text: 
  #include "hypre_lapack.h"
  #include "f2c.h"
  
  /* Subroutine */ HYPRE_Int dsterf_(integer *n, doublereal *d__, doublereal *e, 
  	integer *info)
  {
  /*  -- LAPACK routine (version 3.0) --   
         Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
         Courant Institute, Argonne National Lab, and Rice University   
         June 30, 1999   
  
  
      Purpose   
      =======   
  
      DSTERF computes all eigenvalues of a symmetric tridiagonal matrix   
      using the Pal-Walker-Kahan variant of the QL or QR algorithm.   
  
      Arguments   
      =========   
  
      N       (input) INTEGER   
              The order of the matrix.  N >= 0.   
  
      D       (input/output) DOUBLE PRECISION array, dimension (N)   
              On entry, the n 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.   
  
      INFO    (output) INTEGER   
              = 0:  successful exit   
              < 0:  if INFO = -i, the i-th argument had an illegal value   
              > 0:  the algorithm failed to find all of the eigenvalues in   
                    a total of 30*N iterations; if INFO = i, then i   
                    elements of E have not converged to zero.   
  
      =====================================================================   
  
  
         Test the input parameters.   
  
         Parameter adjustments */
      /* Table of constant values */
      static integer c__0 = 0;
      static integer c__1 = 1;
      static doublereal c_b32 = 1.;
      
      /* System generated locals */
      integer i__1;
      doublereal d__1, d__2, d__3;
      /* Builtin functions */
      double sqrt(doublereal), d_sign(doublereal *, doublereal *);
      /* Local variables */
      static doublereal oldc;
      static integer lend, jtot;
      extern /* Subroutine */ HYPRE_Int dlae2_(doublereal *, doublereal *, doublereal 
  	    *, doublereal *, doublereal *);
      static doublereal c__;
      static integer i__, l, m;
      static doublereal p, gamma, r__, s, alpha, sigma, anorm;
      static integer l1;
      extern doublereal dlapy2_(doublereal *, doublereal *);
      static doublereal bb;
      extern doublereal dlamch_(char *);
      static integer iscale;
      extern /* Subroutine */ HYPRE_Int dlascl_(char *, integer *, integer *, 
  	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
  	    integer *, integer *);
      static doublereal oldgam, safmin;
      extern /* Subroutine */ HYPRE_Int xerbla_(char *, integer *);
      static doublereal safmax;
      extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
      extern /* Subroutine */ HYPRE_Int dlasrt_(char *, integer *, doublereal *, 
  	    integer *);
      static integer lendsv;
      static doublereal ssfmin;
      static integer nmaxit;
      static doublereal ssfmax, rt1, rt2, eps, rte;
      static integer lsv;
      static doublereal eps2;
  
  
      --e;
      --d__;
  
      /* Function Body */
      *info = 0;
  
  /*     Quick return if possible */
  
      if (*n < 0) {
  	*info = -1;
  	i__1 = -(*info);
  	xerbla_("DSTERF", &i__1);
  	return 0;
      }
      if (*n <= 1) {
  	return 0;
      }
  
  /*     Determine the unit roundoff for this environment. */
  
      eps = dlamch_("E");
  /* Computing 2nd power */
      d__1 = eps;
      eps2 = d__1 * d__1;
      safmin = dlamch_("S");
      safmax = 1. / safmin;
      ssfmax = sqrt(safmax) / 3.;
      ssfmin = sqrt(safmin) / eps2;
  
  /*     Compute the eigenvalues of the tridiagonal matrix. */
  
      nmaxit = *n * 30;
      sigma = 0.;
      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;
  
  L10:
      if (l1 > *n) {
  	goto L170;
      }
      if (l1 > 1) {
  	e[l1 - 1] = 0.;
      }
      i__1 = *n - 1;
      for (m = l1; m <= i__1; ++m) {
  	if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * 
  		sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) {
  	    e[m] = 0.;
  	    goto L30;
  	}
  /* L20: */
      }
      m = *n;
  
  L30:
      l = l1;
      lsv = l;
      lend = m;
      lendsv = lend;
      l1 = m + 1;
      if (lend == l) {
  	goto L10;
      }
  
  /*     Scale submatrix in rows and columns L to LEND */
  
      i__1 = lend - l + 1;
      anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
      iscale = 0;
      if (anorm > ssfmax) {
  	iscale = 1;
  	i__1 = lend - l + 1;
  	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
  		info);
  	i__1 = lend - l;
  	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, 
  		info);
      } else if (anorm < ssfmin) {
  	iscale = 2;
  	i__1 = lend - l + 1;
  	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
  		info);
  	i__1 = lend - l;
  	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 
  		info);
      }
  
      i__1 = lend - 1;
      for (i__ = l; i__ <= i__1; ++i__) {
  /* Computing 2nd power */
  	d__1 = e[i__];
  	e[i__] = d__1 * d__1;
  /* L40: */
      }
  
  /*     Choose between QL and QR iteration */
  
      if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
  	lend = lsv;
  	l = lendsv;
      }
  
      if (lend >= l) {
  
  /*        QL Iteration   
  
            Look for small subdiagonal element. */
  
  L50:
  	if (l != lend) {
  	    i__1 = lend - 1;
  	    for (m = l; m <= i__1; ++m) {
  		if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
  			+ 1], abs(d__1))) {
  		    goto L70;
  		}
  /* L60: */
  	    }
  	}
  	m = lend;
  
  L70:
  	if (m < lend) {
  	    e[m] = 0.;
  	}
  	p = d__[l];
  	if (m == l) {
  	    goto L90;
  	}
  
  /*        If remaining matrix is 2 by 2, use DLAE2 to compute its   
            eigenvalues. */
  
  	if (m == l + 1) {
  	    rte = sqrt(e[l]);
  	    dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
  	    d__[l] = rt1;
  	    d__[l + 1] = rt2;
  	    e[l] = 0.;
  	    l += 2;
  	    if (l <= lend) {
  		goto L50;
  	    }
  	    goto L150;
  	}
  
  	if (jtot == nmaxit) {
  	    goto L150;
  	}
  	++jtot;
  
  /*        Form shift. */
  
  	rte = sqrt(e[l]);
  	sigma = (d__[l + 1] - p) / (rte * 2.);
  	r__ = dlapy2_(&sigma, &c_b32);
  	sigma = p - rte / (sigma + d_sign(&r__, &sigma));
  
  	c__ = 1.;
  	s = 0.;
  	gamma = d__[m] - sigma;
  	p = gamma * gamma;
  
  /*        Inner loop */
  
  	i__1 = l;
  	for (i__ = m - 1; i__ >= i__1; --i__) {
  	    bb = e[i__];
  	    r__ = p + bb;
  	    if (i__ != m - 1) {
  		e[i__ + 1] = s * r__;
  	    }
  	    oldc = c__;
  	    c__ = p / r__;
  	    s = bb / r__;
  	    oldgam = gamma;
  	    alpha = d__[i__];
  	    gamma = c__ * (alpha - sigma) - s * oldgam;
  	    d__[i__ + 1] = oldgam + (alpha - gamma);
  	    if (c__ != 0.) {
  		p = gamma * gamma / c__;
  	    } else {
  		p = oldc * bb;
  	    }
  /* L80: */
  	}
  
  	e[l] = s * p;
  	d__[l] = sigma + gamma;
  	goto L50;
  
  /*        Eigenvalue found. */
  
  L90:
  	d__[l] = p;
  
  	++l;
  	if (l <= lend) {
  	    goto L50;
  	}
  	goto L150;
  
      } else {
  
  /*        QR Iteration   
  
            Look for small superdiagonal element. */
  
  L100:
  	i__1 = lend + 1;
  	for (m = l; m >= i__1; --m) {
  	    if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
  		    - 1], abs(d__1))) {
  		goto L120;
  	    }
  /* L110: */
  	}
  	m = lend;
  
  L120:
  	if (m > lend) {
  	    e[m - 1] = 0.;
  	}
  	p = d__[l];
  	if (m == l) {
  	    goto L140;
  	}
  
  /*        If remaining matrix is 2 by 2, use DLAE2 to compute its   
            eigenvalues. */
  
  	if (m == l - 1) {
  	    rte = sqrt(e[l - 1]);
  	    dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
  	    d__[l] = rt1;
  	    d__[l - 1] = rt2;
  	    e[l - 1] = 0.;
  	    l += -2;
  	    if (l >= lend) {
  		goto L100;
  	    }
  	    goto L150;
  	}
  
  	if (jtot == nmaxit) {
  	    goto L150;
  	}
  	++jtot;
  
  /*        Form shift. */
  
  	rte = sqrt(e[l - 1]);
  	sigma = (d__[l - 1] - p) / (rte * 2.);
  	r__ = dlapy2_(&sigma, &c_b32);
  	sigma = p - rte / (sigma + d_sign(&r__, &sigma));
  
  	c__ = 1.;
  	s = 0.;
  	gamma = d__[m] - sigma;
  	p = gamma * gamma;
  
  /*        Inner loop */
  
  	i__1 = l - 1;
  	for (i__ = m; i__ <= i__1; ++i__) {
  	    bb = e[i__];
  	    r__ = p + bb;
  	    if (i__ != m) {
  		e[i__ - 1] = s * r__;
  	    }
  	    oldc = c__;
  	    c__ = p / r__;
  	    s = bb / r__;
  	    oldgam = gamma;
  	    alpha = d__[i__ + 1];
  	    gamma = c__ * (alpha - sigma) - s * oldgam;
  	    d__[i__] = oldgam + (alpha - gamma);
  	    if (c__ != 0.) {
  		p = gamma * gamma / c__;
  	    } else {
  		p = oldc * bb;
  	    }
  /* L130: */
  	}
  
  	e[l - 1] = s * p;
  	d__[l] = sigma + gamma;
  	goto L100;
  
  /*        Eigenvalue found. */
  
  L140:
  	d__[l] = p;
  
  	--l;
  	if (l >= lend) {
  	    goto L100;
  	}
  	goto L150;
  
      }
  
  /*     Undo scaling if necessary */
  
  L150:
      if (iscale == 1) {
  	i__1 = lendsv - lsv + 1;
  	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
  		n, info);
      }
      if (iscale == 2) {
  	i__1 = lendsv - lsv + 1;
  	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], 
  		n, info);
      }
  
  /*     Check for no convergence to an eigenvalue after a total   
         of N*MAXIT iterations. */
  
      if (jtot < nmaxit) {
  	goto L10;
      }
      i__1 = *n - 1;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	if (e[i__] != 0.) {
  	    ++(*info);
  	}
  /* L160: */
      }
      goto L180;
  
  /*     Sort eigenvalues in increasing order. */
  
  L170:
      dlasrt_("I", n, &d__[1], info);
  
  L180:
      return 0;
  
  /*     End of DSTERF */
  
  } /* dsterf_ */
  
  