/* Ergo, version 3.8, a program for linear scaling electronic structure
 * calculations.
 * Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
 * and Anastasia Kruchinina.
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 * 
 * Primary academic reference:
 * Ergo: An open-source program for linear-scaling electronic structure
 * calculations,
 * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
 * Kruchinina,
 * SoftwareX 7, 107 (2018),
 * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
 * 
 * For further information about Ergo, see <http://www.ergoscf.org>.
 */
 
 /* This file belongs to the template_lapack part of the Ergo source 
  * code. The source files in the template_lapack directory are modified
  * versions of files originally distributed as CLAPACK, see the
  * Copyright/license notice in the file template_lapack/COPYING.
  */
 

#ifndef TEMPLATE_LAPACK_STERF_HEADER
#define TEMPLATE_LAPACK_STERF_HEADER

#include "template_lapack_common.h"

template<class Treal>
int template_lapack_sterf(const integer *n, Treal *d__, Treal *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 */
     integer c__0 = 0;
     integer c__1 = 1;
     Treal c_b32 = 1.;
    
    /* System generated locals */
    integer i__1;
    Treal d__1, d__2, d__3;
    /* Local variables */
     Treal oldc;
     integer lend, jtot;
     Treal c__;
     integer i__, l, m;
     Treal p, gamma, r__, s, alpha, sigma, anorm;
     integer l1;
     Treal bb;
     integer iscale;
     Treal oldgam, safmin;
     Treal safmax;
     integer lendsv;
     Treal ssfmin;
     integer nmaxit;
     Treal ssfmax, rt1, rt2, eps, rte;
     integer lsv;
     Treal eps2;


    --e;
    --d__;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    if (*n < 0) {
	*info = -1;
	i__1 = -(*info);
	template_blas_erbla("STERF ", &i__1);
	return 0;
    }
    if (*n <= 1) {
	return 0;
    }

/*     Determine the unit roundoff for this environment. */

    eps = template_lapack_lamch("E", (Treal)0);
/* Computing 2nd power */
    d__1 = eps;
    eps2 = d__1 * d__1;
    safmin = template_lapack_lamch("S", (Treal)0);
    safmax = 1. / safmin;
    ssfmax = template_blas_sqrt(safmax) / 3.;
    ssfmin = template_blas_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], absMACRO(d__3)) <= template_blas_sqrt((d__1 = d__[m], absMACRO(d__1))) * 
		template_blas_sqrt((d__2 = d__[m + 1], absMACRO(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 = template_lapack_lanst("I", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm > ssfmax) {
	iscale = 1;
	i__1 = lend - l + 1;
	template_lapack_lascl("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	template_lapack_lascl("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;
	template_lapack_lascl("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	template_lapack_lascl("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], absMACRO(d__1)) < (d__2 = d__[l], absMACRO(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], absMACRO(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
			+ 1], absMACRO(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 = template_blas_sqrt(e[l]);
	    template_lapack_lae2(&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 = template_blas_sqrt(e[l]);
	sigma = (d__[l + 1] - p) / (rte * 2.);
	r__ = template_lapack_lapy2(&sigma, &c_b32);
	sigma = p - rte / (sigma + template_lapack_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], absMACRO(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
		    - 1], absMACRO(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 = template_blas_sqrt(e[l - 1]);
	    template_lapack_lae2(&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 = template_blas_sqrt(e[l - 1]);
	sigma = (d__[l - 1] - p) / (rte * 2.);
	r__ = template_lapack_lapy2(&sigma, &c_b32);
	sigma = p - rte / (sigma + template_lapack_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;
	template_lapack_lascl("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
    }
    if (iscale == 2) {
	i__1 = lendsv - lsv + 1;
	template_lapack_lascl("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:
    template_lapack_lasrt("I", n, &d__[1], info);

L180:
    return 0;

/*     End of DSTERF */

} /* dsterf_ */

#endif