This a draft for dgecx.f. #1161
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SRC/dgecx.f
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| *> Specifies how the factors of CX factorization | ||
| *> are returned. | ||
| *> | ||
| *> = 'P' or 'p' : return only the column permutaion matrix P |
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Pedantic: LAPACK doesn't normally specify both Uppercase and lowercase. Cf.:
lapack/SRC> grep "^\*> += '\w'" lapack/SRC/zpotrf.f
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
lapack/SRC> grep "^\*> += '\w'" lapack/SRC/*.f`
| *> matrix in the blocked step auxiliary subroutine DLAQP3RK ). | ||
| *> \endverbatim | ||
| *> | ||
| *> \param[out] LIWORK |
SRC/dgecx.f
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| *> The dimension of the array LIWORK. LIWORK >= N | ||
| *> | ||
| *> If LIWORK = -1, then a workspace query is assumed; the routine | ||
| *> only calculates the optimal size of the WORK array, returns |
SRC/dgecx.f
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| * | ||
| * DGECX | ||
| * | ||
| END No newline at end of file |
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Files should end with a newline. Notice ⊖ on Github.
SRC/dgecx.f
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| NBOPT = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 ) | ||
| LWKOPT = 1000 | ||
| END IF | ||
| WORK( 1 ) = DBLE( LWKOPT ) |
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Add:
LWORK( 1 ) = N
or whatever the formula is. Also elsewhere.
SRC/dgecx.f
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| * | ||
| END IF | ||
| * | ||
| WORK( 1 ) = DBLE( LWKOPT ) |
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Add:
LWORK( 1 ) = N
as above.
SRC/dgecx.f
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| * MSUB. | ||
| * | ||
| INFO = -6 | ||
| WORK( 1 ) = DBLE( LWKOPT ) |
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Add:
LWORK( 1 ) = N
or whatever the formula is. Also elsewhere.
|
by mistake 2 branches (one with dgecx.f and one with DGECX.f ) were joined
in a single pull request, the files are identical. DGECX.f can be removed.
…On Wed, Oct 15, 2025 at 11:15 AM Mark Gates ***@***.***> wrote:
***@***.**** requested changes on this pull request.
Some initial comments.
------------------------------
On SRC/DGECX.f
<#1161 (comment)>
:
There is both DGECX.f (incorrect) and dgecx.f (correct) file? This file
should be removed.
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +*> array as the first K elements.
+*> b) If the flag COMP_X is set, then the routine also explicitly
+*> computes and returns the factor X = pseudoinv(C) * A.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] FACT
+*> \verbatim
+*> FACT is CHARACTER*1
+*> Specifies how the factors of CX factorization
+*> are returned.
+*>
+*> = 'P' or 'p' : return only the column permutaion matrix P
Pedantic: LAPACK doesn't normally specify both Uppercase and lowercase.
Cf.:
lapack/SRC> grep "^\*> += '\w'" lapack/SRC/zpotrf.f
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
lapack/SRC> grep "^\*> += '\w'" lapack/SRC/*.f`
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (N).
+*> Is a work array. ( IWORK is used by DGEQP3RK to store indices
+*> of "bad" columns for norm downdating in the residual
+*> matrix in the blocked step auxiliary subroutine DLAQP3RK ).
+*> \endverbatim
+*>
+*> \param[out] LIWORK
Input, right? \param[in]
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (N).
+*> Is a work array. ( IWORK is used by DGEQP3RK to store indices
+*> of "bad" columns for norm downdating in the residual
+*> matrix in the blocked step auxiliary subroutine DLAQP3RK ).
+*> \endverbatim
+*>
+*> \param[out] LIWORK
+*> \verbatim
+*> LIWORK is INTEGER
+*> The dimension of the array LIWORK. LIWORK >= N
+*>
+*> If LIWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
Typo: IWORK array.
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +* Copy matrix C into work array WORK.
+*
+ CALL DLACPY( 'F', M, K, C, LDC, WORK, M )
+*
+ CALL DGELS( 'N', M, K, N, WORK, M, X, LDX,
+ $ WORK( M*K+1 ), LWORK,
+ $ IINFO )
+ INFO = IINFO
+*
+ END IF
+*
+ WORK( 1 ) = DBLE( LWKOPT )
+*
+* DGECX
+*
+ END
Files should end with a newline. Notice ⊖ on Github.
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +* code.
+*
+ IF( INFO.EQ.0 ) THEN
+ MINMN = MIN( M, N )
+ IF( MINMN.EQ.0 ) THEN
+ LWKMIN = 1
+ LWKOPT = 1
+ ELSE
+ LWKMIN = 3*N + 1
+*
+* Assign to NBOPT optimal block size.
+*
+ NBOPT = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 )
+ LWKOPT = 1000
+ END IF
+ WORK( 1 ) = DBLE( LWKOPT )
Add:
LWORK( 1 ) = N
or whatever the formula is. Also elsewhere.
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +* that uses QR factorization. For that purpose, we store C into
+* WORK array WORK(1:M*K), and the matrix A was copied into
+* the array X at the begining of the routine.
+*
+* Copy matrix C into work array WORK.
+*
+ CALL DLACPY( 'F', M, K, C, LDC, WORK, M )
+*
+ CALL DGELS( 'N', M, K, N, WORK, M, X, LDX,
+ $ WORK( M*K+1 ), LWORK,
+ $ IINFO )
+ INFO = IINFO
+*
+ END IF
+*
+ WORK( 1 ) = DBLE( LWKOPT )
Add:
LWORK( 1 ) = N
as above.
------------------------------
In SRC/dgecx.f
<#1161 (comment)>
:
> +*
+ MNSUB = MIN(MSUB, NSUB)
+ MRESID = MSUB-NSEL
+ NRESID = NSUB-NSEL
+ IF( NSEL.GT.0 ) THEN
+ IF( MSUB.LT.NSEL ) THEN
+* TODO: Move this part to the top of the routine.
+* a) Case MSUB < NSEL.
+* When the number of preselected columns
+* is larger than MSUB, hence the factorization of all NSEL
+* columns cannot be completed. Return from the routine with the
+* error of COL_SEL_DESEL parameter. NSEL cannot be larger than
+* MSUB.
+*
+ INFO = -6
+ WORK( 1 ) = DBLE( LWKOPT )
Add:
LWORK( 1 ) = N
or whatever the formula is. Also elsewhere.
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|
changed the description of DGECX
| *> | ||
| *> A * P(K) = C*X + A_resid, where | ||
| *> | ||
| *> C is an M-by-K matrix which is a subset of K columns selected |
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I think with "subset" you mean "spanning the same subspace" or "in the range of K columns of A" here. Is that right?
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No, C is literally a subset of A.
| *> | ||
| *> DGECX computes a CX factorization of a real M-by-N matrix A: | ||
| *> | ||
| *> A * P(K) = C*X + A_resid, where |
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I think P(K) notation is confusing here. It's not a function of K but depends on K parameter.
| *> from the original matrix A, | ||
| *> | ||
| *> X is a K-by-N matrix that minimizes the Frobenius norm of the | ||
| *> residual matrix A_resid, X = pseudoinv(C) * A, |
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You can just say "minimizes "|A - C*X|" in the Frobenius norm".
| *> Column selection stage 1. | ||
| *> ========================= | ||
| *> | ||
| *> The user can select N_sel columns and deselect N_desel columns |
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Why can't I just supply a list of columns that I want and leave this deselect business out? Then it will be two options, "A" is all columns, "S" selected columns. If "A" then cols array is not referenced otherwise it is read from cols array.
I'm afraid this is getting a bit too complicated with explicit deselection. Same goes for the rows
|
We've discussed that this is the expert interface, and we would have a simplified interface (e.g., without all the column selection). Elsewhere in LAPACK, expert interfaces have an extra |
| * http://www.netlib.org/lapack/explore-html/ | ||
| * | ||
| *> \htmlonly | ||
| *> Download DGEQP3RK + dependencies |
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GECXX instead of GEQP3RK.
| *> \author Univ. of Colorado Denver | ||
| *> \author NAG Ltd. | ||
| * | ||
| *> \ingroup gecxx |
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Need to add to DOCS/groups-usr.dox:
@defgroup gecxx gecxx: CX decomposition
We may need a new category. CX doesn't seem to fit in existing categories.
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Jim suggests a category "Low rank factorizations". Given that, I suggest adding this, or a subset of this, to groups-user.dox between unitary_top @{ ... @} and geev_top @{ ... @} top-level groups (line 456):
@defgroup low_rank_top Low-rank factors (CX, CUR, etc.)
@{
@defgroup cx_grp CX
@{
@defgroup gecx gecx: CX factor
@defgroup gecxx gecxx: CX factor, expert interface
@}
@defgroup cur_grp CUR
@{
@defgroup gecur gecur: CUR factor
@defgroup gecurx gecurx: CUR factor, expert interface
@}
@}
| *> On exit, if INFO >= 0, WORK(1) returns the optimal LIWORK. | ||
| *> \endverbatim | ||
| *> | ||
| *> \param[out] LIWORK |
| NFREE = NSUB | ||
| * | ||
| LQUERY = ( LWORK.EQ.-1 ) | ||
| LIQUERY = ( LIWORK.EQ.-1 ) |
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It would be simpler to have just one LQUERY variable. Cf. zheevd.f
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his a draft for dgecx.f. to REVIEW and COMMENT