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|
*> \brief \b CGET37
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, NIN
* ..
* .. Array Arguments ..
* INTEGER LMAX( 3 ), NINFO( 3 )
* REAL RMAX( 3 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGET37 tests CTRSNA, 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 REAL array, dimension (3)
*> Value of the largest test ratio.
*> RMAX(1) = largest ratio comparing different calls to CTRSNA
*> 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 CGEHRD returns INFO nonzero on example i, LMAX(1)=i
*> If CHSEQR returns INFO nonzero on example i, LMAX(2)=i
*> If CTRSNA 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 CGEHRD returned INFO nonzero
*> NINFO(2) = No. of times CHSEQR returned INFO nonzero
*> NINFO(3) = No. of times CTRSNA 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 complex_eig
*
* =====================================================================
SUBROUTINE CGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.4.0) --
* -- 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 )
REAL RMAX( 3 )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
REAL EPSIN
PARAMETER ( EPSIN = 5.9605E-8 )
INTEGER LDT, LWORK
PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) )
* ..
* .. Local Scalars ..
INTEGER I, ICMP, INFO, ISCL, ISRT, J, KMIN, M, N
REAL BIGNUM, EPS, SMLNUM, TNRM, TOL, TOLIN, V,
$ VCMIN, VMAX, VMIN, VMUL
* ..
* .. Local Arrays ..
LOGICAL SELECT( LDT )
INTEGER LCMP( 3 )
REAL DUM( 1 ), RWORK( 2*LDT ), S( LDT ), SEP( LDT ),
$ SEPIN( LDT ), SEPTMP( LDT ), SIN( LDT ),
$ STMP( LDT ), VAL( 3 ), WIIN( LDT ),
$ WRIN( LDT ), WSRT( LDT )
COMPLEX CDUM( 1 ), LE( LDT, LDT ), RE( LDT, LDT ),
$ T( LDT, LDT ), TMP( LDT, LDT ), W( LDT ),
$ WORK( LWORK ), WTMP( LDT )
* ..
* .. External Functions ..
REAL CLANGE, SLAMCH
EXTERNAL CLANGE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CGEHRD, CHSEQR, CLACPY, CSSCAL, CTREVC,
$ CTRSNA, SCOPY, SLABAD, SSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, MAX, REAL, SQRT
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL SLABAD( 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 if ISRT = 0,
* increasing by imaginary part if ISRT = 1)
*
10 CONTINUE
READ( NIN, FMT = * )N, ISRT
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 = CLANGE( 'M', N, N, TMP, LDT, RWORK )
DO 260 ISCL = 1, 3
*
* Scale input matrix
*
KNT = KNT + 1
CALL CLACPY( 'F', N, N, TMP, LDT, T, LDT )
VMUL = VAL( ISCL )
DO 40 I = 1, N
CALL CSSCAL( N, VMUL, T( 1, I ), 1 )
40 CONTINUE
IF( TNRM.EQ.ZERO )
$ VMUL = ONE
*
* Compute eigenvalues and eigenvectors
*
CALL CGEHRD( 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 260
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 CHSEQR( 'S', 'N', N, 1, N, T, LDT, W, CDUM, 1, WORK,
$ LWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 2 ) = KNT
NINFO( 2 ) = NINFO( 2 ) + 1
GO TO 260
END IF
*
* Compute eigenvectors
*
DO 70 I = 1, N
SELECT( I ) = .TRUE.
70 CONTINUE
CALL CTREVC( 'B', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, N,
$ M, WORK, RWORK, INFO )
*
* Compute condition numbers
*
CALL CTRSNA( 'B', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, S,
$ SEP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
*
* Sort eigenvalues and condition numbers lexicographically
* to compare with inputs
*
CALL CCOPY( N, W, 1, WTMP, 1 )
IF( ISRT.EQ.0 ) THEN
*
* Sort by increasing real part
*
DO 80 I = 1, N
WSRT( I ) = REAL( W( I ) )
80 CONTINUE
ELSE
*
* Sort by increasing imaginary part
*
DO 90 I = 1, N
WSRT( I ) = AIMAG( W( I ) )
90 CONTINUE
END IF
CALL SCOPY( N, S, 1, STMP, 1 )
CALL SCOPY( N, SEP, 1, SEPTMP, 1 )
CALL SSCAL( N, ONE / VMUL, SEPTMP, 1 )
DO 110 I = 1, N - 1
KMIN = I
VMIN = WSRT( I )
DO 100 J = I + 1, N
IF( WSRT( J ).LT.VMIN ) THEN
KMIN = J
VMIN = WSRT( J )
END IF
100 CONTINUE
WSRT( KMIN ) = WSRT( I )
WSRT( I ) = VMIN
VCMIN = WTMP( I )
WTMP( I ) = W( KMIN )
WTMP( KMIN ) = VCMIN
VMIN = STMP( KMIN )
STMP( KMIN ) = STMP( I )
STMP( I ) = VMIN
VMIN = SEPTMP( KMIN )
SEPTMP( KMIN ) = SEPTMP( I )
SEPTMP( I ) = VMIN
110 CONTINUE
*
* Compare condition numbers for eigenvalues
* taking their condition numbers into account
*
V = MAX( TWO*REAL( N )*EPS*TNRM, SMLNUM )
IF( TNRM.EQ.ZERO )
$ V = ONE
DO 120 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
120 CONTINUE
*
* Compare condition numbers for eigenvectors
* taking their condition numbers into account
*
DO 130 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
130 CONTINUE
*
* Compare condition numbers for eigenvalues
* without taking their condition numbers into account
*
DO 140 I = 1, N
IF( SIN( I ).LE.REAL( 2*N )*EPS .AND. STMP( I ).LE.
$ REAL( 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
140 CONTINUE
*
* Compare condition numbers for eigenvectors
* without taking their condition numbers into account
*
DO 150 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
150 CONTINUE
*
* Compute eigenvalue condition numbers only and compare
*
VMAX = ZERO
DUM( 1 ) = -ONE
CALL SCOPY( N, DUM, 0, STMP, 1 )
CALL SCOPY( N, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'E', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 160 I = 1, N
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
160 CONTINUE
*
* Compute eigenvector condition numbers only and compare
*
CALL SCOPY( N, DUM, 0, STMP, 1 )
CALL SCOPY( N, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'V', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 170 I = 1, N
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
170 CONTINUE
*
* Compute all condition numbers using SELECT and compare
*
DO 180 I = 1, N
SELECT( I ) = .TRUE.
180 CONTINUE
CALL SCOPY( N, DUM, 0, STMP, 1 )
CALL SCOPY( N, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'B', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 190 I = 1, N
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
190 CONTINUE
*
* Compute eigenvalue condition numbers using SELECT and compare
*
CALL SCOPY( N, DUM, 0, STMP, 1 )
CALL SCOPY( N, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'E', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 200 I = 1, N
IF( STMP( I ).NE.S( I ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
200 CONTINUE
*
* Compute eigenvector condition numbers using SELECT and compare
*
CALL SCOPY( N, DUM, 0, STMP, 1 )
CALL SCOPY( N, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'V', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 210 I = 1, N
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( I ) )
$ VMAX = ONE / EPS
210 CONTINUE
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
*
* Select second and next to last eigenvalues
*
DO 220 I = 1, N
SELECT( I ) = .FALSE.
220 CONTINUE
ICMP = 0
IF( N.GT.1 ) THEN
ICMP = 1
LCMP( 1 ) = 2
SELECT( 2 ) = .TRUE.
CALL CCOPY( N, RE( 1, 2 ), 1, RE( 1, 1 ), 1 )
CALL CCOPY( N, LE( 1, 2 ), 1, LE( 1, 1 ), 1 )
END IF
IF( N.GT.3 ) THEN
ICMP = 2
LCMP( 2 ) = N - 1
SELECT( N-1 ) = .TRUE.
CALL CCOPY( N, RE( 1, N-1 ), 1, RE( 1, 2 ), 1 )
CALL CCOPY( N, LE( 1, N-1 ), 1, LE( 1, 2 ), 1 )
END IF
*
* Compute all selected condition numbers
*
CALL SCOPY( ICMP, DUM, 0, STMP, 1 )
CALL SCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'B', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 230 I = 1, ICMP
J = LCMP( I )
IF( SEPTMP( I ).NE.SEP( J ) )
$ VMAX = ONE / EPS
IF( STMP( I ).NE.S( J ) )
$ VMAX = ONE / EPS
230 CONTINUE
*
* Compute selected eigenvalue condition numbers
*
CALL SCOPY( ICMP, DUM, 0, STMP, 1 )
CALL SCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'E', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 240 I = 1, ICMP
J = LCMP( I )
IF( STMP( I ).NE.S( J ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
240 CONTINUE
*
* Compute selected eigenvector condition numbers
*
CALL SCOPY( ICMP, DUM, 0, STMP, 1 )
CALL SCOPY( ICMP, DUM, 0, SEPTMP, 1 )
CALL CTRSNA( 'V', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT,
$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 260
END IF
DO 250 I = 1, ICMP
J = LCMP( I )
IF( STMP( I ).NE.DUM( 1 ) )
$ VMAX = ONE / EPS
IF( SEPTMP( I ).NE.SEP( J ) )
$ VMAX = ONE / EPS
250 CONTINUE
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
260 CONTINUE
GO TO 10
*
* End of CGET37
*
END
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