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Cohérence Lapack.

    1: *> \brief <b> ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZHEEV + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheev.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheev.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheev.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
   22: *                         INFO )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          JOBZ, UPLO
   26: *       INTEGER            INFO, LDA, LWORK, N
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   RWORK( * ), W( * )
   30: *       COMPLEX*16         A( LDA, * ), WORK( * )
   31: *       ..
   32: *  
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
   40: *> complex Hermitian matrix A.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] JOBZ
   47: *> \verbatim
   48: *>          JOBZ is CHARACTER*1
   49: *>          = 'N':  Compute eigenvalues only;
   50: *>          = 'V':  Compute eigenvalues and eigenvectors.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] UPLO
   54: *> \verbatim
   55: *>          UPLO is CHARACTER*1
   56: *>          = 'U':  Upper triangle of A is stored;
   57: *>          = 'L':  Lower triangle of A is stored.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] N
   61: *> \verbatim
   62: *>          N is INTEGER
   63: *>          The order of the matrix A.  N >= 0.
   64: *> \endverbatim
   65: *>
   66: *> \param[in,out] A
   67: *> \verbatim
   68: *>          A is COMPLEX*16 array, dimension (LDA, N)
   69: *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
   70: *>          leading N-by-N upper triangular part of A contains the
   71: *>          upper triangular part of the matrix A.  If UPLO = 'L',
   72: *>          the leading N-by-N lower triangular part of A contains
   73: *>          the lower triangular part of the matrix A.
   74: *>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
   75: *>          orthonormal eigenvectors of the matrix A.
   76: *>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
   77: *>          or the upper triangle (if UPLO='U') of A, including the
   78: *>          diagonal, is destroyed.
   79: *> \endverbatim
   80: *>
   81: *> \param[in] LDA
   82: *> \verbatim
   83: *>          LDA is INTEGER
   84: *>          The leading dimension of the array A.  LDA >= max(1,N).
   85: *> \endverbatim
   86: *>
   87: *> \param[out] W
   88: *> \verbatim
   89: *>          W is DOUBLE PRECISION array, dimension (N)
   90: *>          If INFO = 0, the eigenvalues in ascending order.
   91: *> \endverbatim
   92: *>
   93: *> \param[out] WORK
   94: *> \verbatim
   95: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   96: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   97: *> \endverbatim
   98: *>
   99: *> \param[in] LWORK
  100: *> \verbatim
  101: *>          LWORK is INTEGER
  102: *>          The length of the array WORK.  LWORK >= max(1,2*N-1).
  103: *>          For optimal efficiency, LWORK >= (NB+1)*N,
  104: *>          where NB is the blocksize for ZHETRD returned by ILAENV.
  105: *>
  106: *>          If LWORK = -1, then a workspace query is assumed; the routine
  107: *>          only calculates the optimal size of the WORK array, returns
  108: *>          this value as the first entry of the WORK array, and no error
  109: *>          message related to LWORK is issued by XERBLA.
  110: *> \endverbatim
  111: *>
  112: *> \param[out] RWORK
  113: *> \verbatim
  114: *>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
  115: *> \endverbatim
  116: *>
  117: *> \param[out] INFO
  118: *> \verbatim
  119: *>          INFO is INTEGER
  120: *>          = 0:  successful exit
  121: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  122: *>          > 0:  if INFO = i, the algorithm failed to converge; i
  123: *>                off-diagonal elements of an intermediate tridiagonal
  124: *>                form did not converge to zero.
  125: *> \endverbatim
  126: *
  127: *  Authors:
  128: *  ========
  129: *
  130: *> \author Univ. of Tennessee 
  131: *> \author Univ. of California Berkeley 
  132: *> \author Univ. of Colorado Denver 
  133: *> \author NAG Ltd. 
  134: *
  135: *> \date November 2011
  136: *
  137: *> \ingroup complex16HEeigen
  138: *
  139: *  =====================================================================
  140:       SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
  141:      $                  INFO )
  142: *
  143: *  -- LAPACK driver routine (version 3.4.0) --
  144: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  145: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  146: *     November 2011
  147: *
  148: *     .. Scalar Arguments ..
  149:       CHARACTER          JOBZ, UPLO
  150:       INTEGER            INFO, LDA, LWORK, N
  151: *     ..
  152: *     .. Array Arguments ..
  153:       DOUBLE PRECISION   RWORK( * ), W( * )
  154:       COMPLEX*16         A( LDA, * ), WORK( * )
  155: *     ..
  156: *
  157: *  =====================================================================
  158: *
  159: *     .. Parameters ..
  160:       DOUBLE PRECISION   ZERO, ONE
  161:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
  162:       COMPLEX*16         CONE
  163:       PARAMETER          ( CONE = ( 1.0D0, 0.0D0 ) )
  164: *     ..
  165: *     .. Local Scalars ..
  166:       LOGICAL            LOWER, LQUERY, WANTZ
  167:       INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
  168:      $                   LLWORK, LWKOPT, NB
  169:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
  170:      $                   SMLNUM
  171: *     ..
  172: *     .. External Functions ..
  173:       LOGICAL            LSAME
  174:       INTEGER            ILAENV
  175:       DOUBLE PRECISION   DLAMCH, ZLANHE
  176:       EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANHE
  177: *     ..
  178: *     .. External Subroutines ..
  179:       EXTERNAL           DSCAL, DSTERF, XERBLA, ZHETRD, ZLASCL, ZSTEQR,
  180:      $                   ZUNGTR
  181: *     ..
  182: *     .. Intrinsic Functions ..
  183:       INTRINSIC          MAX, SQRT
  184: *     ..
  185: *     .. Executable Statements ..
  186: *
  187: *     Test the input parameters.
  188: *
  189:       WANTZ = LSAME( JOBZ, 'V' )
  190:       LOWER = LSAME( UPLO, 'L' )
  191:       LQUERY = ( LWORK.EQ.-1 )
  192: *
  193:       INFO = 0
  194:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  195:          INFO = -1
  196:       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
  197:          INFO = -2
  198:       ELSE IF( N.LT.0 ) THEN
  199:          INFO = -3
  200:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  201:          INFO = -5
  202:       END IF
  203: *
  204:       IF( INFO.EQ.0 ) THEN
  205:          NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
  206:          LWKOPT = MAX( 1, ( NB+1 )*N )
  207:          WORK( 1 ) = LWKOPT
  208: *
  209:          IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY )
  210:      $      INFO = -8
  211:       END IF
  212: *
  213:       IF( INFO.NE.0 ) THEN
  214:          CALL XERBLA( 'ZHEEV ', -INFO )
  215:          RETURN
  216:       ELSE IF( LQUERY ) THEN
  217:          RETURN
  218:       END IF
  219: *
  220: *     Quick return if possible
  221: *
  222:       IF( N.EQ.0 ) THEN
  223:          RETURN
  224:       END IF
  225: *
  226:       IF( N.EQ.1 ) THEN
  227:          W( 1 ) = A( 1, 1 )
  228:          WORK( 1 ) = 1
  229:          IF( WANTZ )
  230:      $      A( 1, 1 ) = CONE
  231:          RETURN
  232:       END IF
  233: *
  234: *     Get machine constants.
  235: *
  236:       SAFMIN = DLAMCH( 'Safe minimum' )
  237:       EPS = DLAMCH( 'Precision' )
  238:       SMLNUM = SAFMIN / EPS
  239:       BIGNUM = ONE / SMLNUM
  240:       RMIN = SQRT( SMLNUM )
  241:       RMAX = SQRT( BIGNUM )
  242: *
  243: *     Scale matrix to allowable range, if necessary.
  244: *
  245:       ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
  246:       ISCALE = 0
  247:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  248:          ISCALE = 1
  249:          SIGMA = RMIN / ANRM
  250:       ELSE IF( ANRM.GT.RMAX ) THEN
  251:          ISCALE = 1
  252:          SIGMA = RMAX / ANRM
  253:       END IF
  254:       IF( ISCALE.EQ.1 )
  255:      $   CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
  256: *
  257: *     Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
  258: *
  259:       INDE = 1
  260:       INDTAU = 1
  261:       INDWRK = INDTAU + N
  262:       LLWORK = LWORK - INDWRK + 1
  263:       CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
  264:      $             WORK( INDWRK ), LLWORK, IINFO )
  265: *
  266: *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
  267: *     ZUNGTR to generate the unitary matrix, then call ZSTEQR.
  268: *
  269:       IF( .NOT.WANTZ ) THEN
  270:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
  271:       ELSE
  272:          CALL ZUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
  273:      $                LLWORK, IINFO )
  274:          INDWRK = INDE + N
  275:          CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA,
  276:      $                RWORK( INDWRK ), INFO )
  277:       END IF
  278: *
  279: *     If matrix was scaled, then rescale eigenvalues appropriately.
  280: *
  281:       IF( ISCALE.EQ.1 ) THEN
  282:          IF( INFO.EQ.0 ) THEN
  283:             IMAX = N
  284:          ELSE
  285:             IMAX = INFO - 1
  286:          END IF
  287:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
  288:       END IF
  289: *
  290: *     Set WORK(1) to optimal complex workspace size.
  291: *
  292:       WORK( 1 ) = LWKOPT
  293: *
  294:       RETURN
  295: *
  296: *     End of ZHEEV
  297: *
  298:       END