/* Ergo, version 3.8.2, a program for linear scaling electronic structure
 * calculations.
 * Copyright (C) 2023 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_LAGTS_HEADER
#define TEMPLATE_LAPACK_LAGTS_HEADER


template<class Treal>
int template_lapack_lagts(const integer *job, const integer *n, const Treal *a, 
	const Treal *b, const Treal *c__, const Treal *d__, const integer *in, 
	Treal *y, Treal *tol, integer *info)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1992   


    Purpose   
    =======   

    DLAGTS may be used to solve one of the systems of equations   

       (T - lambda*I)*x = y   or   (T - lambda*I)'*x = y,   

    where T is an n by n tridiagonal matrix, for x, following the   
    factorization of (T - lambda*I) as   

       (T - lambda*I) = P*L*U ,   

    by routine DLAGTF. The choice of equation to be solved is   
    controlled by the argument JOB, and in each case there is an option   
    to perturb zero or very small diagonal elements of U, this option   
    being intended for use in applications such as inverse iteration.   

    Arguments   
    =========   

    JOB     (input) INTEGER   
            Specifies the job to be performed by DLAGTS as follows:   
            =  1: The equations  (T - lambda*I)x = y  are to be solved,   
                  but diagonal elements of U are not to be perturbed.   
            = -1: The equations  (T - lambda*I)x = y  are to be solved   
                  and, if overflow would otherwise occur, the diagonal   
                  elements of U are to be perturbed. See argument TOL   
                  below.   
            =  2: The equations  (T - lambda*I)'x = y  are to be solved,   
                  but diagonal elements of U are not to be perturbed.   
            = -2: The equations  (T - lambda*I)'x = y  are to be solved   
                  and, if overflow would otherwise occur, the diagonal   
                  elements of U are to be perturbed. See argument TOL   
                  below.   

    N       (input) INTEGER   
            The order of the matrix T.   

    A       (input) DOUBLE PRECISION array, dimension (N)   
            On entry, A must contain the diagonal elements of U as   
            returned from DLAGTF.   

    B       (input) DOUBLE PRECISION array, dimension (N-1)   
            On entry, B must contain the first super-diagonal elements of   
            U as returned from DLAGTF.   

    C       (input) DOUBLE PRECISION array, dimension (N-1)   
            On entry, C must contain the sub-diagonal elements of L as   
            returned from DLAGTF.   

    D       (input) DOUBLE PRECISION array, dimension (N-2)   
            On entry, D must contain the second super-diagonal elements   
            of U as returned from DLAGTF.   

    IN      (input) INTEGER array, dimension (N)   
            On entry, IN must contain details of the matrix P as returned   
            from DLAGTF.   

    Y       (input/output) DOUBLE PRECISION array, dimension (N)   
            On entry, the right hand side vector y.   
            On exit, Y is overwritten by the solution vector x.   

    TOL     (input/output) DOUBLE PRECISION   
            On entry, with  JOB .lt. 0, TOL should be the minimum   
            perturbation to be made to very small diagonal elements of U.   
            TOL should normally be chosen as about eps*norm(U), where eps   
            is the relative machine precision, but if TOL is supplied as   
            non-positive, then it is reset to eps*max( abs( u(i,j) ) ).   
            If  JOB .gt. 0  then TOL is not referenced.   

            On exit, TOL is changed as described above, only if TOL is   
            non-positive on entry. Otherwise TOL is unchanged.   

    INFO    (output) INTEGER   
            = 0   : successful exit   
            .lt. 0: if INFO = -i, the i-th argument had an illegal value   
            .gt. 0: overflow would occur when computing the INFO(th)   
                    element of the solution vector x. This can only occur   
                    when JOB is supplied as positive and either means   
                    that a diagonal element of U is very small, or that   
                    the elements of the right-hand side vector y are very   
                    large.   

    =====================================================================   


       Parameter adjustments */
    /* System generated locals */
    integer i__1;
    Treal d__1, d__2, d__3, d__4, d__5;
    /* Local variables */
     Treal temp, pert;
     integer k;
     Treal absak, sfmin, ak;
     Treal bignum, eps;

    --y;
    --in;
    --d__;
    --c__;
    --b;
    --a;

    /* Function Body */
    *info = 0;
    if (absMACRO(*job) > 2 || *job == 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    }
    if (*info != 0) {
	i__1 = -(*info);
	template_blas_erbla("LAGTS ", &i__1);
	return 0;
    }

    if (*n == 0) {
	return 0;
    }

    eps = template_lapack_lamch("Epsilon", (Treal)0);
    sfmin = template_lapack_lamch("Safe minimum", (Treal)0);
    bignum = 1. / sfmin;

    if (*job < 0) {
	if (*tol <= 0.) {
	    *tol = absMACRO(a[1]);
	    if (*n > 1) {
/* Computing MAX */
		d__1 = *tol, d__2 = absMACRO(a[2]), d__1 = maxMACRO(d__1,d__2), d__2 = 
			absMACRO(b[1]);
		*tol = maxMACRO(d__1,d__2);
	    }
	    i__1 = *n;
	    for (k = 3; k <= i__1; ++k) {
/* Computing MAX */
		d__4 = *tol, d__5 = (d__1 = a[k], absMACRO(d__1)), d__4 = maxMACRO(d__4,
			d__5), d__5 = (d__2 = b[k - 1], absMACRO(d__2)), d__4 = 
			maxMACRO(d__4,d__5), d__5 = (d__3 = d__[k - 2], absMACRO(d__3));
		*tol = maxMACRO(d__4,d__5);
/* L10: */
	    }
	    *tol *= eps;
	    if (*tol == 0.) {
		*tol = eps;
	    }
	}
    }

    if (absMACRO(*job) == 1) {
	i__1 = *n;
	for (k = 2; k <= i__1; ++k) {
	    if (in[k - 1] == 0) {
		y[k] -= c__[k - 1] * y[k - 1];
	    } else {
		temp = y[k - 1];
		y[k - 1] = y[k];
		y[k] = temp - c__[k - 1] * y[k];
	    }
/* L20: */
	}
	if (*job == 1) {
	    for (k = *n; k >= 1; --k) {
		if (k <= *n - 2) {
		    temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
		} else if (k == *n - 1) {
		    temp = y[k] - b[k] * y[k + 1];
		} else {
		    temp = y[k];
		}
		ak = a[k];
		absak = absMACRO(ak);
		if (absak < 1.) {
		    if (absak < sfmin) {
			if (absak == 0. || absMACRO(temp) * sfmin > absak) {
			    *info = k;
			    return 0;
			} else {
			    temp *= bignum;
			    ak *= bignum;
			}
		    } else if (absMACRO(temp) > absak * bignum) {
			*info = k;
			return 0;
		    }
		}
		y[k] = temp / ak;
/* L30: */
	    }
	} else {
	    for (k = *n; k >= 1; --k) {
		if (k <= *n - 2) {
		    temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
		} else if (k == *n - 1) {
		    temp = y[k] - b[k] * y[k + 1];
		} else {
		    temp = y[k];
		}
		ak = a[k];
		pert = template_lapack_d_sign(tol, &ak);
L40:
		absak = absMACRO(ak);
		if (absak < 1.) {
		    if (absak < sfmin) {
			if (absak == 0. || absMACRO(temp) * sfmin > absak) {
			    ak += pert;
			    pert *= 2;
			    goto L40;
			} else {
			    temp *= bignum;
			    ak *= bignum;
			}
		    } else if (absMACRO(temp) > absak * bignum) {
			ak += pert;
			pert *= 2;
			goto L40;
		    }
		}
		y[k] = temp / ak;
/* L50: */
	    }
	}
    } else {

/*        Come to here if  JOB = 2 or -2 */

	if (*job == 2) {
	    i__1 = *n;
	    for (k = 1; k <= i__1; ++k) {
		if (k >= 3) {
		    temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
		} else if (k == 2) {
		    temp = y[k] - b[k - 1] * y[k - 1];
		} else {
		    temp = y[k];
		}
		ak = a[k];
		absak = absMACRO(ak);
		if (absak < 1.) {
		    if (absak < sfmin) {
			if (absak == 0. || absMACRO(temp) * sfmin > absak) {
			    *info = k;
			    return 0;
			} else {
			    temp *= bignum;
			    ak *= bignum;
			}
		    } else if (absMACRO(temp) > absak * bignum) {
			*info = k;
			return 0;
		    }
		}
		y[k] = temp / ak;
/* L60: */
	    }
	} else {
	    i__1 = *n;
	    for (k = 1; k <= i__1; ++k) {
		if (k >= 3) {
		    temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
		} else if (k == 2) {
		    temp = y[k] - b[k - 1] * y[k - 1];
		} else {
		    temp = y[k];
		}
		ak = a[k];
		pert = template_lapack_d_sign(tol, &ak);
L70:
		absak = absMACRO(ak);
		if (absak < 1.) {
		    if (absak < sfmin) {
			if (absak == 0. || absMACRO(temp) * sfmin > absak) {
			    ak += pert;
			    pert *= 2;
			    goto L70;
			} else {
			    temp *= bignum;
			    ak *= bignum;
			}
		    } else if (absMACRO(temp) > absak * bignum) {
			ak += pert;
			pert *= 2;
			goto L70;
		    }
		}
		y[k] = temp / ak;
/* L80: */
	    }
	}

	for (k = *n; k >= 2; --k) {
	    if (in[k - 1] == 0) {
		y[k - 1] -= c__[k - 1] * y[k];
	    } else {
		temp = y[k - 1];
		y[k - 1] = y[k];
		y[k] = temp - c__[k - 1] * y[k];
	    }
/* L90: */
	}
    }

/*     End of DLAGTS */

    return 0;
} /* dlagts_ */

#endif