zhseqr.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 396 行 · 第 1/2 页

*        University of Kansas, USA
*
*     ================================================================
*     References:
*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*       Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*       929--947, 2002.
*
*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*       Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*       of Matrix Analysis, volume 23, pages 948--973, 2002.
*
*     ================================================================
*     .. Parameters ..
*
*     ==== Matrices of order NTINY or smaller must be processed by
*     .    ZLAHQR because of insufficient subdiagonal scratch space.
*     .    (This is a hard limit.) ====
*
*     ==== NL allocates some local workspace to help small matrices
*     .    through a rare ZLAHQR failure.  NL .GT. NTINY = 11 is
*     .    required and NL .LE. NMIN = ILAENV(ISPEC=1,...) is recom-
*     .    mended.  (The default value of NMIN is 75.)  Using NL = 49
*     .    allows up to six simultaneous shifts and a 16-by-16
*     .    deflation window.  ====
*
      INTEGER            NTINY
      PARAMETER          ( NTINY = 11 )
      INTEGER            NL
      PARAMETER          ( NL = 49 )
      COMPLEX*16         ZERO, ONE
      PARAMETER          ( ZERO = ( 0.0d0, 0.0d0 ),
     $                   ONE = ( 1.0d0, 0.0d0 ) )
      DOUBLE PRECISION   RZERO
      PARAMETER          ( RZERO = 0.0d0 )
*     ..
*     .. Local Arrays ..
      COMPLEX*16         HL( NL, NL ), WORKL( NL )
*     ..
*     .. Local Scalars ..
      INTEGER            KBOT, NMIN
      LOGICAL            INITZ, LQUERY, WANTT, WANTZ
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      LOGICAL            LSAME
      EXTERNAL           ILAENV, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZCOPY, ZLACPY, ZLAHQR, ZLAQR0, ZLASET
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE, DCMPLX, MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     ==== Decode and check the input parameters. ====
*
      WANTT = LSAME( JOB, 'S' )
      INITZ = LSAME( COMPZ, 'I' )
      WANTZ = INITZ .OR. LSAME( COMPZ, 'V' )
      WORK( 1 ) = DCMPLX( DBLE( MAX( 1, N ) ), RZERO )
      LQUERY = LWORK.EQ.-1
*
      INFO = 0
      IF( .NOT.LSAME( JOB, 'E' ) .AND. .NOT.WANTT ) THEN
         INFO = -1
      ELSE IF( .NOT.LSAME( COMPZ, 'N' ) .AND. .NOT.WANTZ ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
         INFO = -5
      ELSE IF( LDH.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.MAX( 1, N ) ) ) THEN
         INFO = -10
      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
         INFO = -12
      END IF
*
      IF( INFO.NE.0 ) THEN
*
*        ==== Quick return in case of invalid argument. ====
*
         CALL XERBLA( 'ZHSEQR', -INFO )
         RETURN
*
      ELSE IF( N.EQ.0 ) THEN
*
*        ==== Quick return in case N = 0; nothing to do. ====
*
         RETURN
*
      ELSE IF( LQUERY ) THEN
*
*        ==== Quick return in case of a workspace query ====
*
         CALL ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI, Z,
     $                LDZ, WORK, LWORK, INFO )
*        ==== Ensure reported workspace size is backward-compatible with
*        .    previous LAPACK versions. ====
         WORK( 1 ) = DCMPLX( MAX( DBLE( WORK( 1 ) ), DBLE( MAX( 1,
     $               N ) ) ), RZERO )
         RETURN
*
      ELSE
*
*        ==== copy eigenvalues isolated by ZGEBAL ====
*
         IF( ILO.GT.1 )
     $      CALL ZCOPY( ILO-1, H, LDH+1, W, 1 )
         IF( IHI.LT.N )
     $      CALL ZCOPY( N-IHI, H( IHI+1, IHI+1 ), LDH+1, W( IHI+1 ), 1 )
*
*        ==== Initialize Z, if requested ====
*
         IF( INITZ )
     $      CALL ZLASET( 'A', N, N, ZERO, ONE, Z, LDZ )
*
*        ==== Quick return if possible ====
*
         IF( ILO.EQ.IHI ) THEN
            W( ILO ) = H( ILO, ILO )
            RETURN
         END IF
*
*        ==== ZLAHQR/ZLAQR0 crossover point ====
*
         NMIN = ILAENV( 1, 'ZHSEQR', JOB( : 1 ) // COMPZ( : 1 ), N, ILO,
     $          IHI, LWORK )
         NMIN = MAX( NTINY, NMIN )
*
*        ==== ZLAQR0 for big matrices; ZLAHQR for small ones ====
*
         IF( N.GT.NMIN ) THEN
            CALL ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI,
     $                   Z, LDZ, WORK, LWORK, INFO )
         ELSE
*
*           ==== Small matrix ====
*
            CALL ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI,
     $                   Z, LDZ, INFO )
*
            IF( INFO.GT.0 ) THEN
*
*              ==== A rare ZLAHQR failure!  ZLAQR0 sometimes succeeds
*              .    when ZLAHQR fails. ====
*
               KBOT = INFO
*
               IF( N.GE.NL ) THEN
*
*                 ==== Larger matrices have enough subdiagonal scratch
*                 .    space to call ZLAQR0 directly. ====
*
                  CALL ZLAQR0( WANTT, WANTZ, N, ILO, KBOT, H, LDH, W,
     $                         ILO, IHI, Z, LDZ, WORK, LWORK, INFO )
*
               ELSE
*
*                 ==== Tiny matrices don't have enough subdiagonal
*                 .    scratch space to benefit from ZLAQR0.  Hence,
*                 .    tiny matrices must be copied into a larger
*                 .    array before calling ZLAQR0. ====
*
                  CALL ZLACPY( 'A', N, N, H, LDH, HL, NL )
                  HL( N+1, N ) = ZERO
                  CALL ZLASET( 'A', NL, NL-N, ZERO, ZERO, HL( 1, N+1 ),
     $                         NL )
                  CALL ZLAQR0( WANTT, WANTZ, NL, ILO, KBOT, HL, NL, W,
     $                         ILO, IHI, Z, LDZ, WORKL, NL, INFO )
                  IF( WANTT .OR. INFO.NE.0 )
     $               CALL ZLACPY( 'A', N, N, HL, NL, H, LDH )
               END IF
            END IF
         END IF
*
*        ==== Clear out the trash, if necessary. ====
*
         IF( ( WANTT .OR. INFO.NE.0 ) .AND. N.GT.2 )
     $      CALL ZLASET( 'L', N-2, N-2, ZERO, ZERO, H( 3, 1 ), LDH )
*
*        ==== Ensure reported workspace size is backward-compatible with
*        .    previous LAPACK versions. ====
*
         WORK( 1 ) = DCMPLX( MAX( DBLE( MAX( 1, N ) ),
     $               DBLE( WORK( 1 ) ) ), RZERO )
      END IF
*
*     ==== End of ZHSEQR ====
*
      END