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- SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
- $ ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
- $ LWORK, INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER COMPQ, COMPZ, JOB
- INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION ALPHAI( * ), ALPHAR( * ), BETA( * ),
- $ H( LDH, * ), Q( LDQ, * ), T( LDT, * ),
- $ WORK( * ), Z( LDZ, * )
-* ..
-*
-* Purpose
-* =======
-*
-* DHGEQZ computes the eigenvalues of a real matrix pair (H,T),
-* where H is an upper Hessenberg matrix and T is upper triangular,
-* using the double-shift QZ method.
-* Matrix pairs of this type are produced by the reduction to
-* generalized upper Hessenberg form of a real matrix pair (A,B):
-*
-* A = Q1*H*Z1**T, B = Q1*T*Z1**T,
-*
-* as computed by DGGHRD.
-*
-* If JOB='S', then the Hessenberg-triangular pair (H,T) is
-* also reduced to generalized Schur form,
-*
-* H = Q*S*Z**T, T = Q*P*Z**T,
-*
-* where Q and Z are orthogonal matrices, P is an upper triangular
-* matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2
-* diagonal blocks.
-*
-* The 1-by-1 blocks correspond to real eigenvalues of the matrix pair
-* (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of
-* eigenvalues.
-*
-* Additionally, the 2-by-2 upper triangular diagonal blocks of P
-* corresponding to 2-by-2 blocks of S are reduced to positive diagonal
-* form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0,
-* P(j,j) > 0, and P(j+1,j+1) > 0.
-*
-* Optionally, the orthogonal matrix Q from the generalized Schur
-* factorization may be postmultiplied into an input matrix Q1, and the
-* orthogonal matrix Z may be postmultiplied into an input matrix Z1.
-* If Q1 and Z1 are the orthogonal matrices from DGGHRD that reduced
-* the matrix pair (A,B) to generalized upper Hessenberg form, then the
-* output matrices Q1*Q and Z1*Z are the orthogonal factors from the
-* generalized Schur factorization of (A,B):
-*
-* A = (Q1*Q)*S*(Z1*Z)**T, B = (Q1*Q)*P*(Z1*Z)**T.
-*
-* To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently,
-* of (A,B)) are computed as a pair of values (alpha,beta), where alpha is
-* complex and beta real.
-* If beta is nonzero, lambda = alpha / beta is an eigenvalue of the
-* generalized nonsymmetric eigenvalue problem (GNEP)
-* A*x = lambda*B*x
-* and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
-* alternate form of the GNEP
-* mu*A*y = B*y.
-* Real eigenvalues can be read directly from the generalized Schur
-* form:
-* alpha = S(i,i), beta = P(i,i).
-*
-* Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
-* Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
-* pp. 241--256.
-*
-* Arguments
-* =========
-*
-* JOB (input) CHARACTER*1
-* = 'E': Compute eigenvalues only;
-* = 'S': Compute eigenvalues and the Schur form.
-*
-* COMPQ (input) CHARACTER*1
-* = 'N': Left Schur vectors (Q) are not computed;
-* = 'I': Q is initialized to the unit matrix and the matrix Q
-* of left Schur vectors of (H,T) is returned;
-* = 'V': Q must contain an orthogonal matrix Q1 on entry and
-* the product Q1*Q is returned.
-*
-* COMPZ (input) CHARACTER*1
-* = 'N': Right Schur vectors (Z) are not computed;
-* = 'I': Z is initialized to the unit matrix and the matrix Z
-* of right Schur vectors of (H,T) is returned;
-* = 'V': Z must contain an orthogonal matrix Z1 on entry and
-* the product Z1*Z is returned.
-*
-* N (input) INTEGER
-* The order of the matrices H, T, Q, and Z. N >= 0.
-*
-* ILO (input) INTEGER
-* IHI (input) INTEGER
-* ILO and IHI mark the rows and columns of H which are in
-* Hessenberg form. It is assumed that A is already upper
-* triangular in rows and columns 1:ILO-1 and IHI+1:N.
-* If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
-*
-* H (input/output) DOUBLE PRECISION array, dimension (LDH, N)
-* On entry, the N-by-N upper Hessenberg matrix H.
-* On exit, if JOB = 'S', H contains the upper quasi-triangular
-* matrix S from the generalized Schur factorization;
-* 2-by-2 diagonal blocks (corresponding to complex conjugate
-* pairs of eigenvalues) are returned in standard form, with
-* H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0.
-* If JOB = 'E', the diagonal blocks of H match those of S, but
-* the rest of H is unspecified.
-*
-* LDH (input) INTEGER
-* The leading dimension of the array H. LDH >= max( 1, N ).
-*
-* T (input/output) DOUBLE PRECISION array, dimension (LDT, N)
-* On entry, the N-by-N upper triangular matrix T.
-* On exit, if JOB = 'S', T contains the upper triangular
-* matrix P from the generalized Schur factorization;
-* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S
-* are reduced to positive diagonal form, i.e., if H(j+1,j) is
-* non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and
-* T(j+1,j+1) > 0.
-* If JOB = 'E', the diagonal blocks of T match those of P, but
-* the rest of T is unspecified.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= max( 1, N ).
-*
-* ALPHAR (output) DOUBLE PRECISION array, dimension (N)
-* The real parts of each scalar alpha defining an eigenvalue
-* of GNEP.
-*
-* ALPHAI (output) DOUBLE PRECISION array, dimension (N)
-* The imaginary parts of each scalar alpha defining an
-* eigenvalue of GNEP.
-* If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
-* positive, then the j-th and (j+1)-st eigenvalues are a
-* complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
-*
-* BETA (output) DOUBLE PRECISION array, dimension (N)
-* The scalars beta that define the eigenvalues of GNEP.
-* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
-* beta = BETA(j) represent the j-th eigenvalue of the matrix
-* pair (A,B), in one of the forms lambda = alpha/beta or
-* mu = beta/alpha. Since either lambda or mu may overflow,
-* they should not, in general, be computed.
-*
-* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
-* On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in
-* the reduction of (A,B) to generalized Hessenberg form.
-* On exit, if COMPZ = 'I', the orthogonal matrix of left Schur
-* vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix
-* of left Schur vectors of (A,B).
-* Not referenced if COMPZ = 'N'.
-*
-* LDQ (input) INTEGER
-* The leading dimension of the array Q. LDQ >= 1.
-* If COMPQ='V' or 'I', then LDQ >= N.
-*
-* Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
-* On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in
-* the reduction of (A,B) to generalized Hessenberg form.
-* On exit, if COMPZ = 'I', the orthogonal matrix of
-* right Schur vectors of (H,T), and if COMPZ = 'V', the
-* orthogonal matrix of right Schur vectors of (A,B).
-* Not referenced if COMPZ = 'N'.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1.
-* If COMPZ='V' or 'I', then LDZ >= N.
-*
-* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= max(1,N).
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* = 1,...,N: the QZ iteration did not converge. (H,T) is not
-* in Schur form, but ALPHAR(i), ALPHAI(i), and
-* BETA(i), i=INFO+1,...,N should be correct.
-* = N+1,...,2*N: the shift calculation failed. (H,T) is not
-* in Schur form, but ALPHAR(i), ALPHAI(i), and
-* BETA(i), i=INFO-N+1,...,N should be correct.
-*
-* Further Details
-* ===============
-*
-* Iteration counters:
-*
-* JITER -- counts iterations.
-* IITER -- counts iterations run since ILAST was last
-* changed. This is therefore reset only when a 1-by-1 or
-* 2-by-2 block deflates off the bottom.
-*
-* =====================================================================
-*
-* .. Parameters ..
-* $ SAFETY = 1.0E+0 )
- DOUBLE PRECISION HALF, ZERO, ONE, SAFETY
- PARAMETER ( HALF = 0.5D+0, ZERO = 0.0D+0, ONE = 1.0D+0,
- $ SAFETY = 1.0D+2 )
-* ..
-* .. Local Scalars ..
- LOGICAL ILAZR2, ILAZRO, ILPIVT, ILQ, ILSCHR, ILZ,
- $ LQUERY
- INTEGER ICOMPQ, ICOMPZ, IFIRST, IFRSTM, IITER, ILAST,
- $ ILASTM, IN, ISCHUR, ISTART, J, JC, JCH, JITER,
- $ JR, MAXIT
- DOUBLE PRECISION A11, A12, A1I, A1R, A21, A22, A2I, A2R, AD11,
- $ AD11L, AD12, AD12L, AD21, AD21L, AD22, AD22L,
- $ AD32L, AN, ANORM, ASCALE, ATOL, B11, B1A, B1I,
- $ B1R, B22, B2A, B2I, B2R, BN, BNORM, BSCALE,
- $ BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
- $ CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
- $ SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
- $ TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
- $ U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
- $ WR2
-* ..
-* .. Local Arrays ..
- DOUBLE PRECISION V( 3 )
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- DOUBLE PRECISION DLAMCH, DLANHS, DLAPY2, DLAPY3
- EXTERNAL LSAME, DLAMCH, DLANHS, DLAPY2, DLAPY3
-* ..
-* .. External Subroutines ..
- EXTERNAL DLAG2, DLARFG, DLARTG, DLASET, DLASV2, DROT,
- $ XERBLA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, DBLE, MAX, MIN, SQRT
-* ..
-* .. Executable Statements ..
-*
-* Decode JOB, COMPQ, COMPZ
-*
- IF( LSAME( JOB, 'E' ) ) THEN
- ILSCHR = .FALSE.
- ISCHUR = 1
- ELSE IF( LSAME( JOB, 'S' ) ) THEN
- ILSCHR = .TRUE.
- ISCHUR = 2
- ELSE
- ISCHUR = 0
- END IF
-*
- IF( LSAME( COMPQ, 'N' ) ) THEN
- ILQ = .FALSE.
- ICOMPQ = 1
- ELSE IF( LSAME( COMPQ, 'V' ) ) THEN
- ILQ = .TRUE.
- ICOMPQ = 2
- ELSE IF( LSAME( COMPQ, 'I' ) ) THEN
- ILQ = .TRUE.
- ICOMPQ = 3
- ELSE
- ICOMPQ = 0
- END IF
-*
- IF( LSAME( COMPZ, 'N' ) ) THEN
- ILZ = .FALSE.
- ICOMPZ = 1
- ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
- ILZ = .TRUE.
- ICOMPZ = 2
- ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
- ILZ = .TRUE.
- ICOMPZ = 3
- ELSE
- ICOMPZ = 0
- END IF
-*
-* Check Argument Values
-*
- INFO = 0
- WORK( 1 ) = MAX( 1, N )
- LQUERY = ( LWORK.EQ.-1 )
- IF( ISCHUR.EQ.0 ) THEN
- INFO = -1
- ELSE IF( ICOMPQ.EQ.0 ) THEN
- INFO = -2
- ELSE IF( ICOMPZ.EQ.0 ) THEN
- INFO = -3
- ELSE IF( N.LT.0 ) THEN
- INFO = -4
- ELSE IF( ILO.LT.1 ) THEN
- INFO = -5
- ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN
- INFO = -6
- ELSE IF( LDH.LT.N ) THEN
- INFO = -8
- ELSE IF( LDT.LT.N ) THEN
- INFO = -10
- ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN
- INFO = -15
- ELSE IF( LDZ.LT.1 .OR. ( ILZ .AND. LDZ.LT.N ) ) THEN
- INFO = -17
- ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
- INFO = -19
- END IF
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'DHGEQZ', -INFO )
- RETURN
- ELSE IF( LQUERY ) THEN
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( N.LE.0 ) THEN
- WORK( 1 ) = DBLE( 1 )
- RETURN
- END IF
-*
-* Initialize Q and Z
-*
- IF( ICOMPQ.EQ.3 )
- $ CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
- IF( ICOMPZ.EQ.3 )
- $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ )
-*
-* Machine Constants
-*
- IN = IHI + 1 - ILO
- SAFMIN = DLAMCH( 'S' )
- SAFMAX = ONE / SAFMIN
- ULP = DLAMCH( 'E' )*DLAMCH( 'B' )
- ANORM = DLANHS( 'F', IN, H( ILO, ILO ), LDH, WORK )
- BNORM = DLANHS( 'F', IN, T( ILO, ILO ), LDT, WORK )
- ATOL = MAX( SAFMIN, ULP*ANORM )
- BTOL = MAX( SAFMIN, ULP*BNORM )
- ASCALE = ONE / MAX( SAFMIN, ANORM )
- BSCALE = ONE / MAX( SAFMIN, BNORM )
-*
-* Set Eigenvalues IHI+1:N
-*
- DO 30 J = IHI + 1, N
- IF( T( J, J ).LT.ZERO ) THEN
- IF( ILSCHR ) THEN
- DO 10 JR = 1, J
- H( JR, J ) = -H( JR, J )
- T( JR, J ) = -T( JR, J )
- 10 CONTINUE
- ELSE
- H( J, J ) = -H( J, J )
- T( J, J ) = -T( J, J )
- END IF
- IF( ILZ ) THEN
- DO 20 JR = 1, N
- Z( JR, J ) = -Z( JR, J )
- 20 CONTINUE
- END IF
- END IF
- ALPHAR( J ) = H( J, J )
- ALPHAI( J ) = ZERO
- BETA( J ) = T( J, J )
- 30 CONTINUE
-*
-* If IHI < ILO, skip QZ steps
-*
- IF( IHI.LT.ILO )
- $ GO TO 380
-*
-* MAIN QZ ITERATION LOOP
-*
-* Initialize dynamic indices
-*
-* Eigenvalues ILAST+1:N have been found.
-* Column operations modify rows IFRSTM:whatever.
-* Row operations modify columns whatever:ILASTM.
-*
-* If only eigenvalues are being computed, then
-* IFRSTM is the row of the last splitting row above row ILAST;
-* this is always at least ILO.
-* IITER counts iterations since the last eigenvalue was found,
-* to tell when to use an extraordinary shift.
-* MAXIT is the maximum number of QZ sweeps allowed.
-*
- ILAST = IHI
- IF( ILSCHR ) THEN
- IFRSTM = 1
- ILASTM = N
- ELSE
- IFRSTM = ILO
- ILASTM = IHI
- END IF
- IITER = 0
- ESHIFT = ZERO
- MAXIT = 30*( IHI-ILO+1 )
-*
- DO 360 JITER = 1, MAXIT
-*
-* Split the matrix if possible.
-*
-* Two tests:
-* 1: H(j,j-1)=0 or j=ILO
-* 2: T(j,j)=0
-*
- IF( ILAST.EQ.ILO ) THEN
-*
-* Special case: j=ILAST
-*
- GO TO 80
- ELSE
- IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
- H( ILAST, ILAST-1 ) = ZERO
- GO TO 80
- END IF
- END IF
-*
- IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
- T( ILAST, ILAST ) = ZERO
- GO TO 70
- END IF
-*
-* General case: j<ILAST
-*
- DO 60 J = ILAST - 1, ILO, -1
-*
-* Test 1: for H(j,j-1)=0 or j=ILO
-*
- IF( J.EQ.ILO ) THEN
- ILAZRO = .TRUE.
- ELSE
- IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
- H( J, J-1 ) = ZERO
- ILAZRO = .TRUE.
- ELSE
- ILAZRO = .FALSE.
- END IF
- END IF
-*
-* Test 2: for T(j,j)=0
-*
- IF( ABS( T( J, J ) ).LT.BTOL ) THEN
- T( J, J ) = ZERO
-*
-* Test 1a: Check for 2 consecutive small subdiagonals in A
-*
- ILAZR2 = .FALSE.
- IF( .NOT.ILAZRO ) THEN
- TEMP = ABS( H( J, J-1 ) )
- TEMP2 = ABS( H( J, J ) )
- TEMPR = MAX( TEMP, TEMP2 )
- IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
- TEMP = TEMP / TEMPR
- TEMP2 = TEMP2 / TEMPR
- END IF
- IF( TEMP*( ASCALE*ABS( H( J+1, J ) ) ).LE.TEMP2*
- $ ( ASCALE*ATOL ) )ILAZR2 = .TRUE.
- END IF
-*
-* If both tests pass (1 & 2), i.e., the leading diagonal
-* element of B in the block is zero, split a 1x1 block off
-* at the top. (I.e., at the J-th row/column) The leading
-* diagonal element of the remainder can also be zero, so
-* this may have to be done repeatedly.
-*
- IF( ILAZRO .OR. ILAZR2 ) THEN
- DO 40 JCH = J, ILAST - 1
- TEMP = H( JCH, JCH )
- CALL DLARTG( TEMP, H( JCH+1, JCH ), C, S,
- $ H( JCH, JCH ) )
- H( JCH+1, JCH ) = ZERO
- CALL DROT( ILASTM-JCH, H( JCH, JCH+1 ), LDH,
- $ H( JCH+1, JCH+1 ), LDH, C, S )
- CALL DROT( ILASTM-JCH, T( JCH, JCH+1 ), LDT,
- $ T( JCH+1, JCH+1 ), LDT, C, S )
- IF( ILQ )
- $ CALL DROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
- $ C, S )
- IF( ILAZR2 )
- $ H( JCH, JCH-1 ) = H( JCH, JCH-1 )*C
- ILAZR2 = .FALSE.
- IF( ABS( T( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
- IF( JCH+1.GE.ILAST ) THEN
- GO TO 80
- ELSE
- IFIRST = JCH + 1
- GO TO 110
- END IF
- END IF
- T( JCH+1, JCH+1 ) = ZERO
- 40 CONTINUE
- GO TO 70
- ELSE
-*
-* Only test 2 passed -- chase the zero to T(ILAST,ILAST)
-* Then process as in the case T(ILAST,ILAST)=0
-*
- DO 50 JCH = J, ILAST - 1
- TEMP = T( JCH, JCH+1 )
- CALL DLARTG( TEMP, T( JCH+1, JCH+1 ), C, S,
- $ T( JCH, JCH+1 ) )
- T( JCH+1, JCH+1 ) = ZERO
- IF( JCH.LT.ILASTM-1 )
- $ CALL DROT( ILASTM-JCH-1, T( JCH, JCH+2 ), LDT,
- $ T( JCH+1, JCH+2 ), LDT, C, S )
- CALL DROT( ILASTM-JCH+2, H( JCH, JCH-1 ), LDH,
- $ H( JCH+1, JCH-1 ), LDH, C, S )
- IF( ILQ )
- $ CALL DROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
- $ C, S )
- TEMP = H( JCH+1, JCH )
- CALL DLARTG( TEMP, H( JCH+1, JCH-1 ), C, S,
- $ H( JCH+1, JCH ) )
- H( JCH+1, JCH-1 ) = ZERO
- CALL DROT( JCH+1-IFRSTM, H( IFRSTM, JCH ), 1,
- $ H( IFRSTM, JCH-1 ), 1, C, S )
- CALL DROT( JCH-IFRSTM, T( IFRSTM, JCH ), 1,
- $ T( IFRSTM, JCH-1 ), 1, C, S )
- IF( ILZ )
- $ CALL DROT( N, Z( 1, JCH ), 1, Z( 1, JCH-1 ), 1,
- $ C, S )
- 50 CONTINUE
- GO TO 70
- END IF
- ELSE IF( ILAZRO ) THEN
-*
-* Only test 1 passed -- work on J:ILAST
-*
- IFIRST = J
- GO TO 110
- END IF
-*
-* Neither test passed -- try next J
-*
- 60 CONTINUE
-*
-* (Drop-through is "impossible")
-*
- INFO = N + 1
- GO TO 420
-*
-* T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a
-* 1x1 block.
-*
- 70 CONTINUE
- TEMP = H( ILAST, ILAST )
- CALL DLARTG( TEMP, H( ILAST, ILAST-1 ), C, S,
- $ H( ILAST, ILAST ) )
- H( ILAST, ILAST-1 ) = ZERO
- CALL DROT( ILAST-IFRSTM, H( IFRSTM, ILAST ), 1,
- $ H( IFRSTM, ILAST-1 ), 1, C, S )
- CALL DROT( ILAST-IFRSTM, T( IFRSTM, ILAST ), 1,
- $ T( IFRSTM, ILAST-1 ), 1, C, S )
- IF( ILZ )
- $ CALL DROT( N, Z( 1, ILAST ), 1, Z( 1, ILAST-1 ), 1, C, S )
-*
-* H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
-* and BETA
-*
- 80 CONTINUE
- IF( T( ILAST, ILAST ).LT.ZERO ) THEN
- IF( ILSCHR ) THEN
- DO 90 J = IFRSTM, ILAST
- H( J, ILAST ) = -H( J, ILAST )
- T( J, ILAST ) = -T( J, ILAST )
- 90 CONTINUE
- ELSE
- H( ILAST, ILAST ) = -H( ILAST, ILAST )
- T( ILAST, ILAST ) = -T( ILAST, ILAST )
- END IF
- IF( ILZ ) THEN
- DO 100 J = 1, N
- Z( J, ILAST ) = -Z( J, ILAST )
- 100 CONTINUE
- END IF
- END IF
- ALPHAR( ILAST ) = H( ILAST, ILAST )
- ALPHAI( ILAST ) = ZERO
- BETA( ILAST ) = T( ILAST, ILAST )
-*
-* Go to next block -- exit if finished.
-*
- ILAST = ILAST - 1
- IF( ILAST.LT.ILO )
- $ GO TO 380
-*
-* Reset counters
-*
- IITER = 0
- ESHIFT = ZERO
- IF( .NOT.ILSCHR ) THEN
- ILASTM = ILAST
- IF( IFRSTM.GT.ILAST )
- $ IFRSTM = ILO
- END IF
- GO TO 350
-*
-* QZ step
-*
-* This iteration only involves rows/columns IFIRST:ILAST. We
-* assume IFIRST < ILAST, and that the diagonal of B is non-zero.
-*
- 110 CONTINUE
- IITER = IITER + 1
- IF( .NOT.ILSCHR ) THEN
- IFRSTM = IFIRST
- END IF
-*
-* Compute single shifts.
-*
-* At this point, IFIRST < ILAST, and the diagonal elements of
-* T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
-* magnitude)
-*
- IF( ( IITER / 10 )*10.EQ.IITER ) THEN
-*
-* Exceptional shift. Chosen for no particularly good reason.
-* (Single shift only.)
-*
- IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT.
- $ ABS( T( ILAST-1, ILAST-1 ) ) ) THEN
- ESHIFT = ESHIFT + H( ILAST-1, ILAST ) /
- $ T( ILAST-1, ILAST-1 )
- ELSE
- ESHIFT = ESHIFT + ONE / ( SAFMIN*DBLE( MAXIT ) )
- END IF
- S1 = ONE
- WR = ESHIFT
-*
- ELSE
-*
-* Shifts based on the generalized eigenvalues of the
-* bottom-right 2x2 block of A and B. The first eigenvalue
-* returned by DLAG2 is the Wilkinson shift (AEP p.512),
-*
- CALL DLAG2( H( ILAST-1, ILAST-1 ), LDH,
- $ T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
- $ S2, WR, WR2, WI )
-*
- TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) )
- IF( WI.NE.ZERO )
- $ GO TO 200
- END IF
-*
-* Fiddle with shift to avoid overflow
-*
- TEMP = MIN( ASCALE, ONE )*( HALF*SAFMAX )
- IF( S1.GT.TEMP ) THEN
- SCALE = TEMP / S1
- ELSE
- SCALE = ONE
- END IF
-*
- TEMP = MIN( BSCALE, ONE )*( HALF*SAFMAX )
- IF( ABS( WR ).GT.TEMP )
- $ SCALE = MIN( SCALE, TEMP / ABS( WR ) )
- S1 = SCALE*S1
- WR = SCALE*WR
-*
-* Now check for two consecutive small subdiagonals.
-*
- DO 120 J = ILAST - 1, IFIRST + 1, -1
- ISTART = J
- TEMP = ABS( S1*H( J, J-1 ) )
- TEMP2 = ABS( S1*H( J, J )-WR*T( J, J ) )
- TEMPR = MAX( TEMP, TEMP2 )
- IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
- TEMP = TEMP / TEMPR
- TEMP2 = TEMP2 / TEMPR
- END IF
- IF( ABS( ( ASCALE*H( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
- $ TEMP2 )GO TO 130
- 120 CONTINUE
-*
- ISTART = IFIRST
- 130 CONTINUE
-*
-* Do an implicit single-shift QZ sweep.
-*
-* Initial Q
-*
- TEMP = S1*H( ISTART, ISTART ) - WR*T( ISTART, ISTART )
- TEMP2 = S1*H( ISTART+1, ISTART )
- CALL DLARTG( TEMP, TEMP2, C, S, TEMPR )
-*
-* Sweep
-*
- DO 190 J = ISTART, ILAST - 1
- IF( J.GT.ISTART ) THEN
- TEMP = H( J, J-1 )
- CALL DLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
- H( J+1, J-1 ) = ZERO
- END IF
-*
- DO 140 JC = J, ILASTM
- TEMP = C*H( J, JC ) + S*H( J+1, JC )
- H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
- H( J, JC ) = TEMP
- TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
- T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
- T( J, JC ) = TEMP2
- 140 CONTINUE
- IF( ILQ ) THEN
- DO 150 JR = 1, N
- TEMP = C*Q( JR, J ) + S*Q( JR, J+1 )
- Q( JR, J+1 ) = -S*Q( JR, J ) + C*Q( JR, J+1 )
- Q( JR, J ) = TEMP
- 150 CONTINUE
- END IF
-*
- TEMP = T( J+1, J+1 )
- CALL DLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
- T( J+1, J ) = ZERO
-*
- DO 160 JR = IFRSTM, MIN( J+2, ILAST )
- TEMP = C*H( JR, J+1 ) + S*H( JR, J )
- H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
- H( JR, J+1 ) = TEMP
- 160 CONTINUE
- DO 170 JR = IFRSTM, J
- TEMP = C*T( JR, J+1 ) + S*T( JR, J )
- T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
- T( JR, J+1 ) = TEMP
- 170 CONTINUE
- IF( ILZ ) THEN
- DO 180 JR = 1, N
- TEMP = C*Z( JR, J+1 ) + S*Z( JR, J )
- Z( JR, J ) = -S*Z( JR, J+1 ) + C*Z( JR, J )
- Z( JR, J+1 ) = TEMP
- 180 CONTINUE
- END IF
- 190 CONTINUE
-*
- GO TO 350
-*
-* Use Francis double-shift
-*
-* Note: the Francis double-shift should work with real shifts,
-* but only if the block is at least 3x3.
-* This code may break if this point is reached with
-* a 2x2 block with real eigenvalues.
-*
- 200 CONTINUE
- IF( IFIRST+1.EQ.ILAST ) THEN
-*
-* Special case -- 2x2 block with complex eigenvectors
-*
-* Step 1: Standardize, that is, rotate so that
-*
-* ( B11 0 )
-* B = ( ) with B11 non-negative.
-* ( 0 B22 )
-*
- CALL DLASV2( T( ILAST-1, ILAST-1 ), T( ILAST-1, ILAST ),
- $ T( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
-*
- IF( B11.LT.ZERO ) THEN
- CR = -CR
- SR = -SR
- B11 = -B11
- B22 = -B22
- END IF
-*
- CALL DROT( ILASTM+1-IFIRST, H( ILAST-1, ILAST-1 ), LDH,
- $ H( ILAST, ILAST-1 ), LDH, CL, SL )
- CALL DROT( ILAST+1-IFRSTM, H( IFRSTM, ILAST-1 ), 1,
- $ H( IFRSTM, ILAST ), 1, CR, SR )
-*
- IF( ILAST.LT.ILASTM )
- $ CALL DROT( ILASTM-ILAST, T( ILAST-1, ILAST+1 ), LDT,
- $ T( ILAST, ILAST+1 ), LDH, CL, SL )
- IF( IFRSTM.LT.ILAST-1 )
- $ CALL DROT( IFIRST-IFRSTM, T( IFRSTM, ILAST-1 ), 1,
- $ T( IFRSTM, ILAST ), 1, CR, SR )
-*
- IF( ILQ )
- $ CALL DROT( N, Q( 1, ILAST-1 ), 1, Q( 1, ILAST ), 1, CL,
- $ SL )
- IF( ILZ )
- $ CALL DROT( N, Z( 1, ILAST-1 ), 1, Z( 1, ILAST ), 1, CR,
- $ SR )
-*
- T( ILAST-1, ILAST-1 ) = B11
- T( ILAST-1, ILAST ) = ZERO
- T( ILAST, ILAST-1 ) = ZERO
- T( ILAST, ILAST ) = B22
-*
-* If B22 is negative, negate column ILAST
-*
- IF( B22.LT.ZERO ) THEN
- DO 210 J = IFRSTM, ILAST
- H( J, ILAST ) = -H( J, ILAST )
- T( J, ILAST ) = -T( J, ILAST )
- 210 CONTINUE
-*
- IF( ILZ ) THEN
- DO 220 J = 1, N
- Z( J, ILAST ) = -Z( J, ILAST )
- 220 CONTINUE
- END IF
- END IF
-*
-* Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.)
-*
-* Recompute shift
-*
- CALL DLAG2( H( ILAST-1, ILAST-1 ), LDH,
- $ T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
- $ TEMP, WR, TEMP2, WI )
-*
-* If standardization has perturbed the shift onto real line,
-* do another (real single-shift) QR step.
-*
- IF( WI.EQ.ZERO )
- $ GO TO 350
- S1INV = ONE / S1
-*
-* Do EISPACK (QZVAL) computation of alpha and beta
-*
- A11 = H( ILAST-1, ILAST-1 )
- A21 = H( ILAST, ILAST-1 )
- A12 = H( ILAST-1, ILAST )
- A22 = H( ILAST, ILAST )
-*
-* Compute complex Givens rotation on right
-* (Assume some element of C = (sA - wB) > unfl )
-* __
-* (sA - wB) ( CZ -SZ )
-* ( SZ CZ )
-*
- C11R = S1*A11 - WR*B11
- C11I = -WI*B11
- C12 = S1*A12
- C21 = S1*A21
- C22R = S1*A22 - WR*B22
- C22I = -WI*B22
-*
- IF( ABS( C11R )+ABS( C11I )+ABS( C12 ).GT.ABS( C21 )+
- $ ABS( C22R )+ABS( C22I ) ) THEN
- T1 = DLAPY3( C12, C11R, C11I )
- CZ = C12 / T1
- SZR = -C11R / T1
- SZI = -C11I / T1
- ELSE
- CZ = DLAPY2( C22R, C22I )
- IF( CZ.LE.SAFMIN ) THEN
- CZ = ZERO
- SZR = ONE
- SZI = ZERO
- ELSE
- TEMPR = C22R / CZ
- TEMPI = C22I / CZ
- T1 = DLAPY2( CZ, C21 )
- CZ = CZ / T1
- SZR = -C21*TEMPR / T1
- SZI = C21*TEMPI / T1
- END IF
- END IF
-*
-* Compute Givens rotation on left
-*
-* ( CQ SQ )
-* ( __ ) A or B
-* ( -SQ CQ )
-*
- AN = ABS( A11 ) + ABS( A12 ) + ABS( A21 ) + ABS( A22 )
- BN = ABS( B11 ) + ABS( B22 )
- WABS = ABS( WR ) + ABS( WI )
- IF( S1*AN.GT.WABS*BN ) THEN
- CQ = CZ*B11
- SQR = SZR*B22
- SQI = -SZI*B22
- ELSE
- A1R = CZ*A11 + SZR*A12
- A1I = SZI*A12
- A2R = CZ*A21 + SZR*A22
- A2I = SZI*A22
- CQ = DLAPY2( A1R, A1I )
- IF( CQ.LE.SAFMIN ) THEN
- CQ = ZERO
- SQR = ONE
- SQI = ZERO
- ELSE
- TEMPR = A1R / CQ
- TEMPI = A1I / CQ
- SQR = TEMPR*A2R + TEMPI*A2I
- SQI = TEMPI*A2R - TEMPR*A2I
- END IF
- END IF
- T1 = DLAPY3( CQ, SQR, SQI )
- CQ = CQ / T1
- SQR = SQR / T1
- SQI = SQI / T1
-*
-* Compute diagonal elements of QBZ
-*
- TEMPR = SQR*SZR - SQI*SZI
- TEMPI = SQR*SZI + SQI*SZR
- B1R = CQ*CZ*B11 + TEMPR*B22
- B1I = TEMPI*B22
- B1A = DLAPY2( B1R, B1I )
- B2R = CQ*CZ*B22 + TEMPR*B11
- B2I = -TEMPI*B11
- B2A = DLAPY2( B2R, B2I )
-*
-* Normalize so beta > 0, and Im( alpha1 ) > 0
-*
- BETA( ILAST-1 ) = B1A
- BETA( ILAST ) = B2A
- ALPHAR( ILAST-1 ) = ( WR*B1A )*S1INV
- ALPHAI( ILAST-1 ) = ( WI*B1A )*S1INV
- ALPHAR( ILAST ) = ( WR*B2A )*S1INV
- ALPHAI( ILAST ) = -( WI*B2A )*S1INV
-*
-* Step 3: Go to next block -- exit if finished.
-*
- ILAST = IFIRST - 1
- IF( ILAST.LT.ILO )
- $ GO TO 380
-*
-* Reset counters
-*
- IITER = 0
- ESHIFT = ZERO
- IF( .NOT.ILSCHR ) THEN
- ILASTM = ILAST
- IF( IFRSTM.GT.ILAST )
- $ IFRSTM = ILO
- END IF
- GO TO 350
- ELSE
-*
-* Usual case: 3x3 or larger block, using Francis implicit
-* double-shift
-*
-* 2
-* Eigenvalue equation is w - c w + d = 0,
-*
-* -1 2 -1
-* so compute 1st column of (A B ) - c A B + d
-* using the formula in QZIT (from EISPACK)
-*
-* We assume that the block is at least 3x3
-*
- AD11 = ( ASCALE*H( ILAST-1, ILAST-1 ) ) /
- $ ( BSCALE*T( ILAST-1, ILAST-1 ) )
- AD21 = ( ASCALE*H( ILAST, ILAST-1 ) ) /
- $ ( BSCALE*T( ILAST-1, ILAST-1 ) )
- AD12 = ( ASCALE*H( ILAST-1, ILAST ) ) /
- $ ( BSCALE*T( ILAST, ILAST ) )
- AD22 = ( ASCALE*H( ILAST, ILAST ) ) /
- $ ( BSCALE*T( ILAST, ILAST ) )
- U12 = T( ILAST-1, ILAST ) / T( ILAST, ILAST )
- AD11L = ( ASCALE*H( IFIRST, IFIRST ) ) /
- $ ( BSCALE*T( IFIRST, IFIRST ) )
- AD21L = ( ASCALE*H( IFIRST+1, IFIRST ) ) /
- $ ( BSCALE*T( IFIRST, IFIRST ) )
- AD12L = ( ASCALE*H( IFIRST, IFIRST+1 ) ) /
- $ ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
- AD22L = ( ASCALE*H( IFIRST+1, IFIRST+1 ) ) /
- $ ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
- AD32L = ( ASCALE*H( IFIRST+2, IFIRST+1 ) ) /
- $ ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
- U12L = T( IFIRST, IFIRST+1 ) / T( IFIRST+1, IFIRST+1 )
-*
- V( 1 ) = ( AD11-AD11L )*( AD22-AD11L ) - AD12*AD21 +
- $ AD21*U12*AD11L + ( AD12L-AD11L*U12L )*AD21L
- V( 2 ) = ( ( AD22L-AD11L )-AD21L*U12L-( AD11-AD11L )-
- $ ( AD22-AD11L )+AD21*U12 )*AD21L
- V( 3 ) = AD32L*AD21L
-*
- ISTART = IFIRST
-*
- CALL DLARFG( 3, V( 1 ), V( 2 ), 1, TAU )
- V( 1 ) = ONE
-*
-* Sweep
-*
- DO 290 J = ISTART, ILAST - 2
-*
-* All but last elements: use 3x3 Householder transforms.
-*
-* Zero (j-1)st column of A
-*
- IF( J.GT.ISTART ) THEN
- V( 1 ) = H( J, J-1 )
- V( 2 ) = H( J+1, J-1 )
- V( 3 ) = H( J+2, J-1 )
-*
- CALL DLARFG( 3, H( J, J-1 ), V( 2 ), 1, TAU )
- V( 1 ) = ONE
- H( J+1, J-1 ) = ZERO
- H( J+2, J-1 ) = ZERO
- END IF
-*
- DO 230 JC = J, ILASTM
- TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
- $ H( J+2, JC ) )
- H( J, JC ) = H( J, JC ) - TEMP
- H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
- H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
- TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
- $ T( J+2, JC ) )
- T( J, JC ) = T( J, JC ) - TEMP2
- T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
- T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
- 230 CONTINUE
- IF( ILQ ) THEN
- DO 240 JR = 1, N
- TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
- $ Q( JR, J+2 ) )
- Q( JR, J ) = Q( JR, J ) - TEMP
- Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
- Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
- 240 CONTINUE
- END IF
-*
-* Zero j-th column of B (see DLAGBC for details)
-*
-* Swap rows to pivot
-*
- ILPIVT = .FALSE.
- TEMP = MAX( ABS( T( J+1, J+1 ) ), ABS( T( J+1, J+2 ) ) )
- TEMP2 = MAX( ABS( T( J+2, J+1 ) ), ABS( T( J+2, J+2 ) ) )
- IF( MAX( TEMP, TEMP2 ).LT.SAFMIN ) THEN
- SCALE = ZERO
- U1 = ONE
- U2 = ZERO
- GO TO 250
- ELSE IF( TEMP.GE.TEMP2 ) THEN
- W11 = T( J+1, J+1 )
- W21 = T( J+2, J+1 )
- W12 = T( J+1, J+2 )
- W22 = T( J+2, J+2 )
- U1 = T( J+1, J )
- U2 = T( J+2, J )
- ELSE
- W21 = T( J+1, J+1 )
- W11 = T( J+2, J+1 )
- W22 = T( J+1, J+2 )
- W12 = T( J+2, J+2 )
- U2 = T( J+1, J )
- U1 = T( J+2, J )
- END IF
-*
-* Swap columns if nec.
-*
- IF( ABS( W12 ).GT.ABS( W11 ) ) THEN
- ILPIVT = .TRUE.
- TEMP = W12
- TEMP2 = W22
- W12 = W11
- W22 = W21
- W11 = TEMP
- W21 = TEMP2
- END IF
-*
-* LU-factor
-*
- TEMP = W21 / W11
- U2 = U2 - TEMP*U1
- W22 = W22 - TEMP*W12
- W21 = ZERO
-*
-* Compute SCALE
-*
- SCALE = ONE
- IF( ABS( W22 ).LT.SAFMIN ) THEN
- SCALE = ZERO
- U2 = ONE
- U1 = -W12 / W11
- GO TO 250
- END IF
- IF( ABS( W22 ).LT.ABS( U2 ) )
- $ SCALE = ABS( W22 / U2 )
- IF( ABS( W11 ).LT.ABS( U1 ) )
- $ SCALE = MIN( SCALE, ABS( W11 / U1 ) )
-*
-* Solve
-*
- U2 = ( SCALE*U2 ) / W22
- U1 = ( SCALE*U1-W12*U2 ) / W11
-*
- 250 CONTINUE
- IF( ILPIVT ) THEN
- TEMP = U2
- U2 = U1
- U1 = TEMP
- END IF
-*
-* Compute Householder Vector
-*
- T1 = SQRT( SCALE**2+U1**2+U2**2 )
- TAU = ONE + SCALE / T1
- VS = -ONE / ( SCALE+T1 )
- V( 1 ) = ONE
- V( 2 ) = VS*U1
- V( 3 ) = VS*U2
-*
-* Apply transformations from the right.
-*
- DO 260 JR = IFRSTM, MIN( J+3, ILAST )
- TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
- $ H( JR, J+2 ) )
- H( JR, J ) = H( JR, J ) - TEMP
- H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
- H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
- 260 CONTINUE
- DO 270 JR = IFRSTM, J + 2
- TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
- $ T( JR, J+2 ) )
- T( JR, J ) = T( JR, J ) - TEMP
- T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
- T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
- 270 CONTINUE
- IF( ILZ ) THEN
- DO 280 JR = 1, N
- TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
- $ Z( JR, J+2 ) )
- Z( JR, J ) = Z( JR, J ) - TEMP
- Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
- Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
- 280 CONTINUE
- END IF
- T( J+1, J ) = ZERO
- T( J+2, J ) = ZERO
- 290 CONTINUE
-*
-* Last elements: Use Givens rotations
-*
-* Rotations from the left
-*
- J = ILAST - 1
- TEMP = H( J, J-1 )
- CALL DLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
- H( J+1, J-1 ) = ZERO
-*
- DO 300 JC = J, ILASTM
- TEMP = C*H( J, JC ) + S*H( J+1, JC )
- H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
- H( J, JC ) = TEMP
- TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
- T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
- T( J, JC ) = TEMP2
- 300 CONTINUE
- IF( ILQ ) THEN
- DO 310 JR = 1, N
- TEMP = C*Q( JR, J ) + S*Q( JR, J+1 )
- Q( JR, J+1 ) = -S*Q( JR, J ) + C*Q( JR, J+1 )
- Q( JR, J ) = TEMP
- 310 CONTINUE
- END IF
-*
-* Rotations from the right.
-*
- TEMP = T( J+1, J+1 )
- CALL DLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
- T( J+1, J ) = ZERO
-*
- DO 320 JR = IFRSTM, ILAST
- TEMP = C*H( JR, J+1 ) + S*H( JR, J )
- H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
- H( JR, J+1 ) = TEMP
- 320 CONTINUE
- DO 330 JR = IFRSTM, ILAST - 1
- TEMP = C*T( JR, J+1 ) + S*T( JR, J )
- T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
- T( JR, J+1 ) = TEMP
- 330 CONTINUE
- IF( ILZ ) THEN
- DO 340 JR = 1, N
- TEMP = C*Z( JR, J+1 ) + S*Z( JR, J )
- Z( JR, J ) = -S*Z( JR, J+1 ) + C*Z( JR, J )
- Z( JR, J+1 ) = TEMP
- 340 CONTINUE
- END IF
-*
-* End of Double-Shift code
-*
- END IF
-*
- GO TO 350
-*
-* End of iteration loop
-*
- 350 CONTINUE
- 360 CONTINUE
-*
-* Drop-through = non-convergence
-*
- INFO = ILAST
- GO TO 420
-*
-* Successful completion of all QZ steps
-*
- 380 CONTINUE
-*
-* Set Eigenvalues 1:ILO-1
-*
- DO 410 J = 1, ILO - 1
- IF( T( J, J ).LT.ZERO ) THEN
- IF( ILSCHR ) THEN
- DO 390 JR = 1, J
- H( JR, J ) = -H( JR, J )
- T( JR, J ) = -T( JR, J )
- 390 CONTINUE
- ELSE
- H( J, J ) = -H( J, J )
- T( J, J ) = -T( J, J )
- END IF
- IF( ILZ ) THEN
- DO 400 JR = 1, N
- Z( JR, J ) = -Z( JR, J )
- 400 CONTINUE
- END IF
- END IF
- ALPHAR( J ) = H( J, J )
- ALPHAI( J ) = ZERO
- BETA( J ) = T( J, J )
- 410 CONTINUE
-*
-* Normal Termination
-*
- INFO = 0
-*
-* Exit (other than argument error) -- return optimal workspace size
-*
- 420 CONTINUE
- WORK( 1 ) = DBLE( N )
- RETURN
-*
-* End of DHGEQZ
-*
- END
generated by cgit (git 2.34.1) at 2025-06-04 02:53:41 +0000