This is really old school, but a lot of times we have users sending us
copy pasting of codes, and that is the only way to know the version of
the code.
This is mostly a long term maintenance improvement.
Many coding styles require elimination of trailing whitespace, and
many editors and source code management configurations automatically
gobble up whitespace. When these tools gobble up whitespace, it
complicates reviewing the meaningful code changes.
By removing whitespace on one patch, it makes future
code reviews much easier.
=SCRIPT====================================================================
if which tempfile &>/dev/null; then
TEMPMAKER=tempfile
elif which mktemp &>/dev/null; then
TEMPMAKER=mktemp
else
echo "Cannot find tempfile program." 2>&1
exit 1
fi
MYTEMP=$($TEMPMAKER)
trap 'rm -f $MYTEMP' SIGINT SIGTERM
stripit() {
echo "stripping $1"
sed 's/[ \t]*$//' "$1" > $MYTEMP
cp $MYTEMP "$1"
}
if [ $# -gt 0 ]; then
while [ "$1" != "" ]; do
stripit $1
shift
done
else
while read -t 2; do
stripit $REPLY
done
fi
rm $MYTEMP
=================================================
Items are labelled (a) through (m), omitting (l).
Several are not bugs, just suggestions.
Most bugs are in *gesdd.
There's one bug (g) in *bdsdc. This is the underlying cause of LAPACK bug #111.
There's one bug (m) in [cz]gesvd. I also added an INT() cast in these
assignments to silence compiler warnings. Changed:
LWORK_ZGEQRF=CDUM(1)
to:
LWORK_ZGEQRF = INT( CDUM(1) )
Where possible, I ran a test showing the wrong behavior, then a test showing the
corrected behavior. These use a modified version of the MAGMA SVD tester
(calling LAPACK), because I could adjust the lwork as needed. The last 3 columns
are the lwork type, the lwork size, and the lwork formula. The lwork types are:
doc_old as documented in LAPACK 3.6.
doc as in the attached, updated documentation.
min_old minwrk, as computed in LAPACK 3.6.
min minwrk, as computed in the attached, updated code.
min-1 minimum - 1; this should cause gesdd to return an error.
opt optimal size.
max the maximum size LAPACK will take advantage of;
some cases, the optimal is n*n + work, while the max is m*n + work.
query what gesdd returns for an lwork query; should equal opt or max.
After the lwork, occasionally there is a ! or ? error code indicating:
Error codes: ! error: lwork < min. For (min-1), this ought to appear.
? compatability issue: lwork < min_old, will fail for lapack <= 3.6.
I also tested the update routines on a wide variety of sizes and jobz, with
various lwork.
Besides fixing the bugs below, I made two significant changes.
1) Changed *gesdd from computing each routine's workspace using, e.g.:
N*ilaenv(...)
to querying each routine for its LWORK, e.g.:
CALL ZGEBRD( M, N, CDUM(1), M, CDUM(1), DUM(1), CDUM(1),
$ CDUM(1), CDUM(1), -1, IERR )
LWORK_ZGEBRD_MN = INT( CDUM(1) )
This matches how *gesvd was changed in LAPACK 3.4.0.
2) Changed the Workspace: comments, which were incredibly deceptive.
For instance, in Path 2 before dbdsdc, it said
Workspace: need N + N*N + BDSPAC
since dbdsdc needs the [e] vector, [U] matrix, and bdspac.
However, that ignores that the [tauq, taup] vectors and [R] matrix
are also already allocated, though dbdsdc doesn't need them.
So the workspace needed at that point in the code is actually
Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC
For clarity, I added in [brackets] what matrices or vectors were allocated,
and the order reflects their order in memory.
I may do a similar change for *gesvd eventually. The workspace comments in
MAGMA's *gesvd have already been updated as above.
================================================================================
a) Throughout, to simplify equations, let:
mn = min( M, N )
mx = max( M, N )
================================================================================
b) [sdcz]gesdd Path 4 (m >> n, job="all") has wrong minwrk formula in code:
minwrk = bdspac + mn*mn + 2*mn + mx
= 4*mn*mn + 6*mn + mx
This is an overestimate, needlessly rejecting the documented formula:
doc = 4*mn*mn + 7*mn
In complex, the correct min fails, but the doc matches the wrong minwrk.
Solution: fix code to:
minwrk = mn*mn + max( 3*mn + bdspac, mn + mx )
= mn*mn + max( 3*mn*mn + 7*mn, mn + mx )
Test cases:
m=40, ..., 100; n=20; jobz='A'
See bug (d) showing documentation is also wrong.
Also, see bug (i), complex [cz]gesdd should return -12 instead of -13.
================================================================================
bt) transposed case
[sd]gesdd Path 4t (n >> m, job="all") has a different wrong minwrk; see bug (c).
[cz]gesdd Path 4t exhibits same bug as Path 4.
Test cases:
m=20; n=40, ..., 100; jobz='A'
================================================================================
c) [sd]gesdd Path 4t (n >> m, job="all") has wrong minwrk formula in code,
different than bug (b):
minwrk = bdspac + m*m + 3*m
= 4*mn*mn + 7*mn
This formula lacks any dependence on N, so the code will fail (without
setting info; orglq calls xerbla) if N is too large, N > 3*M*M + 6*M.
Bug does not occur in complex.
Test cases:
m=20; n = 1320; jobz='A' ok with documented lwork
m=20; n > 1320; jobz='A' fails with documented lwork
Solution: as in bug (b), fix code to:
minwrk = mn*mn + max( 3*mn + bdspac, mn + mx )
= mn*mn + max( 3*mn*mn + 7*mn, mn + mx )
See bug (d) showing documentation is also wrong.
================================================================================
d) [sd]gesdd documentation lists the same minimum size for jobz='S' and 'A':
If JOBZ = 'S' or 'A', LWORK >= min(M,N)*(7 + 4*min(M,N))
However, jobz='A' actually also depends on max(M,N):
minwrk = mn*mn + max( 3*mn*mn + 7*mn, mn + mx )
This causes the formula to fail for mx > 3*mn*mn + 6*mn.
Test cases:
m > 1320; n = 20; jobz='A' fails with document lwork, even after fixing bugs (b) and (c).
m = 20; n > 1320; jobz='A' fails also.
Solution: in docs, split these two cases. This fix uses an overestimate,
so that codes using it will be backwards compatible with LAPACK <= 3.6.
If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn.
If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx.
================================================================================
e) [sd]gesdd, Path 5, jobz='A' has wrong maxwrk formula in the code:
MAXWRK = MAX( MAXWRK, BDSPAC + 3*N )
Should be:
MAXWRK = MAX( WRKBL, BDSPAC + 3*N )
This causes the lwork query to ignore WRKBL, and return the minimum
workspace size, BDSPAC + 3*N, instead of the optimal workspace size.
However, it only affects the result for small sizes where min(M,N) < NB.
Path 5t has the correct maxwrk formula.
Complex is correct for both Path 5 and 5t.
Test case:
Compare lwork query with
M = 30, N = 20, jobz='A', lwork query is 1340
M = 20, N = 30, jobz='A', lwork query is 3260
These should be the same.
Solution: fix code as above.
================================================================================
f) Not a bug, just a suggestion.
The lwork minimum sizes are not actually minimums, and can be larger than
the queried lwork size.
Solution: add a comment:
These are not tight minimums in all cases; see comments inside code.
================================================================================
g) [sd]bdsdc segfaults due to too small workspace size. Its documentation claims:
If COMPQ = 'N' then LWORK >= (4 * N).
Based on this, in zgesdd, the rwork size >= 5*min(M,N).
However, LAPACK bug 111 found that rwork size >= 7*min(M,N) was required.
In dbdsdc, if uplo='L', then it rotates lower bidiagonal to upper bidiagonal,
and saves 2 vectors of Givens rotations in work. It shifts WSTART from
1 to 2*N-1. Then it calls dlasdq( ..., work( wstart ), info ).
As dlasdq requires 4*N, dbdsdc would now require 6*N in this case.
This caused zgesdd to require rwork size >= 7*min(M,N) when N > M and jobz='N'.
My preferred solution is to change WSTART to 1 in the DLASDQ call inside dbdsdc:
IF( ICOMPQ.EQ.0 ) THEN
CALL DLASDQ( 'U', 0, N, 0, 0, 0, D, E, VT, LDVT, U, LDU, U,
$ LDU, WORK( WSTART ), INFO )
GO TO 40
END IF
to:
IF( ICOMPQ.EQ.0 ) THEN
* Ignores WSTART, which is needed only for ICOMPQ = 1 or 2;
* using WSTART would change required workspace to 6*N for uplo='L'.
CALL DLASDQ( 'U', 0, N, 0, 0, 0, D, E, VT, LDVT, U, LDU, U,
$ LDU, WORK( 1 ), INFO )
GO TO 40
END IF
The [cz]gesdd documentation, which was changed to 7*min(M,N) in LAPACK 3.6,
may be reverted to 5*min(M,N), if desired.
================================================================================
h) [sd]gesdd for jobz='N' requires bdspac = 7*n for the dbdsdc workspace.
However, dbdsdc requires only 4*n, or 6*n before fixing bug (g).
For backwards compatability, I did not change the code, but added a comment
for clarification.
================================================================================
i) [cz]gesdd returns info = -13 instead of info = -12 for lwork errors.
================================================================================
j) In zgesdd, for computing maxwrk, these paths:
Path 6, jobz=A
Path 6t, jobz=S
Path 6t, jobz=A
query ilaenv( 1, zungbr, ... )
when the code actually calls zunmbr (twice). I corrected it.
================================================================================
k) In zgesdd documentation, currently
lrwork >= max( 5*mn*mn + 7*mn, 2*mx*mn + 2*mn*mn + mn )
It doesn't need that much, particularly for (mx >> mn) case.
If (mx >> mn), lrwork >= 5*mn*mn + 5*mn;
else, lrwork >= max( 5*mn*mn + 5*mn,
2*mx*mn + 2*mn*mn + mn ).
I changed this in the documentation. Feel free to revert if you prefer.
================================================================================
m) [cz]gesvd, Path 10 and 10t, have minwrk inside the wrong conditional:
IF( .NOT.WNTVN ) THEN
MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZUNGBR_P )
MINWRK = 2*N + M
END IF
So Path 10 with jobvt='N', and Path 10t with jobu='N', have minwrk = 1,
so an invalid lwork is not correctly rejected.
================================================================================
mt) transposed case
broken: with old routine, Path 10t with jobu='N' doesn't enforce minwrk
Replace Workspace calculations by calls to the routines with LWORK=-1.
This impacts only three routines: xGESVD, xGELSS, x[OR/UN]GBR
Testing have been run to check that the workspace size return is the same.
In a further effort (next major release probably), LAPACK will need to stick
to that LWORK=-1 rule to compute Workspace size.
Use \par instead of \details for section.
add a Contributors Section and a Reference Section.
Remove (some) verbatim section when not needed.
Those changes have been done by hand so I am not sure I manage to catch them all.
Mark Gates