Move LAPACK trunk into position.

1 files changed, 208 insertions, 0 deletions

diff --git a/SRC/zhbev.f b/SRC/zhbev.f
new file mode 100644
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--- /dev/null
+++ b/SRC/zhbev.f
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+      SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
+     $                  RWORK, INFO )
+*
+*  -- LAPACK driver routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      CHARACTER          JOBZ, UPLO
+      INTEGER            INFO, KD, LDAB, LDZ, N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   RWORK( * ), W( * )
+      COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
+*  a complex Hermitian band matrix A.
+*
+*  Arguments
+*  =========
+*
+*  JOBZ    (input) CHARACTER*1
+*          = 'N':  Compute eigenvalues only;
+*          = 'V':  Compute eigenvalues and eigenvectors.
+*
+*  UPLO    (input) CHARACTER*1
+*          = 'U':  Upper triangle of A is stored;
+*          = 'L':  Lower triangle of A is stored.
+*
+*  N       (input) INTEGER
+*          The order of the matrix A.  N >= 0.
+*
+*  KD      (input) INTEGER
+*          The number of superdiagonals of the matrix A if UPLO = 'U',
+*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
+*
+*  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)
+*          On entry, the upper or lower triangle of the Hermitian band
+*          matrix A, stored in the first KD+1 rows of the array.  The
+*          j-th column of A is stored in the j-th column of the array AB
+*          as follows:
+*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
+*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
+*
+*          On exit, AB is overwritten by values generated during the
+*          reduction to tridiagonal form.  If UPLO = 'U', the first
+*          superdiagonal and the diagonal of the tridiagonal matrix T
+*          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
+*          the diagonal and first subdiagonal of T are returned in the
+*          first two rows of AB.
+*
+*  LDAB    (input) INTEGER
+*          The leading dimension of the array AB.  LDAB >= KD + 1.
+*
+*  W       (output) DOUBLE PRECISION array, dimension (N)
+*          If INFO = 0, the eigenvalues in ascending order.
+*
+*  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
+*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
+*          eigenvectors of the matrix A, with the i-th column of Z
+*          holding the eigenvector associated with W(i).
+*          If JOBZ = 'N', then Z is not referenced.
+*
+*  LDZ     (input) INTEGER
+*          The leading dimension of the array Z.  LDZ >= 1, and if
+*          JOBZ = 'V', LDZ >= max(1,N).
+*
+*  WORK    (workspace) COMPLEX*16 array, dimension (N)
+*
+*  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
+*
+*  INFO    (output) INTEGER
+*          = 0:  successful exit.
+*          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*          > 0:  if INFO = i, the algorithm failed to converge; i
+*                off-diagonal elements of an intermediate tridiagonal
+*                form did not converge to zero.
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO, ONE
+      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            LOWER, WANTZ
+      INTEGER            IINFO, IMAX, INDE, INDRWK, ISCALE
+      DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
+     $                   SMLNUM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      DOUBLE PRECISION   DLAMCH, ZLANHB
+      EXTERNAL           LSAME, DLAMCH, ZLANHB
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      WANTZ = LSAME( JOBZ, 'V' )
+      LOWER = LSAME( UPLO, 'L' )
+*
+      INFO = 0
+      IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
+         INFO = -1
+      ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
+         INFO = -2
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( KD.LT.0 ) THEN
+         INFO = -4
+      ELSE IF( LDAB.LT.KD+1 ) THEN
+         INFO = -6
+      ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
+         INFO = -9
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'ZHBEV ', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.EQ.0 )
+     $   RETURN
+*
+      IF( N.EQ.1 ) THEN
+         IF( LOWER ) THEN
+            W( 1 ) = AB( 1, 1 )
+         ELSE
+            W( 1 ) = AB( KD+1, 1 )
+         END IF
+         IF( WANTZ )
+     $      Z( 1, 1 ) = ONE
+         RETURN
+      END IF
+*
+*     Get machine constants.
+*
+      SAFMIN = DLAMCH( 'Safe minimum' )
+      EPS = DLAMCH( 'Precision' )
+      SMLNUM = SAFMIN / EPS
+      BIGNUM = ONE / SMLNUM
+      RMIN = SQRT( SMLNUM )
+      RMAX = SQRT( BIGNUM )
+*
+*     Scale matrix to allowable range, if necessary.
+*
+      ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
+      ISCALE = 0
+      IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
+         ISCALE = 1
+         SIGMA = RMIN / ANRM
+      ELSE IF( ANRM.GT.RMAX ) THEN
+         ISCALE = 1
+         SIGMA = RMAX / ANRM
+      END IF
+      IF( ISCALE.EQ.1 ) THEN
+         IF( LOWER ) THEN
+            CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
+         ELSE
+            CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
+         END IF
+      END IF
+*
+*     Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
+*
+      INDE = 1
+      CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
+     $             LDZ, WORK, IINFO )
+*
+*     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEQR.
+*
+      IF( .NOT.WANTZ ) THEN
+         CALL DSTERF( N, W, RWORK( INDE ), INFO )
+      ELSE
+         INDRWK = INDE + N
+         CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
+     $                RWORK( INDRWK ), INFO )
+      END IF
+*
+*     If matrix was scaled, then rescale eigenvalues appropriately.
+*
+      IF( ISCALE.EQ.1 ) THEN
+         IF( INFO.EQ.0 ) THEN
+            IMAX = N
+         ELSE
+            IMAX = INFO - 1
+         END IF
+         CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
+      END IF
+*
+      RETURN
+*
+*     End of ZHBEV
+*
+      END