zhetd2.c

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/* zhetd2.f -- translated by f2c (version 20061008).
   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
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

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

/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, 
        integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1;
    doublecomplex z__1, z__2, z__3, z__4;

    /* Local variables */
    integer i__;
    doublecomplex taui;
    extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *);
    doublecomplex alpha;
    extern logical lsame_(char *, char *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, doublecomplex *, integer *);
    logical upper;
    extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
            char *, integer *), zlarfg_(integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

/*  Purpose */
/*  ======= */

/*  ZHETD2 reduces a complex Hermitian matrix A to real symmetric */
/*  tridiagonal form T by a unitary similarity transformation: */
/*  Q' * A * Q = T. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          Hermitian matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) 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 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 unitary */
/*          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 unitary 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) COMPLEX*16 array, dimension (N-1) */
/*          The scalar factors of the elementary reflectors (see Further */
/*          Details). */

/*  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 complex scalar, and v is a complex 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 complex scalar, and v is a complex 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). */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --d__;
    --e;
    --tau;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*n)) {
        *info = -4;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZHETD2", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    if (upper) {

/*        Reduce the upper triangle of A */

        i__1 = *n + *n * a_dim1;
        i__2 = *n + *n * a_dim1;
        d__1 = a[i__2].r;
        a[i__1].r = d__1, a[i__1].i = 0.;
        for (i__ = *n - 1; i__ >= 1; --i__) {

/*           Generate elementary reflector H(i) = I - tau * v * v' */
/*           to annihilate A(1:i-1,i+1) */

            i__1 = i__ + (i__ + 1) * a_dim1;
            alpha.r = a[i__1].r, alpha.i = a[i__1].i;
            zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
            i__1 = i__;
            e[i__1] = alpha.r;

            if (taui.r != 0. || taui.i != 0.) {

/*              Apply H(i) from both sides to A(1:i,1:i) */

                i__1 = i__ + (i__ + 1) * a_dim1;
                a[i__1].r = 1., a[i__1].i = 0.;

/*              Compute  x := tau * A * v  storing x in TAU(1:i) */

                zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * 
                        a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1);

/*              Compute  w := x - 1/2 * tau * (x'*v) * v */

                z__3.r = -.5, z__3.i = -0.;
                z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * 
                        taui.i + z__3.i * taui.r;
                zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * 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;
                zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
                        1], &c__1);

/*              Apply the transformation as a rank-2 update: */
/*                 A := A - v * w' - w * v' */

                z__1.r = -1., z__1.i = -0.;
                zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, &
                        tau[1], &c__1, &a[a_offset], lda);

            } else {
                i__1 = i__ + i__ * a_dim1;
                i__2 = i__ + i__ * a_dim1;
                d__1 = a[i__2].r;
                a[i__1].r = d__1, a[i__1].i = 0.;
            }
            i__1 = i__ + (i__ + 1) * a_dim1;
            i__2 = i__;
            a[i__1].r = e[i__2], a[i__1].i = 0.;
            i__1 = i__ + 1;
            i__2 = i__ + 1 + (i__ + 1) * a_dim1;
            d__[i__1] = a[i__2].r;
            i__1 = i__;
            tau[i__1].r = taui.r, tau[i__1].i = taui.i;
/* L10: */
        }
        i__1 = a_dim1 + 1;
        d__[1] = a[i__1].r;
    } else {

/*        Reduce the lower triangle of A */

        i__1 = a_dim1 + 1;
        i__2 = a_dim1 + 1;
        d__1 = a[i__2].r;
        a[i__1].r = d__1, a[i__1].i = 0.;
        i__1 = *n - 1;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Generate elementary reflector H(i) = I - tau * v * v' */
/*           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, &
                    taui);
            i__2 = i__;
            e[i__2] = alpha.r;

            if (taui.r != 0. || taui.i != 0.) {

/*              Apply H(i) from both sides to A(i+1:n,i+1:n) */

                i__2 = i__ + 1 + i__ * a_dim1;
                a[i__2].r = 1., a[i__2].i = 0.;

/*              Compute  x := tau * A * v  storing y in TAU(i:n-1) */

                i__2 = *n - i__;
                zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], 
                        lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[
                        i__], &c__1);

/*              Compute  w := x - 1/2 * tau * (x'*v) * v */

                z__3.r = -.5, z__3.i = -0.;
                z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * 
                        taui.i + z__3.i * taui.r;
                i__2 = *n - i__;
                zdotc_(&z__4, &i__2, &tau[i__], &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, &tau[
                        i__], &c__1);

/*              Apply the transformation as a rank-2 update: */
/*                 A := A - v * w' - w * v' */

                i__2 = *n - i__;
                z__1.r = -1., z__1.i = -0.;
                zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, 
                        &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], 
                        lda);

            } else {
                i__2 = i__ + 1 + (i__ + 1) * a_dim1;
                i__3 = i__ + 1 + (i__ + 1) * a_dim1;
                d__1 = a[i__3].r;
                a[i__2].r = d__1, a[i__2].i = 0.;
            }
            i__2 = i__ + 1 + i__ * a_dim1;
            i__3 = i__;
            a[i__2].r = e[i__3], a[i__2].i = 0.;
            i__2 = i__;
            i__3 = i__ + i__ * a_dim1;
            d__[i__2] = a[i__3].r;
            i__2 = i__;
            tau[i__2].r = taui.r, tau[i__2].i = taui.i;
/* L20: */
        }
        i__1 = *n;
        i__2 = *n + *n * a_dim1;
        d__[i__1] = a[i__2].r;
    }

    return 0;

/*     End of ZHETD2 */

} /* zhetd2_ */