text: /* dsyevd.f -- translated by f2c (version 20061008).
     You must link the resulting object file with libf2c:
  	on Microsoft Windows system, link with libf2c.lib;
  	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
  	or, if you install libf2c.a in a standard place, with -lf2c -lm
  	-- in that order, at the end of the command line, as in
  		cc *.o -lf2c -lm
  	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
  
  		http://www.netlib.org/f2c/libf2c.zip
  */
  
  #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  static integer c__0 = 0;
  static doublereal c_b17 = 1.;
  
  /* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal *
  	a, integer *lda, doublereal *w, doublereal *work, integer *lwork, 
  	integer *iwork, integer *liwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3;
      doublereal d__1;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      doublereal eps;
      integer inde;
      doublereal anrm, rmin, rmax;
      integer lopt;
      extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
  	    integer *);
      doublereal sigma;
      extern logical lsame_(char *, char *);
      integer iinfo, lwmin, liopt;
      logical lower, wantz;
      integer indwk2, llwrk2;
      extern doublereal dlamch_(char *);
      integer iscale;
      extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
  	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
  	    integer *, integer *), dstedc_(char *, integer *, 
  	    doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
  	     integer *, integer *, integer *, integer *), dlacpy_(
  	    char *, integer *, integer *, doublereal *, integer *, doublereal 
  	    *, integer *);
      doublereal safmin;
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      extern /* Subroutine */ int xerbla_(char *, integer *);
      doublereal bignum;
      integer indtau;
      extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, 
  	     integer *);
      extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
  	    integer *, doublereal *);
      integer indwrk, liwmin;
      extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, 
  	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
  	    integer *, doublereal *, integer *, integer *), dsytrd_(char *, integer *, doublereal *, integer *, 
  	    doublereal *, doublereal *, doublereal *, doublereal *, integer *, 
  	     integer *);
      integer llwork;
      doublereal smlnum;
      logical lquery;
  
  
  /*  -- LAPACK driver routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DSYEVD computes all eigenvalues and, optionally, eigenvectors of a */
  /*  real symmetric matrix A. If eigenvectors are desired, it uses a */
  /*  divide and conquer algorithm. */
  
  /*  The divide and conquer algorithm 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. */
  
  /*  Because of large use of BLAS of level 3, DSYEVD needs N**2 more */
  /*  workspace than DSYEVX. */
  
  /*  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. */
  
  /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
  /*          On entry, the symmetric matrix A.  If UPLO = 'U', the */
  /*          leading N-by-N upper triangular part of A contains the */
  /*          upper triangular part of the matrix A.  If UPLO = 'L', */
  /*          the leading N-by-N lower triangular part of A contains */
  /*          the lower triangular part of the matrix A. */
  /*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
  /*          orthonormal eigenvectors of the matrix A. */
  /*          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
  /*          or the upper triangle (if UPLO='U') of A, including the */
  /*          diagonal, is destroyed. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,N). */
  
  /*  W       (output) DOUBLE PRECISION array, dimension (N) */
  /*          If INFO = 0, the eigenvalues in ascending order. */
  
  /*  WORK    (workspace/output) DOUBLE PRECISION array, */
  /*                                         dimension (LWORK) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The dimension of the array WORK. */
  /*          If N <= 1,               LWORK must be at least 1. */
  /*          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. */
  /*          If JOBZ = 'V' and N > 1, LWORK must be at least */
  /*                                                1 + 6*N + 2*N**2. */
  
  /*          If LWORK = -1, then a workspace query is assumed; the routine */
  /*          only calculates the optimal sizes of the WORK and IWORK */
  /*          arrays, returns these values as the first entries of the WORK */
  /*          and IWORK arrays, and no error message related to LWORK or */
  /*          LIWORK is issued by XERBLA. */
  
  /*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
  /*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
  
  /*  LIWORK  (input) INTEGER */
  /*          The dimension of the array IWORK. */
  /*          If N <= 1,                LIWORK must be at least 1. */
  /*          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1. */
  /*          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */
  
  /*          If LIWORK = -1, then a workspace query is assumed; the */
  /*          routine only calculates the optimal sizes of the WORK and */
  /*          IWORK arrays, returns these values as the first entries of */
  /*          the WORK and IWORK arrays, and no error message related to */
  /*          LWORK or LIWORK is issued by XERBLA. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
  /*          > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed */
  /*                to converge; i off-diagonal elements of an intermediate */
  /*                tridiagonal form did not converge to zero; */
  /*                if INFO = i and JOBZ = 'V', then 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). */
  
  /*  Further Details */
  /*  =============== */
  
  /*  Based on contributions by */
  /*     Jeff Rutter, Computer Science Division, University of California */
  /*     at Berkeley, USA */
  /*  Modified by Francoise Tisseur, University of Tennessee. */
  
  /*  Modified description of INFO. Sven, 16 Feb 05. */
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --w;
      --work;
      --iwork;
  
      /* Function Body */
      wantz = lsame_(jobz, "V");
      lower = lsame_(uplo, "L");
      lquery = *lwork == -1 || *liwork == -1;
  
      *info = 0;
      if (! (wantz || lsame_(jobz, "N"))) {
  	*info = -1;
      } else if (! (lower || lsame_(uplo, "U"))) {
  	*info = -2;
      } else if (*n < 0) {
  	*info = -3;
      } else if (*lda < max(1,*n)) {
  	*info = -5;
      }
  
      if (*info == 0) {
  	if (*n <= 1) {
  	    liwmin = 1;
  	    lwmin = 1;
  	    lopt = lwmin;
  	    liopt = liwmin;
  	} else {
  	    if (wantz) {
  		liwmin = *n * 5 + 3;
  /* Computing 2nd power */
  		i__1 = *n;
  		lwmin = *n * 6 + 1 + (i__1 * i__1 << 1);
  	    } else {
  		liwmin = 1;
  		lwmin = (*n << 1) + 1;
  	    }
  /* Computing MAX */
  	    i__1 = lwmin, i__2 = (*n << 1) + ilaenv_(&c__1, "DSYTRD", uplo, n, 
  		     &c_n1, &c_n1, &c_n1);
  	    lopt = max(i__1,i__2);
  	    liopt = liwmin;
  	}
  	work[1] = (doublereal) lopt;
  	iwork[1] = liopt;
  
  	if (*lwork < lwmin && ! lquery) {
  	    *info = -8;
  	} else if (*liwork < liwmin && ! lquery) {
  	    *info = -10;
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DSYEVD", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n == 0) {
  	return 0;
      }
  
      if (*n == 1) {
  	w[1] = a[a_dim1 + 1];
  	if (wantz) {
  	    a[a_dim1 + 1] = 1.;
  	}
  	return 0;
      }
  
  /*     Get machine constants. */
  
      safmin = dlamch_("Safe minimum");
      eps = dlamch_("Precision");
      smlnum = safmin / eps;
      bignum = 1. / smlnum;
      rmin = sqrt(smlnum);
      rmax = sqrt(bignum);
  
  /*     Scale matrix to allowable range, if necessary. */
  
      anrm = dlansy_("M", uplo, n, &a[a_offset], lda, &work[1]);
      iscale = 0;
      if (anrm > 0. && anrm < rmin) {
  	iscale = 1;
  	sigma = rmin / anrm;
      } else if (anrm > rmax) {
  	iscale = 1;
  	sigma = rmax / anrm;
      }
      if (iscale == 1) {
  	dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, 
  		info);
      }
  
  /*     Call DSYTRD to reduce symmetric matrix to tridiagonal form. */
  
      inde = 1;
      indtau = inde + *n;
      indwrk = indtau + *n;
      llwork = *lwork - indwrk + 1;
      indwk2 = indwrk + *n * *n;
      llwrk2 = *lwork - indwk2 + 1;
  
      dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], &
  	    work[indwrk], &llwork, &iinfo);
      lopt = (integer) ((*n << 1) + work[indwrk]);
  
  /*     For eigenvalues only, call DSTERF.  For eigenvectors, first call */
  /*     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */
  /*     tridiagonal matrix, then call DORMTR to multiply it by the */
  /*     Householder transformations stored in A. */
  
      if (! wantz) {
  	dsterf_(n, &w[1], &work[inde], info);
      } else {
  	dstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], &
  		llwrk2, &iwork[1], liwork, info);
  	dormtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
  		indwrk], n, &work[indwk2], &llwrk2, &iinfo);
  	dlacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
  /* Computing MAX */
  /* Computing 2nd power */
  	i__3 = *n;
  	i__1 = lopt, i__2 = *n * 6 + 1 + (i__3 * i__3 << 1);
  	lopt = max(i__1,i__2);
      }
  
  /*     If matrix was scaled, then rescale eigenvalues appropriately. */
  
      if (iscale == 1) {
  	d__1 = 1. / sigma;
  	dscal_(n, &d__1, &w[1], &c__1);
      }
  
      work[1] = (doublereal) lopt;
      iwork[1] = liopt;
  
      return 0;
  
  /*     End of DSYEVD */
  
  } /* dsyevd_ */
  