dsytd2.c File Reference

(r)

Functions
int	dsytd2_fla (char *uplo, integer *n, doublereal *a, integer *lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info)

Function Documentation

dsytd2_fla()

int dsytd2_fla	(	char *	uplo,
		integer *	n,
		doublereal *	a,
		integer *	lda,
		doublereal *	d__,
		doublereal *	e,
		doublereal *	tau,
		integer *	info
	)

{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    /* Local variables */
    integer i__;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *);
    doublereal taui;
    extern /* Subroutine */
    int dsyr2_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *);
    doublereal alpha;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *);
    logical upper;
    extern /* Subroutine */
    int dsymv_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), 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_("DSYTD2", &i__1);
        return 0;
    }
    /* Quick return if possible */
    if (*n <= 0)
    {
        return 0;
    }
    if (upper)
    {
        /* Reduce the upper triangle of A */
        for (i__ = *n - 1;
                i__ >= 1;
                --i__)
        {
            /* Generate elementary reflector H(i) = I - tau * v * v**T */
            /* to annihilate A(1:i-1,i+1) */
            dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
            e[i__] = a[i__ + (i__ + 1) * a_dim1];
            if (taui != 0.)
            {
                /* Apply H(i) from both sides to A(1:i,1:i) */
                a[i__ + (i__ + 1) * a_dim1] = 1.;
                /* Compute x := tau * A * v storing x in TAU(1:i) */
                dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1);
                /* Compute w := x - 1/2 * tau * (x**T * v) * v */
                alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1], &c__1);
                daxpy_(&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**T - w * v**T */
                dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1, &a[a_offset], lda);
                a[i__ + (i__ + 1) * a_dim1] = e[i__];
            }
            d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1];
            tau[i__] = taui;
            /* L10: */
        }
        d__[1] = a[a_dim1 + 1];
    }
    else
    {
        /* Reduce the lower triangle of A */
        i__1 = *n - 1;
        for (i__ = 1;
                i__ <= i__1;
                ++i__)
        {
            /* Generate elementary reflector H(i) = I - tau * v * v**T */
            /* to annihilate A(i+2:n,i) */
            i__2 = *n - i__;
            /* Computing MIN */
            i__3 = i__ + 2;
            dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * a_dim1], &c__1, &taui);
            e[i__] = a[i__ + 1 + i__ * a_dim1];
            if (taui != 0.)
            {
                /* Apply H(i) from both sides to A(i+1:n,i+1:n) */
                a[i__ + 1 + i__ * a_dim1] = 1.;
                /* Compute x := tau * A * v storing y in TAU(i:n-1) */
                i__2 = *n - i__;
                dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ i__], &c__1);
                /* Compute w := x - 1/2 * tau * (x**T * v) * v */
                i__2 = *n - i__;
                alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
                i__2 = *n - i__;
                daxpy_(&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**T - w * v**T */
                i__2 = *n - i__;
                dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda);
                a[i__ + 1 + i__ * a_dim1] = e[i__];
            }
            d__[i__] = a[i__ + i__ * a_dim1];
            tau[i__] = taui;
            /* L20: */
        }
        d__[*n] = a[*n + *n * a_dim1];
    }
    return 0;
    /* End of DSYTD2 */
}

References i.

Referenced by dsytrd_fla().