chetd2.c File Reference

(r)

Functions
int	chetd2_fla (char *uplo, integer *n, complex *a, integer *lda, real *d__, real *e, complex *tau, integer *info)

Function Documentation

chetd2_fla()

int chetd2_fla	(	char *	uplo,
		integer *	n,
		complex *	a,
		integer *	lda,
		real *	d__,
		real *	e,
		complex *	tau,
		integer *	info
	)

{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    real r__1;
    complex q__1, q__2, q__3, q__4;
    /* Local variables */
    integer i__;
    complex taui;
    extern /* Subroutine */
    int cher2_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, integer *);
    complex alpha;
    extern /* Complex */
    VOID cdotc_f2c_(complex *, integer *, complex *, integer *, complex *, integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int chemv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * ), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *);
    logical upper;
    extern /* Subroutine */
    int clarfg_(integer *, complex *, complex *, integer *, complex *), xerbla_(char *, integer *);
    /* -- LAPACK computational routine (version 3.4.2) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* September 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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_("CHETD2", &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;
        r__1 = a[i__2].r;
        a[i__1].r = r__1;
        a[i__1].i = 0.f; // , expr subst
        for (i__ = *n - 1;
                i__ >= 1;
                --i__)
        {
            /* Generate elementary reflector H(i) = I - tau * v * v**H */
            /* 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; // , expr subst
            clarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
            i__1 = i__;
            e[i__1] = alpha.r;
            if (taui.r != 0.f || taui.i != 0.f)
            {
                /* Apply H(i) from both sides to A(1:i,1:i) */
                i__1 = i__ + (i__ + 1) * a_dim1;
                a[i__1].r = 1.f;
                a[i__1].i = 0.f; // , expr subst
                /* Compute x := tau * A * v storing x in TAU(1:i) */
                chemv_(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**H * v) * v */
                q__3.r = -.5f;
                q__3.i = -0.f; // , expr subst
                q__2.r = q__3.r * taui.r - q__3.i * taui.i;
                q__2.i = q__3.r * taui.i + q__3.i * taui.r; // , expr subst
                cdotc_f2c_(&q__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1] , &c__1);
                q__1.r = q__2.r * q__4.r - q__2.i * q__4.i;
                q__1.i = q__2.r * q__4.i + q__2.i * q__4.r; // , expr subst
                alpha.r = q__1.r;
                alpha.i = q__1.i; // , expr subst
                caxpy_(&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**H - w * v**H */
                q__1.r = -1.f;
                q__1.i = -0.f; // , expr subst
                cher2_(uplo, &i__, &q__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;
                r__1 = a[i__2].r;
                a[i__1].r = r__1;
                a[i__1].i = 0.f; // , expr subst
            }
            i__1 = i__ + (i__ + 1) * a_dim1;
            i__2 = i__;
            a[i__1].r = e[i__2];
            a[i__1].i = 0.f; // , expr subst
            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; // , expr subst
            /* 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;
        r__1 = a[i__2].r;
        a[i__1].r = r__1;
        a[i__1].i = 0.f; // , expr subst
        i__1 = *n - 1;
        for (i__ = 1;
                i__ <= i__1;
                ++i__)
        {
            /* Generate elementary reflector H(i) = I - tau * v * v**H */
            /* 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; // , expr subst
            i__2 = *n - i__;
            /* Computing MIN */
            i__3 = i__ + 2;
            clarfg_(&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.f || taui.i != 0.f)
            {
                /* 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.f;
                a[i__2].i = 0.f; // , expr subst
                /* Compute x := tau * A * v storing y in TAU(i:n-1) */
                i__2 = *n - i__;
                chemv_(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**H * v) * v */
                q__3.r = -.5f;
                q__3.i = -0.f; // , expr subst
                q__2.r = q__3.r * taui.r - q__3.i * taui.i;
                q__2.i = q__3.r * taui.i + q__3.i * taui.r; // , expr subst
                i__2 = *n - i__;
                cdotc_f2c_(&q__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
                q__1.r = q__2.r * q__4.r - q__2.i * q__4.i;
                q__1.i = q__2.r * q__4.i + q__2.i * q__4.r; // , expr subst
                alpha.r = q__1.r;
                alpha.i = q__1.i; // , expr subst
                i__2 = *n - i__;
                caxpy_(&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**H - w * v**H */
                i__2 = *n - i__;
                q__1.r = -1.f;
                q__1.i = -0.f; // , expr subst
                cher2_(uplo, &i__2, &q__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;
                r__1 = a[i__3].r;
                a[i__2].r = r__1;
                a[i__2].i = 0.f; // , expr subst
            }
            i__2 = i__ + 1 + i__ * a_dim1;
            i__3 = i__;
            a[i__2].r = e[i__3];
            a[i__2].i = 0.f; // , expr subst
            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; // , expr subst
            /* L20: */
        }
        i__1 = *n;
        i__2 = *n + *n * a_dim1;
        d__[i__1] = a[i__2].r;
    }
    return 0;
    /* End of CHETD2 */
}

References i.

Referenced by chetrd_fla().