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|
*> \brief \b DGET37
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE DGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, NIN
* ..
* .. Array Arguments ..
* INTEGER LMAX( 3 ), NINFO( 3 )
* DOUBLE PRECISION RMAX( 3 )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> DGET37 tests DTRSNA, a routine for estimating condition numbers of
*> eigenvalues and/or right eigenvectors of a matrix.
*>
*> The test matrices are read from a file with logical unit number NIN.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is DOUBLE PRECISION array, dimension (3)
*> Value of the largest test ratio.
*> RMAX(1) = largest ratio comparing different calls to DTRSNA
*> RMAX(2) = largest error in reciprocal condition
*> numbers taking their conditioning into account
*> RMAX(3) = largest error in reciprocal condition
*> numbers not taking their conditioning into
*> account (may be larger than RMAX(2))
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER array, dimension (3)
*> LMAX(i) is example number where largest test ratio
*> RMAX(i) is achieved. Also:
*> If DGEHRD returns INFO nonzero on example i, LMAX(1)=i
*> If DHSEQR returns INFO nonzero on example i, LMAX(2)=i
*> If DTRSNA returns INFO nonzero on example i, LMAX(3)=i
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER array, dimension (3)
*> NINFO(1) = No. of times DGEHRD returned INFO nonzero
*> NINFO(2) = No. of times DHSEQR returned INFO nonzero
*> NINFO(3) = No. of times DTRSNA returned INFO nonzero
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER KNT, NIN
* ..
* .. Array Arguments ..
INTEGER LMAX( 3 ), NINFO( 3 )
DOUBLE PRECISION RMAX( 3 )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
DOUBLE PRECISION EPSIN
PARAMETER ( EPSIN = 5.9605D-8 )
INTEGER LDT, LWORK
PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) )
* ..
* .. Local Scalars ..
INTEGER I, ICMP, IFND, INFO, ISCL, J, KMIN, M, N
DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TNRM, TOL, TOLIN, V,
$ VIMIN, VMAX, VMUL, VRMIN
* ..
* .. Local Arrays ..
LOGICAL SELECT( LDT )
INTEGER IWORK( 2*LDT ), LCMP( 3 )
DOUBLE PRECISION DUM( 1 ), LE( LDT, LDT ), RE( LDT, LDT ),
$ S( LDT ), SEP( LDT ), SEPIN( LDT ),
$ SEPTMP( LDT ), SIN( LDT ), STMP( LDT ),
$ T( LDT, LDT ), TMP( LDT, LDT ), VAL( 3 ),
$ WI( LDT ), WIIN( LDT ), WITMP( LDT ),
$ WORK( LWORK ), WR( LDT ), WRIN( LDT ),
$ WRTMP( LDT )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE
EXTERNAL DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEHRD, DHSEQR, DLABAD, DLACPY, DSCAL,
$ DTREVC, DTRSNA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, SQRT
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* EPSIN = 2**(-24) = precision to which input data computed
*
EPS = MAX( EPS, EPSIN )
RMAX( 1 ) = ZERO
RMAX( 2 ) = ZERO
RMAX( 3 ) = ZERO
LMAX( 1 ) = 0
LMAX( 2 ) = 0
LMAX( 3 ) = 0
KNT = 0
NINFO( 1 ) = 0
NINFO( 2 ) = 0
NINFO( 3 ) = 0
*
VAL( 1 ) = SQRT( SMLNUM )
VAL( 2 ) = ONE
VAL( 3 ) = SQRT( BIGNUM )
*
* Read input data until N=0. Assume input eigenvalues are sorted
* lexicographically (increasing by real part, then decreasing by
* imaginary part)
*
10 CONTINUE
READ( NIN, FMT = * )N
IF( N.EQ.0 )
$ RETURN
DO 20 I = 1, N
READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
20 CONTINUE
DO 30 I = 1, N
READ( NIN, FMT = * )WRIN( I ), WIIN( I ), SIN( I ), SEPIN( I )
30 CONTINUE
TNRM = DLANGE( 'M', N, N, TMP, LDT, WORK )
*
* Begin test
*
DO 240 ISCL = 1, 3
*
* Scale input matrix
*
KNT = KNT + 1
CALL DLACPY( 'F', N, N, TMP, LDT, T, LDT )
VMUL = VAL( ISCL )
DO 40 I = 1, N
CALL DSCAL( N, VMUL, T( 1, I ), 1 )
40 CONTINUE
IF( TNRM.EQ.ZERO )
$ VMUL = ONE
*
* Compute eigenvalues and eigenvectors
*
CALL DGEHRD( N, 1, N, T, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N,
$ INFO )
IF( INFO.NE.0 ) THEN
LMAX( 1 ) = KNT
NINFO( 1 ) = NINFO( 1 ) + 1
GO TO 240
END IF
DO 60 J = 1, N - 2
DO 50 I = J + 2, N
T( I, J ) = ZERO
50 CONTINUE
60 CONTINUE
*
* Compute Schur form
*
CALL DHSEQR( 'S', 'N', N, 1, N, T, LDT, WR, WI, DUM, 1, WORK,
$ LWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 2 ) = KNT
NINFO( 2 ) = NINFO( 2 ) + 1
GO TO 240
END IF
*
* Compute eigenvectors
*
CALL DTREVC( 'Both', 'All', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, N, M, WORK, INFO )
*
* Compute condition numbers
*
CALL DTRSNA( 'Both', 'All', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, S, SEP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
*
* Sort eigenvalues and condition numbers lexicographically
* to compare with inputs
*
CALL DCOPY( N, WR, 1, WRTMP, 1 )
CALL DCOPY( N, WI, 1, WITMP, 1 )
CALL DCOPY( N, S, 1, STMP, 1 )
CALL DCOPY( N, SEP, 1, SEPTMP, 1 )
CALL DSCAL( N, ONE / VMUL, SEPTMP, 1 )
DO 80 I = 1, N - 1
KMIN = I
VRMIN = WRTMP( I )
VIMIN = WITMP( I )
DO 70 J = I + 1, N
IF( WRTMP( J ).LT.VRMIN ) THEN
KMIN = J
VRMIN = WRTMP( J )
VIMIN = WITMP( J )
END IF
70 CONTINUE
WRTMP( KMIN ) = WRTMP( I )
WITMP( KMIN ) = WITMP( I )
WRTMP( I ) = VRMIN
WITMP( I ) = VIMIN
VRMIN = STMP( KMIN )
STMP( KMIN ) = STMP( I )
STMP( I ) = VRMIN
VRMIN = SEPTMP( KMIN )
SEPTMP( KMIN ) = SEPTMP( I )
SEPTMP( I ) = VRMIN
80 CONTINUE
*
* Compare condition numbers for eigenvalues
* taking their condition numbers into account
*
V = MAX( TWO*DBLE( N )*EPS*TNRM, SMLNUM )
IF( TNRM.EQ.ZERO )
$ V = ONE
DO 90 I = 1, N
IF( V.GT.SEPTMP( I ) ) THEN
TOL = ONE
ELSE
TOL = V / SEPTMP( I )
END IF
IF( V.GT.SEPIN( I ) ) THEN
TOLIN = ONE
ELSE
TOLIN = V / SEPIN( I )
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( SIN( I )-TOLIN ).GT.STMP( I )+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( SIN( I )-TOLIN.GT.STMP( I )+TOL ) THEN
VMAX = ( SIN( I )-TOLIN ) / ( STMP( I )+TOL )
ELSE IF( SIN( I )+TOLIN.LT.EPS*( STMP( I )-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( SIN( I )+TOLIN.LT.STMP( I )-TOL ) THEN
VMAX = ( STMP( I )-TOL ) / ( SIN( I )+TOLIN )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 2 ) ) THEN
RMAX( 2 ) = VMAX
IF( NINFO( 2 ).EQ.0 )
$ LMAX( 2 ) = KNT
END IF
90 CONTINUE
*
* Compare condition numbers for eigenvectors
* taking their condition numbers into account
*
DO 100 I = 1, N
IF( V.GT.SEPTMP( I )*STMP( I ) ) THEN
TOL = SEPTMP( I )
ELSE
TOL = V / STMP( I )
END IF
IF( V.GT.SEPIN( I )*SIN( I ) ) THEN
TOLIN = SEPIN( I )
ELSE
TOLIN = V / SIN( I )
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( SEPIN( I )-TOLIN ).GT.SEPTMP( I )+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN( I )-TOLIN.GT.SEPTMP( I )+TOL ) THEN
VMAX = ( SEPIN( I )-TOLIN ) / ( SEPTMP( I )+TOL )
ELSE IF( SEPIN( I )+TOLIN.LT.EPS*( SEPTMP( I )-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN( I )+TOLIN.LT.SEPTMP( I )-TOL ) THEN
VMAX = ( SEPTMP( I )-TOL ) / ( SEPIN( I )+TOLIN )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 2 ) ) THEN
RMAX( 2 ) = VMAX
IF( NINFO( 2 ).EQ.0 )
$ LMAX( 2 ) = KNT
END IF
100 CONTINUE
*
* Compare condition numbers for eigenvalues
* without taking their condition numbers into account
*
DO 110 I = 1, N
IF( SIN( I ).LE.DBLE( 2*N )*EPS .AND. STMP( I ).LE.
$ DBLE( 2*N )*EPS ) THEN
VMAX = ONE
ELSE IF( EPS*SIN( I ).GT.STMP( I ) ) THEN
VMAX = ONE / EPS
ELSE IF( SIN( I ).GT.STMP( I ) ) THEN
VMAX = SIN( I ) / STMP( I )
ELSE IF( SIN( I ).LT.EPS*STMP( I ) ) THEN
VMAX = ONE / EPS
ELSE IF( SIN( I ).LT.STMP( I ) ) THEN
VMAX = STMP( I ) / SIN( I )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 3 ) ) THEN
RMAX( 3 ) = VMAX
IF( NINFO( 3 ).EQ.0 )
$ LMAX( 3 ) = KNT
END IF
110 CONTINUE
*
* Compare condition numbers for eigenvectors
* without taking their condition numbers into account
*
DO 120 I = 1, N
IF( SEPIN( I ).LE.V .AND. SEPTMP( I ).LE.V ) THEN
VMAX = ONE
ELSE IF( EPS*SEPIN( I ).GT.SEPTMP( I ) ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN( I ).GT.SEPTMP( I ) ) THEN
VMAX = SEPIN( I ) / SEPTMP( I )
ELSE IF( SEPIN( I ).LT.EPS*SEPTMP( I ) ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN( I ).LT.SEPTMP( I ) ) THEN
VMAX = SEPTMP( I ) / SEPIN( I )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 3 ) ) THEN
RMAX( 3 ) = VMAX
IF( NINFO( 3 ).EQ.0 )
$ LMAX( 3 ) = KNT
END IF
120 CONTINUE
*
* Compute eigenvalue condition numbers only and compare
*
VMAX = ZERO
DUM( 1 ) = -ONE
CALL DCOPY( N, DUM, 0, STMP, 1 )
CALL DCOPY( N, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Eigcond', 'All', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 130 I = 1, N
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
130 CONTINUE
*
* Compute eigenvector condition numbers only and compare
*
CALL DCOPY( N, DUM, 0, STMP, 1 )
CALL DCOPY( N, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Veccond', 'All', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 140 I = 1, N
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
140 CONTINUE
*
* Compute all condition numbers using SELECT and compare
*
DO 150 I = 1, N
SELECT( I ) = .TRUE.
150 CONTINUE
CALL DCOPY( N, DUM, 0, STMP, 1 )
CALL DCOPY( N, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Bothcond', 'Some', SELECT, N, T, LDT, LE, LDT,
$ RE, LDT, STMP, SEPTMP, N, M, WORK, N, IWORK,
$ INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 160 I = 1, N
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
160 CONTINUE
*
* Compute eigenvalue condition numbers using SELECT and compare
*
CALL DCOPY( N, DUM, 0, STMP, 1 )
CALL DCOPY( N, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Eigcond', 'Some', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 170 I = 1, N
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
170 CONTINUE
*
* Compute eigenvector condition numbers using SELECT and compare
*
CALL DCOPY( N, DUM, 0, STMP, 1 )
CALL DCOPY( N, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Veccond', 'Some', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 180 I = 1, N
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
180 CONTINUE
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
*
* Select first real and first complex eigenvalue
*
IF( WI( 1 ).EQ.ZERO ) THEN
LCMP( 1 ) = 1
IFND = 0
DO 190 I = 2, N
IF( IFND.EQ.1 .OR. WI( I ).EQ.ZERO ) THEN
SELECT( I ) = .FALSE.
ELSE
IFND = 1
LCMP( 2 ) = I
LCMP( 3 ) = I + 1
CALL DCOPY( N, RE( 1, I ), 1, RE( 1, 2 ), 1 )
CALL DCOPY( N, RE( 1, I+1 ), 1, RE( 1, 3 ), 1 )
CALL DCOPY( N, LE( 1, I ), 1, LE( 1, 2 ), 1 )
CALL DCOPY( N, LE( 1, I+1 ), 1, LE( 1, 3 ), 1 )
END IF
190 CONTINUE
IF( IFND.EQ.0 ) THEN
ICMP = 1
ELSE
ICMP = 3
END IF
ELSE
LCMP( 1 ) = 1
LCMP( 2 ) = 2
IFND = 0
DO 200 I = 3, N
IF( IFND.EQ.1 .OR. WI( I ).NE.ZERO ) THEN
SELECT( I ) = .FALSE.
ELSE
LCMP( 3 ) = I
IFND = 1
CALL DCOPY( N, RE( 1, I ), 1, RE( 1, 3 ), 1 )
CALL DCOPY( N, LE( 1, I ), 1, LE( 1, 3 ), 1 )
END IF
200 CONTINUE
IF( IFND.EQ.0 ) THEN
ICMP = 2
ELSE
ICMP = 3
END IF
END IF
*
* Compute all selected condition numbers
*
CALL DCOPY( ICMP, DUM, 0, STMP, 1 )
CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Bothcond', 'Some', SELECT, N, T, LDT, LE, LDT,
$ RE, LDT, STMP, SEPTMP, N, M, WORK, N, IWORK,
$ INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 210 I = 1, ICMP
J = LCMP( I )
IF( SEPTMP( I ).NE.SEP( J ) )
$ VMAX = ONE / EPS
IF( STMP( I ).NE.S( J ) )
$ VMAX = ONE / EPS
210 CONTINUE
*
* Compute selected eigenvalue condition numbers
*
CALL DCOPY( ICMP, DUM, 0, STMP, 1 )
CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Eigcond', 'Some', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 220 I = 1, ICMP
J = LCMP( I )
IF( STMP( I ).NE.S( J ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
220 CONTINUE
*
* Compute selected eigenvector condition numbers
*
CALL DCOPY( ICMP, DUM, 0, STMP, 1 )
CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL DTRSNA( 'Veccond', 'Some', SELECT, N, T, LDT, LE, LDT, RE,
$ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 240
END IF
DO 230 I = 1, ICMP
J = LCMP( I )
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( J ) )
$ VMAX = ONE / EPS
230 CONTINUE
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
240 CONTINUE
GO TO 10
*
* End of DGET37
*
END
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