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Scale ABSTOL with the matrix in xSTEVX and xSTEVR #1386

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Scale ABSTOL with the matrix in xSTEVX and xSTEVR #1386

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14 changes: 12 additions & 2 deletions SRC/dstevr.f
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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, IMAX, 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 @@ -456,6 +458,14 @@ 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 @@ -522,7 +532,7 @@ 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
14 changes: 12 additions & 2 deletions SRC/dstevx.f
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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, IMAX, 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 @@ -358,6 +360,14 @@ 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 @@ -406,7 +416,7 @@ 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
14 changes: 12 additions & 2 deletions SRC/sstevr.f
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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, IMAX, 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 @@ -458,6 +460,14 @@ 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 @@ -524,7 +534,7 @@ 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
14 changes: 12 additions & 2 deletions SRC/sstevx.f
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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, IMAX, 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 @@ -358,6 +360,14 @@ 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 @@ -406,7 +416,7 @@ 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 TESTING/EIG/dchkee.F
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Original file line number Diff line number Diff line change
Expand Up @@ -1924,7 +1924,7 @@ 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
37 changes: 30 additions & 7 deletions TESTING/EIG/ddrvst.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -479,7 +479,7 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
DOUBLE PRECISION HALF
PARAMETER ( HALF = 0.5D0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 18 )
PARAMETER ( MAXTYP = 19 )
* ..
* .. Local Scalars ..
LOGICAL BADNN
Expand Down Expand Up @@ -519,11 +519,11 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
INTRINSIC ABS, DBLE, INT, LOG, MAX, MIN, SQRT
* ..
* .. Data statements ..
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9 /
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9, 10 /
DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
$ 2, 3, 1, 2, 3 /
$ 2, 3, 1, 2, 3, 2 /
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
$ 0, 0, 4, 4, 4 /
$ 0, 0, 4, 4, 4, 0 /
* ..
* .. Executable Statements ..
*
Expand Down Expand Up @@ -741,6 +741,22 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
A( I, J ) = U( IROW, J )
90 CONTINUE
100 CONTINUE
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Tridiagonal with equal diagonal entries and half that
* off the diagonal, so that the absolute tolerance below
* is a meaningful fraction of the spread of the
* eigenvalues.
*
DO 105 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
105 CONTINUE
DO 106 JCOL = 1, N - 1
A( JCOL, JCOL+1 ) = ANORM / TWO
A( JCOL+1, JCOL ) = A( JCOL, JCOL+1 )
106 CONTINUE
*
ELSE
IINFO = 1
END IF
Expand All @@ -755,6 +771,13 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
110 CONTINUE
*
ABSTOL = UNFL + UNFL
*
* A tolerance at or below the smallest pivot is inert in the
* bisection, so type 19 asks for one that the routine has to
* scale along with the matrix.
*
IF( JTYPE.EQ.19 )
$ ABSTOL = TEN*ULP*ANORM
IF( N.LE.1 ) THEN
IL = 1
IU = N
Expand All @@ -770,7 +793,7 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 3) If matrix is tridiagonal, call DSTEV and DSTEVX.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
NTEST = 1
DO 120 I = 1, N
D1( I ) = A( I, I )
Expand Down Expand Up @@ -2051,7 +2074,7 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 6) Call DSBEV and DSBEVX.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
KD = 1
ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
KD = MAX( N-1, 0 )
Expand Down Expand Up @@ -2555,7 +2578,7 @@ SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 9) Call DSBEVD.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
KD = 1
ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
KD = MAX( N-1, 0 )
Expand Down
2 changes: 1 addition & 1 deletion TESTING/EIG/schkee.F
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1925,7 +1925,7 @@ PROGRAM SCHKEE
$ A( 1, 3 ), D( 1, 12 ), A( 1, 4 ), WORK,
$ LWORK, IWORK, LIWORK, RESULT, INFO )
ELSE
CALL SDRVST( NN, NVAL, 18, DOTYPE, ISEED, THRESH,
CALL SDRVST( 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
37 changes: 30 additions & 7 deletions TESTING/EIG/sdrvst.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -479,7 +479,7 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
REAL HALF
PARAMETER ( HALF = 0.5E0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 18 )
PARAMETER ( MAXTYP = 19 )
* ..
* .. Local Scalars ..
LOGICAL BADNN
Expand Down Expand Up @@ -519,11 +519,11 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
INTRINSIC ABS, INT, LOG, MAX, MIN, REAL, SQRT
* ..
* .. Data statements ..
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9 /
DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9, 10 /
DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
$ 2, 3, 1, 2, 3 /
$ 2, 3, 1, 2, 3, 2 /
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
$ 0, 0, 4, 4, 4 /
$ 0, 0, 4, 4, 4, 0 /
* ..
* .. Executable Statements ..
*
Expand Down Expand Up @@ -741,6 +741,22 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
A( I, J ) = U( IROW, J )
90 CONTINUE
100 CONTINUE
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Tridiagonal with equal diagonal entries and half that
* off the diagonal, so that the absolute tolerance below
* is a meaningful fraction of the spread of the
* eigenvalues.
*
DO 105 JCOL = 1, N
A( JCOL, JCOL ) = ANORM
105 CONTINUE
DO 106 JCOL = 1, N - 1
A( JCOL, JCOL+1 ) = ANORM / TWO
A( JCOL+1, JCOL ) = A( JCOL, JCOL+1 )
106 CONTINUE
*
ELSE
IINFO = 1
END IF
Expand All @@ -755,6 +771,13 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
110 CONTINUE
*
ABSTOL = UNFL + UNFL
*
* A tolerance at or below the smallest pivot is inert in the
* bisection, so type 19 asks for one that the routine has to
* scale along with the matrix.
*
IF( JTYPE.EQ.19 )
$ ABSTOL = TEN*ULP*ANORM
IF( N.LE.1 ) THEN
IL = 1
IU = N
Expand All @@ -770,7 +793,7 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 3) If matrix is tridiagonal, call SSTEV and SSTEVX.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
NTEST = 1
DO 120 I = 1, N
D1( I ) = A( I, I )
Expand Down Expand Up @@ -2051,7 +2074,7 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 6) Call SSBEV and SSBEVX.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
KD = 1
ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
KD = MAX( N-1, 0 )
Expand Down Expand Up @@ -2555,7 +2578,7 @@ SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
*
* 9) Call SSBEVD.
*
IF( JTYPE.LE.7 ) THEN
IF( JTYPE.LE.7 .OR. JTYPE.EQ.19 ) THEN
KD = 1
ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
KD = MAX( N-1, 0 )
Expand Down
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