/* fortran/zlatrd.f -- translated by f2c (version 20200916).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"

/* Table of constant values */

static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;

/* > \brief \b ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago
nal form by an unitary similarity transformation. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download ZLATRD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */

/*       .. Scalar Arguments .. */
/*       CHARACTER          UPLO */
/*       INTEGER            LDA, LDW, N, NB */
/*       .. */
/*       .. Array Arguments .. */
/*       DOUBLE PRECISION   E( * ) */
/*       COMPLEX*16         A( LDA, * ), TAU( * ), W( LDW, * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to */
/* > Hermitian tridiagonal form by a unitary similarity */
/* > transformation Q**H * A * Q, and returns the matrices V and W which are */
/* > needed to apply the transformation to the unreduced part of A. */
/* > */
/* > If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a */
/* > matrix, of which the upper triangle is supplied; */
/* > if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a */
/* > matrix, of which the lower triangle is supplied. */
/* > */
/* > This is an auxiliary routine called by ZHETRD. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          Specifies whether the upper or lower triangular part of the */
/* >          Hermitian matrix A is stored: */
/* >          = 'U': Upper triangular */
/* >          = 'L': Lower triangular */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* >          NB is INTEGER */
/* >          The number of rows and columns to be reduced. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is COMPLEX*16 array, dimension (LDA,N) */
/* >          On entry, the Hermitian 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 last NB columns have been reduced to */
/* >            tridiagonal form, with the diagonal elements overwriting */
/* >            the diagonal elements of A; the elements above the diagonal */
/* >            with the array TAU, represent the unitary matrix Q as a */
/* >            product of elementary reflectors; */
/* >          if UPLO = 'L', the first NB columns have been reduced to */
/* >            tridiagonal form, with the diagonal elements overwriting */
/* >            the diagonal elements of A; the elements below the diagonal */
/* >            with the array TAU, represent the  unitary matrix Q as a */
/* >            product of elementary reflectors. */
/* >          See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N-1) */
/* >          If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
/* >          elements of the last NB columns of the reduced matrix; */
/* >          if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
/* >          the first NB columns of the reduced matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is COMPLEX*16 array, dimension (N-1) */
/* >          The scalar factors of the elementary reflectors, stored in */
/* >          TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
/* >          See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is COMPLEX*16 array, dimension (LDW,NB) */
/* >          The n-by-nb matrix W required to update the unreduced part */
/* >          of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDW */
/* > \verbatim */
/* >          LDW is INTEGER */
/* >          The leading dimension of the array W. LDW >= max(1,N). */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup complex16OTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(n) H(n-1) . . . H(n-nb+1). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - tau * v * v**H */
/* > */
/* >  where tau is a complex scalar, and v is a complex vector with */
/* >  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
/* >  and tau in TAU(i-1). */
/* > */
/* >  If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(nb). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - tau * v * v**H */
/* > */
/* >  where tau is a complex scalar, and v is a complex vector with */
/* >  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* >  and tau in TAU(i). */
/* > */
/* >  The elements of the vectors v together form the n-by-nb matrix V */
/* >  which is needed, with W, to apply the transformation to the unreduced */
/* >  part of the matrix, using a Hermitian rank-2k update of the form: */
/* >  A := A - V*W**H - W*V**H. */
/* > */
/* >  The contents of A on exit are illustrated by the following examples */
/* >  with n = 5 and nb = 2: */
/* > */
/* >  if UPLO = 'U':                       if UPLO = 'L': */
/* > */
/* >    (  a   a   a   v4  v5 )              (  d                  ) */
/* >    (      a   a   v4  v5 )              (  1   d              ) */
/* >    (          a   1   v5 )              (  v1  1   a          ) */
/* >    (              d   1  )              (  v1  v2  a   a      ) */
/* >    (                  d  )              (  v1  v2  a   a   a  ) */
/* > */
/* >  where d denotes a diagonal element of the reduced matrix, a denotes */
/* >  an element of the original matrix that is unchanged, and vi denotes */
/* >  an element of the vector defining H(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb,
        doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau,
        doublecomplex *w, integer *ldw, ftnlen uplo_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
    doublereal d__1;
    doublecomplex z__1, z__2, z__3, z__4;

    /* Local variables */
    integer i__, iw;
    doublecomplex alpha;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
            doublecomplex *, integer *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
            doublecomplex *, doublecomplex *, integer *, doublecomplex *,
            integer *, doublecomplex *, doublecomplex *, integer *, ftnlen),
            zhemv_(char *, integer *, doublecomplex *, doublecomplex *,
            integer *, doublecomplex *, integer *, doublecomplex *,
            doublecomplex *, integer *, ftnlen), zaxpy_(integer *,
            doublecomplex *, doublecomplex *, integer *, doublecomplex *,
            integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
            integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *,
            integer *);


/*  -- LAPACK auxiliary routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick return if possible */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --e;
    --tau;
    w_dim1 = *ldw;
    w_offset = 1 + w_dim1;
    w -= w_offset;

    /* Function Body */
    if (*n <= 0) {
        return 0;
    }

    if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {

/*        Reduce last NB columns of upper triangle */

        i__1 = *n - *nb + 1;
        for (i__ = *n; i__ >= i__1; --i__) {
            iw = i__ - *n + *nb;
            if (i__ < *n) {

/*              Update A(1:i,i) */

                i__2 = i__ + i__ * a_dim1;
                i__3 = i__ + i__ * a_dim1;
                d__1 = a[i__3].r;
                a[i__2].r = d__1, a[i__2].i = 0.;
                i__2 = *n - i__;
                zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
                i__2 = *n - i__;
                z__1.r = -1., z__1.i = -0.;
                zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) *
                        a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
                        c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
                i__2 = *n - i__;
                zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
                i__2 = *n - i__;
                zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
                i__2 = *n - i__;
                z__1.r = -1., z__1.i = -0.;
                zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) *
                        w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
                        c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
                i__2 = *n - i__;
                zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
                i__2 = i__ + i__ * a_dim1;
                i__3 = i__ + i__ * a_dim1;
                d__1 = a[i__3].r;
                a[i__2].r = d__1, a[i__2].i = 0.;
            }
            if (i__ > 1) {

/*              Generate elementary reflector H(i) to annihilate */
/*              A(1:i-2,i) */

                i__2 = i__ - 1 + i__ * a_dim1;
                alpha.r = a[i__2].r, alpha.i = a[i__2].i;
                i__2 = i__ - 1;
                zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__
                        - 1]);
                e[i__ - 1] = alpha.r;
                i__2 = i__ - 1 + i__ * a_dim1;
                a[i__2].r = 1., a[i__2].i = 0.;

/*              Compute W(1:i-1,i) */

                i__2 = i__ - 1;
                zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ *
                        a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1,
                         (ftnlen)5);
                if (i__ < *n) {
                    i__2 = i__ - 1;
                    i__3 = *n - i__;
                    zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw
                            + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &
                            c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, (
                            ftnlen)19);
                    i__2 = i__ - 1;
                    i__3 = *n - i__;
                    z__1.r = -1., z__1.i = -0.;
                    zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) *
                             a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
                            c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
                            12);
                    i__2 = i__ - 1;
                    i__3 = *n - i__;
                    zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[(
                            i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1],
                             &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, (
                            ftnlen)19);
                    i__2 = i__ - 1;
                    i__3 = *n - i__;
                    z__1.r = -1., z__1.i = -0.;
                    zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) *
                            w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
                            c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
                            12);
                }
                i__2 = i__ - 1;
                zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
                z__3.r = -.5, z__3.i = -0.;
                i__2 = i__ - 1;
                z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
                         z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
                i__3 = i__ - 1;
                zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ *
                        a_dim1 + 1], &c__1);
                z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
                        z__4.i + z__2.i * z__4.r;
                alpha.r = z__1.r, alpha.i = z__1.i;
                i__2 = i__ - 1;
                zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
                        w_dim1 + 1], &c__1);
            }

/* L10: */
        }
    } else {

/*        Reduce first NB columns of lower triangle */

        i__1 = *nb;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Update A(i:n,i) */

            i__2 = i__ + i__ * a_dim1;
            i__3 = i__ + i__ * a_dim1;
            d__1 = a[i__3].r;
            a[i__2].r = d__1, a[i__2].i = 0.;
            i__2 = i__ - 1;
            zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
            i__2 = *n - i__ + 1;
            i__3 = i__ - 1;
            z__1.r = -1., z__1.i = -0.;
            zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda,
                     &w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], &
                    c__1, (ftnlen)12);
            i__2 = i__ - 1;
            zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
            i__2 = i__ - 1;
            zlacgv_(&i__2, &a[i__ + a_dim1], lda);
            i__2 = *n - i__ + 1;
            i__3 = i__ - 1;
            z__1.r = -1., z__1.i = -0.;
            zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw,
                     &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], &
                    c__1, (ftnlen)12);
            i__2 = i__ - 1;
            zlacgv_(&i__2, &a[i__ + a_dim1], lda);
            i__2 = i__ + i__ * a_dim1;
            i__3 = i__ + i__ * a_dim1;
            d__1 = a[i__3].r;
            a[i__2].r = d__1, a[i__2].i = 0.;
            if (i__ < *n) {

/*              Generate elementary reflector H(i) to annihilate */
/*              A(i+2:n,i) */

                i__2 = i__ + 1 + i__ * a_dim1;
                alpha.r = a[i__2].r, alpha.i = a[i__2].i;
                i__2 = *n - i__;
/* Computing MIN */
                i__3 = i__ + 2;
                zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1,
                         &tau[i__]);
                e[i__] = alpha.r;
                i__2 = i__ + 1 + i__ * a_dim1;
                a[i__2].r = 1., a[i__2].i = 0.;

/*              Compute W(i+1:n,i) */

                i__2 = *n - i__;
                zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1]
                        , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[
                        i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5);
                i__2 = *n - i__;
                i__3 = i__ - 1;
                zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1
                        + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &
                        c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19);
                i__2 = *n - i__;
                i__3 = i__ - 1;
                z__1.r = -1., z__1.i = -0.;
                zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 +
                        a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
                        i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
                i__2 = *n - i__;
                i__3 = i__ - 1;
                zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
                        + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
                        c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19);
                i__2 = *n - i__;
                i__3 = i__ - 1;
                z__1.r = -1., z__1.i = -0.;
                zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 +
                        w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
                        i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
                i__2 = *n - i__;
                zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
                z__3.r = -.5, z__3.i = -0.;
                i__2 = i__;
                z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
                         z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
                i__3 = *n - i__;
                zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[
                        i__ + 1 + i__ * a_dim1], &c__1);
                z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
                        z__4.i + z__2.i * z__4.r;
                alpha.r = z__1.r, alpha.i = z__1.i;
                i__2 = *n - i__;
                zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
                        i__ + 1 + i__ * w_dim1], &c__1);
            }

/* L20: */
        }
    }

    return 0;

/*     End of ZLATRD */

} /* zlatrd_ */

#ifdef __cplusplus
        }
#endif