householder transforms associated with UR1 and T11 to // AR2: // // ( A21 A22 ) := ( A21 A22 ) Q1 // // where QR1 is formed from UR1 and T11. FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE, AR1, T11, W12, AR2, FLA_Cntl_sub_apqut( cntl ) ); } // Update T // // T01 = conj(A01) * U11^T + conj(A02) * U12^T; // // Recall: U11 = triuu( A11 ); // U12 = A12; FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, A01, T01 ); FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_TRANSPOSE, FLA_UNIT_DIAG, FLA_ONE, A11, T01 ); FLA_Gemm_external( FLA_CONJ_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A02, A12, 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_LQ_UT_blk_var3 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
fla_lqut_t * | cntl | ||
) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_LQ_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 AR1, AR2; 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_1x2( A11, A12, &AR1 ); // Perform an LQ factorization via the UT transform on AR1: // // ( A11 A12 ) -> L11 QR1 // // where: // - QR1 is formed from UR1 (which is stored row-wise above the // diagonal of AR1) and T11 (which is stored to the upper triangle // of T11). // - L11 is stored to the lower triangle of AR1. FLA_LQ_UT_internal( AR1, T11, FLA_Cntl_sub_lqut( cntl ) ); if ( FLA_Obj_length( A21 ) > 0 ) { FLA_Merge_1x2( A21, A22, &AR2 ); // Apply the Householder transforms associated with UR1 and T11 to // AR2: // // ( A21 A22 ) := ( A21 A22 ) Q1 // // where QR1 is formed from UR1 and T11. FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE, AR1, T11, W12, AR2, 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_LQ_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_r_opc_var1(), and FLA_Househ2_UT_r_opc().
Referenced by FLA_LQ_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_RIGHT, alpha11, a12t // tau1 ); FLA_Househ2_UT_r_opc( n_ahead, alpha11, a12t, cs_A, tau1 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opc_var1( m_ahead, n_ahead, tau1, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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 bl1_ccopyv(), bl1_cgemv(), BLIS1_CONJ_NO_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, FLA_Apply_H2_UT_r_opc_var1(), FLA_Househ2_UT_r_opc(), and FLA_ONE.
Referenced by FLA_LQ_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* a01 = buff_A + (i )*cs_A + (0 )*rs_A; scomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A; scomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A; scomplex* A02 = buff_A + (i+1)*cs_A + (0 )*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 m_behind = i; /*------------------------------------------------------------*/ // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t // tau11 ); FLA_Househ2_UT_r_opc( n_ahead, alpha11, a12t, cs_A, tau11 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opc_var1( m_ahead, n_ahead, tau11, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); bl1_ccopyv( BLIS1_CONJUGATE, m_behind, a01, rs_A, t01, rs_T ); // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, // FLA_ONE, A02, a12t, FLA_ONE, t01 ); bl1_cgemv( BLIS1_CONJ_NO_TRANSPOSE, BLIS1_NO_CONJUGATE, m_behind, n_ahead, buff_1, A02, rs_A, cs_A, a12t, cs_A, buff_1, t01, rs_T ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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_r_opd_var1(), and FLA_Househ2_UT_r_opd().
Referenced by FLA_LQ_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_RIGHT, alpha11, a12t // tau1 ); FLA_Househ2_UT_r_opd( n_ahead, alpha11, a12t, cs_A, tau1 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opd_var1( m_ahead, n_ahead, tau1, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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 bl1_dcopyv(), bl1_dgemv(), BLIS1_CONJ_NO_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, FLA_Apply_H2_UT_r_opd_var1(), FLA_Househ2_UT_r_opd(), and FLA_ONE.
Referenced by FLA_LQ_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* a01 = buff_A + (i )*cs_A + (0 )*rs_A; double* alpha11 = buff_A + (i )*cs_A + (i )*rs_A; double* a21 = buff_A + (i )*cs_A + (i+1)*rs_A; double* A02 = buff_A + (i+1)*cs_A + (0 )*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 m_behind = i; /*------------------------------------------------------------*/ // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t // tau11 ); FLA_Househ2_UT_r_opd( n_ahead, alpha11, a12t, cs_A, tau11 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opd_var1( m_ahead, n_ahead, tau11, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); bl1_dcopyv( BLIS1_CONJUGATE, m_behind, a01, rs_A, t01, rs_T ); // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, // FLA_ONE, A02, a12t, FLA_ONE, t01 ); bl1_dgemv( BLIS1_CONJ_NO_TRANSPOSE, BLIS1_NO_CONJUGATE, m_behind, n_ahead, buff_1, A02, rs_A, cs_A, a12t, cs_A, buff_1, t01, rs_T ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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_r_ops_var1(), and FLA_Househ2_UT_r_ops().
Referenced by FLA_LQ_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_RIGHT, alpha11, a12t // tau1 ); FLA_Househ2_UT_r_ops( n_ahead, alpha11, a12t, cs_A, tau1 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 ); FLA_Apply_H2_UT_r_ops_var1( m_ahead, n_ahead, tau1, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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 bl1_scopyv(), bl1_sgemv(), BLIS1_CONJ_NO_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, FLA_Apply_H2_UT_r_ops_var1(), FLA_Househ2_UT_r_ops(), and FLA_ONE.
Referenced by FLA_LQ_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* a01 = buff_A + (i )*cs_A + (0 )*rs_A; float* alpha11 = buff_A + (i )*cs_A + (i )*rs_A; float* a21 = buff_A + (i )*cs_A + (i+1)*rs_A; float* A02 = buff_A + (i+1)*cs_A + (0 )*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 m_behind = i; /*------------------------------------------------------------*/ // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t // tau11 ); FLA_Househ2_UT_r_ops( n_ahead, alpha11, a12t, cs_A, tau11 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); FLA_Apply_H2_UT_r_ops_var1( m_ahead, n_ahead, tau11, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); bl1_scopyv( BLIS1_CONJUGATE, m_behind, a01, rs_A, t01, rs_T ); // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, // FLA_ONE, A02, a12t, FLA_ONE, t01 ); bl1_sgemv( BLIS1_CONJ_NO_TRANSPOSE, BLIS1_NO_CONJUGATE, m_behind, n_ahead, buff_1, A02, rs_A, cs_A, a12t, cs_A, buff_1, t01, rs_T ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_UT_opt_var1 | ( | FLA_Obj | A, |
FLA_Obj | t | ||
) |
References FLA_LQ_UT_opc_var1(), FLA_LQ_UT_opd_var1(), FLA_LQ_UT_ops_var1(), FLA_LQ_UT_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), and FLA_Obj_width().
Referenced by FLA_LQ_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_LQ_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_LQ_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_LQ_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_LQ_UT_opz_var1( m_A, n_A, buff_A, rs_A, cs_A, buff_t, inc_t ); break; } } return FLA_SUCCESS; }
FLA_Error FLA_LQ_UT_opt_var2 | ( | FLA_Obj | A, |
FLA_Obj | T | ||
) |
References FLA_LQ_UT_opc_var2(), FLA_LQ_UT_opd_var2(), FLA_LQ_UT_ops_var2(), FLA_LQ_UT_opz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), and FLA_Obj_width().
Referenced by FLA_LQ_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_LQ_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_LQ_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_LQ_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_LQ_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_LQ_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_r_opz_var1(), and FLA_Househ2_UT_r_opz().
Referenced by FLA_LQ_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_RIGHT, alpha11, a12t // tau1 ); FLA_Househ2_UT_r_opz( n_ahead, alpha11, a12t, cs_A, tau1 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opz_var1( m_ahead, n_ahead, tau1, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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 bl1_zcopyv(), bl1_zgemv(), BLIS1_CONJ_NO_TRANSPOSE, BLIS1_CONJUGATE, BLIS1_NO_CONJUGATE, FLA_Apply_H2_UT_r_opz_var1(), FLA_Househ2_UT_r_opz(), and FLA_ONE.
Referenced by FLA_LQ_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* a01 = buff_A + (i )*cs_A + (0 )*rs_A; dcomplex* alpha11 = buff_A + (i )*cs_A + (i )*rs_A; dcomplex* a21 = buff_A + (i )*cs_A + (i+1)*rs_A; dcomplex* A02 = buff_A + (i+1)*cs_A + (0 )*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 m_behind = i; /*------------------------------------------------------------*/ // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t // tau11 ); FLA_Househ2_UT_r_opz( n_ahead, alpha11, a12t, cs_A, tau11 ); // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); FLA_Apply_H2_UT_r_opz_var1( m_ahead, n_ahead, tau11, a12t, cs_A, a21, rs_A, A22, rs_A, cs_A ); // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); bl1_zcopyv( BLIS1_CONJUGATE, m_behind, a01, rs_A, t01, rs_T ); // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, // FLA_ONE, A02, a12t, FLA_ONE, t01 ); bl1_zgemv( BLIS1_CONJ_NO_TRANSPOSE, BLIS1_NO_CONJUGATE, m_behind, n_ahead, buff_1, A02, rs_A, cs_A, a12t, cs_A, buff_1, t01, rs_T ); /*------------------------------------------------------------*/ } return FLA_SUCCESS; }
FLA_Error FLA_LQ_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_LQ_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 u12t from alpha11 and a12t such that tau11 and u12t // determine a Householder transform H such that applying H from the // right to the row vector consisting of alpha11 and a12t annihilates // the entries in a12t (and updates alpha11). FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t, tau1 ); // ( a21 A22 ) = ( a21 A22 ) H // // where H is formed from tau11 and u12t. FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, 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_LQ_UT_unb_var2 | ( | FLA_Obj | A, |
FLA_Obj | T | ||
) |
References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemvc_external(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_LQ_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 u12t from alpha11 and a12t such that tau11 and u12t // determine a Householder transform H such that applying H from the // right to the row vector consisting of alpha11 and a12t annihilates // the entries in a12t (and updates alpha11). FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t, tau11 ); // ( a21 A22 ) = ( a21 A22 ) H // // where H is formed from tau11 and u12t. FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); // t01 = conj(a01) + conj(A02) * u12t^T; FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A02, a12t, 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; }