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SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
$ LRWORK, IWORK, LIWORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
REAL D( * ), E( * ), RWORK( * )
COMPLEX WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
* symmetric tridiagonal matrix using the divide and conquer method.
* The eigenvectors of a full or band complex Hermitian matrix can also
* be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
* matrix to tridiagonal form.
*
* This code makes very mild assumptions about floating point
* arithmetic. It will work on machines with a guard digit in
* add/subtract, or on those binary machines without guard digits
* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
* It could conceivably fail on hexadecimal or decimal machines
* without guard digits, but we know of none. See SLAED3 for details.
*
* Arguments
* =========
*
* COMPZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only.
* = 'I': Compute eigenvectors of tridiagonal matrix also.
* = 'V': Compute eigenvectors of original Hermitian matrix
* also. On entry, Z contains the unitary matrix used
* to reduce the original matrix to tridiagonal form.
*
* N (input) INTEGER
* The dimension of the symmetric tridiagonal matrix. N >= 0.
*
* D (input/output) REAL array, dimension (N)
* On entry, the diagonal elements of the tridiagonal matrix.
* On exit, if INFO = 0, the eigenvalues in ascending order.
*
* E (input/output) REAL array, dimension (N-1)
* On entry, the subdiagonal elements of the tridiagonal matrix.
* On exit, E has been destroyed.
*
* Z (input/output) COMPLEX array, dimension (LDZ,N)
* On entry, if COMPZ = 'V', then Z contains the unitary
* matrix used in the reduction to tridiagonal form.
* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
* orthonormal eigenvectors of the original Hermitian matrix,
* and if COMPZ = 'I', Z contains the orthonormal eigenvectors
* of the symmetric tridiagonal matrix.
* If COMPZ = 'N', then Z is not referenced.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1.
* If eigenvectors are desired, then LDZ >= max(1,N).
*
* WORK (workspace/output) COMPLEX array, dimension (LWORK)
* On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
* If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
* If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
*
* RWORK (workspace/output) REAL array,
* dimension (LRWORK)
* On exit, if LRWORK > 0, RWORK(1) returns the optimal LRWORK.
*
* LRWORK (input) INTEGER
* The dimension of the array RWORK.
* If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
* If COMPZ = 'V' and N > 1, LRWORK must be at least
* 1 + 3*N + 2*N*lg N + 3*N**2 ,
* where lg( N ) = smallest integer k such
* that 2**k >= N.
* If COMPZ = 'I' and N > 1, LRWORK must be at least
* 1 + 3*N + 2*N*lg N + 3*N**2 .
*
* IWORK (workspace/output) INTEGER array, dimension (LIWORK)
* On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
* If COMPZ = 'V' or N > 1, LIWORK must be at least
* 6 + 6*N + 5*N*lg N.
* If COMPZ = 'I' or N > 1, LIWORK must be at least
* 2 + 5*N .
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: The algorithm failed to compute an eigenvalue while
* working on the submatrix lying in rows and columns
* INFO/(N+1) through mod(INFO,N+1).
*
* =====================================================================
*
* .. Parameters ..
INTEGER SMLSIZ
PARAMETER ( SMLSIZ = 25 )
REAL ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
* ..
* .. Local Scalars ..
INTEGER END, I, ICOMPZ, II, J, K, LGN, LIWMIN, LL,
$ LRWMIN, LWMIN, M, NM1, START
REAL EPS, ORGNRM, P, TINY
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANST
EXTERNAL LSAME, SLAMCH, SLANST
* ..
* .. External Subroutines ..
EXTERNAL CLACPY, CLACRM, CLAED0, CSTEQR, CSWAP, SLASCL,
$ SLASET, SSTEDC, SSTEQR, SSTERF, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, INT, LOG, MAX, MOD, REAL, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
*
IF( LSAME( COMPZ, 'N' ) ) THEN
ICOMPZ = 0
ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
ICOMPZ = 1
ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
ICOMPZ = 2
ELSE
ICOMPZ = -1
END IF
IF( N.LE.1 .OR. ICOMPZ.LE.0 ) THEN
LWMIN = 1
LIWMIN = 1
LRWMIN = 1
ELSE
LGN = INT( LOG( REAL( N ) ) / LOG( TWO ) )
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IF( ICOMPZ.EQ.1 ) THEN
LWMIN = N*N
LRWMIN = 1 + 3*N + 2*N*LGN + 3*N**2
LIWMIN = 6 + 6*N + 5*N*LGN
ELSE IF( ICOMPZ.EQ.2 ) THEN
LWMIN = 1
LRWMIN = 1 + 3*N + 2*N*LGN + 3*N**2
LIWMIN = 2 + 5*N
END IF
END IF
IF( ICOMPZ.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
$ N ) ) ) THEN
INFO = -6
ELSE IF( LWORK.LT.LWMIN ) THEN
INFO = -8
ELSE IF( LRWORK.LT.LRWMIN ) THEN
INFO = -10
ELSE IF( LIWORK.LT.LIWMIN ) THEN
INFO = -12
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CSTEDC', -INFO )
GO TO 70
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ GO TO 70
IF( N.EQ.1 ) THEN
IF( ICOMPZ.NE.0 )
$ Z( 1, 1 ) = ONE
GO TO 70
END IF
*
* If the following conditional clause is removed, then the routine
* will use the Divide and Conquer routine to compute only the
* eigenvalues, which requires (3N + 3N**2) real workspace and
* (2 + 5N + 2N lg(N)) integer workspace.
* Since on many architectures SSTERF is much faster than any other
* algorithm for finding eigenvalues only, it is used here
* as the default.
*
* If COMPZ = 'N', use SSTERF to compute the eigenvalues.
*
IF( ICOMPZ.EQ.0 ) THEN
CALL SSTERF( N, D, E, INFO )
GO TO 70
END IF
*
* If N is smaller than the minimum divide size (SMLSIZ+1), then
* solve the problem with another solver.
*
IF( N.LE.SMLSIZ ) THEN
IF( ICOMPZ.EQ.0 ) THEN
CALL SSTERF( N, D, E, INFO )
GO TO 70
ELSE IF( ICOMPZ.EQ.2 ) THEN
CALL CSTEQR( 'I', N, D, E, Z, LDZ, RWORK, INFO )
GO TO 70
ELSE
CALL CSTEQR( 'V', N, D, E, Z, LDZ, RWORK, INFO )
GO TO 70
END IF
END IF
*
* If COMPZ = 'I', we simply call SSTEDC instead.
*
IF( ICOMPZ.EQ.2 ) THEN
CALL SLASET( 'Full', N, N, ZERO, ONE, RWORK, N )
LL = N*N + 1
CALL SSTEDC( 'I', N, D, E, RWORK, N, RWORK( LL ), LRWORK-LL+1,
$ IWORK, LIWORK, INFO )
DO 20 J = 1, N
DO 10 I = 1, N
Z( I, J ) = RWORK( ( J-1 )*N+I )
10 CONTINUE
20 CONTINUE
GO TO 70
END IF
*
* From now on, only option left to be handled is COMPZ = 'V',
* i.e. ICOMPZ = 1.
*
* Scale.
*
NM1 = N - 1
ORGNRM = SLANST( 'M', N, D, E )
IF( ORGNRM.EQ.ZERO )
$ GO TO 70
*
EPS = SLAMCH( 'Epsilon' )
*
START = 1
*
* while ( START <= N )
*
30 CONTINUE
IF( START.LE.N ) THEN
*
* Let END be the position of the next subdiagonal entry such that
* E( END ) <= TINY or END = N if no such subdiagonal exists. The
* matrix identified by the elements between START and END
* constitutes an independent sub-problem.
*
END = START
40 CONTINUE
IF( END.LT.N ) THEN
TINY = EPS*SQRT( ABS( D( END ) ) )*SQRT( ABS( D( END+1 ) ) )
IF( ABS( E( END ) ).GT.TINY ) THEN
END = END + 1
GO TO 40
END IF
END IF
*
* (Sub) Problem determined. Compute its size and solve it.
*
M = END - START + 1
IF( M.GT.SMLSIZ ) THEN
INFO = SMLSIZ
*
* Scale.
*
ORGNRM = SLANST( 'M', M, D( START ), E( START ) )
CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M,
$ INFO )
CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ),
$ M-1, INFO )
*
CALL CLAED0( N, M, D( START ), E( START ), Z( 1, START ),
$ LDZ, WORK, N, RWORK, IWORK, INFO )
IF( INFO.GT.0 ) THEN
INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) +
$ MOD( INFO, ( M+1 ) ) + START - 1
GO TO 70
END IF
*
* Scale back.
*
CALL SLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M,
$ INFO )
*
ELSE
CALL SSTEQR( 'I', M, D( START ), E( START ), RWORK, M,
$ RWORK( M*M+1 ), INFO )
CALL CLACRM( N, M, Z( 1, START ), LDZ, RWORK, M, WORK, N,
$ RWORK( M*M+1 ) )
CALL CLACPY( 'A', N, M, WORK, N, Z( 1, START ), LDZ )
IF( INFO.GT.0 ) THEN
INFO = START*( N+1 ) + END
GO TO 70
END IF
END IF
*
START = END + 1
GO TO 30
END IF
*
* endwhile
*
* If the problem split any number of times, then the eigenvalues
* will not be properly ordered. Here we permute the eigenvalues
* (and the associated eigenvectors) into ascending order.
*
IF( M.NE.N ) THEN
*
* Use Selection Sort to minimize swaps of eigenvectors
*
DO 60 II = 2, N
I = II - 1
K = I
P = D( I )
DO 50 J = II, N
IF( D( J ).LT.P ) THEN
K = J
P = D( J )
END IF
50 CONTINUE
IF( K.NE.I ) THEN
D( K ) = D( I )
D( I ) = P
CALL CSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 )
END IF
60 CONTINUE
END IF
*
70 CONTINUE
IF( LWORK.GT.0 )
$ WORK( 1 ) = LWMIN
IF( LRWORK.GT.0 )
$ RWORK( 1 ) = LRWMIN
IF( LIWORK.GT.0 )
$ IWORK( 1 ) = LIWMIN
RETURN
*
* End of CSTEDC
*
END
|
