dsptrd.c

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/* dsptrd.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 integer c__1 = 1;
static doublereal c_b8 = 0.;
static doublereal c_b14 = -1.;

/* Subroutine */ int dsptrd_(char *uplo, integer *n, doublereal *ap, 
        doublereal *d__, doublereal *e, doublereal *tau, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    integer i__, i1, ii, i1i1;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    doublereal taui;
    extern /* Subroutine */ int dspr2_(char *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *);
    doublereal alpha;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *), dspmv_(char *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
             doublereal *, integer *);
    logical upper;
    extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *), xerbla_(char *, integer *);


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

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

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

/*  DSPTRD reduces a real symmetric matrix A stored in packed form to */
/*  symmetric tridiagonal form T by an orthogonal similarity */
/*  transformation: Q**T * A * Q = T. */

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

/*  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. */

/*  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/*          On entry, the upper or lower triangle of the symmetric matrix */
/*          A, packed columnwise in a linear array.  The j-th column of A */
/*          is stored in the array AP as follows: */
/*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
/*          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. */

/*  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 AP, */
/*  overwriting A(1:i-1,i+1), and tau is stored 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 AP, */
/*  overwriting A(i+2:n,i), and tau is stored in TAU(i). */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    --tau;
    --e;
    --d__;
    --ap;

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

/*     Quick return if possible */

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

    if (upper) {

/*        Reduce the upper triangle of A. */
/*        I1 is the index in AP of A(1,I+1). */

        i1 = *n * (*n - 1) / 2 + 1;
        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__, &ap[i1 + i__ - 1], &ap[i1], &c__1, &taui);
            e[i__] = ap[i1 + i__ - 1];

            if (taui != 0.) {

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

                ap[i1 + i__ - 1] = 1.;

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

                dspmv_(uplo, &i__, &taui, &ap[1], &ap[i1], &c__1, &c_b8, &tau[
                        1], &c__1);

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

                alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &ap[i1], &
                        c__1);
                daxpy_(&i__, &alpha, &ap[i1], &c__1, &tau[1], &c__1);

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

                dspr2_(uplo, &i__, &c_b14, &ap[i1], &c__1, &tau[1], &c__1, &
                        ap[1]);

                ap[i1 + i__ - 1] = e[i__];
            }
            d__[i__ + 1] = ap[i1 + i__];
            tau[i__] = taui;
            i1 -= i__;
/* L10: */
        }
        d__[1] = ap[1];
    } else {

/*        Reduce the lower triangle of A. II is the index in AP of */
/*        A(i,i) and I1I1 is the index of A(i+1,i+1). */

        ii = 1;
        i__1 = *n - 1;
        for (i__ = 1; i__ <= i__1; ++i__) {
            i1i1 = ii + *n - i__ + 1;

/*           Generate elementary reflector H(i) = I - tau * v * v' */
/*           to annihilate A(i+2:n,i) */

            i__2 = *n - i__;
            dlarfg_(&i__2, &ap[ii + 1], &ap[ii + 2], &c__1, &taui);
            e[i__] = ap[ii + 1];

            if (taui != 0.) {

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

                ap[ii + 1] = 1.;

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

                i__2 = *n - i__;
                dspmv_(uplo, &i__2, &taui, &ap[i1i1], &ap[ii + 1], &c__1, &
                        c_b8, &tau[i__], &c__1);

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

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

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

                i__2 = *n - i__;
                dspr2_(uplo, &i__2, &c_b14, &ap[ii + 1], &c__1, &tau[i__], &
                        c__1, &ap[i1i1]);

                ap[ii + 1] = e[i__];
            }
            d__[i__] = ap[ii];
            tau[i__] = taui;
            ii = i1i1;
/* L20: */
        }
        d__[*n] = ap[ii];
    }

    return 0;

/*     End of DSPTRD */

} /* dsptrd_ */