/* 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_SYTRD_HEADER
#define TEMPLATE_LAPACK_SYTRD_HEADER

#include "template_lapack_common.h"

template<class Treal>
int template_lapack_sytrd(const char *uplo, const integer *n, Treal *a, const integer *
	lda, Treal *d__, Treal *e, Treal *tau, Treal *
	work, const integer *lwork, 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   
    =======   

    DSYTRD reduces a real symmetric matrix A to real symmetric   
    tridiagonal form T by an orthogonal similarity transformation:   
    Q**T * A * Q = T.   

    Arguments   
    =========   

    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, and the strictly lower   
            triangular part of A is not referenced.  If UPLO = 'L', the   
            leading N-by-N lower triangular part of A contains the lower   
            triangular part of the matrix A, and the strictly upper   
            triangular part of A is not referenced.   
            On exit, if UPLO = 'U', the diagonal and first superdiagonal   
            of A are overwritten by the corresponding elements of the   
            tridiagonal matrix T, and the elements above the first   
            superdiagonal, with the array TAU, represent the orthogonal   
            matrix Q as a product of elementary reflectors; if UPLO   
            = 'L', the diagonal and first subdiagonal of A are over-   
            written by the corresponding elements of the tridiagonal   
            matrix T, and the elements below the first subdiagonal, with   
            the array TAU, represent the orthogonal matrix Q as a product   
            of elementary reflectors. See Further Details.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.  LDA >= max(1,N).   

    D       (output) DOUBLE PRECISION array, dimension (N)   
            The diagonal elements of the tridiagonal matrix T:   
            D(i) = A(i,i).   

    E       (output) DOUBLE PRECISION array, dimension (N-1)   
            The off-diagonal elements of the tridiagonal matrix T:   
            E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.   

    TAU     (output) DOUBLE PRECISION array, dimension (N-1)   
            The scalar factors of the elementary reflectors (see Further   
            Details).   

    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.  LWORK >= 1.   
            For optimum performance LWORK >= N*NB, where NB is the   
            optimal blocksize.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   

    Further Details   
    ===============   

    If UPLO = 'U', the matrix Q is represented as a product of elementary   
    reflectors   

       Q = H(n-1) . . . H(2) H(1).   

    Each H(i) has the form   

       H(i) = I - tau * v * v'   

    where tau is a real scalar, and v is a real vector with   
    v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in   
    A(1:i-1,i+1), and tau in TAU(i).   

    If UPLO = 'L', the matrix Q is represented as a product of elementary   
    reflectors   

       Q = H(1) H(2) . . . H(n-1).   

    Each H(i) has the form   

       H(i) = I - tau * v * v'   

    where tau is a real scalar, and v is a real vector with   
    v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),   
    and tau in TAU(i).   

    The contents of A on exit are illustrated by the following examples   
    with n = 5:   

    if UPLO = 'U':                       if UPLO = 'L':   

      (  d   e   v2  v3  v4 )              (  d                  )   
      (      d   e   v3  v4 )              (  e   d              )   
      (          d   e   v4 )              (  v1  e   d          )   
      (              d   e  )              (  v1  v2  e   d      )   
      (                  d  )              (  v1  v2  v3  e   d  )   

    where d and e denote diagonal and off-diagonal elements of T, and vi   
    denotes an element of the vector defining H(i).   

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


       Test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
     integer c__1 = 1;
     integer c_n1 = -1;
     integer c__3 = 3;
     integer c__2 = 2;
     Treal c_b22 = -1.;
     Treal c_b23 = 1.;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    /* Local variables */
     integer i__, j;
     integer nbmin, iinfo;
     logical upper;
     integer nb, kk, nx;
     integer ldwork, lwkopt;
     logical lquery;
     integer iws;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --d__;
    --e;
    --tau;
    --work;

    /* Initialization added by Elias to get rid of compiler warnings. */
    lwkopt = 0;
    /* Function Body */
    *info = 0;
    upper = template_blas_lsame(uplo, "U");
    lquery = *lwork == -1;
    if (! upper && ! template_blas_lsame(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < maxMACRO(1,*n)) {
	*info = -4;
    } else if (*lwork < 1 && ! lquery) {
	*info = -9;
    }

    if (*info == 0) {

/*        Determine the block size. */

	nb = template_lapack_ilaenv(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
		 (ftnlen)1);
	lwkopt = *n * nb;
	work[1] = (Treal) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	template_blas_erbla("SYTRD ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	work[1] = 1.;
	return 0;
    }

    nx = *n;
    iws = 1;
    if (nb > 1 && nb < *n) {

/*        Determine when to cross over from blocked to unblocked code   
          (last block is always handled by unblocked code).   

   Computing MAX */
	i__1 = nb, i__2 = template_lapack_ilaenv(&c__3, "DSYTRD", uplo, n, &c_n1, &c_n1, &
		c_n1, (ftnlen)6, (ftnlen)1);
	nx = maxMACRO(i__1,i__2);
	if (nx < *n) {

/*           Determine if workspace is large enough for blocked code. */

	    ldwork = *n;
	    iws = ldwork * nb;
	    if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  determine the   
                minimum value of NB, and reduce NB or force use of   
                unblocked code by setting NX = N.   

   Computing MAX */
		i__1 = *lwork / ldwork;
		nb = maxMACRO(i__1,1);
		nbmin = template_lapack_ilaenv(&c__2, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1,
			 (ftnlen)6, (ftnlen)1);
		if (nb < nbmin) {
		    nx = *n;
		}
	    }
	} else {
	    nx = *n;
	}
    } else {
	nb = 1;
    }

    if (upper) {

/*        Reduce the upper triangle of A.   
          Columns 1:kk are handled by the unblocked method. */

	kk = *n - (*n - nx + nb - 1) / nb * nb;
	i__1 = kk + 1;
	i__2 = -nb;
	for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
		i__2) {

/*           Reduce columns i:i+nb-1 to tridiagonal form and form the   
             matrix W which is needed to update the unreduced part of   
             the matrix */

	    i__3 = i__ + nb - 1;
	    template_lapack_latrd(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
		    work[1], &ldwork);

/*           Update the unreduced submatrix A(1:i-1,1:i-1), using an   
             update of the form:  A := A - V*W' - W*V' */

	    i__3 = i__ - 1;
	    template_blas_syr2k(uplo, "No transpose", &i__3, &nb, &c_b22, &a_ref(1, i__), 
		    lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);

/*           Copy superdiagonal elements back into A, and diagonal   
             elements into D */

	    i__3 = i__ + nb - 1;
	    for (j = i__; j <= i__3; ++j) {
		a_ref(j - 1, j) = e[j - 1];
		d__[j] = a_ref(j, j);
/* L10: */
	    }
/* L20: */
	}

/*        Use unblocked code to reduce the last or only block */

	template_lapack_sytd2(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
    } else {

/*        Reduce the lower triangle of A */

	i__2 = *n - nx;
	i__1 = nb;
	for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {

/*           Reduce columns i:i+nb-1 to tridiagonal form and form the   
             matrix W which is needed to update the unreduced part of   
             the matrix */

	    i__3 = *n - i__ + 1;
	    template_lapack_latrd(uplo, &i__3, &nb, &a_ref(i__, i__), lda, &e[i__], &tau[
		    i__], &work[1], &ldwork);

/*           Update the unreduced submatrix A(i+ib:n,i+ib:n), using   
             an update of the form:  A := A - V*W' - W*V' */

	    i__3 = *n - i__ - nb + 1;
	    template_blas_syr2k(uplo, "No transpose", &i__3, &nb, &c_b22, &a_ref(i__ + nb,
		     i__), lda, &work[nb + 1], &ldwork, &c_b23, &a_ref(i__ + 
		    nb, i__ + nb), lda);

/*           Copy subdiagonal elements back into A, and diagonal   
             elements into D */

	    i__3 = i__ + nb - 1;
	    for (j = i__; j <= i__3; ++j) {
		a_ref(j + 1, j) = e[j];
		d__[j] = a_ref(j, j);
/* L30: */
	    }
/* L40: */
	}

/*        Use unblocked code to reduce the last or only block */

	i__1 = *n - i__ + 1;
	template_lapack_sytd2(uplo, &i__1, &a_ref(i__, i__), lda, &d__[i__], &e[i__], &tau[
		i__], &iinfo);
    }

    work[1] = (Treal) lwkopt;
    return 0;

/*     End of DSYTRD */

} /* dsytrd_ */

#undef a_ref


#endif