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

/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer *
	lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1992   


    Purpose   
    =======   

    DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal   
    form T by an orthogonal similarity transformation: Q' * A * Q = T.   

    Arguments   
    =========   

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

    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).   

    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 */
    static integer c__1 = 1;
    static doublereal c_b8 = 0.;
    static doublereal c_b14 = -1.;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static doublereal taui;
    extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static integer i__;
    static doublereal alpha;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    static 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 *
	    );
#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;

    /* 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'   
             to annihilate A(1:i-1,i+1) */

	    dlarfg_(&i__, &a_ref(i__, i__ + 1), &a_ref(1, i__ + 1), &c__1, &
		    taui);
	    e[i__] = a_ref(i__, i__ + 1);

	    if (taui != 0.) {

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

		a_ref(i__, i__ + 1) = 1.;

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

		dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a_ref(1, i__ + 
			1), &c__1, &c_b8, &tau[1], &c__1);

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

		alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a_ref(1, 
			i__ + 1), &c__1);
		daxpy_(&i__, &alpha, &a_ref(1, i__ + 1), &c__1, &tau[1], &
			c__1);

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

		dsyr2_(uplo, &i__, &c_b14, &a_ref(1, i__ + 1), &c__1, &tau[1],
			 &c__1, &a[a_offset], lda);

		a_ref(i__, i__ + 1) = e[i__];
	    }
	    d__[i__ + 1] = a_ref(i__ + 1, i__ + 1);
	    tau[i__] = taui;
/* L10: */
	}
	d__[1] = a_ref(1, 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'   
             to annihilate A(i+2:n,i)   

   Computing MIN */
	    i__2 = i__ + 2;
	    i__3 = *n - i__;
	    dlarfg_(&i__3, &a_ref(i__ + 1, i__), &a_ref(min(i__2,*n), i__), &
		    c__1, &taui);
	    e[i__] = a_ref(i__ + 1, i__);

	    if (taui != 0.) {

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

		a_ref(i__ + 1, i__) = 1.;

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

		i__2 = *n - i__;
		dsymv_(uplo, &i__2, &taui, &a_ref(i__ + 1, i__ + 1), lda, &
			a_ref(i__ + 1, i__), &c__1, &c_b8, &tau[i__], &c__1);

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

		i__2 = *n - i__;
		alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a_ref(
			i__ + 1, i__), &c__1);
		i__2 = *n - i__;
		daxpy_(&i__2, &alpha, &a_ref(i__ + 1, i__), &c__1, &tau[i__], 
			&c__1);

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

		i__2 = *n - i__;
		dsyr2_(uplo, &i__2, &c_b14, &a_ref(i__ + 1, i__), &c__1, &tau[
			i__], &c__1, &a_ref(i__ + 1, i__ + 1), lda)
			;

		a_ref(i__ + 1, i__) = e[i__];
	    }
	    d__[i__] = a_ref(i__, i__);
	    tau[i__] = taui;
/* L20: */
	}
	d__[*n] = a_ref(*n, *n);
    }

    return 0;

/*     End of DSYTD2 */

} /* dsytd2_ */

#undef a_ref


