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C
C SPDX-License-Identifier: BSD-3-Clause
C
* MB03WD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER NMAX, PMAX
PARAMETER ( NMAX = 20, PMAX = 20 )
INTEGER LDA1, LDA2, LDTAU, LDZ1, LDZ2, LDZTA
PARAMETER ( LDA1 = NMAX, LDA2 = NMAX, LDTAU = NMAX-1,
$ LDZ1 = NMAX, LDZ2 = NMAX, LDZTA = NMAX )
INTEGER LDWORK
PARAMETER ( LDWORK = MAX( NMAX, NMAX + PMAX - 2 ) )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* .. Local Scalars ..
DOUBLE PRECISION SSQ
INTEGER I, IHI, IHIZ, ILO, ILOZ, INFO, J, K, KP1, N, P
CHARACTER COMPZ, JOB
* .. Local Arrays ..
DOUBLE PRECISION A(LDA1,LDA2,PMAX), AS(LDA1,LDA2,PMAX),
$ DWORK(LDWORK), TAU(LDTAU,PMAX), WI(NMAX),
$ WR(NMAX), Z(LDZ1,LDZ2,PMAX), ZTA(LDZTA,NMAX)
* .. External Functions ..
DOUBLE PRECISION DLANGE, DLAPY2
LOGICAL LSAME
EXTERNAL DLANGE, DLAPY2, LSAME
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY, MB03VD, MB03VY, MB03WD, MB03WX
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* .. Executable Statements ..
WRITE (NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N, P, ILO, IHI, ILOZ, IHIZ, JOB, COMPZ
IF ( N.LT.0 .OR. N.GT.MIN( LDA1, LDA2 ) ) THEN
WRITE ( NOUT, FMT = 99988 ) N
ELSE
IF ( P.LE.0 .OR. P.GT.PMAX ) THEN
WRITE ( NOUT, FMT = 99987 ) P
ELSE
* Read matrices A_1, ..., A_p from the input file.
DO 10 K = 1, P
READ ( NIN, FMT = * )
$ ( ( A(I,J,K), J = 1, N ), I = 1, N )
CALL DLACPY( 'F', N, N, A(1,1,K), LDA1, AS(1,1,K), LDA1 )
10 CONTINUE
* Reduce to the periodic Hessenberg form.
CALL MB03VD( N, P, ILO, IHI, A, LDA1, LDA2, TAU, LDTAU,
$ DWORK, INFO )
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99997 ) INFO
ELSE
IF ( LSAME( COMPZ, 'V' ) ) THEN
DO 20 K = 1, P
CALL DLACPY( 'L', N, N, A(1,1,K), LDA1, Z(1,1,K),
$ LDZ1 )
20 CONTINUE
* Accumulate the transformations.
CALL MB03VY( N, P, ILO, IHI, Z, LDZ1, LDZ2, TAU,
$ LDTAU, DWORK, LDWORK, INFO )
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99996 ) INFO
STOP
ELSE
* Reduce to the periodic Schur form.
CALL MB03WD( JOB, COMPZ, N, P, ILO, IHI, ILOZ,
$ IHIZ, A, LDA1, LDA2, Z, LDZ1, LDZ2,
$ WR, WI, DWORK, LDWORK, INFO )
IF ( INFO.GT.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
WRITE ( NOUT, FMT = 99991 )
DO 30 I = MAX( ILO, INFO + 1 ), IHI
WRITE ( NOUT, FMT = 99990 ) WR(I), WI(I)
30 CONTINUE
STOP
END IF
IF ( INFO.LT.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
* Store the isolated eigenvalues.
CALL MB03WX( ILO-1, P, A, LDA1, LDA2, WR, WI,
$ INFO )
IF ( IHI.LT.N )
$ CALL MB03WX( N-IHI, P, A(IHI+1,IHI+1,1),
$ LDA1, LDA2, WR(IHI+1),
$ WI(IHI+1), INFO )
WRITE ( NOUT, FMT = 99991 )
DO 40 I = 1, N
WRITE ( NOUT, FMT = 99990 ) WR(I), WI(I)
40 CONTINUE
WRITE ( NOUT, FMT = 99995 )
DO 60 K = 1, P
WRITE ( NOUT, FMT = 99994 ) K
DO 50 I = 1, N
WRITE ( NOUT, FMT = 99993 )
$ ( A(I,J,K), J = 1, N )
50 CONTINUE
60 CONTINUE
WRITE ( NOUT, FMT = 99992 )
DO 80 K = 1, P
WRITE ( NOUT, FMT = 99994 ) K
DO 70 I = 1, N
WRITE ( NOUT, FMT = 99993 )
$ ( Z(I,J,K), J = 1, N )
70 CONTINUE
80 CONTINUE
* Compute error.
SSQ = ZERO
DO 90 K = 1, P
KP1 = K+1
IF( KP1.GT.P ) KP1 = 1
* Compute NORM (Z' * A * Z - Aout)
CALL DGEMM( 'T', 'N', N, N, N, ONE, Z(1,1,K),
$ LDZ1, AS(1,1,K), LDA1, ZERO, ZTA,
$ LDZTA )
CALL DGEMM( 'N', 'N', N, N, N, ONE, ZTA,
$ LDZTA, Z(1,1,KP1), LDZ1, -ONE,
$ A(1,1,K), LDA1 )
SSQ = DLAPY2( SSQ,
$ DLANGE( 'Frobenius', N, N,
$ A(1,1,K), LDA1,
$ DWORK ) )
90 CONTINUE
WRITE ( NOUT, FMT = 99989 ) SSQ
END IF
END IF
END IF
END IF
END IF
END IF
STOP
99999 FORMAT (' MB03WD EXAMPLE PROGRAM RESULTS', /1X)
99998 FORMAT (' INFO on exit from MB03WD = ', I2)
99997 FORMAT (' INFO on exit from MB03VD = ', I2)
99996 FORMAT (' INFO on exit from MB03VY = ', I2)
99995 FORMAT (/' Reduced matrices')
99994 FORMAT (/' K = ', I5)
99993 FORMAT (8F8.4)
99992 FORMAT (/' Transformation matrices')
99991 FORMAT ( ' Computed eigenvalues'/)
99990 FORMAT (4X,'( ', F17.6,' ,', F17.6,' )')
99989 FORMAT (/,' NORM (Z''*A*Z - Aout) = ', 1PD12.5)
99988 FORMAT (/, ' N is out of range.',/' N = ', I5)
99987 FORMAT (/, ' P is out of range.',/' P = ', I5)
END
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