text: /* sspev.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;
  
  /* Subroutine */ int sspev_(char *jobz, char *uplo, integer *n, real *ap, 
  	real *w, real *z__, integer *ldz, real *work, integer *info)
  {
      /* System generated locals */
      integer z_dim1, z_offset, i__1;
      real r__1;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      real eps;
      integer inde;
      real anrm;
      integer imax;
      real rmin, rmax, sigma;
      extern logical lsame_(char *, char *);
      integer iinfo;
      extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
      logical wantz;
      integer iscale;
      extern doublereal slamch_(char *);
      real safmin;
      extern /* Subroutine */ int xerbla_(char *, integer *);
      real bignum;
      integer indtau, indwrk;
      extern doublereal slansp_(char *, char *, integer *, real *, real *);
      extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
      real smlnum;
      extern /* Subroutine */ int sopgtr_(char *, integer *, real *, real *, 
  	    real *, integer *, real *, integer *), ssptrd_(char *, 
  	    integer *, real *, real *, real *, real *, integer *), 
  	    ssteqr_(char *, integer *, real *, real *, real *, integer *, 
  	    real *, integer *);
  
  
  /*  -- LAPACK driver routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SSPEV computes all the eigenvalues and, optionally, eigenvectors of a */
  /*  real symmetric matrix A in packed storage. */
  
  /*  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. */
  
  /*  AP      (input/output) REAL array, dimension (N*(N+1)/2) */
  /*          On entry, the upper or lower triangle of the symmetric matrix */
  /*          A, packed columnwise in a linear array.  The j-th column of A */
  /*          is stored in the array AP as follows: */
  /*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
  /*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
  
  /*          On exit, AP is overwritten by values generated during the */
  /*          reduction to tridiagonal form.  If UPLO = 'U', the diagonal */
  /*          and first superdiagonal of the tridiagonal matrix T overwrite */
  /*          the corresponding elements of A, and if UPLO = 'L', the */
  /*          diagonal and first subdiagonal of T overwrite the */
  /*          corresponding elements of A. */
  
  /*  W       (output) REAL array, dimension (N) */
  /*          If INFO = 0, the eigenvalues in ascending order. */
  
  /*  Z       (output) REAL 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) REAL array, dimension (3*N) */
  
  /*  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 .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      --ap;
      --w;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --work;
  
      /* Function Body */
      wantz = lsame_(jobz, "V");
  
      *info = 0;
      if (! (wantz || lsame_(jobz, "N"))) {
  	*info = -1;
      } else if (! (lsame_(uplo, "U") || lsame_(uplo, 
  	    "L"))) {
  	*info = -2;
      } else if (*n < 0) {
  	*info = -3;
      } else if (*ldz < 1 || wantz && *ldz < *n) {
  	*info = -7;
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SSPEV ", &i__1);
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n == 0) {
  	return 0;
      }
  
      if (*n == 1) {
  	w[1] = ap[1];
  	if (wantz) {
  	    z__[z_dim1 + 1] = 1.f;
  	}
  	return 0;
      }
  
  /*     Get machine constants. */
  
      safmin = slamch_("Safe minimum");
      eps = slamch_("Precision");
      smlnum = safmin / eps;
      bignum = 1.f / smlnum;
      rmin = sqrt(smlnum);
      rmax = sqrt(bignum);
  
  /*     Scale matrix to allowable range, if necessary. */
  
      anrm = slansp_("M", uplo, n, &ap[1], &work[1]);
      iscale = 0;
      if (anrm > 0.f && anrm < rmin) {
  	iscale = 1;
  	sigma = rmin / anrm;
      } else if (anrm > rmax) {
  	iscale = 1;
  	sigma = rmax / anrm;
      }
      if (iscale == 1) {
  	i__1 = *n * (*n + 1) / 2;
  	sscal_(&i__1, &sigma, &ap[1], &c__1);
      }
  
  /*     Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. */
  
      inde = 1;
      indtau = inde + *n;
      ssptrd_(uplo, n, &ap[1], &w[1], &work[inde], &work[indtau], &iinfo);
  
  /*     For eigenvalues only, call SSTERF.  For eigenvectors, first call */
  /*     SOPGTR to generate the orthogonal matrix, then call SSTEQR. */
  
      if (! wantz) {
  	ssterf_(n, &w[1], &work[inde], info);
      } else {
  	indwrk = indtau + *n;
  	sopgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[
  		indwrk], &iinfo);
  	ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[
  		indtau], info);
      }
  
  /*     If matrix was scaled, then rescale eigenvalues appropriately. */
  
      if (iscale == 1) {
  	if (*info == 0) {
  	    imax = *n;
  	} else {
  	    imax = *info - 1;
  	}
  	r__1 = 1.f / sigma;
  	sscal_(&imax, &r__1, &w[1], &c__1);
      }
  
      return 0;
  
  /*     End of SSPEV */
  
  } /* sspev_ */
  