```      SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          COMPZ
INTEGER            INFO, LDZ, N
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   D( * ), E( * ), WORK( * )
COMPLEX*16         Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a
*  symmetric tridiagonal matrix using the implicit QL or QR method.
*  The eigenvectors of a full or band complex Hermitian matrix can also
*  be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
*  matrix to tridiagonal form.
*
*  Arguments
*  =========
*
*  COMPZ   (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only.
*          = 'V':  Compute eigenvalues and eigenvectors of the original
*                  Hermitian matrix.  On entry, Z must contain the
*                  unitary matrix used to reduce the original matrix
*                  to tridiagonal form.
*          = 'I':  Compute eigenvalues and eigenvectors of the
*                  tridiagonal matrix.  Z is initialized to the identity
*                  matrix.
*
*  N       (input) INTEGER
*          The order of the matrix.  N >= 0.
*
*  D       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
*          On entry, the (n-1) subdiagonal elements of the tridiagonal
*          matrix.
*          On exit, E has been destroyed.
*
*  Z       (input/output) COMPLEX*16 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, and if
*          eigenvectors are desired, then  LDZ >= max(1,N).
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
*          If COMPZ = 'N', then WORK is not referenced.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  the algorithm has failed to find all the eigenvalues in
*                a total of 30*N iterations; if INFO = i, then i
*                elements of E have not converged to zero; on exit, D
*                and E contain the elements of a symmetric tridiagonal
*                matrix which is unitarily similar to the original
*                matrix.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE, TWO, THREE
PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
\$                   THREE = 3.0D0 )
COMPLEX*16         CZERO, CONE
PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
\$                   CONE = ( 1.0D0, 0.0D0 ) )
INTEGER            MAXIT
PARAMETER          ( MAXIT = 30 )
*     ..
*     .. Local Scalars ..
INTEGER            I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND,
\$                   LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1,
\$                   NM1, NMAXIT
DOUBLE PRECISION   ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2,
\$                   S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DLAMCH, DLANST, DLAPY2
EXTERNAL           LSAME, DLAMCH, DLANST, DLAPY2
*     ..
*     .. External Subroutines ..
EXTERNAL           DLAE2, DLAEV2, DLARTG, DLASCL, DLASRT, XERBLA,
\$                   ZLASET, ZLASR, ZSWAP
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, MAX, SIGN, 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( 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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSTEQR', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
IF( ICOMPZ.EQ.2 )
\$      Z( 1, 1 ) = CONE
RETURN
END IF
*
*     Determine the unit roundoff and over/underflow thresholds.
*
EPS = DLAMCH( 'E' )
EPS2 = EPS**2
SAFMIN = DLAMCH( 'S' )
SAFMAX = ONE / SAFMIN
SSFMAX = SQRT( SAFMAX ) / THREE
SSFMIN = SQRT( SAFMIN ) / EPS2
*
*     Compute the eigenvalues and eigenvectors of the tridiagonal
*     matrix.
*
IF( ICOMPZ.EQ.2 )
\$   CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
*
NMAXIT = N*MAXIT
JTOT = 0
*
*     Determine where the matrix splits and choose QL or QR iteration
*     for each block, according to whether top or bottom diagonal
*     element is smaller.
*
L1 = 1
NM1 = N - 1
*
10 CONTINUE
IF( L1.GT.N )
\$   GO TO 160
IF( L1.GT.1 )
\$   E( L1-1 ) = ZERO
IF( L1.LE.NM1 ) THEN
DO 20 M = L1, NM1
TST = ABS( E( M ) )
IF( TST.EQ.ZERO )
\$         GO TO 30
IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+
\$          1 ) ) ) )*EPS ) THEN
E( M ) = ZERO
GO TO 30
END IF
20    CONTINUE
END IF
M = N
*
30 CONTINUE
L = L1
LSV = L
LEND = M
LENDSV = LEND
L1 = M + 1
IF( LEND.EQ.L )
\$   GO TO 10
*
*     Scale submatrix in rows and columns L to LEND
*
ANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) )
ISCALE = 0
IF( ANORM.EQ.ZERO )
\$   GO TO 10
IF( ANORM.GT.SSFMAX ) THEN
ISCALE = 1
CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N,
\$                INFO )
CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N,
\$                INFO )
ELSE IF( ANORM.LT.SSFMIN ) THEN
ISCALE = 2
CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N,
\$                INFO )
CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N,
\$                INFO )
END IF
*
*     Choose between QL and QR iteration
*
IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN
LEND = LSV
L = LENDSV
END IF
*
IF( LEND.GT.L ) THEN
*
*        QL Iteration
*
*        Look for small subdiagonal element.
*
40    CONTINUE
IF( L.NE.LEND ) THEN
LENDM1 = LEND - 1
DO 50 M = L, LENDM1
TST = ABS( E( M ) )**2
IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+
\$             SAFMIN )GO TO 60
50       CONTINUE
END IF
*
M = LEND
*
60    CONTINUE
IF( M.LT.LEND )
\$      E( M ) = ZERO
P = D( L )
IF( M.EQ.L )
\$      GO TO 80
*
*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
*        to compute its eigensystem.
*
IF( M.EQ.L+1 ) THEN
IF( ICOMPZ.GT.0 ) THEN
CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S )
WORK( L ) = C
WORK( N-1+L ) = S
CALL ZLASR( 'R', 'V', 'B', N, 2, WORK( L ),
\$                     WORK( N-1+L ), Z( 1, L ), LDZ )
ELSE
CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 )
END IF
D( L ) = RT1
D( L+1 ) = RT2
E( L ) = ZERO
L = L + 2
IF( L.LE.LEND )
\$         GO TO 40
GO TO 140
END IF
*
IF( JTOT.EQ.NMAXIT )
\$      GO TO 140
JTOT = JTOT + 1
*
*        Form shift.
*
G = ( D( L+1 )-P ) / ( TWO*E( L ) )
R = DLAPY2( G, ONE )
G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) )
*
S = ONE
C = ONE
P = ZERO
*
*        Inner loop
*
MM1 = M - 1
DO 70 I = MM1, L, -1
F = S*E( I )
B = C*E( I )
CALL DLARTG( G, F, C, S, R )
IF( I.NE.M-1 )
\$         E( I+1 ) = R
G = D( I+1 ) - P
R = ( D( I )-G )*S + TWO*C*B
P = S*R
D( I+1 ) = G + P
G = C*R - B
*
*           If eigenvectors are desired, then save rotations.
*
IF( ICOMPZ.GT.0 ) THEN
WORK( I ) = C
WORK( N-1+I ) = -S
END IF
*
70    CONTINUE
*
*        If eigenvectors are desired, then apply saved rotations.
*
IF( ICOMPZ.GT.0 ) THEN
MM = M - L + 1
CALL ZLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ),
\$                  Z( 1, L ), LDZ )
END IF
*
D( L ) = D( L ) - P
E( L ) = G
GO TO 40
*
*        Eigenvalue found.
*
80    CONTINUE
D( L ) = P
*
L = L + 1
IF( L.LE.LEND )
\$      GO TO 40
GO TO 140
*
ELSE
*
*        QR Iteration
*
*        Look for small superdiagonal element.
*
90    CONTINUE
IF( L.NE.LEND ) THEN
LENDP1 = LEND + 1
DO 100 M = L, LENDP1, -1
TST = ABS( E( M-1 ) )**2
IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+
\$             SAFMIN )GO TO 110
100       CONTINUE
END IF
*
M = LEND
*
110    CONTINUE
IF( M.GT.LEND )
\$      E( M-1 ) = ZERO
P = D( L )
IF( M.EQ.L )
\$      GO TO 130
*
*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
*        to compute its eigensystem.
*
IF( M.EQ.L-1 ) THEN
IF( ICOMPZ.GT.0 ) THEN
CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S )
WORK( M ) = C
WORK( N-1+M ) = S
CALL ZLASR( 'R', 'V', 'F', N, 2, WORK( M ),
\$                     WORK( N-1+M ), Z( 1, L-1 ), LDZ )
ELSE
CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 )
END IF
D( L-1 ) = RT1
D( L ) = RT2
E( L-1 ) = ZERO
L = L - 2
IF( L.GE.LEND )
\$         GO TO 90
GO TO 140
END IF
*
IF( JTOT.EQ.NMAXIT )
\$      GO TO 140
JTOT = JTOT + 1
*
*        Form shift.
*
G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) )
R = DLAPY2( G, ONE )
G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) )
*
S = ONE
C = ONE
P = ZERO
*
*        Inner loop
*
LM1 = L - 1
DO 120 I = M, LM1
F = S*E( I )
B = C*E( I )
CALL DLARTG( G, F, C, S, R )
IF( I.NE.M )
\$         E( I-1 ) = R
G = D( I ) - P
R = ( D( I+1 )-G )*S + TWO*C*B
P = S*R
D( I ) = G + P
G = C*R - B
*
*           If eigenvectors are desired, then save rotations.
*
IF( ICOMPZ.GT.0 ) THEN
WORK( I ) = C
WORK( N-1+I ) = S
END IF
*
120    CONTINUE
*
*        If eigenvectors are desired, then apply saved rotations.
*
IF( ICOMPZ.GT.0 ) THEN
MM = L - M + 1
CALL ZLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ),
\$                  Z( 1, M ), LDZ )
END IF
*
D( L ) = D( L ) - P
E( LM1 ) = G
GO TO 90
*
*        Eigenvalue found.
*
130    CONTINUE
D( L ) = P
*
L = L - 1
IF( L.GE.LEND )
\$      GO TO 90
GO TO 140
*
END IF
*
*     Undo scaling if necessary
*
140 CONTINUE
IF( ISCALE.EQ.1 ) THEN
CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1,
\$                D( LSV ), N, INFO )
CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ),
\$                N, INFO )
ELSE IF( ISCALE.EQ.2 ) THEN
CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1,
\$                D( LSV ), N, INFO )
CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ),
\$                N, INFO )
END IF
*
*     Check for no convergence to an eigenvalue after a total
*     of N*MAXIT iterations.
*
IF( JTOT.EQ.NMAXIT ) THEN
DO 150 I = 1, N - 1
IF( E( I ).NE.ZERO )
\$         INFO = INFO + 1
150    CONTINUE
RETURN
END IF
GO TO 10
*
*     Order eigenvalues and eigenvectors.
*
160 CONTINUE
IF( ICOMPZ.EQ.0 ) THEN
*
*        Use Quick Sort
*
CALL DLASRT( 'I', N, D, INFO )
*
ELSE
*
*        Use Selection Sort to minimize swaps of eigenvectors
*
DO 180 II = 2, N
I = II - 1
K = I
P = D( I )
DO 170 J = II, N
IF( D( J ).LT.P ) THEN
K = J
P = D( J )
END IF
170       CONTINUE
IF( K.NE.I ) THEN
D( K ) = D( I )
D( I ) = P
CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 )
END IF
180    CONTINUE
END IF
RETURN
*
*     End of ZSTEQR
*
END

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