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Functions | |
FLA_Error | FLA_QR_UT_piv_unb_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p) |
FLA_Error | FLA_QR_UT_piv_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p, fla_qrut_t *cntl) |
FLA_Error | FLA_QR_UT_piv_unb_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p) |
FLA_Error | FLA_QR_UT_piv_blk_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p, fla_qrut_t *cntl) |
FLA_Error | FLA_Apply_H2_UT_piv_row (FLA_Obj tau, FLA_Obj a1t, FLA_Obj u1t, FLA_Obj W, FLA_Obj u2, FLA_Obj A2, FLA_Obj U2, FLA_Obj w1t, FLA_Obj vt) |
FLA_Error FLA_Apply_H2_UT_piv_row | ( | FLA_Obj | tau, |
FLA_Obj | a1t, | ||
FLA_Obj | u1t, | ||
FLA_Obj | W, | ||
FLA_Obj | u2, | ||
FLA_Obj | A2, | ||
FLA_Obj | U2, | ||
FLA_Obj | w1t, | ||
FLA_Obj | vt | ||
) |
References FLA_Axpy_external(), FLA_Copy_external(), FLA_Gemvc_external(), FLA_Inv_scalc_external(), FLA_MINUS_ONE, FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), and FLA_ZERO.
Referenced by FLA_QR_UT_piv_unb_var2().
{ // a1t -= u1t W = 1 a1t -1 W^T u1t; FLA_Gemvc_external( FLA_TRANSPOSE, FLA_NO_CONJUGATE, FLA_MINUS_ONE, W, u1t, FLA_ONE, a1t ); // w1t := a1t; FLA_Copy_external( a1t, w1t ); // w1t += u2' A2 = 1 w1t + 1 A2^T conj(u2); FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, A2, u2, FLA_ONE, w1t ); if ( FLA_Obj_min_dim( U2 ) > 0 ) { FLA_Obj vtR; // Partition the workspace (a row vector matching the width of a1t) FLA_Part_1x2( vt, &vt, &vtR, FLA_Obj_width( U2 ), FLA_LEFT ); // vt := u2'U2 = 0 vt + 1 U2^T conj(u2); FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, U2, u2, FLA_ZERO, vt ); // w1t -= - vt W = 1 w1t -1 W^T vt; FLA_Gemvc_external( FLA_TRANSPOSE, FLA_NO_CONJUGATE, FLA_MINUS_ONE, W, vt, FLA_ONE, w1t ); } // w1t = w1t / tau; FLA_Inv_scalc_external( FLA_NO_CONJUGATE, tau, w1t ); // a1t = a1t - w1t; FLA_Axpy_external( FLA_MINUS_ONE, w1t, a1t ); return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_piv_blk_var1 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
FLA_Obj | w, | ||
FLA_Obj | p, | ||
fla_qrut_t * | cntl | ||
) |
References FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_internal(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_piv_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 pT, p0, pB, p1, p2; FLA_Obj wT, w0, wB, w1, w2; 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 ); FLA_Part_2x1( p, &pT, &pB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); // Loop over A; T is properly truncated. 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_Repart_2x1_to_3x1( pT, &p0, /* ** */ /* ** */ &p1, pB, &p2, b, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w0, /* ** */ /* ** */ &w1, wB, &w2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ FLA_Part_2x1( T1, &T1T, &T2B, b, FLA_TOP ); // Perform a unblocked (BLAS2-oriented) QR factorization // with pivoting via the UT transform on ABR: // // ABR -> QB1 R11 // // where: // - QB1 is formed from UB1 (which is stored column-wise below the // diagonal of ( A11 A21 )^T and T1T (which is stored to the upper triangle // of T11). // - R11 is stored to ( A11 A12 ). FLA_QR_UT_piv_internal( ABR, T1T, wB, p1, FLA_Cntl_sub_qrut( cntl ) ); // Apply pivots to previous columns. FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, p1, ATR ); /*------------------------------------------------------------*/ 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 ); FLA_Cont_with_3x1_to_2x1( &pT, p0, p1, /* ** */ /* ** */ &pB, p2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w0, w1, /* ** */ /* ** */ &wB, w2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_QR_UT_piv_blk_var2 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
FLA_Obj | w, | ||
FLA_Obj | p, | ||
fla_qrut_t * | cntl | ||
) |
References FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Gemm_external(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_internal(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_QR_UT_piv_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 TT, TB; FLA_Obj pT, p0, pB, p1, p2; FLA_Obj wT, w0, wB, w1, w2; 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 ); FLA_Part_2x1( p, &pT, &pB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); 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_Repart_2x1_to_3x1( pT, &p0, /* ** */ /* ** */ &p1, pB, &p2, b, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w0, /* ** */ /* ** */ &w1, wB, &w2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ // ** Reshape T matrices to match the blocksize b FLA_Part_2x1( TR, &TT, &TB, b, FLA_TOP ); // ** Perform a unblocked (BLAS2-oriented) QR factorization // with pivoting via the UT transform on ABR: // // ABR -> QB1 R11 // // where: // - QB1 is formed from UB1 (which is stored column-wise below the // diagonal of ( A11 A21 )^T and the upper-triangle of T1. // - R11 is stored to ( A11 A12 ). // - W12 stores T and partial updates for FLA_Apply_Q_UT_piv_var. FLA_QR_UT_piv_internal( ABR, TT, wB, p1, FLA_Cntl_sub_qrut( cntl ) ); if ( FLA_Obj_width( A12 ) > 0 ) { // ** Block update FLA_Part_2x1( W12, &TT, &TB, b, FLA_TOP ); FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A21, TT, FLA_ONE, A22 ); } // ** Apply pivots to previous columns. FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, p1, ATR ); /*------------------------------------------------------------*/ 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 ); FLA_Cont_with_3x1_to_2x1( &pT, p0, p1, /* ** */ /* ** */ &pB, p2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w0, w1, /* ** */ /* ** */ &wB, w2, FLA_TOP ); } return FLA_SUCCESS; }
References FLA_Amax_external(), FLA_Apply_H2_UT(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_1x2(), FLA_MINUS_ONE, FLA_Obj_le(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_colnorm(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Set(), and FLA_ZERO.
Referenced by FLA_QR_UT_piv_internal().
{ FLA_Obj AL, AR; FLA_Obj ATL, ATR, A00, a01, A02, ABL, ABR, a10t, alpha11, a12t, A20, a21, A22; FLA_Obj AT, A0, AB, a1t, A2; FLA_Obj AB1, AT1, at1; FLA_Obj TTL, TTR, T00, t01, T02, TBL, TBR, t10t, tau11, t12t, T20, t21, T22; FLA_Obj pT, p0, pB, pi1, p2; FLA_Obj wT, w0, wB, omega1, w2; dim_t nb = FLA_Obj_width ( A ) - FLA_Obj_width( T ); //dim_t mb = FLA_Obj_length( A ) - FLA_Obj_width( T ); FLA_Part_1x2( A, &AL, &AR, nb, FLA_RIGHT ); FLA_Part_2x2( AL, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x1( AR, &AT, &AB, 0, FLA_TOP ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); FLA_Part_2x1( p, &pT, &pB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); 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_2x1_to_3x1( AT, &A0, /* ** */ /* *** */ &a1t, AB, &A2, 1, FLA_BOTTOM ); 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( pT, &p0, /* ** */ /* *** */ &pi1, pB, &p2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w0, /* ** */ /* *** */ &omega1, wB, &w2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ // Ignore minus inputs for LAPACK compatability. if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE ) { // Determine pivot index FLA_Amax_external( wB, pi1 ); FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, wB ); // Apply pivots FLA_Merge_1x2( ABR, AB, &AB1 ); FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AB1 ); } else { // Do not pivot. FLA_Set( FLA_ZERO, pi1 ); } // 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 ); // Apply H to (a12t A22)^T // / a12t \ = H / a12t \ // \ A22 / \ A22 / // // where H is formed from tau11 and u21. FLA_Merge_1x2( A22, A2, &AB1 ); FLA_Merge_1x2( a12t, a1t, &at1 ); FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, at1, AB1 ); // 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 ); // Apply pivots to previous rows if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE ) { FLA_Merge_1x2( ATR, AT, &AT1 ); FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AT1 ); } // Norm downdate w2 = alpha w2 + beta columnwisenorm2(a12t) FLA_QR_UT_piv_colnorm( FLA_MINUS_ONE, at1, w2 ); /*------------------------------------------------------------*/ 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( &AT, A0, a1t, /* ** */ /* *** */ &AB, A2, FLA_TOP ); 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( &pT, p0, pi1, /* ** */ /* *** */ &pB, p2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w0, omega1, /* ** */ /* *** */ &wB, w2, FLA_TOP ); } return FLA_SUCCESS; }
References FLA_Amax_external(), FLA_Apply_H2_UT_piv_row(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_lt(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_colnorm(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Set(), and FLA_ZERO.
Referenced by FLA_QR_UT_piv_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_Obj pT, p0, pB, pi1, p2; FLA_Obj wT, w0, wB, omega1, w2; FLA_Obj ab1, v; // Create workspace FLA_Obj_create( FLA_Obj_datatype( T ), 1, FLA_Obj_width( T ), 0, 0, &v ); 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( p, &pT, &pB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); while ( FLA_Obj_min_dim( pB ) > 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 ); FLA_Repart_2x1_to_3x1( pT, &p0, /* ** */ /* *** */ &pi1, pB, &p2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w0, /* ** */ /* *** */ &omega1, wB, &w2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ // ** Ignore minus inputs for LAPACK compatability. if ( FLA_Obj_lt( pi1, FLA_ZERO ) == FALSE ) { // ** Determine pivot index FLA_Amax_external( wB, pi1 ); // ** BLIS returns -1 if it fails to search the maximum value if ( FLA_Obj_lt( pi1, FLA_ZERO ) == TRUE ) FLA_Set( FLA_ZERO, pi1 ); // ** Apply a pivot on column norms FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, wB ); // ** Apply a pivot on ABR FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, ABR ); // ** Apply a pivot on TTR FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, TTR ); } else { // ** Do not pivot. FLA_Set( FLA_ZERO, pi1 ); } // ** Update the pivot column FLA_Merge_2x1( alpha11, a21, &ab1 ); // ab1 = ab1 - ABL t01 FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, ABL, t01, FLA_ONE, ab1 ); // ** Find the householder reflector on that column FLA_Househ2_UT( FLA_LEFT, alpha11, a21, tau11 ); // ** Update the pivot row FLA_Apply_H2_UT_piv_row( tau11, a12t, a10t, T02, a21, A22, A20, t12t, v ); // ** Apply pivots on ATR FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, ATR ); // ** Norm downdate w2 = w2 - columnwisenorm2(a12t) FLA_QR_UT_piv_colnorm( FLA_MINUS_ONE, a12t, w2 ); // ** Update T matrix // 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 ); FLA_Cont_with_3x1_to_2x1( &pT, p0, pi1, /* ** */ /* *** */ &pB, p2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w0, omega1, /* ** */ /* *** */ &wB, w2, FLA_TOP ); } // Free the workspace FLA_Obj_free( &v); return FLA_SUCCESS; }