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Scale ABSTOL with the matrix in ?STEVR/?STEVX (Reference-LAPACK PR 1386) #6191

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martin-frbg merged 2 commits into from
Oct 29, 2026
Merged

Scale ABSTOL with the matrix in ?STEVR/?STEVX (Reference-LAPACK PR 1386) #6191

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Scale ABSTOL with the matrix (Reference-LAPACK PR 1386)
martin-frbg Oct 28, 2026
0645127
Scale ABSTOL in ?STEVR/?STEVX with the matrix (Reference-LAPACK PR 1386)
martin-frbg Oct 28, 2026
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16 changes: 14 additions & 2 deletions lapack-netlib/SRC/dstevr.c
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Original file line number Diff line number Diff line change
Expand Up @@ -566,7 +566,7 @@ f"> */
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ void xerbla_(char *, integer *, ftnlen);
doublereal bignum;
doublereal abstll, bignum;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
integer indisp;
extern /* Subroutine */ void dstein_(integer *, doublereal *, doublereal *,
Expand Down Expand Up @@ -713,6 +713,7 @@ f"> */
/* Scale matrix to allowable range, if necessary. */

iscale = 0;
abstll = *abstol;
if (valeig) {
vll = *vl;
vuu = *vu;
Expand All @@ -734,6 +735,17 @@ f"> */
dscal_(n, &sigma, &d__[1], &c__1);
i__1 = *n - 1;
dscal_(&i__1, &sigma, &e[1], &c__1);

/* Scale a positive ABSTOL with the matrix. Keep the product */
/* positive, as DSTEBZ takes ABSTOL <= 0 as a request for its */
/* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the */
/* product cannot overflow. */

if (*abstol > 0.) {
/* Computing MAX */
d__1 = f2cmin(*abstol,tnrm) * sigma;
abstll = f2cmax(d__1,safmin);
}
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
Expand Down Expand Up @@ -799,7 +811,7 @@ f"> */
} else {
*(unsigned char *)order = 'E';
}
dstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, &
dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &d__[1], &e[1], m, &
nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[1], &iwork[
indiwo], info);

Expand Down
14 changes: 12 additions & 2 deletions lapack-netlib/SRC/dstevr.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -329,7 +329,8 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
INTEGER I, IEEEOK, INDIBL, INDIFL, INDISP,
$ INDIWO, ISCALE, ITMP1, J, JJ, LIWMIN, LWMIN,
$ NSPLIT
DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
DOUBLE PRECISION ABSTLL, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM,
$ TMP1, TNRM, VLL, VUU
* ..
* .. External Functions ..
Expand Down Expand Up @@ -440,6 +441,7 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
ABSTLL = ABSTOL
IF( VALEIG ) THEN
VLL = VL
VUU = VU
Expand All @@ -459,6 +461,14 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
IF( ISCALE.EQ.1 ) THEN
CALL DSCAL( N, SIGMA, D, 1 )
CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
*
* Scale a positive ABSTOL with the matrix. Keep the product
* positive, as DSTEBZ takes ABSTOL <= 0 as a request for its
* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the
* product cannot overflow.
*
IF( ABSTOL.GT.ZERO )
$ ABSTLL = MAX( MIN( ABSTOL, TNRM )*SIGMA, SAFMIN )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
Expand Down Expand Up @@ -525,7 +535,7 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
ORDER = 'E'
END IF

CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E,
CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, D, E,
$ M,
$ NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ), WORK,
$ IWORK( INDIWO ), INFO )
Expand Down
16 changes: 14 additions & 2 deletions lapack-netlib/SRC/dstevx.c
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -485,7 +485,7 @@ f"> */
logical alleig, indeig, valeig;
doublereal safmin;
extern /* Subroutine */ void xerbla_(char *, integer *, ftnlen);
doublereal bignum;
doublereal abstll, bignum;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
integer indisp;
extern /* Subroutine */ void dstein_(integer *, doublereal *, doublereal *,
Expand Down Expand Up @@ -600,6 +600,7 @@ f"> */
/* Scale matrix to allowable range, if necessary. */

iscale = 0;
abstll = *abstol;
if (valeig) {
vll = *vl;
vuu = *vu;
Expand All @@ -623,6 +624,17 @@ f"> */
dscal_(n, &sigma, &d__[1], &c__1);
i__1 = *n - 1;
dscal_(&i__1, &sigma, &e[1], &c__1);

/* Scale a positive ABSTOL with the matrix. Keep the product */
/* positive, as DSTEBZ takes ABSTOL <= 0 as a request for its */
/* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the */
/* product cannot overflow. */

if (*abstol > 0.) {
/* Computing MAX */
d__1 = f2cmin(*abstol,tnrm) * sigma;
abstll = f2cmax(d__1,safmin);
}
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
Expand Down Expand Up @@ -674,7 +686,7 @@ f"> */
indwrk = 1;
indisp = *n + 1;
indiwo = indisp + *n;
dstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, &
dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &d__[1], &e[1], m, &
nsplit, &w[1], &iwork[1], &iwork[indisp], &work[indwrk], &iwork[
indiwo], &iinfo);
if (iinfo != 0) {
Expand Down
14 changes: 12 additions & 2 deletions lapack-netlib/SRC/dstevx.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -253,7 +253,8 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
CHARACTER ORDER
INTEGER I, IINFO, INDISP, INDIWO, INDWRK,
$ ISCALE, ITMP1, J, JJ, NSPLIT
DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
DOUBLE PRECISION ABSTLL, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM,
$ TMP1, TNRM, VLL, VUU
* ..
* .. External Functions ..
Expand Down Expand Up @@ -340,6 +341,7 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
ABSTLL = ABSTOL
IF( VALEIG ) THEN
VLL = VL
VUU = VU
Expand All @@ -361,6 +363,14 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
IF( ISCALE.EQ.1 ) THEN
CALL DSCAL( N, SIGMA, D, 1 )
CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
*
* Scale a positive ABSTOL with the matrix. Keep the product
* positive, as DSTEBZ takes ABSTOL <= 0 as a request for its
* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the
* product cannot overflow.
*
IF( ABSTOL.GT.ZERO )
$ ABSTLL = MAX( MIN( ABSTOL, TNRM )*SIGMA, SAFMIN )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
Expand Down Expand Up @@ -409,7 +419,7 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
INDWRK = 1
INDISP = 1 + N
INDIWO = INDISP + N
CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E,
CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, D, E,
$ M,
$ NSPLIT, W, IWORK( 1 ), IWORK( INDISP ),
$ WORK( INDWRK ), IWORK( INDIWO ), IINFO )
Expand Down
16 changes: 14 additions & 2 deletions lapack-netlib/SRC/sstevr.c
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -558,7 +558,7 @@ f"> */
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ void xerbla_(char *, integer *, ftnlen);
real bignum;
real abstll, bignum;
integer indisp, indiwo, liwmin;
logical tryrac;
extern real slanst_(char *, integer *, real *, real *);
Expand Down Expand Up @@ -703,6 +703,7 @@ f"> */
/* Scale matrix to allowable range, if necessary. */

iscale = 0;
abstll = *abstol;
if (valeig) {
vll = *vl;
vuu = *vu;
Expand All @@ -724,6 +725,17 @@ f"> */
sscal_(n, &sigma, &d__[1], &c__1);
i__1 = *n - 1;
sscal_(&i__1, &sigma, &e[1], &c__1);

/* Scale a positive ABSTOL with the matrix. Keep the product */
/* positive, as SSTEBZ takes ABSTOL <= 0 as a request for its */
/* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the */
/* product cannot overflow. */

if (*abstol > 0.f) {
/* Computing MAX */
r__1 = f2cmin(*abstol,tnrm) * sigma;
abstll = f2cmax(r__1,safmin);
}
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
Expand Down Expand Up @@ -789,7 +801,7 @@ f"> */
} else {
*(unsigned char *)order = 'E';
}
sstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, &
sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &d__[1], &e[1], m, &
nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[1], &iwork[
indiwo], info);

Expand Down
14 changes: 12 additions & 2 deletions lapack-netlib/SRC/sstevr.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -330,7 +330,8 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
CHARACTER ORDER
INTEGER I, IEEEOK, INDIBL, INDIFL, INDISP,
$ INDIWO, ISCALE, J, JJ, LIWMIN, LWMIN, NSPLIT
REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
REAL ABSTLL, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM,
$ TMP1, TNRM, VLL, VUU
* ..
* .. External Functions ..
Expand Down Expand Up @@ -442,6 +443,7 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
ABSTLL = ABSTOL
IF( VALEIG ) THEN
VLL = VL
VUU = VU
Expand All @@ -461,6 +463,14 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
IF( ISCALE.EQ.1 ) THEN
CALL SSCAL( N, SIGMA, D, 1 )
CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
*
* Scale a positive ABSTOL with the matrix. Keep the product
* positive, as SSTEBZ takes ABSTOL <= 0 as a request for its
* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the
* product cannot overflow.
*
IF( ABSTOL.GT.ZERO )
$ ABSTLL = MAX( MIN( ABSTOL, TNRM )*SIGMA, SAFMIN )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
Expand Down Expand Up @@ -527,7 +537,7 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
ORDER = 'E'
END IF

CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E,
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, D, E,
$ M,
$ NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ), WORK,
$ IWORK( INDIWO ), INFO )
Expand Down
16 changes: 14 additions & 2 deletions lapack-netlib/SRC/sstevx.c
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -477,7 +477,7 @@ f"> */
extern real slamch_(char *);
real safmin;
extern /* Subroutine */ void xerbla_(char *, integer *, ftnlen);
real bignum;
real abstll, bignum;
integer indisp, indiwo, indwrk;
extern real slanst_(char *, integer *, real *, real *);
extern /* Subroutine */ void sstein_(integer *, real *, real *, integer *,
Expand Down Expand Up @@ -590,6 +590,7 @@ f"> */
/* Scale matrix to allowable range, if necessary. */

iscale = 0;
abstll = *abstol;
if (valeig) {
vll = *vl;
vuu = *vu;
Expand All @@ -613,6 +614,17 @@ f"> */
sscal_(n, &sigma, &d__[1], &c__1);
i__1 = *n - 1;
sscal_(&i__1, &sigma, &e[1], &c__1);

/* Scale a positive ABSTOL with the matrix. Keep the product */
/* positive, as SSTEBZ takes ABSTOL <= 0 as a request for its */
/* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the */
/* product cannot overflow. */

if (*abstol > 0.f) {
/* Computing MAX */
r__1 = f2cmin(*abstol,tnrm) * sigma;
abstll = f2cmax(r__1,safmin);
}
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
Expand Down Expand Up @@ -664,7 +676,7 @@ f"> */
indwrk = 1;
indisp = *n + 1;
indiwo = indisp + *n;
sstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, &
sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &d__[1], &e[1], m, &
nsplit, &w[1], &iwork[1], &iwork[indisp], &work[indwrk], &iwork[
indiwo], &iinfo);
if (iinfo != 0) {
Expand Down
14 changes: 12 additions & 2 deletions lapack-netlib/SRC/sstevx.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -253,7 +253,8 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
CHARACTER ORDER
INTEGER I, IINFO, INDISP, INDIWO, INDWRK,
$ ISCALE, ITMP1, J, JJ, NSPLIT
REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
REAL ABSTLL, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM,
$ TMP1, TNRM, VLL, VUU
* ..
* .. External Functions ..
Expand Down Expand Up @@ -340,6 +341,7 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
ABSTLL = ABSTOL
IF ( VALEIG ) THEN
VLL = VL
VUU = VU
Expand All @@ -361,6 +363,14 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
IF( ISCALE.EQ.1 ) THEN
CALL SSCAL( N, SIGMA, D, 1 )
CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
*
* Scale a positive ABSTOL with the matrix. Keep the product
* positive, as SSTEBZ takes ABSTOL <= 0 as a request for its
* default tolerance EPS*|T|, and cap ABSTOL at |T| so that the
* product cannot overflow.
*
IF( ABSTOL.GT.ZERO )
$ ABSTLL = MAX( MIN( ABSTOL, TNRM )*SIGMA, SAFMIN )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
Expand Down Expand Up @@ -409,7 +419,7 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
INDWRK = 1
INDISP = 1 + N
INDIWO = INDISP + N
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E,
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, D, E,
$ M,
$ NSPLIT, W, IWORK( 1 ), IWORK( INDISP ),
$ WORK( INDWRK ), IWORK( INDIWO ), IINFO )
Expand Down
2 changes: 1 addition & 1 deletion lapack-netlib/TESTING/EIG/dchkee.F
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1942,7 +1942,7 @@ PROGRAM DCHKEE
$ A( 1, 3 ), D( 1, 12 ), A( 1, 4 ), WORK,
$ LWORK, IWORK, LIWORK, RESULT, INFO )
ELSE
CALL DDRVST( NN, NVAL, 18, DOTYPE, ISEED, THRESH, NOUT,
CALL DDRVST( NN, NVAL, 19, DOTYPE, ISEED, THRESH, NOUT,
$ A( 1, 1 ), NMAX, D( 1, 3 ), D( 1, 4 ),
$ D( 1, 5 ), D( 1, 6 ), D( 1, 8 ), D( 1, 9 ),
$ D( 1, 10 ), D( 1, 11 ), A( 1, 2 ), NMAX,
Expand Down
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