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Functions | |
FLA_Error | FLA_QR_UT_form_Q (FLA_Obj A, FLA_Obj T, FLA_Obj Q) |
FLA_Error | FLA_QR_UT_form_Q_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W) |
FLA_Error | FLA_QR_UT_form_Q_opt_var1 (FLA_Obj A, FLA_Obj T) |
FLA_Error | FLA_QR_UT_form_Q_ops_var1 (int m_A, int n_A, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T) |
FLA_Error | FLA_QR_UT_form_Q_opd_var1 (int m_A, int n_A, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T) |
FLA_Error | FLA_QR_UT_form_Q_opc_var1 (int m_A, int n_A, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T) |
FLA_Error | FLA_QR_UT_form_Q_opz_var1 (int m_A, int n_A, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T) |
FLA_Error FLA_QR_UT_form_Q | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
FLA_Obj | Q | ||
) |
References FLA_Apply_Q_UT_create_workspace(), FLA_Check_error_level(), FLA_Copyr(), FLA_Merge_2x1(), FLA_Obj_free(), FLA_Obj_is(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x2(), FLA_QR_UT_form_Q_blk_var1(), FLA_QR_UT_form_Q_check(), FLA_Set_diag(), FLA_Setr(), and FLA_ZERO.
Referenced by FLA_Bidiag_UT_form_U(), FLA_Bidiag_UT_form_V(), FLA_Random_unitary_matrix(), FLA_Svd_uv_unb_var1(), FLA_Svd_uv_unb_var2(), and FLA_Tridiag_UT_form_Q().
{ FLA_Error r_val = FLA_SUCCESS; FLA_Obj QTL, QTR, QBL, QBR; FLA_Obj QL; FLA_Obj W; dim_t n_A; if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING ) FLA_QR_UT_form_Q_check( A, T, Q ); // Zero out the upper triangle of Q. FLA_Setr( FLA_UPPER_TRIANGULAR, FLA_ZERO, Q ); // If A and Q are different objects, copy the Householder vectors // from A to QT, and zero out the lower triangle of QBR. If they // are the same object, we don't need to do the copy, and don't // need to zero anything out since the user should only have A and // Q be the same object if A is square, since Q needs to be square // (specifically, dim(Q) needs to equal m(A)). if ( FLA_Obj_is( A, Q ) == FALSE ) { n_A = FLA_Obj_width( A ); FLA_Part_2x2( Q, &QTL, &QTR, &QBL, &QBR, n_A, n_A, FLA_TL ); FLA_Merge_2x1( QTL, QBL, &QL ); // Copy the Householder vectors in A to QL. FLA_Copyr( FLA_LOWER_TRIANGULAR, A, QL ); // Zero out the lower triangle of QBR. FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, QBR ); } // Set the digaonal to one. FLA_Set_diag( FLA_ONE, Q ); // Create workspace for applying the block Householder transforms. FLA_Apply_Q_UT_create_workspace( T, Q, &W ); // Overwrite Q, which currently contains Householder vectors in the // strictly lower triangle and identity in the upper triangle, with // the unitary matrix associated with those Householder transforms. r_val = FLA_QR_UT_form_Q_blk_var1( Q, T, W ); // Free the temporary workspace. FLA_Obj_free( &W ); /* FLA_Apply_Q_UT_create_workspace( T, Q, &W ); FLA_Set_to_identity( Q ); FLA_Apply_Q_UT( FLA_LEFT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE, A, T, W, Q ); FLA_Obj_free( &W ); FLA_Obj_show( "Q", Q, "%8.1e %8.1e ", "" ); */ return r_val; }
FLA_Error FLA_QR_UT_form_Q_blk_var1 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
FLA_Obj | W | ||
) |
References FLA_Apply_Q_UT(), 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_form_Q_opt_var1(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_form_Q().
{ FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj TL, TR, T0, T1, T2; FLA_Obj T1T, T2B; FLA_Obj WTL, WTR, WBL, WBR; FLA_Obj AB1, AB2; dim_t b, b_alg; dim_t m_BR, n_BR; b_alg = FLA_Obj_length( T ); // If A is wider than T, then we need to position ourseves carefully // within the matrix for the initial partitioning. if ( FLA_Obj_width( A ) > FLA_Obj_width( T ) ) { m_BR = FLA_Obj_length( A ) - FLA_Obj_width( T ); n_BR = FLA_Obj_width( A ) - FLA_Obj_width( T ); } else { m_BR = 0; n_BR = 0; } //printf( "\nn(A) n(T) = %d %d\n", FLA_Obj_width( A ), FLA_Obj_width( T ) ); //printf( "m_BR n_BR = %d %d\n", m_BR, n_BR ); FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, m_BR, n_BR, FLA_BR ); FLA_Part_1x2( T, &TL, &TR, 0, FLA_RIGHT ); while ( FLA_Obj_length( ATL ) > 0 ) { b = min( b_alg, FLA_Obj_min_dim( ATL ) ); // Since T was filled from left to right, and since we need to access them // in reverse order, we need to handle the case where the last block is // smaller than the other b x b blocks. if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 ) b = FLA_Obj_width( T ) % b_alg; FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, &T1, /**/ &T2, b, FLA_LEFT ); /*------------------------------------------------------------*/ FLA_Part_2x1( T1, &T1T, &T2B, b, FLA_TOP ); FLA_Part_2x2( W, &WTL, &WTR, &WBL, &WBR, b, FLA_Obj_width( A12 ), FLA_TL ); // Use an unblocked algorithm for the first (or only) block. if ( FLA_Obj_length( ABR ) == 0 ) { FLA_QR_UT_form_Q_opt_var1( A11, T1T ); } else { FLA_Merge_2x1( A11, A21, &AB1 ); FLA_Merge_2x1( A12, A22, &AB2 ); // Apply the block Householder transforms to A12 and A22. FLA_Apply_Q_UT( FLA_LEFT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE, AB1, T1T, WTL, AB2 ); // Apply H to the current block panel consisting of A11 and A21. FLA_QR_UT_form_Q_opt_var1( AB1, T1T ); } /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, /**/ T1, T2, FLA_RIGHT ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_form_Q_opc_var1 | ( | int | m_A, |
int | n_A, | ||
scomplex * | buff_A, | ||
int | rs_A, | ||
int | cs_A, | ||
scomplex * | buff_T, | ||
int | rs_T, | ||
int | cs_T | ||
) |
References bli_c0(), bli_c1(), bli_cscalv(), BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opc_var1(), scomplex::imag, and scomplex::real.
Referenced by FLA_QR_UT_form_Q_opt_var1().
{ scomplex zero = bli_c0(); scomplex one = bli_c1(); int min_m_n = min( m_A, n_A ); int i; for ( i = min_m_n - 1; i >= 0; --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* 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 minus_inv_tau11; //int m_behind = i; int n_ahead = n_A - i - 1; int m_ahead = m_A - i - 1; FLA_Apply_H2_UT_l_opc_var1( m_ahead, n_ahead, tau11, a21, rs_A, a12t, cs_A, A22, rs_A, cs_A ); minus_inv_tau11.real = -one.real / tau11->real; minus_inv_tau11.imag = zero.imag; alpha11->real = one.real + minus_inv_tau11.real; alpha11->imag = zero.imag; bli_cscalv( BLIS_NO_CONJUGATE, m_ahead, &minus_inv_tau11, a21, rs_A ); // Not necessary if upper triangle of A is initialized to identity. //bli_csetv( m_behind, // &zero, // a01, rs_A ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_form_Q_opd_var1 | ( | int | m_A, |
int | n_A, | ||
double * | buff_A, | ||
int | rs_A, | ||
int | cs_A, | ||
double * | buff_T, | ||
int | rs_T, | ||
int | cs_T | ||
) |
References bli_d1(), bli_dscalv(), BLIS_NO_CONJUGATE, and FLA_Apply_H2_UT_l_opd_var1().
Referenced by FLA_QR_UT_form_Q_opt_var1().
{ double one = bli_d1(); int min_m_n = min( m_A, n_A ); int i; for ( i = min_m_n - 1; i >= 0; --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* 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 minus_inv_tau11; //int m_behind = i; int n_ahead = n_A - i - 1; int m_ahead = m_A - i - 1; FLA_Apply_H2_UT_l_opd_var1( m_ahead, n_ahead, tau11, a21, rs_A, a12t, cs_A, A22, rs_A, cs_A ); minus_inv_tau11 = -one / *tau11; *alpha11 = one + minus_inv_tau11; bli_dscalv( BLIS_NO_CONJUGATE, m_ahead, &minus_inv_tau11, a21, rs_A ); // Not necessary if upper triangle of A is initialized to identity. //bli_dsetv( m_behind, // &zero, // a01, rs_A ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_form_Q_ops_var1 | ( | int | m_A, |
int | n_A, | ||
float * | buff_A, | ||
int | rs_A, | ||
int | cs_A, | ||
float * | buff_T, | ||
int | rs_T, | ||
int | cs_T | ||
) |
References bli_d1(), bli_sscalv(), BLIS_NO_CONJUGATE, and FLA_Apply_H2_UT_l_ops_var1().
Referenced by FLA_QR_UT_form_Q_opt_var1().
{ float one = bli_d1(); int min_m_n = min( m_A, n_A ); int i; for ( i = min_m_n - 1; i >= 0; --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* 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 minus_inv_tau11; //int m_behind = i; int n_ahead = n_A - i - 1; int m_ahead = m_A - i - 1; FLA_Apply_H2_UT_l_ops_var1( m_ahead, n_ahead, tau11, a21, rs_A, a12t, cs_A, A22, rs_A, cs_A ); minus_inv_tau11 = -one / *tau11; *alpha11 = one + minus_inv_tau11; bli_sscalv( BLIS_NO_CONJUGATE, m_ahead, &minus_inv_tau11, a21, rs_A ); // Not necessary if upper triangle of A is initialized to identity. //bli_ssetv( m_behind, // &zero, // a01, rs_A ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_form_Q_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_width(), FLA_QR_UT_form_Q_opc_var1(), FLA_QR_UT_form_Q_opd_var1(), FLA_QR_UT_form_Q_ops_var1(), and FLA_QR_UT_form_Q_opz_var1().
Referenced by FLA_QR_UT_form_Q_blk_var1().
{ 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 = ( float* ) FLA_FLOAT_PTR( A ); float* buff_T = ( float* ) FLA_FLOAT_PTR( T ); FLA_QR_UT_form_Q_ops_var1( m_A, n_A, buff_A, rs_A, cs_A, buff_T, rs_T, cs_T ); break; } case FLA_DOUBLE: { double* buff_A = ( double* ) FLA_DOUBLE_PTR( A ); double* buff_T = ( double* ) FLA_DOUBLE_PTR( T ); FLA_QR_UT_form_Q_opd_var1( m_A, n_A, buff_A, rs_A, cs_A, buff_T, rs_T, cs_T ); break; } case FLA_COMPLEX: { scomplex* buff_A = ( scomplex* ) FLA_COMPLEX_PTR( A ); scomplex* buff_T = ( scomplex* ) FLA_COMPLEX_PTR( T ); FLA_QR_UT_form_Q_opc_var1( m_A, n_A, buff_A, rs_A, cs_A, buff_T, rs_T, cs_T ); break; } case FLA_DOUBLE_COMPLEX: { dcomplex* buff_A = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( A ); dcomplex* buff_T = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( T ); FLA_QR_UT_form_Q_opz_var1( 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_form_Q_opz_var1 | ( | int | m_A, |
int | n_A, | ||
dcomplex * | buff_A, | ||
int | rs_A, | ||
int | cs_A, | ||
dcomplex * | buff_T, | ||
int | rs_T, | ||
int | cs_T | ||
) |
References bli_z0(), bli_z1(), bli_zscalv(), BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opz_var1(), dcomplex::imag, and dcomplex::real.
Referenced by FLA_QR_UT_form_Q_opt_var1().
{ dcomplex zero = bli_z0(); dcomplex one = bli_z1(); int min_m_n = min( m_A, n_A ); int i; for ( i = min_m_n - 1; i >= 0; --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* 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 minus_inv_tau11; //int m_behind = i; int n_ahead = n_A - i - 1; int m_ahead = m_A - i - 1; FLA_Apply_H2_UT_l_opz_var1( m_ahead, n_ahead, tau11, a21, rs_A, a12t, cs_A, A22, rs_A, cs_A ); minus_inv_tau11.real = -one.real / tau11->real; minus_inv_tau11.imag = zero.imag; alpha11->real = one.real + minus_inv_tau11.real; alpha11->imag = zero.imag; bli_zscalv( BLIS_NO_CONJUGATE, m_ahead, &minus_inv_tau11, a21, rs_A ); // Not necessary if upper triangle of A is initialized to identity. //bli_zsetv( m_behind, // &zero, // a01, rs_A ); } return FLA_SUCCESS; }