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

/* Subroutine */ int dsbtrd_(char *vect, char *uplo, integer *n, integer *kd, 
	doublereal *ab, integer *ldab, doublereal *d__, doublereal *e, 
	doublereal *q, integer *ldq, doublereal *work, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    DSBTRD reduces a real symmetric band matrix A to symmetric   
    tridiagonal form T by an orthogonal similarity transformation:   
    Q**T * A * Q = T.   

    Arguments   
    =========   

    VECT    (input) CHARACTER*1   
            = 'N':  do not form Q;   
            = 'V':  form Q;   
            = 'U':  update a matrix X, by forming X*Q.   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangle of A is stored;   
            = 'L':  Lower triangle of A is stored.   

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

    KD      (input) INTEGER   
            The number of superdiagonals of the matrix A if UPLO = 'U',   
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.   

    AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)   
            On entry, the upper or lower triangle of the symmetric band   
            matrix A, stored in the first KD+1 rows of the array.  The   
            j-th column of A is stored in the j-th column of the array AB   
            as follows:   
            if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;   
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).   
            On exit, the diagonal elements of AB are overwritten by the   
            diagonal elements of the tridiagonal matrix T; if KD > 0, the   
            elements on the first superdiagonal (if UPLO = 'U') or the   
            first subdiagonal (if UPLO = 'L') are overwritten by the   
            off-diagonal elements of T; the rest of AB is overwritten by   
            values generated during the reduction.   

    LDAB    (input) INTEGER   
            The leading dimension of the array AB.  LDAB >= KD+1.   

    D       (output) DOUBLE PRECISION array, dimension (N)   
            The diagonal elements of the tridiagonal matrix T.   

    E       (output) DOUBLE PRECISION array, dimension (N-1)   
            The off-diagonal elements of the tridiagonal matrix T:   
            E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.   

    Q       (input/output) DOUBLE PRECISION array, dimension (LDQ,N)   
            On entry, if VECT = 'U', then Q must contain an N-by-N   
            matrix X; if VECT = 'N' or 'V', then Q need not be set.   

            On exit:   
            if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;   
            if VECT = 'U', Q contains the product X*Q;   
            if VECT = 'N', the array Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q.   
            LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.   

    WORK    (workspace) DOUBLE PRECISION array, dimension (N)   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   

    Further Details   
    ===============   

    Modified by Linda Kaufman, Bell Labs.   

    =====================================================================   


       Test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static doublereal c_b9 = 0.;
    static doublereal c_b10 = 1.;
    static integer c__1 = 1;
    
    /* System generated locals */
    integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4, 
	    i__5;
    /* Local variables */
    static integer inca, jend, lend, jinc, incx, last;
    static doublereal temp;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *);
    static integer j1end, j1inc, i__, j, k, l, iqend;
    extern logical lsame_(char *, char *);
    static logical initq, wantq, upper;
    static integer i2, j1, j2;
    extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *,
	     doublereal *, integer *, doublereal *, doublereal *, integer *);
    static integer nq, nr, iqaend;
    extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *), 
	    dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *), xerbla_(char *, integer *), dlargv_(
	    integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *), dlartv_(integer *, doublereal *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *);
    static integer kd1, ibl, iqb, kdn, jin, nrt, kdm1;
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]


    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --d__;
    --e;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --work;

    /* Function Body */
    initq = lsame_(vect, "V");
    wantq = initq || lsame_(vect, "U");
    upper = lsame_(uplo, "U");
    kd1 = *kd + 1;
    kdm1 = *kd - 1;
    incx = *ldab - 1;
    iqend = 1;

    *info = 0;
    if (! wantq && ! lsame_(vect, "N")) {
	*info = -1;
    } else if (! upper && ! lsame_(uplo, "L")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*kd < 0) {
	*info = -4;
    } else if (*ldab < kd1) {
	*info = -6;
    } else if (*ldq < max(1,*n) && wantq) {
	*info = -10;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSBTRD", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Initialize Q to the unit matrix, if needed */

    if (initq) {
	dlaset_("Full", n, n, &c_b9, &c_b10, &q[q_offset], ldq);
    }

/*     Wherever possible, plane rotations are generated and applied in   
       vector operations of length NR over the index set J1:J2:KD1.   

       The cosines and sines of the plane rotations are stored in the   
       arrays D and WORK. */

    inca = kd1 * *ldab;
/* Computing MIN */
    i__1 = *n - 1;
    kdn = min(i__1,*kd);
    if (upper) {

	if (*kd > 1) {

/*           Reduce to tridiagonal form, working with upper triangle */

	    nr = 0;
	    j1 = kdn + 2;
	    j2 = 1;

	    i__1 = *n - 2;
	    for (i__ = 1; i__ <= i__1; ++i__) {

/*              Reduce i-th row of matrix to tridiagonal form */

		for (k = kdn + 1; k >= 2; --k) {
		    j1 += kdn;
		    j2 += kdn;

		    if (nr > 0) {

/*                    generate plane rotations to annihilate nonzero   
                      elements which have been created outside the band */

			dlargv_(&nr, &ab_ref(1, j1 - 1), &inca, &work[j1], &
				kd1, &d__[j1], &kd1);

/*                    apply rotations from the right   


                      Dependent on the the number of diagonals either   
                      DLARTV or DROT is used */

			if (nr >= (*kd << 1) - 1) {
			    i__2 = *kd - 1;
			    for (l = 1; l <= i__2; ++l) {
				dlartv_(&nr, &ab_ref(l + 1, j1 - 1), &inca, &
					ab_ref(l, j1), &inca, &d__[j1], &work[
					j1], &kd1);
/* L10: */
			    }

			} else {
			    jend = j1 + (nr - 1) * kd1;
			    i__2 = jend;
			    i__3 = kd1;
			    for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <= 
				    i__2; jinc += i__3) {
				drot_(&kdm1, &ab_ref(2, jinc - 1), &c__1, &
					ab_ref(1, jinc), &c__1, &d__[jinc], &
					work[jinc]);
/* L20: */
			    }
			}
		    }


		    if (k > 2) {
			if (k <= *n - i__ + 1) {

/*                       generate plane rotation to annihilate a(i,i+k-1)   
                         within the band */

			    dlartg_(&ab_ref(*kd - k + 3, i__ + k - 2), &
				    ab_ref(*kd - k + 2, i__ + k - 1), &d__[
				    i__ + k - 1], &work[i__ + k - 1], &temp);
			    ab_ref(*kd - k + 3, i__ + k - 2) = temp;

/*                       apply rotation from the right */

			    i__3 = k - 3;
			    drot_(&i__3, &ab_ref(*kd - k + 4, i__ + k - 2), &
				    c__1, &ab_ref(*kd - k + 3, i__ + k - 1), &
				    c__1, &d__[i__ + k - 1], &work[i__ + k - 
				    1]);
			}
			++nr;
			j1 = j1 - kdn - 1;
		    }

/*                 apply plane rotations from both sides to diagonal   
                   blocks */

		    if (nr > 0) {
			dlar2v_(&nr, &ab_ref(kd1, j1 - 1), &ab_ref(kd1, j1), &
				ab_ref(*kd, j1), &inca, &d__[j1], &work[j1], &
				kd1);
		    }

/*                 apply plane rotations from the left */

		    if (nr > 0) {
			if ((*kd << 1) - 1 < nr) {

/*                    Dependent on the the number of diagonals either   
                      DLARTV or DROT is used */

			    i__3 = *kd - 1;
			    for (l = 1; l <= i__3; ++l) {
				if (j2 + l > *n) {
				    nrt = nr - 1;
				} else {
				    nrt = nr;
				}
				if (nrt > 0) {
				    dlartv_(&nrt, &ab_ref(*kd - l, j1 + l), &
					    inca, &ab_ref(*kd - l + 1, j1 + l)
					    , &inca, &d__[j1], &work[j1], &
					    kd1);
				}
/* L30: */
			    }
			} else {
			    j1end = j1 + kd1 * (nr - 2);
			    if (j1end >= j1) {
				i__3 = j1end;
				i__2 = kd1;
				for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <=
					 i__3; jin += i__2) {
				    i__4 = *kd - 1;
				    drot_(&i__4, &ab_ref(*kd - 1, jin + 1), &
					    incx, &ab_ref(*kd, jin + 1), &
					    incx, &d__[jin], &work[jin]);
/* L40: */
				}
			    }
/* Computing MIN */
			    i__2 = kdm1, i__3 = *n - j2;
			    lend = min(i__2,i__3);
			    last = j1end + kd1;
			    if (lend > 0) {
				drot_(&lend, &ab_ref(*kd - 1, last + 1), &
					incx, &ab_ref(*kd, last + 1), &incx, &
					d__[last], &work[last]);
			    }
			}
		    }

		    if (wantq) {

/*                    accumulate product of plane rotations in Q */

			if (initq) {

/*                 take advantage of the fact that Q was   
                   initially the Identity matrix */

			    iqend = max(iqend,j2);
/* Computing MAX */
			    i__2 = 0, i__3 = k - 3;
			    i2 = max(i__2,i__3);
			    iqaend = i__ * *kd + 1;
			    if (k == 2) {
				iqaend += *kd;
			    }
			    iqaend = min(iqaend,iqend);
			    i__2 = j2;
			    i__3 = kd1;
			    for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j 
				    += i__3) {
				ibl = i__ - i2 / kdm1;
				++i2;
/* Computing MAX */
				i__4 = 1, i__5 = j - ibl;
				iqb = max(i__4,i__5);
				nq = iqaend + 1 - iqb;
/* Computing MIN */
				i__4 = iqaend + *kd;
				iqaend = min(i__4,iqend);
				drot_(&nq, &q_ref(iqb, j - 1), &c__1, &q_ref(
					iqb, j), &c__1, &d__[j], &work[j]);
/* L50: */
			    }
			} else {

			    i__3 = j2;
			    i__2 = kd1;
			    for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j 
				    += i__2) {
				drot_(n, &q_ref(1, j - 1), &c__1, &q_ref(1, j)
					, &c__1, &d__[j], &work[j]);
/* L60: */
			    }
			}

		    }

		    if (j2 + kdn > *n) {

/*                    adjust J2 to keep within the bounds of the matrix */

			--nr;
			j2 = j2 - kdn - 1;
		    }

		    i__2 = j2;
		    i__3 = kd1;
		    for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) 
			    {

/*                    create nonzero element a(j-1,j+kd) outside the band   
                      and store it in WORK */

			work[j + *kd] = work[j] * ab_ref(1, j + *kd);
			ab_ref(1, j + *kd) = d__[j] * ab_ref(1, j + *kd);
/* L70: */
		    }
/* L80: */
		}
/* L90: */
	    }
	}

	if (*kd > 0) {

/*           copy off-diagonal elements to E */

	    i__1 = *n - 1;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		e[i__] = ab_ref(*kd, i__ + 1);
/* L100: */
	    }
	} else {

/*           set E to zero if original matrix was diagonal */

	    i__1 = *n - 1;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		e[i__] = 0.;
/* L110: */
	    }
	}

/*        copy diagonal elements to D */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    d__[i__] = ab_ref(kd1, i__);
/* L120: */
	}

    } else {

	if (*kd > 1) {

/*           Reduce to tridiagonal form, working with lower triangle */

	    nr = 0;
	    j1 = kdn + 2;
	    j2 = 1;

	    i__1 = *n - 2;
	    for (i__ = 1; i__ <= i__1; ++i__) {

/*              Reduce i-th column of matrix to tridiagonal form */

		for (k = kdn + 1; k >= 2; --k) {
		    j1 += kdn;
		    j2 += kdn;

		    if (nr > 0) {

/*                    generate plane rotations to annihilate nonzero   
                      elements which have been created outside the band */

			dlargv_(&nr, &ab_ref(kd1, j1 - kd1), &inca, &work[j1],
				 &kd1, &d__[j1], &kd1);

/*                    apply plane rotations from one side   


                      Dependent on the the number of diagonals either   
                      DLARTV or DROT is used */

			if (nr > (*kd << 1) - 1) {
			    i__3 = *kd - 1;
			    for (l = 1; l <= i__3; ++l) {
				dlartv_(&nr, &ab_ref(kd1 - l, j1 - kd1 + l), &
					inca, &ab_ref(kd1 - l + 1, j1 - kd1 + 
					l), &inca, &d__[j1], &work[j1], &kd1);
/* L130: */
			    }
			} else {
			    jend = j1 + kd1 * (nr - 1);
			    i__3 = jend;
			    i__2 = kd1;
			    for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <= 
				    i__3; jinc += i__2) {
				drot_(&kdm1, &ab_ref(*kd, jinc - *kd), &incx, 
					&ab_ref(kd1, jinc - *kd), &incx, &d__[
					jinc], &work[jinc]);
/* L140: */
			    }
			}

		    }

		    if (k > 2) {
			if (k <= *n - i__ + 1) {

/*                       generate plane rotation to annihilate a(i+k-1,i)   
                         within the band */

			    dlartg_(&ab_ref(k - 1, i__), &ab_ref(k, i__), &
				    d__[i__ + k - 1], &work[i__ + k - 1], &
				    temp);
			    ab_ref(k - 1, i__) = temp;

/*                       apply rotation from the left */

			    i__2 = k - 3;
			    i__3 = *ldab - 1;
			    i__4 = *ldab - 1;
			    drot_(&i__2, &ab_ref(k - 2, i__ + 1), &i__3, &
				    ab_ref(k - 1, i__ + 1), &i__4, &d__[i__ + 
				    k - 1], &work[i__ + k - 1]);
			}
			++nr;
			j1 = j1 - kdn - 1;
		    }

/*                 apply plane rotations from both sides to diagonal   
                   blocks */

		    if (nr > 0) {
			dlar2v_(&nr, &ab_ref(1, j1 - 1), &ab_ref(1, j1), &
				ab_ref(2, j1 - 1), &inca, &d__[j1], &work[j1],
				 &kd1);
		    }

/*                 apply plane rotations from the right   


                      Dependent on the the number of diagonals either   
                      DLARTV or DROT is used */

		    if (nr > 0) {
			if (nr > (*kd << 1) - 1) {
			    i__2 = *kd - 1;
			    for (l = 1; l <= i__2; ++l) {
				if (j2 + l > *n) {
				    nrt = nr - 1;
				} else {
				    nrt = nr;
				}
				if (nrt > 0) {
				    dlartv_(&nrt, &ab_ref(l + 2, j1 - 1), &
					    inca, &ab_ref(l + 1, j1), &inca, &
					    d__[j1], &work[j1], &kd1);
				}
/* L150: */
			    }
			} else {
			    j1end = j1 + kd1 * (nr - 2);
			    if (j1end >= j1) {
				i__2 = j1end;
				i__3 = kd1;
				for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 : 
					j1inc <= i__2; j1inc += i__3) {
				    drot_(&kdm1, &ab_ref(3, j1inc - 1), &c__1,
					     &ab_ref(2, j1inc), &c__1, &d__[
					    j1inc], &work[j1inc]);
/* L160: */
				}
			    }
/* Computing MIN */
			    i__3 = kdm1, i__2 = *n - j2;
			    lend = min(i__3,i__2);
			    last = j1end + kd1;
			    if (lend > 0) {
				drot_(&lend, &ab_ref(3, last - 1), &c__1, &
					ab_ref(2, last), &c__1, &d__[last], &
					work[last]);
			    }
			}
		    }



		    if (wantq) {

/*                    accumulate product of plane rotations in Q */

			if (initq) {

/*                 take advantage of the fact that Q was   
                   initially the Identity matrix */

			    iqend = max(iqend,j2);
/* Computing MAX */
			    i__3 = 0, i__2 = k - 3;
			    i2 = max(i__3,i__2);
			    iqaend = i__ * *kd + 1;
			    if (k == 2) {
				iqaend += *kd;
			    }
			    iqaend = min(iqaend,iqend);
			    i__3 = j2;
			    i__2 = kd1;
			    for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j 
				    += i__2) {
				ibl = i__ - i2 / kdm1;
				++i2;
/* Computing MAX */
				i__4 = 1, i__5 = j - ibl;
				iqb = max(i__4,i__5);
				nq = iqaend + 1 - iqb;
/* Computing MIN */
				i__4 = iqaend + *kd;
				iqaend = min(i__4,iqend);
				drot_(&nq, &q_ref(iqb, j - 1), &c__1, &q_ref(
					iqb, j), &c__1, &d__[j], &work[j]);
/* L170: */
			    }
			} else {

			    i__2 = j2;
			    i__3 = kd1;
			    for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j 
				    += i__3) {
				drot_(n, &q_ref(1, j - 1), &c__1, &q_ref(1, j)
					, &c__1, &d__[j], &work[j]);
/* L180: */
			    }
			}
		    }

		    if (j2 + kdn > *n) {

/*                    adjust J2 to keep within the bounds of the matrix */

			--nr;
			j2 = j2 - kdn - 1;
		    }

		    i__3 = j2;
		    i__2 = kd1;
		    for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) 
			    {

/*                    create nonzero element a(j+kd,j-1) outside the   
                      band and store it in WORK */

			work[j + *kd] = work[j] * ab_ref(kd1, j);
			ab_ref(kd1, j) = d__[j] * ab_ref(kd1, j);
/* L190: */
		    }
/* L200: */
		}
/* L210: */
	    }
	}

	if (*kd > 0) {

/*           copy off-diagonal elements to E */

	    i__1 = *n - 1;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		e[i__] = ab_ref(2, i__);
/* L220: */
	    }
	} else {

/*           set E to zero if original matrix was diagonal */

	    i__1 = *n - 1;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		e[i__] = 0.;
/* L230: */
	    }
	}

/*        copy diagonal elements to D */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    d__[i__] = ab_ref(1, i__);
/* L240: */
	}
    }

    return 0;

/*     End of DSBTRD */

} /* dsbtrd_ */

#undef ab_ref
#undef q_ref


